ABSTRACT A STUDY OF THE PROBLEM OF DETERMINING ONTOLOGICAL COMMITMENTS IN WITTGENSTEIN'S TRACTATUS By Jan Arden Smucker The fundamental purpose of Wittgenstein's Tractatus a as the author states in his preface to that work, ". . is to set a limit to thought, or rather--not to thought, but to ““3 expression of thoughts . . . " Wittgenstein asserts that ordinary language, because of the vagueness and ambi- quilty of its expressions, fails to function as an adequate Vehicle for the setting of such limits. Hence the program of the Tractatus consists substantially in the recommendation of a language whose structure is so perspicuous that we can- IKNS make the mistakes which ordinary language allows us to make. It is, however, a program only, and the problems pertaining to the application of the program are not dis- cuSsed in full in the Tractatus. One such problem is the determination of the nature 0f the basic entities of the system, the objects; for if the nature of these entities cannot be determined, the I tug 5'1- df‘tz" ‘ ...ola-~‘ V1 ' fl :Lvokh&a‘s, n: :::.iversals a 22 states that 2;: iniversals 5221'. hypothesis The pra never, is co: Llanguages 1 Kim the syste Ethis essay), iliiussed by t? .. “ Fat ~ hubb exnihit ~= essay). i :..I: “5‘8": Jan Arden Smucker Tractatus has no application. This essay attempts to deter- mine the status of the basic entities, and does this through 1mm consideration of two hypotheses concerning the nature of tme Objects. Hypothesis I states that the objects are bare particulars, having no empirical qualities, and hence that ru>universals are to be found among the objects. Hypothesis II states that not only are particulars to be found there, but universals as well. The textual evidence in favor of each hypothesis is closely examined. The problem of determining the status of the objects, hOwever, is complicated by the fact that we must speak of -Qfla languages in the Tractatus: there is the language in whichthe system is presented (termed the "ladder language" inthis essay), and there is also the language which is discussed by the ladder language (the language discussed, tun; not exhibited, is called the "perspicuous language" in this essay). The problem is raised concerning whether the 11“Iplications of the two languages for the ontology of the Tractatus are similar, for if they are not, it must be \—__ deCtided which ontology is "the" ontology of the Tractatus. It is finally decided that the two languages to assume different ontologies, and that that of the perspicuous lan- guage must be regarded as primary. The difficulties con- heCted with the decision are discussed in detail. It is the parallelism of structure between the per- sDicuous language and the world described by it that forms the basis for our decision concerning the status of the .5 L...” . 3 v 1 n: fift‘opA-JOJS 1a ‘ A..‘A' “7‘0 :J:Jo.vu, ab: is reintroduce 25in sources 0 ‘I failure to “.1 "‘65 that . :3? s tnEip ban u"... '4qu we p :E'P‘t the ‘ 1 obuec 4N E's? h g p. . tion Etta Jan Arden Smucker objects. The form of the elementary propositions of the perspicuous language is regarded as central to the main question, and a serious attempt is made to determine how an elementary proposition would actually appear. After the theory of substance and relations in the Tractatus is discussed, the decision is made that the ob- jects are particulars. The question of whether the two languages found in the Tractatus imply different ontologies is reintroduced, and it is there argued that one of the nmin sources of difficulty in understanding the Tractatus is the failure to differentiate between these two languages. In the concluding chapter, various problems relating to the application of the system of the Tractatus to actual cases of analysis are brieflydiscussed. It is argued there that, given our interpretation of the nature of the objects, the applicability of the system of the Tractatus to actual cases is problematic indeed, and this constitutes the primary rea- son for Wittgenstein's partial abandonment of the viewpoint eXpressed in that early work. The major conclusion, then, is that textual evidence implies that the objects indeed are bare particulars, and that their bare particularity implies their unobservability. Although we present an argument in Chapter III to the effect that the objects are indeed observable under a certain interpretation of 'object', this is conjecture which is based on extrapolation from very scanty textual evidence a3 ['1‘ . m ‘ . a nv‘q:;a .ndvu . oars, are ui lit. I... III, .15] 151,13. .. 7, m! Jan Arden Smucker indeed. Thus we conclude that the objects, as bare parti- culars, are ultimately unobservable. 1‘“. L.‘ . oi l . ...|Ir.d r. . .. inli . .. a is: in 1 A STUDY OF THE PROBLEM OF DETERMINING ONTOLOGICAL COMMITMENTS IN WITTGENSTEIN’S TRACTATUS By Jan Arden Smucker A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Philosophy 1969 7 1y: ‘ V -——‘_ 7 v I' -. . r—wv- l {'7 . V “'1' I- q .‘_ cult dd“ Une e. "‘ :phire’ be so. l.\,‘ U ; ;:“‘nt: “Wall". E ”'1‘; “My“; h a ‘ L... “JD val. -"A l \ ‘3‘ \ H‘tn‘ t INF“ ‘r'y'l 1.- N V. “early I: I“ no ---5 ‘vi iii-{.3 \ ACKNOWLEDGEMENTS The writer is deeply indebted to many people for their help and aSSistance during the writing of the disserta- tion and the total doctoral program. Special thanks are due to Dr. Herbert H. Hendry and Dr. Rhoda H. Kotzin, under whose direction a substantial number of the ideas herein expressed were crystallized. Thanks are also due to Dr. Ronald Suter, Mmose help was instrumental in clarifying many of the diffi— mflt and complex ideas of Frege, and in connecting these ideas with the system of the Tractatus. Appreciation and acknowledgement is also extended to ma Henry E. Van Leeuwen and Dr. Robert H. Rosenthal, collea- Qmm of mine in the Department of Philosophy, Hanover College. They have been very much responsible for the development of many of my philosophical ideas, and have been most helpful in the clarification of a number of topics discussed in this dissertation. And finally, to Bobbie, who unknowingly provided the ‘Lfltimate impetus for this work, special thanks. ii I-‘ny‘lhvvv nq'fim‘vr: - nu 3-15». WJLUUs-at --— m e r '”’€P bee-LU ‘v . T""T:n — M Lin. c- C '11, pl' -. 71"" ‘.‘ _ lur- . " Kath n 5"“ -i b.‘ I V 91. . V. .‘ I a‘ I 'VI N. LII .._ ”V" .. H“ ‘_.,." 5‘ J-AnL‘_ ‘1‘ P'“ ‘U‘ “ b- A»! n 'J ‘v T "0 anfiuvl 0“,“‘l ler V‘u -. q N 1| a H 'L I -Y 1 fl 0 VA ‘ L1‘."‘ v vg‘lx‘ ‘- ’1“. ¢..; i~‘ - e ‘ ‘ ~“‘u 5., I. ‘v’u‘ LE‘" H,“ *4} . TABLE OF CONTENTS Page ACKNOWLEDGEMENTS . . . . . . . . . . . . ii Chapter I. INTRODUCTION: THE PROBLEM OF THE ONTOLOGY OF THE TRACTATUS . . . . . . . . . l A. The Problem at Hand . . . . . . l B. Frege: His Theory of Meaning . . . 17 C. Wittgenstein: The Early Writings . 35 II. THE WORLD ACCORDING TO THE LADDER LANGUAGE: A SKETCH . . . . . . . . . . . . 6A A. Facts . . . . . . . . . . . 6A B. Sachverhalte . . . . . . . . 89 C. Sachverhalte and Facts . . . . . 97 D. Objects (Gegenstande) . . . . . 106 III. THOUGHTS AND PROPOSITIONS: 'THE PICTURE THEORY . . . . . . . . . . 123 A. Pictures and Possibilities in Logical Space . . . . . . . . 123 B. The Sense of a Picture . . . . . 154 C. The Proposition (Satz) as a Picture . . . . . . . . . . 168 IV. ATOMIC PROPOSITIONS AND THE ONTOLOGICAL STATUS OF THE OBJECTS . . . . . . . 187 A. Introduction . . . . . . . 187 B. Two Hypotheses Concerning Objects and Elementary Propositions . . . 203 V. CONCLUSION: THE IDENTIFIABILITY OF THE OBJECTS . . . . . . . . . . . 2A7 BIBLIOGRAPHY . . . . . . . . . . . . . 269 iii .r‘.r :‘ I L. o. a «o .w. a; si 3‘ GS l. L. s v .7“. VA. ‘1 «H» VIM 0‘ A 0‘ ‘ .‘C o. s a ‘ mi. a. . o. . 4 A t ,. s ,.. To :1; ~ . h it «.1. fly: t .c .. . Y . L; L .. AC YA L L. V» AC . ”1.. .. A u‘- « are .«u .er a . r .. Ct. 02 vi. Lb LI» OI. nt. .4” .nu .. a ”an T.» v.. ”Pu o u Q» ~. a 5 ‘ 2.. my vl~ no r .. a. n .. mu. Mu 3: I 1. h. 5.: 3 c 2 . n v. 9:. rlu Cu. O» fit. r w DUI / .. .x a C. 1:. raw 2* a. a la ‘ 1.; n. s I . .— .u . \ . L . V .. t . w ,. r c fin ‘ \U A .dH ‘7). t ,- r . s, e u. . e . a. v F . k 1. a \u a :1 . is » Mu]. ‘ . .. . . a a. . ._. .... ~ .. .f a 1 k .. . J! .~ \.~ . . .. . x . . , . .. . . . y . . . . l t CHAPTER I INTRODUCTION: THE PROBLEM OF THE ONTOLOGY OF THE TRACTATUS A. The Problem At Hand According to Brand Blanchard, ”Wittgenstein has the strange distinction of having produced a work on logic beside which the Logic of Helel is luminously intelligible."l While perhaps overstated, this is as apt a description of Wittgenstein's Tractatus Logico-Philosophicus as has ever been penned, for this work is indeed one of the most difficult in the Western philosophical tradition. The style of the German text is simple and beautiful, the tone of its pro- nouncements oracular and almost dramatic. But the text is difficult indeed, and certainly one of the reasons for this difficulty is the fact that Wittgenstein assumes an easy, working familiarity with both Russell's and Frege's logical and metaphysical doctrines. But even given such background, the reader is faced With prodigious difficulties in interpreting Wittgenstein's teXt- Little concession is made to the reader, little \— W' 1Quoted in Irving Copi and Robert Beard, Essays on éfllffiflstein's Tractatus (New York, 1966), p. x. o A ‘ yvy‘fi Mi.“ P“ A ”I” LgyolhA . ..,_ iv!” AAII .. r4 4 V‘L C A.” r- .. .\. : . v r... a. P.» A: h. A; A3. .... . y... A A .i H. NAL -. a PMI A. t v r. vs. A. ”1 TI ~a +e "1. Q. . I. .w u u- . e . so a: F. :i h. (rt Pa ~ m «not A: I .19 wC Dy at as r. I J. I. aft i. . VA Ox h . t .4 AN; ‘IJ L 1. Hr.» .NK ~ A“ 3‘ a Cy I. . Y .. 1,.5 v..v .14. 5 Av v r .n u w u . v .. y . r . «a . A... 5 . i. :w u. ‘ V “Guy Sir.“ A”. an ... 4 . v . u, , a 4 s A n u .s . «.4 . pi. “ Q a is F e a .1 Au Q A. .y n§v —1& t . 1.. I," n... 1 "3.. W... . .4 .... .. fifl -. .. .en . background is provided by Wittgenstein for the understanding of his pronouncements. Rarely is any warning given that, at a particular point in the text, Wittgenstein is discuss- ing Frege's theory of meaning or Russellis theory of types, or any issues pertaining thereto. Nor are we warned at every point that Frege's distinction between the sense. (Sinn) and the reference (Bedeutung) of a term has undergone radical change and reinterpretation at Wittgenstein's hands. All this we must puzzle out for ourselves. Further, an understanding of the Tractatus requires extremely close attention to the use of various crucial terms in various places throughout the text: words such as 'Sachverhalt' (translated as "state of affairs" in the Pears— McGuinness English translation), 'Tatsache' (fact), 'Wirklich- 3313' (reality), and 'Sachlage' (situation). Each time that such a term occurs in the text, the context of its occurrence may give it a different meaning; and hence an understanding (n‘the term requires that all contexts of its occurrence in the text be sought out and compared. Of particular interest is the fact that the Tractatus is a metaphysical system based on an analysis of all language. Its Outcome is that many of the expressions used in everyday (fiscourse are not merely false (in the case of statements), tum nonsensical. And this conclusion is urged particularly inthe case of philosophy. But more to the point, the Efifliéfigg attempts among other things to answer the questions: what must the world be in order that communication be possi- ble by means of language? How is it that expressions of language have meaning, so that such communication can take place? These questions, presumably, are answered in the course of the construction of a metaphysical system which Urmson, for one, has interpreted as a system of logical he questions of the ct atomism.2 Thus, according to Urms on, nature of language and of meaning are to he answered by the construction of an atomistic metaphysics in which certain P€lations hold between the expressions of language and the worlri, But the Tractatus immediately presents one with a diffdxmflt problem of interpretation, a problem which is bUI"iied in the very structure of the Tractatus. For the pur- FWSéES of our study of the Tractatus, tnere are two languages LA.) xflfixch we must consider. Following Bernstein, we may dis— tirlguish between what might be called the ”ladder language" (th63 language actually used in the Tractatus to exposit the ”Et&iphys ics) and the "perspicuous language" (tt e language WhCVSe main features are discussed by the ladder—Ian nguage textl). We shall argue that it is the perspi cuOus language Whig”? most clearly indicates the fundamental commitments of \ T J I (‘1‘ I V j) ('3 * l 2J. O. Urmson, Philosophical Analysis: . releg— EEIH; between the Two World Wars (Oxford, l9g3), pp. 5’—60. hl U1 ree Langu— 3Richard J. Bernstein, "Wittgenstein’s T 2, Dec. 1961, ageS," The Review of Metaphysics, Vol. 15, no. 9- 281, 282. a: -r\~AR .a I" -.~\ ." ._-.4,.—-~’ .. - ""'."'.’JV‘"‘: I.“ -.. -.‘u.g *- ‘Y 5 3s ’0 .V’ -~ C.-. “‘~ CO . -, u\ l .v-.J__~ ‘ y. 00 ‘ rhpwnrbqr'lp .. e... .\,_‘_-“\', . .‘ D F:'5Y?r~ - A. 1.- b.4gk‘buv" .. ,fip,,“_‘g u. ..., k‘vvd‘ ‘J‘ . . ‘ »,. ‘ A - Ti"; ‘2'- III. “““\‘ "‘.. ... ‘ . rear-2,...“ f‘ *- .Nawnlhdeu U 6 A, A ‘ . "'9‘" ‘Q ‘nbha .» QM ‘1‘ . x. ”e. . ‘ . ‘N ‘- 1... «J ‘b ”:7.- ~._\\ .,‘ .‘ ,. .. ,wc erfl‘fcp “y .\ VJ»..,~“. . .1. . A‘. ‘ " ‘ .‘. Q a : ‘i a. .t mlrpb, . -‘ h‘v.‘* ~. ‘ {n ""4 "VA 'u' A ‘ d §.. : :QTTVK: q. .“L‘L"I“P|", . (_ K,“ .H 1.,‘0 P“ L‘r ‘A ~‘. ‘ 1“! “a: .. “‘99 1.x . 2‘. ~. ~ “‘R:hl .g N ‘Aasnkf:,l v a 2»- ‘\‘¢ ,, ‘. eh ‘4 u, ‘ ‘qer‘,. V: --.«. \I h!” ' I.‘ h .v.‘ , use A .. V .a\. .1. . ‘zrm ‘IAK - \— of the Tractatus. But in distinguishing between these two languages, we are presented with a difficult problem, for we shall find that the types of entities to which the two lan- guages are committed are quite different, and indeed the commitments are incompatible. Yet it is in the ladder language that the major features of the recOmmended perspicuous language are de- veloped; and if the commitments of the two languages are inmompatible, how accurate a guide to the commitments of the pnerspicuous language can the ladder language be? Yet, hitnie course of its exposition of the perspicuous language, mu? ladder language finds itself committed to entities not mnuitenanced by the other. In the text of the Tractatus, therwe is introduced the notion of the "object" (Gegenstand), and :it is these objects that are the fundamental entities 0f tdae system. From these objects is constructed all of I'eatliity, and statements of the perspicuous language are saiCi to "mirror" or "picture" that reality. It is this ObSérvation which forms the basis of our contention that Um; perspicuous language provides the main clue to the flatware of the fundamental entities. By the nature of that 1a"niguage, its well-formed sentences bear a definite rela- tiofl to the world, and because they have such contact, they a“? Umaningful. For the Tractatus, language and the world 81"are an identity of structure. It is therefore the pri- mapy purpose of the Tractatus to sketch out a picture of both language and the world in order to exhibit this .‘O«-nl‘ _,.J-..¢- .A- l u.- r.~v1~r‘ "o‘ . . u'v‘,‘ . . . _.. ., f A E : . A c a. CO at \ . r .. .. a Q. A; v” A1 . . . a. ..n .. . a .. . i .. 1 z . l .n. Ad. Ad -nu Tc ... . .. 2... t). «L P. a. [it :i h. at L. :i n; .2 u ~. #I. fly. :. M4 o‘. a. .c L,” a; Q» .l M r“ I 1,“ *1 Ac L. .3 a. m...- 6.. is .r... «L M». G. u «i. s . s . «0 Wu ..4 5. 3» AH. tie n!» JV, r: A g AH. 0. g L. W . A» J. a «u» r .n A. .. . 5 .BH .n.. 11); “a .n.. s a r.. rflq .r.. «\C rt. A I . 1, r,“ a . A? 5.: s a ‘ t s a u ,1 s a x .. A: e i x .i. . .. v. . x . . . A .. . u r... s . .. i r, . .. . . .. A .L a I i \a . l a. . 5 x .0 . . . . v .u u. / y - . n . ”1‘. . u . A o 4 1 . . . n~ t I . \ .v A ‘ . structural identity and to justify postulating it. And this structural identity of language and world is the basis for our: claim that, if we can determine the basic properties of thee perspicuous language, we can determine the nature of the basix: entities of the system. Wittgenstein, then, must do several things in the Tra<3tatus: (l) he must sketch out a scheme for the descrip- tiori of the world so that the elementary entities from whicfli the world is constructed are postulated, and the com- ple)( entities of the world are constructed out of them; (2) lie must show that language can, in some sense, be re- duceci to elements of a certain kind, and that composite lingniistic entities (e.g., sentences) can be constructed out Of tliem; (3) he must show how to perform such linguistic constzructions, and (A) he must show how the basic entities of tile world are assembled into complex entities. No claim 13 "made here that Wittgenstein succeeds in performing all Cfi'tiiese tasks. For now, we assert that some suggested modiffiication of the language of the Principia Mathematica humus the basis of the improved language suggested by Wittgenstein; in fact, it determines the form which the "Etaiflfiysics of the Tractatus takes. Our primary interest, again, is the metaphysics of thelyactatus, the construction of which is the first of the tasks which the Tractatus must perform. But so subtly interwoven are the ontology and the theory of language of the Tractatus, that it is ultimately impossible to consider _‘ . .I. H... -L‘v I‘m‘ , ~‘t a. . ; '~~- ...-~ -\ y _ .4 ,. . . .. . . _. T—r .4 v“ » . .A..~.-.... D -... L/A K A . . C " ~-r,~A - 1 n. .. ...A.-...— . :r-v» -A ,‘J‘ - Ha a.-»~.- \, . . _ . .’ ’W'r-\~~ , , , 5.; ’ H... g. t \ A v 5 -‘ _. _' 7'3"“ . x M ‘-‘~-»-Av.. .. u . hY.‘r'p 0., . .....l..:: -.. 'r ,1,‘ . 5“. F“V‘.‘ A. "'“\L. _o --.,I. _‘ v" “ . . , .. ‘ «I I— u.._ c... “v~,“ . H‘ "~\-.~ C *. \4—\ v L‘. 4‘ -"v»’ , -4 ~ r: 0. -,‘_ . , i '5. Q . ‘-- ,, A "A ~ § .JH“ ,. _‘ ‘4' A. ,‘_: A I _ ~ .‘~ ‘- _ e ‘.‘“"i\;' LI .. ‘ A , A_ fine." 1 ‘- 'fiM . ' .-‘v.| {V3 _ ‘ h“ :;- ‘ no" .- 51 ' a .‘. h" _ \ r-A «,‘N ~ . ‘_ ‘I,h ’-. A .. -‘-:Cn . y" p- . _. .4._‘ L. . .. v . . ,. \ .\‘ 5.4!" . ‘V F‘ “o - is. . J}; 6.‘ «HCVF 'Ll r-V ‘\ .Z\_ ,‘ ~_‘ A0 4" .‘- \.~ A, s r , 'o‘g 1“ u ‘ 1“": *'U . « .f -.'1 V Y! ‘ {4"}: . r . A __p- ‘_ them separately. The structure of the perspicuous language seems to determine the nature of the metaphysics which Wittgenstein exposits in the ladder language. The theory which proposes this scheme must answer such questions as: Moat meaning can we give to the individual constants and wariables of an improved or perspicuous language such as fliat proposed in the Tractatus? What meaning is to be given tc> sentences of an improved language in which all variables cxscurring therein are bound by quantifiers? Or indeed, are such constructions possible in the perspicuous language pro- posed by the Tractatus? The answers to these questions Cormtitute the ontology of the Tractatus. But the answers to these questions are difficult to GGtermine, for if they are given at all, they are given in the ladder language; and ontological issues are not clearly distinguished in that language. The last of these questions is particularly crucial, since we wish to determine the relevance of Quine's criterion of ontic commitment to the System of the Tractatus. It is not at all clear that quanti- fied (or quantifiable) sentences do occur in the perspicuous language, and if they do not, then Quine's criterion cannot be applied. Therefore we must be able to determine what an Elementary sentence of the perspicuous language looks like, 399 how they are reached in the process of analysis of States of affairs as they are found in the world. But for Quine, the ultimate criterion of ontic commitment is the tYDe of variable we are willing to bind by use of our I I I I I II I I II II I . L . a r A .. . . . ..... 3‘ A.» .'.. .rL :44 p: a. I u. A . v . a a .w a -r a w . bu Win L.» t A. u h-.. I; n. 71.- .1" V \ ills er ht «4...; P y P anM a . V. m c ‘0 A44 «Kg h A. AIK P A W a, ’u « L .v 55. I C “LA \I)‘ LIV I is ‘ n J P 1.. n c h .. .w i v. . .14 hi L t A: C In” yuv , xi h . .fiu AC nlv h. A Q. HNL A: ~\u I w. .., Wu. :4 I A c a: A: r r)». LL 3: «I. .71. A: hi n; A». utu . . A v n. a fit hlu sis A...» .n a \c .A.. emu. A A |o u... 3. hi hi A44 .5 u p: «v a a a u . C... 3.x :1. .r .. 1 . .1 v 3 \ . .4 a.» .u. us... ~.\ u ,., A. . s . a a. .4. s.‘ A.“ It A » ... .11. 2. I» r. L. A . . s a . A u . .. ..:. r... r... ... . .1. u... ... .. \ -..... .;. i .. . . . quantifiersfl This is the only way in which we can involve mnwuelves in such commitment. The use of names via the employnmmm of nonlogical constants in quantificational logic: is no criterion for ontic commitment. "For," says Quine , . . We can repudiate their namehood at the drop of a hat, unless the assumption of a corresponding entity can be spotted in the things we affirm in terms of bound variables. 5 Namess, says Quine, are irrelevant to the ontological issue, and tkie reason for this is that names can be paraphrased away 13y descriptions, and descriptions can be eliminated by Russelgl's method of paraphrasing them away. _ll singular ternms, according to Quine, can be eliminated from discourse in fkivor of bound variables, and hence Quine's insistence mltflie primacy of quantification over types of variables as 232 Ckriterion of ontological commitment. But with the Tractatus some serious questions arise With :regard to the ontological issue. Quine's criterion is PeleVHant to the commitments of discourse within a language, bUt it is problematic to speak of the commitments of a JBDEAMage. And the perspicuous language of the Tractatus 1821 formal language, not a piece of natural language; hence it 13 doubthl that pieces of discourse can be distinguished \ P “W. V. O. Quine, "On What There Is," in From g Logical m o_ View (Cambridge, Mass., 1961), pp. 12-13. 51bid., p. 12. 6Ibid. p 12 A; .“ r.~ I. ‘ .rri Eb. .~. .~\)‘ xflthin it. It is even difficult to determine whether or not iflw perspicuous language allows Tor a stock of variables and a quantificational mechanism to bind them. The lack of a quantificational mechanism, however, is not per i: evidence for the criterion's relevance: ‘The above critcwdrri of ontclryfi1M11 commit— ment is of course inapplicable to discc.rae constructed by means of combinatows. Once we know the systematic method «f ' bggquimp back and forth between statements which use combinators and statements which are vapia— bles, however, there is no Ol.ficulty in devising an equivalent criterion Of entrie- gical commitment for combinatory stcourse.l The use of a combinatorial logic, then, does not alter our mmmnitments, inn:rmarely altxnx; our’ynqx(\f *fip18321TQ3l319m. We must, then, determine what sort Of system the DGPSpicuous language is, though it is uncl'ar whether ren— tences of that language occur at all anywhv"e in the m ‘- - , f» . - . ~ .r‘,.». . ‘i ifiéélfiififlfig 'The ruflnare of‘iflie pewK411c“oan. «anpuanw: muii: be determined from the statements made about it in o" lancer C 1anEuage. And if the two languages curt r.* in assume the ex1stence of different types of entities, T1?» lhsrwug»;s a new elenent of perplexity into the problem ff inieag“*t mg the'PPactatus. For then it must be detecmg ed what the relation between the two languages is, and which ccmhitments haVe (f) >v‘ L.) L_J L“. a primacy in the system. But we argue thwt it is the perspicuous language which gives u: ts. altimetp Club to the nature of the objects. \ 7lbid., p. 10A. ( Tt 23pf3?arK3, tflieri, tluat sniy zitt63npt to <*orn 1th r tile 0 l ontology of the Tractatus must also COnsiOgI'iJM¥TRM&3P¥ o weaning developed therein. This requires a consideration of H . -. ,. r1 til‘WJI'y’ WhiCil the so-called "picture theory of meaning, has given rise to no small controversy. Edi; con ideratien is necessary because of the close correspcherce, already mentioned, between the elements of a sentehcc of the pergpic~ uous language and the elementary entitfxr v_fi ~>: “ ;P~O-,v ‘ 4 ( | ‘ . L'.‘—. - ‘ ‘ \ ._i .' ‘A V ‘ J --. ‘: -f\ , .‘1 -\‘~ ’- .. M“. .V l ‘, .‘ ~ 2—. «'fi ‘ ‘ r m,‘ ‘_ ;. . J... a | ' n "kn“ 'r ‘P I I‘- >. ‘u, ' u‘ “.‘f.\ L /‘ M‘ . . .7,~ . ,A .m—«A "‘ r I I-“nr . \, "J~V"‘“l .‘ 7. t .- ." .. ’ l .1» ' ~~ r ~ . . t» 41' ‘ .k ‘ v x v N -‘ “— k. A ‘7 MF". “ .V . .‘ . .h 4"] ‘ ‘ '- V, 4‘ . y. L4 ‘L ‘-4\»' '4' 4‘ ~ . ‘1," «I ‘r ‘ ’ ”N 4‘ (~‘f_ " ’NN . “h \ r... ‘. f2. . -." 1‘ :‘\ ~_\ r: ._‘c, l r 4_,.‘ ‘ , ‘l‘ A.‘ vlr“ ‘ \ 10 The cent’al issue, however, is that concerning the rumure of the objects, the basic entities which the ladder language introduces, and from which he composite entities Cf the world are constructed. The question to he answered 3 this: are the objects only particulars, or are universals b—J' included as well? Are they q‘alitied particulars, in the sense that they are entities which somehow ”sugport” material qualities? Or are they hare particula: , in the sen e that they do not have material qualities hut orly formal ones? Our answer to this question will determlae our answer to the final question of the nature of relations in the system exposited in the Tractatus' ladder langte c. All there ques— \ tiorms are extremely difficult to answer, for there are many gaps {and lacumae at crucial points in the equmd the Eudswers must generally be inferred from a close comptri« “N1 of various parts of the text. But tnere seems to he a way in: make progress toward answering ttose qawstiuns through mnnsideration of the elementary sentences cf the tOTUpiCdOHS lanenuage and the Tractatus' theory of nnxor. it is .;J:: must (decide whether or not only names of particulars r-t1: hltflie elementary sentences, or whether Lfiflnl cf Pigger trier alSO c>ccur. But as already remarked in our disens {on of Quixe A critelfiion, we must decide which variables a? tne elementary seUtences are to be bound by quantifiers (a_ axing that Var'lables do occur therein). We mist there ure nuy parti— c . . . Ularly Close attention to the theory of the Vhrl&bl€ ll exposited in the ladder language, and determine precisely what it is that a generalized proposition asserts. gut Jhile quantified sentences do occur in the text of the Tractatus, it is hardly clear that such sentences are genuinely elemen— tary. They may be merely illustrative deVices used to f 7 as - s' ' . s‘ci n“opcsitlcis as ;.e fac1lit1te the ex 0 ition In ucl kl _) l r , a *h y occur in the text of the Tractatus, functional varieties are bommj by quantifiers. But we must in iiit cake determine whemaer'such quantifications are consistent with what Witt— gensterin has to say about the basic sentenve; of‘the pe1~ SPiCULius language. The 'ssue of the meaning of quantified sentences is acnnicial one for other reasons. We have already pointed out that, according to Wittengenstein, atomic «r e eventary sen— I , 3 tencess consist of names only. What is the vote of variables -~. is Sucfli sentences? Do atomic sentences use variables a; all? fIf they do not, we of course cannot use quontLiicatibn at al]_, since there would be no variables To bind. As we pointexj out, one or two cases do occur it 18» Leader langu- age prwbpositions in which first-order varia;les are bound by quenitifiers; and it is true that no expl‘ i: re uyirtforr are Pliiced on the binding of variables by qwentifiers. Yet (T C CD }__1 ‘ 3 C T Q I weffluill argue that, on the basis of certair tax i n . . . 81° lri the Tractatus, variables and constn_:; acuve Type "On (“3 not occur in elementary sentences. The neues, we Sha . . i 7 JJ- argue, are names of particulars, and axe language an?) fi 0 0 ' ' ° Umeo the ex1stence of particulars alone ufi awe basic l2 entities of the system. This is similar to Capi's thesis concerning the form of elementary sentences: we shall argue that, if Copi if right in this matter, there can be no quantifications over functional variables . . . since, according to Copi's thesis, functional variables do not occur in the perspicuous language. What thesis we adopt concerning the nature of the basic entities of the system will have great inOPtance in our treatment of the themn31<3f relations in the Tractatus. If the atomic propositions contain only haze; for particu— lars, then our treatment of relations will differ consider- _1 a ably from that which would result from our allowing universals into the set of objects. Consider the sentences '5(a)' and 'affib ' th _, . ‘ ‘ ‘ “ T. Y ‘ '1' ': ~.., \ 'l‘f «“r‘ v" 'u ‘i ‘ "a ‘ ’\ , e latter being an expression Ami n c.cen octuis in the ladder language of the Tractatus. Let us interpret the first as asserting that an entity named by 'a’ has a certain property here indicated by the express'on 'r . Tye use 0 the Word 'indicated' is deliberately vague. Does 'h' name some object or other? If '8' names an okjr~t, hen fiHesum— ably We must be able to construct a sentence, e.g., {r} ((X)F(X))', in which 'x' and 'F' are var axles of d??? rent (4‘ L.‘ U "f‘f (‘3 1.. V types and are bound by quantifiers. But on |~+ (U L_c H U r» K]; . *4 \ wehaye two objects composing this state of a“?: there a relation holding among them? we mutt ask what tte “atUPe of that relation is then. Concernity this problem, ..,. V n. .. A. ! .o 4. ‘hV A» « ..;.. u. « L. . u 3 v.-. .3 a. pr. 7 .1 P\‘ \«V \ . .n. 2,... ~ , ;. e .. . \ . .s‘ n‘ . ~ a 0 l3 9 . . . ,. , . Bergmann’ has raised the issue of the nature o1 tne exempli— Iication "relation.” Since presumably 'B(a)' states that some object designated by 'a' exemplifies a universal, there arises the question of the ontological status of exemplifi— H cation. if universals are objects, and biidable predicate variables occur in elementary sentences, can we accord any status at all to a predicate such as 'exemrlifTes . Would it OCCLU‘in the perspicuous language at all. ssruming a mxnflxificational mechanism for the peéspicuo‘s language, thecquestion arises whether or not we woulu be able to Quantify over it, so as to commit ourselves to the existence Ofea relation such as exemplification. unfi yet it syrpirn Umn;\Ne must do so if we allow universals among our stock or Objects. A different, but analogous proolem arises when we comEider the other sentence 'aRb'. Presumably, this says that ‘the relation R holds between two distinct entities ruflneCi by 'zi' arm} 'b'. But Ch) 'a' curl 'b ’THYNCL61“6?HTL£Lllf1 R? Rather we might say that the (ordered) ;'iw exenlplifies the universal R. But in that case, we st? 3 have the exemplification problem. And fur ger,sa;mdr is not a particular, but a set. So shall we regorl sets and classes as being among the basic entities of the SYSldm “f theTractatus? We shall argue that we can; t do so. Cer- t O O O I l ainly it is not our intention to answer suns QUPCCJHCJ in _\~‘~__g 9 . p -. l... H Gustav Bergmann, Logic and healii; (t disoh, Hlfl., 196“), 13- 55. a "s u‘_\ h .\ “‘1‘ » is» (V, .k V‘v; . ~ q. "1+ N H. ’«..A. .4 ‘ C ... ..,.Aq+‘ u ‘ "‘1 V .t ‘ . .. - .. L ‘. :7 tr; Pov)“vv .. ..... Lg“ . “ -»"Vv V'A." ‘l .l (‘1'; w ~ L n1-.D‘W 1‘,‘>'_\ ' .;," ~J‘-.l ,_ . .j. , q~, 1 . .. , ‘« .4,” AA. JL‘ ;JI . 1 n".'m. "nn . ‘l \ ”H.v““u, n, ‘ ‘ ‘ ._ may“, 5;: r ‘.‘.'\"“"»J k rzwcc '32" .. sun“; .“1‘ s: a . " “f APWG‘ . '9'... __ J.‘ ‘~, - “irrfifih: "y hm..." 44.. .‘_ ‘ L iptcpr‘ 'T ' ... ..,._. ‘ .‘ Wirr‘.‘ ’ ' .A,.,1. 7“: PA" ‘ .. by Ll-“(A- ‘. .1." h LL41 C: A: ‘, ‘ \. VG 'a‘: -..- LS'fl-x fl 4"“; ’7 a,“- U; .m. an *H . .41 '«Ce .h‘ ‘5; ._ ~ “3‘ “a h V] ._ E “ .o , ‘ a I! ' ‘ - A a A ‘- h‘NrCrt. .. ‘IRHVC; L .‘ ‘r, a M b "u ’h ' 7' ‘4‘ L Ch . "M '.~\ \~"\ 1" c .Cnnn“ 1 “\JL’ \ .‘72'.’ 1“ this section, but rather to raise them. However, it may be that such problems can be solved by the assumption that the objects are bare particulars, that the names which occur in the perspicuous language are signs which correspond in many ways to the individual non-logical constants of a system such as the Principia Mathematica. For then, under such an assumption, relations can obtain only among such particulars, and configurations of such particulars can be represented by configurations of names; and such a "nexus" of names can be significant, as Copi shows. The configura- tion of names thus replaces the functional symbol, which disappears under analysis. And hence expressions such as the letter 'R' cannot occur in elementary sentences, and cannot be bound by quantifiers. But apparently this is precisely the way the problem Of the basic entities of the Tractatus stands. For the System of the Tractatus, as exposited in the ladder language, once we have reached the configurations of names which form the elementary sentences of the perspicuous language, there is no further analysis possible. Hence it may be that names cannot be eliminated from perspicuous discourse by paraphrasing them by means of descriptions. This is the question as it stands now: what sort of clue to the ultimate nature of the basic entities, the "objects," is afforded by inspection of elementary sentences? Much of our effort Will be directed to the answering of this question. And the discussion of this question will take us through a treatment lll|| . . I II III I - I. . .. y .. ., a . c A . .14 as 0 . .. . .A .u I . . . v. -, ,v. ..>. o . \ .r . 6 six . c .. . 5., .o i .. r . n :1 Cu . .... r, . . if A. . in v . ._r .. .T‘ a o .r .. -n ,- . . .. o... v. . l . o . .v . t... w . a _. v ,1 r n 4 4 Q; I Z a.» . . .. l a. O n‘. a . . - , PC. a ‘ no a a vi Q. 11‘ L .4 \. L L l v 4 .u. h; o . PM I. a r... r o c an r5? 0 7b .4 n U. k.« )u w -4 y” A Ly. . c . 3.. o . . . A C. “k. L. «L C , n. ._ ... ._ Lo 3. .. ... r. n. 7.. r. x. a .. 3: i ii .3: a o A; .1» 3 w. ~ ». .. r” . L. .>~ a... L. r: l. y: , . e 0 . i. no . . , ... . . 2 .. . .i x... C. .. .L a 4 vi. ._ x 4 . i .4 i. -. ., ,. » ._. a . C. . 5. .. .1u . . ~ n... . \ .1. . . .~. 3 x .. . u up v y . . , ._ p n . . .. z 4. m. .. vs . w. . h. . . p... a .. ..,. . . t .. . . . , of the Tractatus picture theory of meaning, s) that we may determine what sort of connection exists ietween the elemen— tary sentences of the perspicuous language and the reality referred to by them. since we are posing the problem of the nature of the basic entities of the Tractatus' system by reference to its theory of meaning, the procedure will be as follows: the remainder of this chapter will be devoted to on examination Of certain doctrines of Frege, which strongly influenced Wittgenstein in the writing of the Tractatwh; we shall also look briefly at some of Russell's early work en the theory Of descriptions, and then we shall proceed it a more detailed study of the earlier works of Wittgenstein which bear on the problem at hand. in the second Chapter of thS essay, we shall proceed to a discussion of the Tractatus' doctrine of H H the nature of the world, as it is presented in the ladder language. In the third chapter of the essay, we shall pro— ceed to a study of the picture theory of h hfllfif so far as it is applied to the elementary sentence» n“ the perspicuoun language. We shall, in that chapter, be es fr . . r ‘ ’ 2 . ,‘ ‘ ,-,. 1 \ /1 “.3 t: L. l. :1 i. if C. on C t: I l .1 E ' u With the correspondence between the reality wnich the ser— k Spicuous language describes and the perspicuous language itself. In the fourth chapter, we shall be concerned to decide the issue of the ontological status «f the ob‘ccti. TO accomplish that, we shall introduce two hypotheses con— sis which asserts that names of universals do occur in elementary pro— positions, and try to argue for it on the basis of textual evidence for it. We shall decide in favor of the first hypothesis, however. In the fifth and final chapter, we shall dis uss some problems concerning the application of the theory of analysis presented in the erctstuc, particu- larly with regard to our adoption of the ”nominalistic" hypothesis. Indeed, on this hypothesis, the Tractatus may appear to be inapplicable to any actual aialysis of situations in the world. But this is not to deny its merit as a philoso— phical work. The Tractatus contains a wealth of profound suggestions concerning the nature of language and meaning, the nature of logic, and the nature of the world to which 0UP language must ultimately be applied. The essential cor~ ti“Uity between the major themes of the Tractatus and torso Of Frege's and Russell's work cannot be denied, and there iSTND doubt that Wittgenstein believed that he had solved Uwst (3f the major problems which both had rcised." Se 3 10Wittgenstein, op. cit., p. S. , . "V'.“. V - .— P- .“-,. I "';' nu ” o1 . ,\ _. I. . '1 :nn [‘ -\o'_. ~ ~ '. ’h .‘r -,, ._. ‘ “~V‘ "‘ "M \-_ . 2| ~I pt .4 : u ' re . _ .I h ' k‘ H u, ..A p a ‘r'. : q — r u. ;3 w- H‘ .. ._ '1 I ‘ ~ ‘ ’ a t-I .’”- o.‘ '~»‘ H ‘ -- ‘O 'I - . .g " "__ _;;v. . ",‘H ‘f I“?\. “.4, ..«I'WN 3 .i ‘ ‘ .M . ‘g ‘ . . v. 1 ‘i l.‘ ';"‘1, .1“. r; a. ‘.~4:1 R "o “in” _ ‘L. . V‘H.‘ J._ “r «1‘. _‘ ‘4 _ ‘L. 5",L ~Iv‘-l' ) f, L. . ,V\ - c ‘-. , a .i‘, ,V‘ «A. 'u ’4. .‘. \ \ \ .a $- . r;- v a ‘1. 1"; *_. ' 1’; L. ‘ . 1, ’ ‘ . ‘ l H kq «u. s .g‘ ‘~‘.’ .:~ ‘ - u v ‘e \ -. L '.\ - r ‘,~?‘$ l‘ o P“ 3 r1 4 .~ ‘ .’. v . “ ‘. 1‘ r Ea l7 believed himself to have solved the problems raised by Frege's Sinn/Redeutung distinction, those raised by Russell's theory of descriptions, and some of the major methodological certain that (f) problems of the Prinicipia Mathematica. It i |\ nmjor themes which occur in Frege's works (the Sinn/hodeutung distinction, and the concept/object distinction, the nature 1 of the thought) are reworked extensively in the Ni ,. 4.. ,. iractatus L and in the earlier writings. Hence to a c nsiieration of mud) problems we now turn, with a view to referring to them fnmn time to time in order to s'ow how the: are transformed athittgenstein's hands. 5. Frege: his Theory Of Meaning Fl Much of the discussion in the Practitun is directed in p-4 towarwi issues raised by Frege's theory of meaning, ant this :section we shall exposit and discuss time of these issues;. Frege's work on functions, on the association of functicuiand concept, on the contrast between concept and Object;, on the famous Sinn/Bedeutung distinction is impor- tant txa an understanding of the Tractatus and to its dis— cussiorlcd'language in general. And by extension, it is important for an understanding of the questions arising about the ultimate constituents of the world which are dis— cusmai in Wittgenstein's early work. The cnnhection betwe~n ' O I a 0 fl Frege:3 work and the pre—Tractatus writing: is particularly ianPtant; all of which is not to say that all of Pro vunk on these issues is carried over into ice Tractatus III I I I I .I Z . . . A . v. .. V. . . . . . .. . c .. w J r . . . . x x _ .. .J . .. a” _ fl. .i .... l ,4 . .. r. ... .1 ..J a: . Y. O. . Tn ;. .5 -.. ...a .t ». ...- e ,. ... v. .u Ly .... .1 Q. m! A I ».l 4 .I x . , ..pu & v u v . A ..44 c~ . .4 u. .« VA. fluv— n.U “\V k a fig AN~ .. .Q .2. . .. i . . .. .... S .. .u .... .14 T? .r» a. .2 w . H. 7. 2. . . .-n 1... . .8. ... r. v. c . . r .. } at. r . F L.. L my” .... ..‘n . .ru r. r. .. V“ r: u . f: It A: o. M at. t J T. J h. f .. ... C .1 -.. . .. . T. T n. ...: - A ... u . ‘ . .y—L \1 u. . a raw x. a . w x. . f. . ... 4 3:» .r.A .h- r .. .... TL . . 7.; .. .. r;_ ~ .1 n. .. t. ... l. a . .. . ;. V . ;.. A. . . . w . . . (I. .u. r .. _ , . v . . . s . . . . r , l , , ... . . . , . . . a ... . ._ .. . ‘ .... .f. . . 3 . q .. ... . v . t T. A, . . . . r , . X . ‘ 18 vfllfinaut modification.' One of the central concerns of the Tractatus is to modify the doctrines of Frege (and Russell) in such a way that these doctrines come to form an ade— quate, coherent theory of language. Wittgenstein's earlv ’ u gropings toward such a theory are found in the early Note- books, lQlU—lglb, and in the Notes on Logic of 191?. The L) latten'work from the basis of much of Russell's subsequent wordc, which found fruition in the 1918 lGUlnth on logical atcnnism. But we are more immediately concerned with Frege's work. In the cou‘se of his researches into the founfs‘iore Of rnathematics, Frege came into collision thh various pro- blenus regarding such basic mathematical notions as those of finiction, variable, argument, and the like. it became necessary to provide some sort of systematic treapnent of these notions, so that a clear account of the foundations of mathematics could be reached. As a result, much of Frege's work is directed toward their clarification. One of these notions is that of a function tut according to Frege, the term 'function' is difficult to ex- plicate because of the various confusions which attasned themselves to it over the course of mathematical historv. Firstly, says Frege, it is Clear that an e:»fp1":‘;;:sf1on L‘.’l";"“h designates a function does not designate some particular determinate number (assuming that variable; rang1n* ortr mmmers occupy the argument-places of the expression degir~ if: ruming the function). Consider, e.g., the expression 'F(x)/b'. 19 If we substitute numerals for the variable 'x' occurring in the expression, we get a different value for each substitu— tion. Thus it appears that when a numeral is substituted for 'x', what is yielded is an expression which designates a specific number. In expressions such as '2(l)/6', '2(3)/6', etc., we seem to be able to discern a common factor. It is this "common element" in the expressions, says Frege, "that contains the essential peculiarity of a function . . . "11 The common element is indicated by the €Xpression which has the variable 'x' in an argument—place: '2(x)/6', as indicated. But the argument is not part of the function; it is WHEN: completes the function.12 The function alone is what FPegge calls incomplete, or "unsaturated.” The function is I“QCOgnized as the common factor which a set of expressions ”figflit have, such as the two expressions mentioned above. 1h”? in both cases, the function is completed or "saturated” ~-L by 51 different number. The number is the ergdment of tVe VAJ\v f1«111Ction, and the argument is complete, not in no . ’Y\, ‘d of sup— plementation. We can say that an expression unsignatin; the arguwent of the function is complete in itself, uni does not neEd supplementation by another expression in order that it should have meaning. The function itself, on the other 11 . . . . . Gottlob Frege, Translations from the fhllOffll'L“¢ §Ffl£lflg§ of Gottlob Frege, Peter Geach and E7: Black { Xford, 1§Eb), I3- 2“. 12Ibid., p. 2a. 20 hand, is incomplete, and does need supplementation by the addition of the argument-entity. The argument itself does not belong to the function, is not a part of it. This dis— cussion suggests that, for Frege, both function and argu— ment are not to be identified with expressions, but are entities in their own right. And Frege due: take such a stand; the function—entity is supplemented by the argument— entity. This supplementation of one (incomglete) entity by another'(conmlete) entity is what concerns us now. In gen- eral we can say that, corresponding to each supplementation Of the function by an argument, there is yielded a unique value. Further, corresponding to the total range of possi— ble snapplementatitnnsa b 3. .4 > Au. . »~. Fla ~— .. . . . ‘ :.. 3.. .. A & uE. . r . r. . s . .I. L... 22 '3 . . . '2" = 14' stands for the True as, say, 2 - 2 '2L' stands for A. And '2 = 1' stands for the False.lu As Frege goes on to explain, all true statements designate the same thing, viz., the True. Correspondingly, all false statements, no matter what their content might be, designate the False. This is the basis for Frege's introduction of a distinction which is of the greatest importance for the Tractatus: the distinction between the sense (Sinn) and Umarwaference (Bedeutung) of an expression. For Frege, differwant expressions can designate the same truth—value, butrnot express the same thought. As distinguished in the essay "Function and Concept," which we have .een discussing, the rexference of a saturated functional expression (contain— ing thee identity-sign as the major functional symbol) is the trnith-value. The sense, on the other hand, is the thoughn: expressed by that saturated functional expression. And FTTEge argues here that expressions may have the same refererice, i.e., be both true or both false, but differ in 13m trKDught expressed. The expressions spoken of here are statements; it jfi thezmg alone which have truth—values. Thus it seems, at least 117 the case of functional expression: containing the identito-sign, that what results from the saturation of th 0 o o o u o e furlCtion is a statement which is either true or ialse. _i___“___ 1A Ibid., p. 28—29. 23 In the case of an identity statement, signs for non—func- tions (such as the numeral '1') can fill the argument- places of the functional expression. Let us first consider the propositional function indicated by the expression 2 'x = 1'. There are two, and only two numerals which can replace the variable 'x', viz., the numeral '1' and the numeral '-l'. When either of these numerals is substituted fbr the variable 'x' in the functional expression, the re— sulting;equation is a statement which designates the True as We say, then, that both the number 1 and the 15 In its reference. lumber“ —1 fall under the concept: square root of l. generaJ_, then, "a concept is a function whose value is always EitPUtri—value."l6 In other words, all concepts are functions, but not; all functions are concepts. Of great importance for Frege is that the notion of functicnq and that of argument have been extended beyond the realm c>f numbers. Indeed, the extension is radical; in Frege ' 8 words , Not merely numbers, but objects in general, are now admissible (as arguments); and here persons must assuredly be counted as objects. The two truth—values have already been intro— duced as values of a function; We must go further and admit objects without restriction as values of a function.17 Chm tYDee of function in which we are interested, however, is the cubncept: and the concept is that type of function \ lSIbid., p. 30. p l6Ibid., 3o. 17Ibid., p. 31. J .Jmahh—w—u If“ - v ‘ iv A .u - a)! . A ‘loVL‘ ha ‘ D ‘ S u :n n: V‘ .1..».U V..-“ — r“ “ 32‘ ...-1‘ use A u- a ‘ ‘ . cC-¢r‘-’S V ‘3‘? ‘n i- coy‘u gleVWEO “JR 5 M' "\QI‘UIV . ‘2' 3 ‘~ ’ IMJ “mung W: r R“, y.< "v‘ Q” on Q Infl'fiens I u WV“; c v, “ w o.“ 'H A A ‘ €89; fiflt, \vj “In: a 1* ~ ...u‘ete ,Y ‘t .. I ""9“ c 2A which takes a truth-value as a value as we saw. Notice that Frege designates objects as the type of entity which can complete or "saturate" a function. But objects are now called values of functions; since the truth-values, the True and the False, are values of functions which are concepts, it follows that the True and the False both are considered by Frege to be objects. Indeed, this is just what he does say.18 The point to be stressed here is the sharp distinc- tion.between function and argument, and between concept and Maject. The latter distinction is put by Frege in the following words: The concept (as I understand the word) is predicative. On the other hand, a name of an object, a proper name, is quite incapable of being used as a grammatical predicate.19 AcOncept, it should be said, is not a psychological notion for. Frege; it does not depend for its existence on the‘ everms of our mental lives. We may, of course, think abggt colTlcepts, but we do not manufacture them, as it were, in the! course of our thinking. A concept is a type of func- tiOnwhich, when saturated by an object as argument, yields am3ther object as value: that is, one of the truth-values, the TTme or the False. An object, on the other hand, is an entity which can be designated by a proper name. It is complete in itself, requiring no supplementation by any other entity. Thus, we predicate concepts of objects, we 18 19 Ibid., p. 32. Ibid., p. A3. ‘ I no ‘. ”V‘“ . .1- .i¢0 &..¢\ '0. - .‘r: ‘v ‘rl uva 4.1.I‘J‘. Lisa: ~.; gr“::;\‘ '0 «-~ Ah”; Hb‘b ' I 2' «0-559 :4 ..., "L‘ , “4" ...;e o ... H~~ ‘ . . ‘- i... J$;VQCC-: ' i a P“ I.‘ n . "? nu‘ ‘4‘ SD” ”1 . h ‘J i ' ;: “H‘s ‘ . ."A:'Efl 7". M V! l h,‘ ‘ whi"‘~‘\'r:‘. M‘u‘ )4. ~‘i d0 0:. a h l‘t.c . t ‘- ‘ In . .‘_' y,” . ‘ "Cue “. ~ I. “‘ ah-w- ‘31 \_. . ‘\ n “K. . "w‘2"" ~ ‘1“! . I‘l ‘ I... . u an“! A » v‘ , “Q51 bl. 4A‘ ‘1?“ k cy c U T}. ‘I‘M? a4; ‘-.‘ ... .'D \ \ 'c I ‘the '5 25 tie predicate terms to subject—terms. This means, according to Frege, that words and phrases beginning with the definite article, when they do refer, designate objects. And proper names also designate objects, when they designate anything at all. This is equally true of cases in which one might not think that the principle would hold: take for example the phrase 'the concept 'horse". This phrase designates an object, if anything, just as does any phrase beginning with 'the'. Thus the complex term 'the concept which I am now discussing' designates an object rather than a concept, and thus cannot function in a sentence as a term designating a cormept. Frege accepts this apparent anomaly with equani- nutyr, apparently regarding this phenomenon as a freak con- seqLuence of his discussion of the concept rather than as being of serious concern. To repeat then: a concept is a function which, when satlurated by an object as argument of the function, yields a tPEWh-value. These truth-values are themselves objects, and \ve find that when an expression for an object (i.e., a propen'name or a phrase beginning with the definite article) SUDFXlements an expression for a concept by filling the latten”s argument—place, the result is a sentence expressing a13hought. But further we find that such a sentence, so formed, designates or refers to the truth—value which is yielded by such supplementation. Thus we are brought again to the famous distinction whiCh‘Frege draws between the reference (Bedeutung) of an A!) A l 26 expression and its sense (Sinn), which we have already introduced. Frege begins his discussion of the distinction with a treatment of the problem of identity and the problem of predication. Identity, for Frege, is a function whose arguments are objects; for we saw that by filling the argu— ment places in the sign for the identity function, a proposi— tion is produced. Now identity may be a relation; hut the question is, is it a relation holding hethgn objects or between signs designating objects? In his important work of 1879, Begriffsschrift, Frege answered this question (temporarily) by opting for the latter: in that work, iden— tity is assumed to be a relation between signs and objects. But this answer is rejected in both "Uber Sinn und Bedeutung” ~W and "Begriff und Gegenstand," both of which appeared in 189-. \) The relevant notion here is the idea that ohjec“s can "fall under” concepts, and that concepts themselves can ”fal }__J 61 . . under" concepts of greater scope.c But objects can never be predicated either of concepts, or of other objects. Now at first sight there seem to be caunter-instrntes to this: e.g., 'Venus is the morning star' seems to ye a Sentence in which one name is predicated of another, so that the corresponding situation in reality would be one in which micmject "completes" or ”saturates” another. hut this is rmt quite so: we are indeed saying that the morning star multhe planet Venus are identical, but the sentence is no: x 201212., P- 56- 2ll‘oid., p. U3, ,1 27 nerely an ”equation" with two proper names standing on either side of the copula. Rather, the sentence is saying that the morning star is no other than Venus.22 Here the expression 'no other than Venus' is analyzed as designating a concept which is completed by the object designated by 'the morning star'. In this way Frege analyzes identity as a problem falling under the concept/object dichotomy and analyzable by means of the dichotomy. This noun: that it cannot be regarded as a relation between names of objects; and the paper Sinn und Bedeutung rejects this earlier solu- tion, as does the paper on concepts and objects. But identity raises problems still. Sometimes the discovery that two objects previously thought to be dis— tinct are identical contributes markedly to our store of information. True, the object in question falls under a concept which is completed by only one object, but the Concept/object distinction is still used to solve the pro— blem, even though the identity-concept would seem to require 2&9 objects for its completion. Let us try to bring the process into relief by which identity contributes to and extends our knowledge. We know that a sign can refer to something; at least we can say that it purports to refer to something. hut if we are trying to determine how we understand this sign, pOlnting to the referent of a sign is not enough. We under~ Stand that the referent of the two expressions 'Venus' and x 28 'the morning star' is the same for each expression. Each n‘them, that is, designates the same object. But the expressions are different. To complete his theory of mean— ing, therefore, Frege says: It is natural now to think of there bein‘ 3 ) connected with th, sign (name, combination of words, letter), besides that to which the sign refers, which may be called the reference of the sign, also what I would like to call the sense of a sign, wherein the rode of pre— H’T—“‘ . . '3 sentation is CODt&lfl€d.2J Thus, as mentioned, the reference of the sign 'Vénus' would be the same as that of 'the morning star'. But the sense Of the two expressions would not be the same. Now we know that proper names designate objects. but one and the same object can be the reference of different Signs, some consisting of one, others of several, WWTdS. The Signs themselves however may differ in sense. .c a sense COrresponds one and only one reference; and to that sense there corres onds one and only one sign hut to the refer— p t. E) ’ PM , ehce there may correspond several signs.” But we mu. :1mmediatel ualif what has been said. Some sighs clfidgj y q y a a a they ma have a sense ma fail to have a reference' as 3 3 Frege says, The words 'the celestial body most distant from earth' have a sense, but it is very doubtful if they also have a reference. The expression 'the least rapidly converg rt series' has a sense but demonstrably no reference . . . In grasping a sen c, ’re is O '1 ‘ 'rwa not certainly assured of a reierence.e» \ 2 . f) [- . _ r, 31b1d., p. 57. C3lh1d., o. bd. 2ulbid., p. 58. 29 As in the case of concepts and objects, the sense and refer- ence of a sign is not produced by one's mental activity in grasping them. The consideration of the sense of a sign may indeed rise to certain ideas about the sense, but these ideas must be distinguished from the sense. The sense is what can be grasped by many different persons, though the idea of this sense may differ radically from person to person. Not returning to the reference of proper names, this, says Frege, is the object which we designate by that name.26 We may have an idea of this object; but again, the idea and the corresponding object must be sharply distin- guished. Frege distinguishes three different ways in which the difference of signs can be considered: one, the idea, the subjective process of thinking; two, the senses of the different signs; and three, the references of the signs as well. People may differ with respect to the first, as noted, but they grasp the same sense in the case of each sign. We say, along with Frege, that a proper name expresses its sense, and designates its reference. But what about sentences? We have intimated several times that it might be appropriate to speak of sentences as if much of the same treatment accorded to names might also be appropriate to sentences as well. Frege spoke of differ- ent senses being expressed by different names, although the 26Ibid., p. 60. 10 ~ reference might be the same for all the names. And it seems that, according to Frege, the same thing might be true of sentences as well. Sentences with both sense and reference, 27 says Frege, contain a thought. The question is whether the thought is to be regarded as either a sense or a refer— ence. We have already said, however, that the reference of any expression is an object, and so the question becomes: is a thought considered to be an object, ard is this object referred to by the sentence? Let us consider any sentence, say 8. Let us assume that S has reference. Now, says Frege, if we replace one word in S by another having the same reference, the refer— ence of S does not change, but the thought expressed by S does. The thought, according to Frege, is the sense 01 the sentence.28 But the question then arises concerning wnat the reference of the sentence is. Above we said that a sentence results from the supplementation of an expression for a function—~or rather a concept--by a proper name of an object. And we said that the truth value y eldei by such supplementation was in fact the reference of the resulting expression. And the same situation obtain: in the ease of sentence. The sentence designates an object, either t True or the False, depending on whether the sentence is true or false, respectively. And the True and the fui;e ave the sole referents of any sentence, assuming that the sentvnee ?8 27lbid., p. 62. ‘ IhiQ-> r. 53- » . x b A l a .a r, n A ‘1 . i. .1, .~ \ V, s . ’ I. 1‘ ~ :_ ... .. ‘L. r‘o .— . ~.<. t..lr>.l: ‘- . ‘I-I'mlxlll . g 4 o \ .n . .v . zd _‘ . ol‘ - . . . c . 3 a A; .r.. r C» ‘ .s I . . v ,N PM» .v‘. .1 . U.‘ is A]. ‘4. r; e . d u s « .-.. n h. ,1. .r. w .. a T I. L . r .. L. a. . | .H H . y M 0‘14 I 1 t fifl‘ ’ LA L. r . ;, l . ,I. L» . . . r . . c . £2. H ‘1, . .‘ saw 5 .~ v.. Q. ..s r u r.. c s . -.« .... . y r . \l. L h 1 .h . » “~ A uh.. v \ t t r . v n H K .r . « ... l I a A A .. 31 does have a truth value.29 Sentences, then, are complex names whose references are truth-values. It is this latter claim with which Wittgenstein struggles in his early writings, many of whose themes appear in the Tractatus itself. Many of the claims about the mean— ing of sentences which one finds developed in the ladder language of the Tamunxfinxs are directed trwnnri;h sues raised by Frege. And while many of Frege's doctrine; concerning meaning are disputed and often rejected in the Tractatus it is often useful to contrast Wittgenstein's revision of, e.g., Frege's Sinn/Hedeutung distinction with the original distinc- tion. It is also useful to determine the mifference between Wittgenstein's notion of an object and Frege's, since this I '1 Ixflxion, as we shall see, undergoes considerable revision at Wittgenstein's hands. Thus far we have discussed Frege's treatnmnt of (l) the concept/object distinction, (2) the correlation of the notions of function and ctncept, (3) the treatnnent of sentences as names of a certain tyne of object, ““1 (H) the Sinn/Redeutung distinction. All c1 these come 1n for’analysis in the Tractatus, and under this analysis they experience considerable transformation. rut our claim is that such transformation provides us with consiierab-e insight into Wittgenstein's treatment of the terspicumus hflguage, whose properties we shall be concrrnvd to study at length. \ 2 91hid., p. 63. It is to be noted, howeve names also came under scrutiny fr Ins theory of descriptions from h Wittgenstein was also dee mly infl and the latter a r, that Frege's theory of om Russell who evolved 3 is study of Frege's theory. uenced by Russell's theory 130 comes in for revision 1V the Tractatus. Therefore we shall briefly summarize some salient features of the theory which are expceitsd in ’2‘”; '1 ’ 1 Russell's early article ”On Denoting.”' h;e pa: 3: the discussion occurring in that article in which we are inter- ested is that concerning the meanirgf of ”denoting phrfises" beginning with the definite article. A denc ing phrase is a pharase which refers to objects in the W(nld 'scme man' ' 4., any nen', 'every man', 'all men', 'a man', 'the man' are al] ,3 31 ‘ _ £— . .. . i . . 4-“ - denoting phrases. we are presently CQMCGPLCJ w.tn derKDting phrases such “3 the last one, which CWNCHLHS the def‘inite article. Russell regards denoting pirases Containing the ( o o a o - . . Jef‘inite article as raising a number of DPCGJOES wic* renter arTNJnd the distinction drawn by Frege between the :j* """ and Lh€?.bedeutung of such a phrase. Russell construe: Frege's lvlevl as follows: a name, in fact any expre sign mitn L‘Lu ‘glrrl and Bedeutung, seems to have sign“1lca.*e in isolation fPCNn any occurrence in an actual sentence Thu: the n«n~ \ 30 o I’ .v_ 7 j -1. Bertrand Russell, Logic and an vle1ww, ad. t~pert Ck‘iar‘les Marsh (LOUdOn, 1956): pp' 3llbid., 31—56. Jflu a . ...-..tiiliul» . ~ '17 (....I~. 'Venus' has both Sinn and Bedeutung as it stands, apart from an occurrence in some sentence. ”Nessus', the name of the centaur whose shirt caused the death of hercules, has Sinn but not Redeutung, so far (s we know. But Russell's view is that no denoting phrase has any significance in isola— tion from some occurrence in a sentence. The prohlem is that v Frege seemed to treat proper names and what Russell calls rn (mnoting phrases in much the same way. they both have objects as their Hedeutungen when they do refer. But for Frege, when either proper names or descriptions fail to refer, the sen— tences in which they occur are devoid of truth—value. Thus when the denoting phrase containing 'the' (which Russell calls a "description") or a proper name which is the subject Of a sentence has no Bedeutung, the sentence itself has no Bedeutung (or "denotation" as Russell would say). But for Russell's argument the central point is that names and des— criptions in isolation, for Frege, can have sense (or ing" as Russell construes it). It is this View which Russell wishes to combat. Consider the sentence 'Scott was a ran'; this is an l—h nstance of the propositional function 'x was a man', with 'Scott' the name which fills the argument—place indicated by 'x'. But Scott was the author of the Waverley novels, hence we ought to be able to say: The author of :ierliv was a man. But this is not a sentence of the form, e.g., 'flanfxl’. What this says is: 'One and only one entity wrote Wayerley, I I ll . I II | c t >7 A, £ .. H A . .. . o . . ...; , C u . u. . who ‘L .nJ n.» v... NC hi 3C 3C G: Ll... n U» s ,_ Wu .2 a: a . n u r .. .5 G u 4i P... r .. er . rim 4 + {i : i. AM. ”H n\.. Th . u 2 .1 A. a0 AG ..U ..c ...d O s '1‘ ‘14 C h .. oi.H WC may. «in o. . ‘AH MW 4 I :4 u: an kw. , \ LH4 no n0 -3 h. n . .. $ 1 o . n . . H 9. G v A c «\u ~l‘ «I. Q» 3,» Lu” n». nAu - . a» ' 2. L w r1 F... fly AH. Ck r.. h.» Q. £2 + . L Ai. w. . ab 5.. e . a l .c . u v 2 «\U an» «A» ...—r. 9 «C i. Cu A .. ~. . a: 3 . s L .1. 7 a . u 7.. n .. ‘ AH. ..Wi . s u: .1 a ya) r.. . u . . . . a y . A 1 . ~ x v. . r l i u . . p“ r C; a.» . . c n. ; x C4 a.» a v 1. i 1. ; u ,r .. .. ..5. .p1.. .J )p’ t. - uIJ r.‘ ' |£ . .Il.‘ ‘~\ I L. “k U u‘ .x. .I. F h u .I u Q.» U i. I 3M and that was a man'. Given this exposition, Russell is now in a position to explain his construal of the notion of denotation. We construe 'Scott was the author of Waverley as follows: 'It is not always false of x (or equivalently, 'There is at least one object x') that x wrote Waverley, and it is always true of y (i.e., for all objects y) that y wrote Waverley, only if y and x are identical, and x is Scott'.32 This construal, says Russell, solves a number of puzzles. George IV, it is said, wished to know whether Scott was the author of Waverley. Now presumably, since 'Scott' and 'the author of Waverley' designate the same man, we can substitute 'Scott' for 'the author of Waverley' and get the sentence: George IV wished to know whether Scott was Scott. But this, given Russell's construal of denoting phrases, is precisely what we cannot do. The fully para— phrased form of 'Scott was the author of Waverley' contains no denoting phrase 'the author of Waverley'; and hence we cannot substitute the name 'Scott' for it.33‘ In fact, Rus- sell's scheme allows us to paraphrase away all denoting phrases; it provides us a method of analysis which allows us to determine the truth—value of the whole by determining the truth-value of the constituent sentence in the paraphrase. And this means that all denoting phrases can be eliminated by this process. 32Ibid., p. 51. 33Ibid., p. 51. Fl 4...... .... , Elia 35 This theory also allows us to deal satisfactorily with nonentities such as the round square or the solid-gold mountain. We no longer need, a'la Meinong, to postulate realms of being in which such entities subsist, but which do not exist in this realm. 'The round square pot-holder is on my desk' becomes: 'There is an entity x such that x is round and x is square and x is a pot-holder, and for all en- tities y, if y is round and y is square, then y and x are identical, and x is resting on my desk'. At least one of the constituent sentences containing the bound variable is false . . . and thus the whole is false. Barring such cases as negations of true sentences containing denoting phrases, this is, according to Russell, the fate of all sentences which contain denoting phrases which fail to denote anything: they are false. In contrast, Frege analyzes sentences con- taining terms or denoting phrases without Bedeutung as being without truth-value. An exception to this is the type called a belief-sentence: 'Jones believes that Santa Claus is fat' depends for its truth-value, not on whether Santa is fat, but on whether Jones believes it. Q. Wittgenstein: The Early Writings The foregoing considerations bear heavily on the thought of the early Wittgenstein, but precisely hgw they bear on it remains to be seen. The ensuing discussion of the pre-Tractatus writings of Wittgenstein affords a con— venient bridge to the Tractatus itself, since issues which mhi vli f\ 5. cl. I I1 : .Px .K. .... a: h . a: a: ; v Q,» .. at a c an to n c s t a v .... ..3 . i U... n. p1 r1 u ...u 2. r“ ... .5 w” . l C .C a. .... e. . D. n v » .. C. is .w u to Q. .a u .3 ~35» Ar.» 0 .c 6V nxv \ v s .. «m» s v s b . v ‘\v ‘fih t .- n, M s .u .C 7 .,. -.. 7. r. .u .4 3 fl. .. . ... ... . . . u. . c .. i. 3» rd 3. «b» r.» B. 2. ..a r... .. ~ p .. pu~ -. . Pun ~\» n ., n b 1. :p » us.» I u u .. or n ‘v n n. . u u min .A .- . 1B. .A I: 36 are introduced in the early writings also are discussed in some detail in the later work. We shall concentrate on the "Notes on Logic" September, 1913. And in particular, let us concentrate on the problems of the atomic proposition as this idea is developed in the early writings. As one turns to the ”Notes on Logic," it immediately becomes clear that Wittgenstein rejects Frege's position that 34 sentences with Sinn and Bedeutung are names. Wittgenstein seems to think that Frege regarded propositions as being names of facts instead of being names of objects called truth-values. But Frege under no circumstances argues that facts are objects. Nor does he argue that truth-values are facts, and nowhere does he argue that facts can be named. This claim, whether or not Frege made it, is explicitly de- nied by Wittgenstein.35 But it is difficult to determine whether or not he is disagreeing as sharply with Frege as he maintains, for Frege does not hold the view with which Wittgenstein credits him. For Wittgenstein, however, we can be sure that sen— tences are not names in any sense, and in particular they 36 are not names of complex entities. It can be gleaned from the text that for the Wittgenstein of the "Notes on Logic" facts are composite entities: whence it follows that facts 3“Ludwig Wittgenstein, Notebooks l9lU-1916, ed. G. H. von Wright and G. E. M. Anscombe (New York, 19613, p. 93. 36 bid., p. 93. Ibid., p. 93—9u. . l. g. ...l 'a‘-I734 H. .9- Nu .‘fim- mm 1.... P L . . NR. . .w réz... .. L 37 or states of affairs cannot be named, for it will become clear in the equal that only simple entities can be named at all. This means that Wittgenstein must show how complex entities which are purportedly named can be analyzed in such a way that the name disappears and is replaced by an expression which represents the result of that analysis. here Wittgen— stein can draw upon Russell's theory of descriptions, pre- viously discussed. But this theory undergoes considerable revision at Wittgenstein's hands, as we shall show. What we shall concentrate on, for now, will be the theory of the atomic proposition as developed in some of the early writings of Wittgenstein, as well as the transformation which some of Frege's doctrines concerning meaning underwent at Wittgen— stein's hands. At any rate, we may say tentatively that, for the early Wittgenstein, what corresponded to a sentence was not an object, not a truth—value, but a fact. What sort of fact a sentence corresponds to depends on the truth—value of the sentence. Or, in Wittgenstein's own words, What corresponds in reality to a proposition depends upon whether it is true or false. But we must be able to understand a proposition without knowing if it is true or false. Wha, we know when we understand a proposition is this: we know what is the case if it 's true and what is the case if it is false. But we do not necessarily know whether or not it is actually true or false. To understand a proposition is to know what is the case if it is true and what is the case if it is false. It appears 37Ibid., p. 93—9“. 38 that the above :uxxMhit of understandirmqtdn:rmeaning of a sentence dovetails with Erege's account of the sense of a s-ntence: we do not need, according to the theory there developed, to know the reference of a sentence in order to be able to understand what it says. Rather, we need to know its sense, the thought which it expresses. Wittgenstein amends this to read: we understand the sentence if we know what is the case if it is true. The two formu.ations appear at first sight to be remarkably similar, since for Frege a thought is "an objective content, which can be the property P 3J Wittgenstein's formulation of the of several thinkers. problem might be thought to be a more explicit version of Frege's "thought." In this formulation, a thought would not appear to be identical with a state of affairs, nor would it be identifiable with the subjective mental image of that state of affairs. Presumably it would be something sui generis, a sort of representation of a possible state of affairs, and this representation could be the common proper- ty of several thinkers. But Wittgenstein's next pronouncemen' makes this seem somewhat doubtful. "Every proposition is essentie 39 true-false," he says. A proposition, that is, is essen— tially bipolar; one pole is the case in which it is true, and the other is the case in which it is false. So far, no real deviation from Frege. However, the relation of the 38Frege, op. cit., p. 62. 39 Wittgenstein, op. cit., p. 9U. following pronouncement to Frege's formulation seeks to be quite another matter: says Wittgenstein, "We call this (i.e., the bi-polarity of a proposition) the sense of a pro— position. The meaning (Bedeutung) of a proposition is the A0 fact which actually corresponds to it. Thus, the true— false olarit of a sentence is its sense' the fact corres— 3 ”meaning”). ponding to it is its reference (or Here there is already divergence from Frege's posi— tion. The sense—reference dichotomy is from Frege, but it suffers a reinterpretation at Wittgenstein's hands, even in these early writings. For Frege, the reference of a sentence is either of the objects the True or the False, depending on the truth or falsity of the sentence. This assumes that, on Frege's view, the subject of the sentence has a reference, for if it does not, the sentence has no truth—value at all, and hence no reference. Now Wittgenstein does not seem to be talking of such a thing here. "Neither the sense nor the h‘ l I H - “nan. ,\ .‘r' lie ()Ci‘)’ A) ) CLHCi \v‘fillle meaning of a proposition is a thing, Frege seems not to be explicit concerning what is to count J as a thing, it is possible to regard all objects as ”things” in some sense. According to this view, both the True and the False may be regarded as (abstract) things. hut (still in line with this view) a thing cannot be the reference of the sentence, according to Wittgenstein, be ause in such a case the proposition would become a name. And Wittgenstein U0 A1 .Tbid., p. 9A. 'Ibid., p. 9’4. HO wants to avoid saying this at all costs. hence, Frege's idea that the Bedeutung of a (declarative) sentence is either the True or the False is rejected and the idea that the reference of a sentence is the fact corresponding to it is put in its place. Hence it remains that, for Wittgenstein, the sense of the proposition is the circumstance that it is ei Cf Aer true or false, plus our grasp of what is the case in either instance. And in fact, it seems that to understand the pro— U2 position is precisely to nderstand its sense. For Witt— of a m sens o genstein it is also true that to understand th all its con- (3 proposition we m st also understand what he Cf) stituents and its forms. He continues: If we know the meaning of 'a', and '1' and if we know what 'XRy' means for all §'s and y's, then we also understand 'ahb'.‘4 The words 'constituents' and 'forms' are Wittgenstein's own; the constituents of this proposition are (here) the names 'a' and 'b' and (presumably) the functional c nstant 'h'. The form, however, is represented by the uniVersal Quantifi— cation over the variables which replace the names in the propositional function 'ny'. '(x)(y).ny' is a generalized proposition which says something, not about the individuals named by 'a' and 'b', but about all the entities whose names can replace the variables 'x' and 'y' in the proposi— tional function 'ny'. According to Wittgenstein writing u ’ 21bid., p. 9n. “hm-1., an. Al in "Notes on Logic," then, the generalized proposition '(x)(y).ny' represents the form of the proposition 'aRb'; if we understand what '(x)(y).sRy' means, and what each of 'a' and 'b' mean, we grasp the sense of 'aRb', a genuine atomic proposition. Thus, when we understand a proposition, we understand its sense; we understand what makes it true or false. Tius, to understand 'aRb' we need to understand not only what 'a' and 'b' mean, but we need to know what substitution instances of the propositional function 'XRy' turn it into a genuine proposition, true or false. It need not be the case that the universal quantification of 'ny' should be true; we need merely to understand it. And that is, apparently, the same thing as knowing which substitution instances of 'xhy' verify it and which falsify it. So far as the reference of the sentence is concerned, #— however, we may find ourselves in considerable difficulty. (1 At this stage of his development, Wittgenstein identifies the reference of a sentence as the fact with which it is correlated; and we shall spend considerable effort in the discussion of the problem of the reference of a sentence. We wish, therefore, to discuss the notion of ac as it is given in the early writings. Take the declarative sentence 'The rose is red'. This is true just in care the rose is indeed red; but suppose that we make a judgment to the effect that the rose is not red. What corresponds to this 0 negative proposition in case it is true; Wittgenstein answers: a negative fact. But how does he understand the term: 'negative fact'? The answer is not easy to determine, but there are many indications from the text. Suppose that the sentence 'The rose is not red' is true. But if this proposition is true, then according to Wittgenstein ”what it signifies is negative."uu ‘The demand for negative facts seems to be motivated by Wittgenstein's notion of the reference of a sentence as the fact to which it corresponds. Since there are negative sentences, negative facts must function as their reference. However, says Wittgenstein, we cannot infer in all cases that the occurrence of 'not' in a sentence signi— 0 o c . o u C fies that its reference is a negative fact. ) We know this only if we know that the reference of the unnegated version of the sentence is a positive fact when that sentence is true. For example, suppose that the sentence 'ire rose is nega— U1 red' is false at the time of its production. Then it: tion has a positive fact as its reference. Wittgenstein is saying that we must know that the (true) sentence 'The rose is red' has a positive fact as its reference before we can say that 'The rose is not red' has a negative fact as its reference (when it is true). However, Wittgenstein adds a parenthetical yarning: (We are not here speaking of the negation: of general propositions, i.e., of such as MM “5 lbid., p. 9“. Ibid., p. 9M. “3 contain apparent variables. Negative facts only justify the negations of atomic pro— positions.) Positive and negative facts there are, but not true and false facts. l ._) It is at this point that "Notes on Logic" introduces the notion of atomic proposition. From the quotation above (the only passage in this section of the ”Notes" in which the term occurs) we may at least conclude of atomic propositions that no variables bound by quantifiers occur in them. Nor, appar— ently, the only sort of individual symbol which can occur in atomic propositions is the individual name, and these are names of entities whose nature is as yet urspecified. But '? Do these occur :13 what about predicate letters such as ' in atomic propositions? If s., are they constants or are they variables? Do they name entities? If so, what sort of entity? The final answer to these questions, unfortunately, is not specified in this section of "Notes on Logic." Witt- genstein speaks only of individual variables and individual names. At any rate, from the passage quoted above, we pan conclude that atomic propositions are genuine sentences in which occur only names. Wittgenstein begins his most extended discussion of the nature of atomic propositions with the following, rather enigmatic pronouncement: It may be doubted whether, if we formed all possible atomic propositions, ”the world wouli be completely described if we declared the truth or falsehood of each (Russell).“ Ibid., p. 9“. u7lbid., p. 93. UH The statement is enigmatic because of the comparison which one can make of it to the following proposition of the Tractatus: (8.26) If all true elementary propositions are given, the result is a complete description of the world. The world is completely described by giving all elementary propositions, and adding which of them are true or false. "T‘ 1 One possible interpretation of this passage from the Jotes' is that Wittgenstein had changed his mind between the writ— ing of the "Notes on Logic" and that of the Tractatus. The a discrepancy between the two passages is indeed somewhat . difficult to explain, although it may perhaps be explained away by saying that the ideas presented in the firs quota- tion are presented as surprising, but whose truth becomes evident upon reflection. If so, then we have one of the main motivations for the introduction of the theory of atomic propositions: the desire to construe language in such a way that analysis reveals the possibility of obtaining (in principle) a com— plete description of the world. It is easy to conjecture, however, that Wittgenstein introduced his discussion of the atomic proposition as part and parcel of his reconstrual of T? A rexe, C~2 Frege's Sinn-Bedeutung distinction. Statements, for 4. I have both Sinn and Bedeutung, and at this stage of his devel- opment, Wittgenstein concurs. But Wittgenstein rebel; against the idea that the truth-value of a statement should be its reference, as we have already pointed cut. Yet he “5 still feels that a statement must have reference (i.e., at this juncture in his thought, be correlated with something— or—other). Hence if he can emerge with a coherent theory of the reference of a statement, he will also emerge with a theory of the nature of the ultimate constituent entities of the world. But a question now arises concerning the connec- tion of the nature of the sense and reference of the state- of U) ment with the issues concerning the constituent entitie the world. It is ssumed that atomic propositions have to have constituents of one sort or another. We saw that, according to our interpretation of the text, atomic propositions must in some sense consist of names. No variables bound by quantifiers (or "apparent" variables) can occur in them; nor, A apparently, can free (or "real") variables. or this point again Wittgenstein is extremely cryptic: No world can be created in which a proposition is true, unless the congtitutents of the proposi— tion are created also. One might amend this proposition to read: ro world can be created unless its constitutents are also created, and no proposition can be true unless its constituents have some relation to the constituents of that world. On the other hand, one might argue that since the atomic proposition also has constituents, these constituents are arranged in some sort of order with respect to each other. The proposition, u81bid., p. 98. ~ my‘ _. .. IL M6 like the world, thus becomes a structured entity, and this structure bears some relation (as yet unspecified) to that world. The world, which presumably is a collection of facts, has a structure; and indeed, so do its component facts each have a structure. Hence, in some sense the linguistic pro- position also is a fact. And indeed, this is precisely what Wittgenstein szys: Propositions, which are symbols having . 0 reference to facts, are themselves facts.1U It appears that we may have some sort of correlation between Lg the sentence— (or proposition-) fact and the fact which is the reference of the sentence. Both facts, so far as we can see now, are complex entities which are in some sense com- posed of elements, and it is possible now to ask the question: what is the nature of these elements of the proposition? Suppose that we wish to analyze a proposition into the elementary entities which compose it. The question arises whether there is a point at which the analysis must stop. If we can reach this point, we reach the end-point of analysis, in which we have discovered symbols which cannot be further H analyzed. Wittgenstein calls such symbols indefinables, H f‘f‘ . u and asserts that they are of two sorts: names ano forms.) We have already met with these in connection with the issue of understanding the sense of a (purportedly) qtoxic prope;i~ tion 'aRb'. We now wish to ask how the indefinable parts 0: an atomic proposition get their meaning. 50 Ibid., p. 98. lbid., p. 98. U7 The question is by no means easy to answer for these early writings, since the doctrine of indefinable elements of atomic propositions is not clearly drawn in "Notes on Logic." We may start, however, by considering the following rather difficult pronouncement: We must be able to understand propositions we have never heard before. But not every proposition is a new symbol. Hence we must have general undefinable symbols; these are unavoidable if propositions are not all indefinable.5l The pronouncement is difficult because there are several steps missing in the argument. The first step is: even though we may never have seen or heard expressed a certain proposition, we are able to understand it . . . presumably because we know its sense. Understanding a proposition is not dependent on previous exposure to it. The second step is as follows: every proposition is new in the sense that, as stated, recog— nition Of its meaning does not depend on our re—identification of that particular pattern of symbols. Rather, as Griffin has put it: "we do not remember propositions as wholes; we know the meaning of the elements, and the rules for their assembly."52 It is this knowledge of the meaning of the pro— position's elements, Wittgenstein seems to be suggesting, that explains this phenomenon. The third step is what causes the most difficulty. Wittgenstein infers from the two preceding steps the Sllbid., p. 98. 52James Griffin, Wittgenstein's Logical Atomism (Oxford, 196“), p. 6. M8 requirement that there should be general indefinables. But what are they? Are they names for universals (properties, relations) rather than particulars? Clearly there are par— ticular indefinables, and the reasonable candidate for these are the individual names of whatever language we are talking about: 'a', 'b', and the like. The present problem is to F- determine what general indefinables are; and there are at least a few indications from the text. But these indications are obscure to say the least! L In a letter to Russell postmarked "IV Alleegasse" and dated :‘ January 1913, Wittgenstein analyzes the sentence 'R(a,b)' into two sorts of constituents: the names 'a' and 'b' and the generalized (quantified) proposition i(Ex)(hy)R(s,y)’. A proposition is, for Wittgenstein, ”generalized” when the names in the original proposition are replaced by variables and the latter are bound by quantifiers. In the passage in question, Wittgenstein specifically designates the general- ized proposition '(Ex)(Ey)R(x,y)' as not being complex. The set of two names can at least be resolved into two elements, 'a' and 'b' each. Apparently there is no way in which we can resolve the generalized proposition into ccnstitzents: it apparently has none, according to the position which Wittgenstein takes at this stage of his development. Accord— ingly we may tentatively accept such propositicns into the class of "general indefinables." “9 In fact, the generalized proposition may be regarded as exhibiting a £33m: it exhibits the form which such pro- positions as 'R(a,b)', 'R(c,d', 'R(e,f)', etc., take. To derive genuine sentences from such a form, drop the quanti— fiers and replace the variables by names. The generalized form of these atomic sentences seems to be part (at least) of what Wittgenstein means when he introduces the notion of the general indefinable. Indeed, this also seems to be what Wittgenstein is talking about when he says that indefinables I are of two sorts: names and forms.53 Names cannot be defined, since they are simple symbols. And now we find that forms (such as are exhibited by the generalized proposi— tion) cannot be defined either. Now Wittgenstein inferred the third step of the argu— ment from the previous two by overleaping several steps. The requirement was that we must have general indefinable symbols. Now we decided that we cannot define names by substituting simpler expressions for them. Names are the simple symbols. Are there predicates (of any number of places) which are undefinable in precisely the same sense? Apparently, accord— (1'1" .L H PG 7.1.”; (“I”) J: ing to Wittgenstein at this stage, there must be. for this is that if there are no indefinable predisates, there can be no unanalyzable propositions either. Griffin's reconstruction of Wittgenstein's argument is interesting: Suppose that the function were 's is a triangle', and suppose that we rejected the Ibid., p. 98. 50 doctrine of general undefinables. Then we must say that we understand this function because we can define it. We define it as: 'x is a plane figure bounded by three straight sides'. But then we understand 'x is a tri- angle' only if we understand 'x is in plane'. 'x is a figure', 'x is bounded', etc.5 Here, 'function' is used in the sense of 'propositional function': a function is a propositional function if, and 1 i only if, there occur free variables in the sentence express— ing the function. Now the result of the progression sketched in the above quotation is an infinite regress, if there is no L3 such thing as an indefinable general term. This also may be V the point of Wittgenstein's remark: Only the doctrine of general indefinables permits us to understand the nature of functions. Neglect of this doctrine leads us to an impenetrable thicket.55 The "impenetrable thicket,” conjectures Griffin, is precisely this regress. The idea is that if we are not to have an infinite chain of propositional functions, each definable in terms of the others in the chain, we must somewhere in the chain encounter such "general indefinables" as Wittgen— stein has introduced. But there seems to be a central problem with Griffin's argunmnt. Wittgenstein has explicitly introduced general imnhefinables as quantified propositional functions, whereas l"\ V“ 1" Griffdxfls argument uses unquantified prOpositienal functian . SM 55 Griffin, op. cit., p. 7. ‘VO (’1‘ Anscombe and Von Wright, op. cit., p. Does this mean that only when we get to the end of the chain, and arrive at our general indefinables, we are free to quan- tify over the variables in this final propositional function containing an unanalyzable general term? Apparently it does mean this. But Griffin gives no explanation of the reason for this. One may, however, conjecture that only when we reach the end of the chain, and arrive thereby at our pro- positional function or functions with unanalyzable general terms, are we justified in turning these functions into assertions by quantifying over the variable or variables. Thus the problem seems to be solved. We now have to inquire how the indefinables get their meaning. We discussed the form of a proposition, and we dis- cussed the fact that, according to Wittgenstein, this form is best exhibited by the quantification (or "generalization”) of this proposition. Wittgenstein, as we saw, argued for the indefinability of such propositions. Names are also un— definable according to this theory, and their indefinability is a feature of their being names. This is not argued for explicitly in the "Notes on Logic," but it is argued in some 56 of the other early writings. Names, apparently, name some— thing unanalyzable since genuine names cannot be further ana- lyzed into constituents. This suggests that, for Wittgen— stein, the reference of a proposition (i.e., the fact with 4-‘ l. ' its which are H which it is correlated) itself consists of eleme 56888, for. example, the NotebOCfl/fifi, p. 52' not further analyzable. We discussed the contention that a true proposition is correlated with a fact, or corresponds to it. The nature of this correspondence, so far as the early writings of Wittgenstein are concerned, is now becoming clearer. Let us explore this further. We said that atomic propositions consist of names for some sort of entity; and we conjectured that the names are "labels" for entities which, like their names, are not further analyzable. We may call these entities, in accordance with Wittgenstein's usage, "simple objects.” In this connection, Wittgenstein asks: What is my fundamental thought when I talk about simple objects? Do not 'complex ob- jects' in the end satisfy just the demands which I apparently made on the simple ones? If I give this book a name 'N' and now talk about N, is not the relation of N to that 'complex object', to those forms and contents, essentially the same as‘I imagined only be- tween name and simple object?J( Why, in short, must we regard names (the "simple symbols") as designating objects of corresponding simplicity? It is perfectly passible, as Wittgenstein points out, to attach a name to a complex thing such as a book. What, therefore, is the difference between naming a simple object and naming a complex entity? This perplexity may well have its origin in Frege's work. Objects for Frege are, as we saw, the sort of en- tities to which names, sentences, and definite descriptions 57Ibid., p. 59e—60e. -...- L—l 53 refer. But in Frege's text there was no explicit suggestion of simplicity for the objects. A proper name such as 'George' may designate a man, but a man is a complex entity indeed. Wittgenstein, then, is asking whether or not a name can genuinely designate something complex. Rather, isn't it true that we can use Russell's theory of descriptions to paraphrase the name away, getting in its place an eXpression which describes the entity without naming it? For something complex, apparently, it is always to eliminate its name in favor of an expression which describes it. That is, the des— cribing expression contains sentences which describe various features of the complex without naming that complex. But it appears as well that sooner or later we must find ourselves at a level of analysis past which we cannot go——as a matter of fact, no further analysis is possible. Apparenlly, at this ultimate level of analysis, we get a set of propositional functions whose variables in their argument places do not range over entities which are further analyzable; and what we end up with is a set of "indefinables" which can either be named, or which are in the range of variables which are bound by quantifiers. And apparently what we have reached are the atomic propositions discussed previously by Wittgen- stein, in which the "simple symbols" fill the argument places. And these simple symbols, these names, refer to objects. But these are simple objects, and are not further analyzable. So, Wittgenstein drastically restricts the notion of 'object' 5A to entities of a certain kind, and deprives the term of the wide range of applicability which Frege gave to it. But if facts are complex, then clearly facts cannot be named, for if we tried to name a fact, we could always use a description to paraphrase the name away. And if facts are complex, Wittgenstein seems to be saying, if we wish to have a correspondence between sentence and fact (thus guaran- teeing a reference for the sentence, in Wittgenstein's usage of the term) the true sentence corresponding with the fact must have a corresponding analyzability. This is Wittgen— stein's demand, not only in the early writings but in the Tractatus as well. It is essentially a demand for so con— struing our language that we can account for the meaningful— ness of at least some of our utterances. Thus if facts are complex, the demand is that we must be able to analyze them into their constituents. Or, as Wittgenstein says: It seems that the idea of the SIMPLE is already to be found in that of the complex and in the idea of analysis, and in such a way that we come to this idea quite apart from any examples of simple objects, or of propositions which mention them, and we realize the existence of simple obiects-— a priori——as a logical necessity.5E There is here no suggestion that, in order to realize the existence of simple objects, we must somehow be directly acquainted with them. We apparently assume that facts are Ibid., p. 60e. £4- 55 in some (unspecified) sense complex. Certainly Wittgenstein makes this assumption. And it appears that, if the result of the analysis is to be unique, if we are to get the same result each time we perform the analysis, there must be a unique point at which the analysis must stop. So it looks as if the existence of the simple objects were related to that of the complex ones as the sense of 'not-P' is to the sence of 'P': the simple object is prejudged (prajudiziert) in the complex.59 The remark about the sense of 'not-P' is supported by Witt— genstein's earlier discussion of negative facts in "Notes on Logic:" to understand the sense of the negated proposition, we must first understand the sense of the unnegated one. Hence to judge that 'not-P', we must first be able to judge that 'P', i.e., we must understand its sense. Likewise, the existence of the simple object is pre-judged in the complex. A complex, whatever its nature, must consist of simples, and presumably a proposition making an assertion about a complex must imply a set of assertions about its simple constituents. This, at least, seems to be the point of the assertion in the Tractatus: (3.2M) A proposition about a complex stands in an internal relation to a proposition about a constituent of the complex. The "internal relation" spoken of in 3.2M is, presumably, that of implication; and this seems to support the contention that a proposition about a complex implies one about a constituent 591b1d., p. 60e. 1 I. w“ ‘u. ... ..x v n le- r L .. u”. u ' P. r4 u L v DC a n .3: f . »r\ I . r A. :7 .o A . AN 7 56 of that complex. However, what must come first is a process of analysis of that complex. Let us now, says Wittgenstein, apply these considera— tions to an actual case. Consider, he says, the case of his watch ticking before him. It is perfectly possible to name F: this complex. And it seems troublesome to think that this name might fulfill all the requirements for the names of simple objects.6O Does the watch, therefore, fulfill al_ . the requirements for being a simple object? And a further l question: In order to know the syntactical treatment of a name, must I know the composition of its reference? If so, then the whole composition is alreadr expressed in the unanalyzed pro- position. 1 ‘ The ultimate answer to the first question asked above is No. It is affirmed again that what seem to be names occurring in unanalyzed propositions do in fact disappear upon analysis.62 This is in fact the upshot of Russell's theory of descriptions, which allows us to paraphrase names away in favor of propositions in which the name does not occur. The expression which seems to be the name of a watch is not a name, as Wittgenstein wishes to understand the term; for the watch is further analyzable into its constituents. We have already indicated the process: we keep paraphrasing, deriving more and.more propositional functions the deeper we 62 60Ibid., p. 60e. Ibid., p. GCe. 61Ibid., p. 60e. 57 go into the analysis, until we reach a "fully analyzed" form of the original proposition. The original name has long since disappeared, to be replaced with expressions whose appearance during the course of the analysis represents ever deeper levels of analysis. Finally we reach the presumed ultimate level of analysis in which occur propositional func— tions containing, perhaps, the "general indefinables" which we discussed, and variables, which may be replaced by names. This outcome is at least suggested by the program which Wittgenstein puts forth. What we seem to have left are names: names of simple entities whose a—pearance under the analysis represents its endpoint. At the end of this analysis, we are, it appears, left with names only: the genuine names. These names designate the simple constituents of the original com- plex which corresponded to the original assertion. From this it would now seem as if in a certain sense all names were genuine names. Or, as I might also say, as if all objects were in a certain sense simple objects. I certainly seem to know what if the analysis were completely carried out, its result would have to be a prOposition which once more contained names relations, etc.05 But our general indefinables seemed to be quantified proposi- tional functions. And there is no mention of quantification here. Rather, the end-point of a process of analysis seems to leave us with constants, and not with bound variables. It may be at this point that Wittgenstein is leaving off 58 consideration of "general indefinables' as ultimate con- stituents of propositions, since there is no mention of these whatsoever in the Tractatus. Consider what happens when, a'la Moore, we try to ”define" the term 'horse'. Here we read 'analyze' for 'define', and thus we direct our attention to the horse itself: in which case we attempt to dissect the poor horse into its various parts and to show how these parts are related to one another. Presumably, then, we can attach names to each one of these parts. But each part turns out to be an "indefinable" (unanalyzable) particular entity, assuming for the sake of the argument that we have reached a point at which, as a matter of fact, we can analyze no further. But where are the general inde— finables at the putative end—point of this analysis? Assum- ing the horse to be a fact, we do not come across them in the course of analysis of this fact. Thus the general indefin— ables, as constituents of a fact, seem to drop out of consid— eration. But particular entities remain. We are, however, in a better position to understand how propositions get their meaning. We understand the con— stituents of a proposition; we know the rules for their assembly, though we may never have formulated these rules explicitly. The constituents, we said, are its "indefinables. Hence, says Wittgenstein, A proposition must be understood when all of its definables are understood. H -v .i. ... ... .f ... L4. ... r4 5. .. 4,. r. ...~ 59 We are not concerned in logic with the relation of any specific name to its meaning and just as little with the relation of a given proposition to reality. We do want to know that our names have Eganings and our propositions sense . . . Consider a propositional function 'ny', to use Wittgenstein's .1) notation. To obtain a genuine proposition from it, replace the variables 'x' and 'y' with the names, e.g., 'a' and 'b'. lb this propositional function correspond »airs of objects standing in a certain relation. For some such pairs, says Wittgenstein, 'ny' will be meaningful; some substitutions k in, 'ny' will yield true statements. Now, says Wittgenstein, I now determine the sense of 'ny' by laying down the rule: when the facts behave in regard to 'ny' so that the meaning of 'x’ stands in the relation R to the meaning of 'y', then I say that these facts are "of like sense" (gleichsinnig) with the proposition 'ny'; ( otherwise, "of opposite sense" (entgegengesetzt).U5 Rut 'x' and 'y' are variables. Does Wittgenstein wish to say that they designate anything? Or is he simply being careless with the notation he is using? Since he calls 'ny' a pro— position rather than a propositional function, one suspects that the latter is the case. But what about 'R'? The ques— tion naturally suggests itself whether or not 'R' is a name of a constituent of the situation whose form is given by the function 'ny'. There is, in fact, no indication whatso— ever from the text which would suggest this; in fact it seems contraindflcated, since the dissection of the horse or watch 6“Ibid., p. 98e. 65Ibid., p. 98e—99e. xl owl-‘- l‘.-‘V'—F"- - ~; ‘ .... ~ =.‘ 7‘. ‘ “txun‘ I I I .1». “ F, ‘7‘; “mod VAA\ .0 . A .v- H“: 3...”; “ a. “ o 4...”. “ ... ‘ yuaydu‘k‘ ’ J 60 yields particular parts, and Wittgenstein nowhere suggests that the relations among the parts are themselves parts of the horse or watch. Nor, as we have established, are general indefinables to be counted among the parts of an analyzed entity. But general indefinable expressions must also be correlated with something; it simply is not clear from the text what they are correlated with. 'ny' becomes a general indefinable ex- pression when its variables are bound by quantifiers. 'ny', however, gets its sense not from its correlation with single objects, but with pairs of objects; and this suggests that, certainly, it is not a name, for pairs of objects are not objects per s3. They are, if we like, "configurations" of objects. To give sense to the expression 'ny', we search the world, as it were, for pairs of objects which are related by that relation. We see that the world divides into those states of affairs in which the entities ranged over by the variable 'x' do stand in the relation R to the entities ranged over by 'y', and those which do not so stand. According to a way of speaking adopted at this point by Wittgenstein, we speak of the "sense of a fact," and this we take to be the actual arrangement of elements of a config— uration such as that described, e.g., by 'aRb'. Thus the indefinable 'ny‘ gets its meaning from the correlation of its sense with the sense of the fact described. Or, in Wittgenstein's words: 61 I correlate the facts to the symbol 'ny' by thus dividing them into those of like sense and those of opposite sense. To this correlation corresponds the correlation of name and meaning. Corresponds, to be sure, but not identical with. The proposi- tional form 'ny' allows us to discriminate the pairs of objects which stand in the relation R to each other from those pairs which do not. Thus I understand the form 'ny' when I know that it discriminates the behavior of 'x' and 'y' according as these stand in the relation R or not. In this way I extract from all possi- ble relations the relation R, as by a name, I extract its meaning from among all possible things. A propositional form such as 'ny', then, is indefinable: but it is not a name of anything. Facts, as we say, cannot be named, because facts are not simple but can be further analyzed into constituents. Given a prOposition such as 'aRb', however, can we analyze this proposition into the elements 'a', 'R', and 'b'? Certainly insofar as 'a' and 'b' are names, we can. This much is agreed upon. But is 'R' the name of anything? Wittgenstein answers negatively: Symbols are not what they seem to be. In "aRb" "R" looks like a substantive but it is not one. What symbolizes in "aRb" is that "R" occurs between "a" and "b". gence "R" is not the indefinable in "aRb".6 If 'R' is not a substantive, does this mean that 'R' can be either eliminated or defined away? Apparently it does; but av ' j 66 68 Ibid., p, 99. Ibid., p. 99. 67Ib1d., p. 99. u w I E 3. i s ; Q . 54¢ ‘5' -l :. q qr .' V Rh. Imp”! V .~,.\ W ...n... ‘ ‘ H fin'”fin~.‘- hvfboit h ‘f'rt‘WHQ .x‘..~ 4‘ 4»... am... .‘ I“. . \‘ Q [‘3‘ 2"fipl. 0,- “WV“, 3\ a “p '“V on. Vllb‘ . ‘ H ‘5." ~h; \b'j‘ . ‘ h V ‘5: ‘Nr 'l.‘ yfi‘. . “N & 5.9.“: A .. '1. “97-3; 1 nu: JEVJE ‘ 'v. ‘52:, I Q ‘1. . .J j " "‘I I Cc . 62 if this is the case, is 'aRb' a genuine atomic proposition? Apparently not, since the text suggests that, even in the early writings, atomic propositions are such as to contain only indefinables. 'a' and 'b' are names; they have meaning standing alone, for they are "labels" for simple objects. But it is apparent that 'R' standing alone has no meaning, if it is understood as a two—place relational symbol. Its meaning is dependent on its occurrence in the context of a proposition, e.g., of the form 'ny'. No matter how we may construe Wittgenstein's words, it does not appear to be the name of anything. 'ny' is a propositional function-expres- sion; for Frege, it refers to an "unsaturated" function. The expression corresponding to the function has a sense for both Frege and Wittgenstein. But the difference between the two positions is also apparent: for Frege, the proposi- tional function—expression does have a reference (Bedeutung). For Wittgenstein, it does not. For the latter, it appears to express a way in which objects can be related to form 5 facts; it expresses a £233, a possibility, as we shall see. We have tried to trace some Fregean themes through the development of Wittgenstein's early writings on the understanding of functions, the sense/reference distinction, and the nature of logical notation. Particularly we have distinguished Wittgenstein's version of the distinction from Frege's. Since Wittgenstein did not accept Frege's conclu— sion that the truth-value of a proposition in its reference, 63 he had to work out an entirely different theory. And in the process of working out this theory he came to the notion of the atomic sentence and the problem of the correlation of facts with statements. And in this way he developed a meta- physics which carried over essentially unchanged into the Tractatus. However, there are many issues which still are not clear. There is, for example, the issue of the simplicity of the objects, the issue of the status of relations and of properties, and that of the status of quantified propositions. Since from this point we are aiming at Chapter III, which deals with the so—called "picture theory" of meaning, we want, in the next chapter, to treat in some detail the sketch of the world which Wittgenstein traces out in the early part of the Tractatus. From this early discussion, we can see that Wittgenstein wishes to hold that the facts are the correlates of the basic propositions, or "atomic" proposi- tions as Wittgenstein puts it. We wish to describe the world, and the nature of the facts in it, particularly as this is exposited in the ladder language of the Tractatus. Hence to that work we now turn, keeping in mind that some doctrines of the early works do not carry over unchanged into the later work of 1919-1920. v... ‘H‘IC‘ a : CHAPTER II in. THE WORLD ACCORDING TO THE LADDER LANGUAGE: A SKETCH A. Facts 4 The metaphysical system sketched out in the early 3' writings of Wittgenstein results directly from Wittgenstein's wrestlings with problems posed by Frege's sense/reference distinction. For Wittgenstein in the Notebooks and "Notes on Logic" the reference of a sentence is the fact with which it is associated. The metaphysical questions, however, seem to be subordinated to the problems associated with Wittgen- stein's reworking of the sense/reference distinction. The metaphysics is developed as an adjunct (albeit an important, even necessary one) to the theory of meaning developed in these early writings, and we should expect that something similar is the case in the Tractatus. Nonetheless the development of the metaphysical issue is much.more explicit in the Tractatus than in the early writings. The first two sections of the Tractatus are de- votexi almost entirely to the sketching out of the metaphysi- cal background to the ensuing analysis of language. Central to this; exposition are such terms as 'fact' (Tatsache), 6A « - u ‘b “J nu km a; ... v” ~M .. <,.\ ‘R‘ ANA f~ y ..s. r4“ L. a. . L. w c _. L .... .. . «a r? 5.. '. . b v ~.L I. o . . m ! 7” a c LL .r u 2.. t .. .5 .1 r u , .4 : . s... 4. 65 'state of affairs' (the Pears and McGuinnes rendering of 'Sachverhalt'), 'reality' (Wirklichkeit), 'situation' (Sachlage), and 'object' (Gegenstand). Indeed, all of these terms are central to the development of the metaphy— sics in the Tractatus, for the development of the central ideas in the book requires an explanation of them. Nonetheless, it should be remembered that the devel— opment of the metaphysics is performed in the ladder language. We must remember that there are two languages in the Tractatus: (l) the ladder language, which is the language actually used in the Tractatus, and (2) the perspicuous language, the lan— guage which is recommended and talked about. But it is questionable indeed whether or not the perspicuous language is actually exhibited in the text of the Tractatus whether sentences of it actually occur. Further, the situation is complicated by the distinct possibility that the two lan- guages have different ontological commitments. It may be that the ladder language commits us to the existence of facts, states of affairs, properties, situations, as well as objects. The perspicuous language has an entirely different set OI commitments. And this seriously complicates the problem of the ontology of the Tractatus, for we may have two distinct ontologies. But which ontology then has primacy? In a sense, to answer this we have to answer the question of what the func— tion of each language is. Perhaps, however, we can answer .v - a hp‘ LII‘ >‘n it. (I, (I) I“! U) .r.e serve 5 Ar "‘- ..,_- 'i r: ~- ¢ P‘ u;,‘ «.5 ~ ‘ P! ». ‘Vk I! «h: t (D ”f { ) I {1) A1,. ‘Vfl 66 this by returning to the question of what the purpose of the Tractatus is. Major purposes is to provide an analysis of meaning in language, to determine the conditions which make it possible fer a significant sentence to have both sense and reference. It is the function of the perspicuous language clearly to exhibit the preconditions for the mean- ingfulness of linguistic expressions. Thus we shall show that for Wittgenstein this requires a theory which connects the perspicuous language to the world with which it is correlated. This is one of the functions which the ladder language performs. And this suggests another interpretation of the Tractatus: that the two languages are different ways of looking at the same world. That is, there may not actually be two distinct ontologies assumed by the two languages, but rather there may be some sort of common ground between the two. In which case it might follow that there is only one assumed ontology and that the two languages constitute dif- ferent ways of looking at those commitments. But since it is the function of the ladder language to present both fea- tures of the world which make the perspicuous language possible and the perspicuous language itself, it appears that the ontology implied by the perspicuous language must take precedence over that exhibited by the ladder language, if they are different. This conclusion is buttressed particularly by the following passage of the Tractatus: w 67 (6.5“) My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical (unsinnig), when he has used them——as steps-- to climb up beyond them. (He must, so to speak, away the ladder after he has climbed up it.) He must transcend these propositions, and then he will see the world aright. It appears, therefore, that if we are to take one of these ontologies as the ontology of the Tractatu , we must take that of the pe*spicuous language as primary. Notice that the "propositions" of the ladder language are unsinnig-— without sense (Sinn). This is a direct consequence of their not being correlated with facts and states of affairs. ihe sentences of the perspicuous language, however, are so correlated, and from this they get their sense. And this is another reason for taking the ontology implied by the perspi- cuous language as being primary. But as Wittgenstein points out, the ladder language has its uses. Its propositions do not really have sense, but they do have some sort of explanatory power, for it is clear that Wittgenstein did not think that he could write the Tractatus in the perspicuous language. The ladder lan- guage gives us intuitive hints concerning the presupposi— tions of the perspicuous language, not only as regards the construction of its propositions, but also regarding the nature of the world. Thus in this chapter we shall discuss the ladder language's conception of the world, always keep— ing in mind that the perspicuous language is the ultimate 68 arbiter of the commitments of the Tractatus. A description of the ladder language's sketch of the world is necessary because of the correlation of the perspicuous language with that world. And this will become important in our treatment of the picture theory of meaning, since we shall wish to know what is pictured. The first proposition of the Tractatus is very gen— eral in scope: (l) The world is all that is the case. This proposition of the Tractatus might be regarded as a definition: 'the world' is to be understood as meaning the same as 'whatever is the case'. It is the case that I am sitting on a swivel chair in my study, working at the type— writer. The world therefore includes this situation, for the latter is the case. The world, however, does not include my listening to Beethoven's Ninth Symphony at exactly 6:08 p.m., February 29, 1968, for I am not doing that at this moment. We might say: the world is all that is going on, everything that is occurring at a given moment. Notice, however, that this does not say that the +— .1 CD world is the totality of things which happen to exist a given moment. This is not consistent with the assertions of the Tractatus, for the second proposition of the ladder language reads: (1.1) The world is the totality of facts, not of things. ;. ~14. «U, . u X: A . .rL. (r4. .. . . .. A 1 . . J I ..M .: ... r: 1. L. e . x c . ..u +. 1.; 1» r; 'J L. ;. a. :2 ‘. .:. 3i. .H «o . ._ . J {hi ”I .. .... . u ... 7.. s ,, h-, Hz..- a; ... . 4“[. ‘L‘ 6Q / The ladder language seems to commit us to the existence of facts, and these facts are among the "building blocks" of the world. So, since I am typing now, this fact is a part of the world. But is it a fact that I am $23 listening to Beethoven's Ninth? Apparently, according to the early p: Wittgenstein, it lg. We saw that Wittgenstein, in "Notes on Logic," did countenance negative facts, and indeed so does Russell. How, otherwise, would it be possible for a true g negative sentence to correspond to something? There is no— thing to say that I could not be listening to the Ninth, but my listening to the Ninth is not a part of the world at the moment. Therefore it is not a (positive) fact. Wittgenstein apparently asserts proposition 1.1 as a consequence of his answer to the question: how may the world be described? It might be thought that the world could be described by making a list of the things in it. But what is a thing? Clearly Wittgenstein will insist that a fact is not a thing, and yet though we are committed to the existence of things, we are apparently committed (in the ladder language) to facts as well. And things occur in facts. We may, perhaps, assume that "bodies" or physical objects are to be accounted as things. Can we therefore say that the room in which I am working is a collection of things? If it is a mere collection, then a description of this room would be complete if we were merely to list the things in it: pictures, file cabinets, books, and so forth. But 7O Wittgenstein would not accept this as a description. A description of a state of affai’s is not given merely by a list of the things in it. Does this room constitute a state of affairs? One thinks not, for a room can be regarded just as well as a thing among things: it is, after all, an en- , i closure. But at the same time, we may consider facts about the room: namely, that there are such and such things in the room, that they are in various relations to one another. The question now arises whether a fact consists of a set of things 2122 their properties and pigs the relations holding among the things. This is at least more plausible than saying that a fact is merely a heap of things. But there is, at least, a problem in the word 'consist'. For we might say that a thing consists of its parts, just as an automobile consists of the engine and its parts, the chassis, the suspension system, and so on. Does this mean (conceiving facts in analogy to the car) that facts also have parts, just as things do? If the ladder language 13 genuinely committed to saying such a thing, then according to the previous dis- " H cussion the fact's parts include at least (1) the things in it, (2) their properties, and (3) the relations (if any) holding among them. Will the ladder language countenance facts containing particular things plus their properties and the relations among the things? It seems, indeed, that the ladder language does countenance just such a position. The ladder language is 71 committed to facts. But the situation is considerably less clear with the perspicuous language, which at this point is not even discussed in the Tractatus. But we have already ‘indicated that "Notes on Logic" did not completely support the view that the symbol 'R' in 'aRb' is a name of anything. The 'R' seems to be a sort of convenient way of indicating that a relation holds among certain entities which the Tractatus later calls "objects." If 'aRb' has sense ('sense' being defined as in "Notes on Logic"), and if it is true, there is a fact corresponding to it. But there seems to be no indication in "Notes on Logic" that, at the end—point of the analysis of some state of affairs, we find relations as well as things related, among the constituents of that state. Thus, at least for the "Notes," relational constants do not name anything, and relational variables do not range over anything. It therefore appears that we cannot see our way clear to quantify over relational variables. But, if we were to try to translate the sentences of the ladder—language into some quantificational language, might we find a symbol for 'fact' that would allow us to quantify over it? And if we did manufacture such a symbol, would we then be committed to the existence of facts, even though we are apparently not committed to the existence of relations? An affirmative answer to this question, on the face of it, seems to go counter to everything which Wittgenstein says in J D—ij the "Notes" concerning the unnameability of fact . acts b 72 cannot be named, but only described. This means that there are no names, and in particular, no variables which take facts as values; and hence there is no way in which we can quantify over variables ranging over facts as entities. This Wittgenstein completely disallows in "Notes on Logic." But this apparently means that the ladder language cannot be translated into whatever notational scheme is to be recom— mended for the perspicuous language. And this is merely additional confirmation for Wittgenstein's View that the "1. I-n .. _ ladder language does not contain sentences with Elfifl' There is no rigorously formal way in which we can determine its commitments. And indeed, perhaps this is one of the reasons why Wittgenstein rules out the propositions of the ladder lan- guage as being unsinnig--nonsensical. And since it is unsinnig , there seems no precise way in which to determine what the commitments of the language are. This, of course, complicates the problem of determin- ing what the ontology of the Tractatus is. But it also re— inforces our determination to treat the perspicuous language of the Tractatus as the main source of our knowledge of the nature of the objects. It suggests that we treat the ladder language as a loose, informal exposition of the main presup- positions of the perspicuous language. In e fect, what the ladder language does is to present a metaphys'cal system whose propositions are unsinnig, and what it claims about the existence of certain types of entities is also literally unsinnig——nonsensical. 73 Nonetheless, it is useful to examine the question of what sorts of entities are claimed to exist by the ladder language of the Tractatus. For one thing, the sentences of the perspicuous language are claimed to have gigg, and Witt- genstein must describe how this can be. It is claimed in the early writings as we saw, that the reference of a sen— tence is a fact, with which it is correlated. The correla- tion of sentence with fact will play a major role in the ladder language's development of the theme of meaning. So we must, at least, have an informal understanding of the role which the ladder language's conception of the nature of facts plays in the meaning of sentences of the perspicuous language. It is Wittgenstein's contention that we cannot really talk about such matters in a sensible way. But however this may be, we Egg act as if we could talk in such a way. And this is precisely what the ladder language does. Hence if we are to speak of the correlates of the sentences of the perspicuous language, we must discuss these correlates as they are exposited in the ladder language. The world, then, is the totality of acts, not things. So far as ordinary uses of the term 'fact' are concerned, however, Black1 has suggested that most such uses of the term are eliminable from discourse without undue damage to the sense of the sentence in which it occurs. Thus, for example, 1Max Black, (Ithaca, 1965), p. 3 A Companion to Wittgenstein's Tractatus 2 o ' 7M from the sentence "It is a fact that he died” we can pre— sumably eliminate the clause 'it is a fact that', since on this view the above assertion is equivalent to the assertion "he died.” However this may be for ordinary language, the ladder— P_ language of the Tractatus is distinctly not ordinary; to quote 6.5M again: (6.5“) My propositions serve as elucidations in the following way: anyone who understands me recognizes them as nonsensical, when he has used them—-as steps—-to climb up beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.) “M‘..§Q. -. . m \ If the ladder language of the Tractatus is not ordinary, its extra—ordinary nature may help explain why we can generally not remove all occurrences of 'fact' from the propositions of that language. Certainly we cannot remove its occurrence from the first few propositions of the ladder language in the Tractatus, a point which Black freely admits.2 'Fact' is a term which belongs integrally to the ladder language, and is generally uneliminable from it. If we were in a position to talk freely about the commitments of the ladder language, we might say that the ladder language is committed to facts as genuine entities. The way in which to determine this precise- ly might be to attempt to formalize the language, determine a domain of interpretation for this language, and then assign each element in this domain to one of the primitive terms of the formalized language. But it may also be Wittgenstein's 2Ibid., p. 32. 75 conviction that the ladder language cannot be formalized in such a way as to do this. It is, in short, the very circum- stance that the ladder language cannot be formalized in such a way as to present its ontological commitments clearly that constitutes its Sinnlosigkeit . . . its "meaningfulness." F Now if the ladder language is committed to the exist— ence of facts as genuine entities, and if we were, per impossible, to try to formalize this language, we must have a stock of names which "label" these irreducible entities. We must also be able to replace these names with variables wherever they occur in the sentences of the formalism, and thence to bind these variables with quantifiers. If we can do this, we have an application of Quine's criterion of onto— logical commitment. But this flies directly in the face of Wittgenstein's discussion of facts in the earliest writings. Facts cannot be named; and presumably, if we are committed to the exist- ence of facts, we must be able to name them, just as we must be able to name anything to whose existence we are committed. And yet, the word 'fact' occurs constantly in sections 1 and 2 of the Tractatus, and we have maintained that these occur— rences of 'fact' cannot be eliminated from the language. It is distinctly possible that in at least this circumstance consists the Sinnlosigkeit of the ladder-language. Wittgen— stein, indeed, will argue that the term 'fact' does not occur in the perspicuous language, as we shall see. 76 Meanwhile, it appears that we can lay down at least this principle: that the ladder language, being ultimately sinnlos does not perspicuously exhibit the ultimate commit— ments of the system of the Tractatus. It is what might be called an informal aid to the understanding of the language F' that is really at issue in the system: the perspicuous lan— guage. It is in the ladder language that the metaphysics ; of the Tractatus is developed. And the metaphysics itself is expressed in pseudo—propositions, that is, proposition without .w‘.n:0 Sigg. Sentences in which the term 'fact' occurs are them- selves sinnlos. But the Sinnlosigkeit of the ladder language does not imply its uselessness, since it can be said that the ladder language states the conditions under which a sentence can be said to have Sign. To Wittgenstein, it seem apparent that sentences with Sigg cannot state the conditions under which sentences are sinnvoll , i.e., have sense. So the ladder language has a definite use in the system of the Eggg— tatus, and while this language is not, strictly speaking, ordinary, it is constructed according to the rules of German grammar, using German words. And correspondingly the English translation of the Tractatus' text has the same relation to ordinary language: words of the English language are used, and sentences are constructed from these words using the same rules of English grammar as are used in the construction of sentences of ordinary, non-philosophical English. Hence it seems that, if we are to understand what Wittgenstein is 77 trying to accomplish with his ladder language, and thereby to understand how the term 'fact' is to be understood in its employment in that language, further study of its use in the ladder-language is necessary. What considerations led to the peculiar use of 'fact' I" which is to be found in the Tractatus? One way to try to answer this question is to refer to recent discussions of the problem of the nature of facts. One such discussion is that 4 which took place between Austin and Strawson in 1950 as a L symposium published in the Proceedings 9: the Aristotelian Society. Let us therefore expend some effort in the exposi- tion and discussion of this symposium for whatever light it casts on the considerations bearing on Wittgenstein's use of 'fact'. Undoubtedly 'fact' is a problematic word; Strawson finds it so, and his attack on the problem is an attack dir— ected against a position taken by Austin in a paper presented at the same symposium. Austin asks the innocent question: when is a statement true? What makes it true? And he goes on to say: The temptation is to answer . . . ”When it corresponds to the facts." And as a piece of standard English this can hardly be wrong. Indeed, I must confess I do not really think it is wrong at all One minimum condition for the occurrence of any pro— cess of communication is the existence of a correlate to a 3J. L. Austin, "Truth,” Proceedings of the Aristol— telian Society, supplementary volume XXIV, 1950, p. llS. 78 statement: namely the world. The existence of a world is a necessary condition for communication by means of language. And according to Austin, the relation of the symbols of lan— guage to the world is entirely conventional. Indeed, he distinguishes between two different sets of conventions: Descriptive conventions correlating the words (sentences? the types of situation, thing, event, etc., to be found in the world Demonstrative conventions correlating the words (statements) with the historic situations, etc., to be found in the world. Brim The statement made via the sentence is correlated with the world by means of these conventions. And this leads to the following statement: A statement is true when the historic state of affairs with which it is correlated by the demonstrative conventions (the one to which it "refers") is of a type with which it is corre- lated by the descriptive conventions.5 It is interesting to note here that the correlates of the statement are termed things, states _£ affairs, situations, and events by Austin. Notice that Austin makes no obvious distinction between these four terms. One wonders whether or not it is a matter of indifference to Austin whether or not such distinctions are to be made. He does not discuss the point, but reintroduces the term 'fact' for our consider- ation as the correlates of true statements. And it appears from this discussion that facts are genuine entities with an existence of their own. U Ibid., p. 116. 5Ibid., p. 116. 79 On the other hand, 'fact' seems rarely to occur in ordinary English apart from the word 'that': it is a fact that P, the fact that P is frightening, etc. And all this implies that it would be correct in such circumstances to assert the corresponding proposition 'P'. But 'fact that' is simply a locution which we use when we wish to circumvent the necessity of distinguishing between the true statement which we are asserting and the fact which makes it true.6 Facts themselves are still re— garded as the nonlinguistic correlates of true statements, and for Austin it is clear that facts are ”in the world,” and even in some sense are constituents of the world. Strawson, however, takes strong exception to Austin's conception of the notion of fact. Austin's scheme requires a two—termed correlation of statement and world, says Straw- son, and Austin fails to discriminate sufficiently well between words such as 'thing', 'fact', 'event', or 'situa— tion'. And Strawson accuses Austin of encouraging the identification of facts with things by failing to make the distinction.7 Indeed, a true statement corresponds to nothing. It refers to a thing, and describes a thing, but does not correspond to it. A statement fits the facts, or fails to fit them; but, says Strawson, 6 7P. F. Strawson, "Truth," Proceedings 23 the Aristol— telian Society, supplementary volume XXIV, 1950, p. 115. Ibid., p. 116—117. 80 What "makes the statement" that the cat has the mange ”true" is not the cat, but the condition of the cat, i.e., the fact that the cat has the mange. The only plausible candi— date for the position of what (in the world) makes the statement true is the fact it states; but thg fact it states is not something in the world. A statement, as we saw, is (in some unspecified and unrestricted sense) about some thing or some person. But things and persons are in the world, and hence they are not facts, according to Strawson. Therefore, whatever a true I statement is "about,' it is not "about" a fact. Rather, the fact is what the statement states. Statements are about things, but they £3323 facts; they are not gbggt the facts. The central point of Strawson's discussion is reflected in the following statement: "Fact," like "true," "states," and "state- ment," is wedded to "that—" clauses; and there is nothing unholy about this union. Facts are known, stated, learned, forgotten, commented upon, communicated or noticed. (Each of these verbs may be followed by a "that-” clause or a "the fact that-" clause). Facts are what statements (when true) state; they are not what statements are about.9 Facts are not entities which can be kicked, heard, seen, broken, or mended. Facts, in short, do not seem to be things that can be referred to. What Strawson seems to be denying here is that facts are entities. The fact that, for example, the H-bomb exists and has various properties is not a constituent of the world, though the H-bombs themselves are. Strawson argues that the 8 9 Ibid., p. 116. Ibid., p. 135. 81 only way in which we can construe facts as being constituents of the world is that somehow we assimilate them to things or objects. Physical objects d9 form the "building blocks" of the world, and the fundamental mistake is to speak of facts in the same sense as we do of things. Austin, however, will not buy this. One of Strawson;s main objections to Austin's discussion was that the latter fails to make the necessary distinction between such terms as 'thing ', 'fact', 'state of affairs' and 'situation.' But Austin asks: how are we to show that there is a distinction of type between such terms? We can, after all, say of things, events, states of affairs, and situations that they are facts, as well as being things, etc. And things and events are in the world. Austin, indeed, would seem to identify the condition of a mangy cat with the fact that the cat has the mange: or, more generally, to identify a condition with the fact that the condition obtains. This apparently is the heart of the difference between Austin and Strawson on the nature of facts. Both Austin and Strawson, I think, will agree in regarding the condition of the cat as something that is in the world. For Strawson, the cat's condition can be regarded as a particular (though not as a "basic particular").10 According to the scheme adopted by Strawson in Individuals, the cat is a basic particular, a 1OP. F. Strawson, Individuals: An Essay in Descrip— tive Metaphysics (Garden City, N. Y., 196?), pp. 29—30. 82 particular belonging to the most fundamental category of particulars. The cat's condition, however, is a particular which belongs to a category entirely distinct from that to which the cat itself belongs: say, the category of events, conditions, processes or states, all of which Strawson seems to subsume under one category.1 The mange is then a condition of the cat, and as such it is a particular whose identification is dependent upon the existence of the cat, which in turn belongs to the category of basic particulars. A mange is a dermatological disease caused by infestation of the animals' fur and skin by mites, which are basic particulars in Strawson's scheme, but the disease itself is not basic but is rather a particular which is dependent on more fundamental ones. Still, the disease, the condition, is just as much "in the world" as is the cat. But, according to Strawson, the fact that the cat has the mange is not a particular of any sort whatever, and is not in the world. The nub of the controversy between Austin and Straw- son, therefore, seems to be this: for Austin, if it is a fact that X (e.g., a condition) obtains, then the fact is part of the world, and can be regarded as a constituent of it. For Strawson, there seems to be a complete refusal to make this latter inference. For him, to say that X is a fact is to say something about the fact that X obtains; and llIbid., p. 36. 83 this seems to be the greater part of the difference, the crucial point on which the distinction turns. X may indeed be in the world; the fact that X obtains is not in the world in any sense. If one now applies this discussion to the framework of the Tractatus one sees that the Tractatus' discussion of facts seems to bear a number of similarities to Austin's position. We mentioned that the concept of fact as developed by the Tractatus seems to be such that occurrences of that term in the ladder—language are non—eliminable from its pro— positions: (1) The world is all that is the case. (1.1) The world is the totality of facts, not of things. (1.11) The world is determined by the facts, and by their being all the facts. (1.2) The world divides into facts. The question arises whether or not facts are in some sense constituents of the world, much like the parts of the auto- mobile are its constituents. We may then say that for Witt- genstein in the ladder—language of the Tractatus, facts are genuine entities, and given that the world is an entity, facts are the entities which are constituents of that world. But among the many strange features of this way of speaking, we might note the following one: a car is a complex entity composed of many parts. Can we say that the car lg the totality of its parts? Not at all, because we can take it ..re-r'ln-fl l 8A apart and lay the thousands of parts neatly in a row and not have a car. A car is constituted by having its parts put together in a determinate way; it is an entity composed of thousands of reciprocating parts, each bearing various relations to all the others. Presumably the opera— tions of the various parts of, e.g., the engine, are casually related to the operations of all its other parts. But again we therefore cannot say that the engine (or the entire car) is the totality of its constituents. But if facts are the constituents of the world, apparently Wittgenstein is saying that the world ii the totality of its constituents. This seems to suggest that the relations holding between the facts (whatever their nature may be . . . or if there are such things as relations) are a matter of indifference to the nature of the world. Or, to put it more clearly: the simple enumeration of the con— stituents of an automobile does not constitute a description of the car, but apparently an enumeration of the facts gggg constitute a complete description of the world. The con— stituents of a car are things; facts are not things, it appears from proposition 1.1, and their difference from things seems to be indicated by our previous discussion. And yet, in spite of this difference, Strawson may justly accuse Wittgenstein of Austin's "error:” namely, the assimilation of facts to things. Wittgenstein, Strawson might say, seems in the ladder language to be using 'fact' in 85 much the same way as ‘thing' is ordinarily used. Things have parts, constituents. If we conceive facts on this ana- logy, facts also have constituents. And the world (still conceived on this analogy) becomes an enormous collection of fact-things, which are its constituents. Apparently the only difference one might detect between Wittgenstein's use of 'fact' and the ordinary use of 'thing' is in the connection of these terms with the notion of constituent. The constitu— ents of a thing are themselves things, and such constituents bear various (spatial, causal) relations one to another. But nothing of the sort is suggested by Wittgenstein's text when it speaks of facts as constituting the world. Thus Strawson might still accuse Wittgenstein of using 'fact' in close analogy with 'thing'. Further corroboration of this view of Wittgenstein's use of the term 'fact' seems to come from Russell's discus— sion of what is to be understood by that term. Russell's lectures of 1918 (published a year later as The Philosophy of Logical Atomism) were influenced by a series of discus— sions which he had held with Wittgenstein in the years 1912— 191“. It was during that time that Wittgenstein penned "Notes on Logic," and Russell's lectures reflect the influ- ence of Wittgenstein's thought in the period of the "Notes," rather than that of the Tractatus. Nonetheless, the position of Russell is sufficiently close to that of the Tractatus that we may briefly refer to Russell's discussion. 86 It is a truism, says Russell, that "the world con- tains facts, which are what they are whatever we may choose to think about them."12 A fact, says Russell, is "the kind 13 of thing that makes a proposition true or false." Cer- tainly the locution "kind of thing" might be regarded as a mere manner of speaking; but Strawson would very probably regard this in a much more serious light. The very fact that this locution is used at all suggests the assimilation of facts to things, the conception of a fact on the analogy of a thing. This, at any rate, is what Strawson warned against. Russell, however, continues: If I say 'It is raining', what I say is true in a certain condition of the weather, and is false in other conditions of weather. The condition of weather that makes my statement true (or false as the Ease may be) is what I should call a 'fact'.1 We have our ambiguity again: is the fact to be identified with a condition, or are we to speak of the fact that the condition obtains? No such distinction is made, either in Russell's work, or in Wittgenstein's "Notes on Logic." Nor, for that matter, does the Tractatus make the explicit dis— tinction. Nonetheless Russell is careful to deny that he is identifying facts and things, at least in these lectures. This distinction was blurred in some of Russell's later work 12Bertrand Russell, Logic and Knowledge, ed. Robert C. Marsh (London, 1956), p. 182. 1 3Ibid., p. 182. 1“Ibid., p. 182. 87 (cf. his Human Knowledge: Its Scope and Limits, in which the statement is made that a fact is "everything there is in the world.")15 It is, for example, not Socrates himself who makes the statement 'Socrates died' true, but the £323 that Socrates died. Socrates the man can be the referent of a r name, but not the referent of a sentence. Statements assert facts about Socrates, if the statements are true. Thus, says ; Russell, a fact is not a particular, for the latter can be I named. Yet Russell's description of what a fact is is rather k vague. A fact, according to him, is the gggg 9: Ehggg that makes a statement true or false. We do, he says, make the distinction between particular facts (such as make the sen- tence 'Socrates is mortal' express a true statement) and general facts (such as make true the statement that all men are mortal). The distinction is made on the basis of whether or not the subject—term of the sentence is a particular or general term. But the distinction is still not made between facts as constituents of the world, and locutions such as 'fact that'. And again this is not permissible according to Strawson. The distinction must be made. And it appears that the distinction is not made in the Tractatus either, for in that work facts appear, in the ladder language, to be genuine entities, much as they are in Russell's lectures. 15Bertrand Russell, Human Knowledge: Its Scope and Limits (New York, 1962), p. lU2. 88 We may conclude at least this about the notion of fact as it is developed in the ladder—language of the nggf Eggggz that, in that language, facts are entities in their own right, and that they are in a sense thus far unspecified the constituents of the world. They make up the world; in- deed, from proposition 1.1 of the ladder language it is clear that the total set of facts lg the world. And this seems to mean that a description of all the facts is equivalent to a description of the world. Much in line with Russell's and Austin's position, facts are nonlinguistic entities whose existence can be asserted and which can be described by statements. But they cannot be named, according to the point already established in our discussion of the material pre— sented in the Notebooks and in the ”Notes on Logic." The ladder language of the Tractatus, then, appears to be committed to the existence of facts as non—linguistic entities. But we have already asserted that Wittgenstein deals with another language in the Tractatus, which we have called the "perspicuous" language. The question arises concerning whether or not this language is also committed to facts as entities. The argument toward an answer to this is long, subtle, and complicated. But suffice it to say here that we shall argue in the negative, on the basis of consid— erations pertaining to the non—nameability of facts, and con- siderations to be introduced later. And we have said that we shall take the commitments of the perspicuous language as 89 primary, owing to the greater likelihood of our being able to determine the commitments of that language with greater precision. But even more, we take it as primary because Wittgenstein takes it as the language whose constituent sen- tences exhibit their sense explicitly and precisely. Yet, since the ladder language might be regarded as setting forth the presuppositions of that language, that is, the conditions under which a sentence is said to have sense, we shall still be concerned with what the ladder language has to tell us about the world, about facts, and about states of affairs. Such was the reason for dwelling at such length on the nature of facts as this nature was presented in the ladder language. E- Sachverhalte Given this discussion of facts, the next problem posed for us is indicated in the following proposition of the Tagg— Leela: (1.13) The facts in logical space are the world. What does Wittgenstein mean by the term: '1ogical space'? There are various divergent explanations and interpretations of this term. We shall attempt to provide an interpretation of this difficult concept using the concept of state-descrip— tion as developed by Carnap in his book The Logical Founda- tions 93 Probability. We will first introduce the basic fea— tures of this language as Carnap develops it, and then we will apply it to the scheme of the Tractatus as developed in 90 the ladder language.16 The coincidence of the two different schemes may not be exact, but our belief is that Wittgenstein's concept of logical space can be illuminated considerably by Carnap's concept of state-description, with the attendent lin— guistic machinery bearing heavily on what we shall say con- cerning Wittgenstein's perspicuous language later in this essay. And further, we shall gradually introduce various concepts related to the problem of Sachverhalte (translated by the locution 'state of affairs' in the English text of the Tractatus), relating the concept of Sachverhalt to the scheme given by Carnap. Carnap advances his theory of state-descriptions as an explication of the notion of "possible state of affairs" and states that this explication is to be carried out rela- tive to a specific language-system.l7 This statement raises one of the major points of contact between Carnap's and Witt— genstein's schemes: the notion of possible state of affairs is very close to Wittgenstein's use of the term 'Sachverhalt' in the ladder language. Can Carnap's symbolic language as developed in the Logical Foundations 9£ Probability function as an adequate explicans for the concept of Sachverhalt in the ladder language? It will for the moment. But whether or not it will ultimately serve as the explication of that con— cept is another question. We shall treat this question in 16Rudolf Carnap, Logical Foundations 9i Probability, 2nd edition (Chicago, 1963). l7Ibid., p. 71. 91 detail in Chapter IV. Our interests here are directed toward an approximate understanding of the concept of Sachverhalt, and we are taking Carnap's 'logically possible states of affairs' as an approximate analogue to 'Sachverhalt'. The concept of logically possible state of affairs is to be re— placed by the notion of a state of individuals of the domain of interpretation assumed by a given language. This state is to be represented in the language through the use of primitive predicates which designate properties of the indi— viduals and the relations which hold among them. Then Car- nap's thesis is that each such state can be represented by sentences of the language, and such sentences are to be called state-descriptions. Let us be more explicit concerning the properties of the language in which state-descriptions are to be formed. One requirement on state descriptions for some language L is, in Carnap's words, the following: A state-description for a system . . . must state for every individual of L and for every property designated by a primitive predicate of L whether or not this individual has t is property; and analogously for relations.l Let us suppose that a sentence, say 'P', is an atomic sen- tence of L. A state-description in L must contain either the affirmation or the denial of 'P', as Carnap says. Let us 19 render the negation of 'P' as '-P') a basic pair. Then every state of the world described by L "can be described by 18Ibid., p. 71. 19Ibid., p. 67. V! w— i.I—A 92 a class of sentences in L which contains exactly one sentence 0 I 20 from every basic pair in L. Such a class of sentences of L is called a state—description (in L). In the case of a finite system a state—description will consist of a conjunction of a finite number of sentences, each sentence being one of each pair in the language. Thus, in a simple language whose primitive basis contains (1) three individual constants and (2) one primitive predicate (say, 'P'), the following would be a state-descrip— tion in that language: —P(a) & P(b) & -P(C). Here the property represented by 'P' is asserted to hold or not to hold of each of the objects designated by 'a', 'b', and 'c'. h In the case of a domain of denumerably many individ- uals, we would need a language whose primitive basis contains denumerably many individual constants. And there is no ques— tion here of a state-description consisting of a conjunction of denumerably many sentences, each of which is a member of each basic pair of the system. Here we are limited to speak- ing of a denumerable g3: of sentences, but not of a conjunc— tion of such sentences, since the construction of such a conjunction would be impossible. Thus, again, a state-des- cription in a language containing finitely many individual constants in its primitive basis in a conjunction of sentences 2OIbid., p. 71. Arr“: ( y.4‘4nl 'y‘. a \.‘.x -I 1 ul’ ("If (3' ‘0 .7 + 93 each of which is a member of each basic pair constructible in the language. In the case of a language whose primitive basis contains denumerably many individual constants, a state—description is a set of denumerably many sentences each of which is a member of each basic pair constructible in the language.21 In order to link Carnap's scheme with Wittgenstein's, ‘ let us introduce the term object, which will be a neutral term referring to any entity which can be designated by an —_'—‘ .—‘ - individual constant of a language-system. We said that the term 'object' has great importance for the metaphysics de— veloped in the ladder language of the Tractatus, and it first makes its appearance in the following proposition: (2.01) A state of affairs (a state of things) is a combination of objects (things). The German word Sachverhalt is translated, as we have noted, by the English locution 'state of affairs'. The English word 'object' is a tranlation of the German Gegenstand. Let us suppose now, and only for now, that objects have various properties, that we can distinguish between the object and the properties which it has. The distinction is parallel to Aristotle's distinction between the substratum of a sub- stance and its form. The present distinction is made for the sake of the language we are developing, for we wish to be able to refer to the object by means of an individual con— stant of the language, and its properties by the primitive 211bid., p. 72. 9U predicates of the language. Let us suppose further that relations can obtain among objects. We do not assume merely dyadic relational predicates, but predicates of any number of places. Now a state—description of this universe of objects will consist, in the case of a finite number of objects in the universe, of a conjunction containing a member of each basic pair of the language. Thus it will contain both atomic sentences and negations of atomic sentences; it is assumed that each member of the conjunction is true, for we wish to have a true description of the state of the world. If there is a finite number of objects in the domain, the conjunction will also be finite. This requirement is laid down as condi— tion number two in Carnap's statement of requirements on state descriptions, and it guarantees that, if there is a finite number of objects in the domain, and if the objects differ from one another in a finite number of respects, the number of states of affairs in the world is finite. Hence the number of atomic sentences of the language is finite, since each atomic sentence of the language describes one and only one state of affairs. And thus it follows that the evaluation of a truth-functional conjunction of atomic sen— tences or their negations is effective. Suppose that we were to list Ell possible state-des— criptions expressible in the language under discussion. This would amount to a listing of all possible states of affairs, 95 not merely the actual states of affairs, whatever they might be. They would be listed in all possible combinations, so that whatever states of affairs might be possible in that world, the description of that state would appear in the list. And this seems to echo something that Wittgenstein himself says about the same subject: (2.012“) If all objects are given, then at the same time all possible states of affairs are given. The list of all possible state-descriptions, then, would include all possible descriptions of all possible states of affairs; each member of the list would describe an atomic state of affairs, and by means of truth-functional conjunc- tion, we could represent them as occurring in all possible combinations with each other. The view of Wittgenstein's Sachverhalte presumed here is that they are very much analogous to what we have called "atomic states of affairs" above. Why atomic? We call them so for two reasons essentially: (l) for the sake of the model developed here, in which it is required (by Carnap) that the atomic sentences of our language be independent of one another, in the sense specified by him, and (2) because of what Wittgenstein himself says about Sachverhalte: (2.062) States of affairs (Sachverhalte) are independent of one another. (2.063) From the existence or non-existence of one state of affairs it is impossible to infer the existence or non—existence of another. 96 Atomic sentences are logically independent in the sense specified by Carnap. But Wittgenstein talks of Sachverhalte, which are described by atomic sentences, as being "independent." Does he mean causal independence here? It appears that Wittgenstein does have causal independence of Sachverhalte in mind. And it appears that the causal inde— T pendence of Sachverhalte is represented by the logical independence of the atomic propositions which describe the . Sachverhalte. g But there is more to be said about what sort of causal connections Wittgenstein is denying to hold among Sachverhalte. Apparently a causal relation holding among Sachverhalte could be represented by a truth-functional con— ditional, say, one holding between an atomic proposition 'P' and another one 'Q'. And such a conditional would be equiv— alent by definition to the sentence '-(P & -Q)'. Let us suppose, then, that 'P' and 'Q' each describe Sachverhalte. And let us construe the notion of causal relation among Sachverhalte as follows: to say that a Sachverhalt described by 'P' is the cause of a Sachverhalt described by 'Q' is to say that the occurrence of the former is a sufficient condi- tion for the occurrence of the latter. And such a relation, we have said, could be asserted to exist by the assertion of a truth-functional conditional with 'P' as antecedent and 'Q' as consequent. 97 Is Wittgenstein saying in 2.062 that we are never justified in asserting such a conditional, that g9 sentence of the form '-(P & —Q)' is ever true under any circumstances, where both 'P' and 'Q' are atomic? He would not be justified in doing so, since this would seem to be tantamount to saying that sentences of the form '-(P & —Q)' are all logically false. And this conflicts with the fact that '-(P & -Q)' is contingent, given the atomicity of 'P' and 'Q'. Apparently Wittgenstein is saying that, since truth-functional condi— tionals with atomic sentences as antecedent and consequent are one and all contingent, any determination of a causal connection between states of affairs will always be subject to this contingence. Wittgenstein, with Hume, is denying that we can know the existence of necessary connections between Sachverhalte. Sachverhalte are causally independent only in the sense that there is no knowable necessary connection between them. And this contingency is in the contingency of the truth—functional conditionals consisting of atomic sen- tences as antecedent and consequent. Q. Sachverhalte and Facts We have thus far spoken more about the representabil- ityof‘Sachverhalte in a language with truth-functional con- nectives, using some of the resources of the first—order functional calculus. We have thus far, however, spoken very little about the nature of the Sachverhalte and the relation «of these to facts, as these concepts occur in the exposition of tflie ladder language. 98 We put forward Carnap's theory of state—descriptions as a possible explication of the notion of logical space as it was introduced in the ladder—language: .(l.l3) The facts in lcgical space are the world. The theory of state-descriptions presumes that the world can be described by conjoining a sentence from each basic pair of the language used. Each atomic sentence in the descrip- tion can be called a cggponent of that description, and each component is independent of all the others, in the sense which we specified at length above. Now, following Stenius' work on the explication of logical space in the Tractatus: . We could therefore generalize the concept of 'dimension' by stating that a world has as many dimensions as it has mutually independent components of des- cription. According to Stenius' scheme of interpretation, a logical space will have as many dimensions as the world has possible states of affairs; or, if we connect the concept of logical space with the language describing that world, the world lias as many logical dimensions as there are atomic sentences iji‘the language. Each state—description constructable in ttme language becomes a description of a possible state of true world. Or, following Leibniz, each state-description cornstructible in the language describes a possible world. Btu: each possible world may differ from other possible worlds 22Erik Stenius, Wittgenstein's Tractatus: A Critical Irnnerpretation 9: its Main Lines 9L Thought (Ithaca, N. Y., 1960), p. ”O. 99 only in one component of description, or in one state of affairs. As Wittgenstein says: (1.21) Each item can be the case or not be the case while everything else remains the same. This follows from the independence of the Sachverhalte, both the causal independence of the Sachverhalte and the logical fl independence of the atomic sentences describing them. Logical space, then, can be described by the state- descriptions constructible in the language. The space has as many dimensions as there are possible states of affairs, Sachverhalte, in it. And the causal independence of the Sachverhalte guarantees that, upon determination of the existence of a single Sachverhalt, the other Sachverhalte remain undetermined. Notice that the word 'dimension' is not being used in a spatial sense; a logical dimension, as we use the word, is a component of the description of the world: a state-description, that is. A state—description summarizes all information about the world as it is at the time at which the state—description is produced. But we still need to determine what it is about Sachverhaltethat atomic sentences describe. To begin such a determdnation, let us examine the first relevant proposi- tion of‘the Tractatus' ladder-language: (2) What is the case—-a fact--is the existence of states of affairs (Sachverhalte). It appears that from proposition (2) above we have the fol- lowing definition: lOO Df. 'Fact' for 'existing Sachverhalt or Sachverhalte'. It seems that this is precisely what Wittgenstein means by asserting proposition (2). In our definition we allow for the possibility that a fact might be constituted by several Sachverhalte, as well as by one only. In the ladder lan- guage of the Tractatus, we are talking about facts and Sachverhalte not merely as pseudo-entities but as genuine entities. If a Sachverhalt exists, it is a fact. But we might question the part of our definition which allows facts to be constituted by several Sachverhalte. And we might put the question thus: are all facts Sachverhalte? Are facts to be considered as independent from one another, as Sachverhalte are? This is a difficult question to answer on the basis of textual evidence, but let us begin the attempt by noting the following propositions of the ladder—language: (2.03“) The structure of a fact consists of the structures of states of affairs (Sachverhalte). (2.09) The totality of existing states of affairs is the world. (2.05) The totality of existing states of affairs also determines which states of affairs do not exist. (2.06) The existence and non—existence of states of affairs is reality. (We also call the existence of states of affairs a positive fact, and their non-exist- ence a negative fact). These pnwmmeitions give us some crucial information about Ekufliverhalte, and about their relation to facts. For example, 101 it is clear from proposition 2.05 that Sachverhalte can fail to exist as well as exist. But from 2.0“ we can infer that facts and existing Sachverhalte can be one and the same. According to proposition (1), the world is all that is the case. According to (1.1), the world is the totality of facts. According to (2), what is the case-—namely, a fact—- is the existence of states of affairs. Facts, then, are existing states of affairs, existing Sachverhalte: they are identified with existing states of affairs. But since we are explicitly told that Sachverhalte can fail to exist, we cannot identify the fact with all possible Sachverhalte; we can identify facts only with those Sachverhalte that gglgg: or perhaps with clusters of them (cf. proposition 2.039). The totality of existing states of affairs, Sachverhalte, is the world. But more explicitly the question can be raised: can a fact consist of more than one Sachverhalt? It appears that it can; whether a fact consists of one Sachverhalt or more than one depends on the breadth of our purview of the world. The world might be said to be ”superfact," the totality of all existing Sachverhalte. But, relative to a particular scientific inquiry into this world, not all Sachverhalte will be relevant to this inquiry. We investigate only those Sachverhalte which are relevant to the inquiry in question, and these are the facts which interest us. Let us say that we are investigating the properties of a boiling liquid in r14 74A 1h. .; . j. 5. a i'li: ILPI .. o...‘ W\‘k a 7;“ u" .0 p n)— 1‘ .. A1. A ‘ 102 beaker. We designate the liquid by the letter 'a', and then proceed to investigate its properties: (1) Liquid a boils at 200°C. (2) Liquid a has a specific gravity of 1.3. (3) Liquid a has a reddish color. Each of these findings may be represented in a symbolic language which contains atomic _ sentences describing them. We might, for the moment, suppose F: that each of these findings represents the discovery of a Sachverhalt. Each of them is a fact, since the Sachverhalte “I‘VE . T- here discovered are existent. And yet we might say that all of them taken together constitute a fact in toto. If we accept the implication of this example, a fact can consist of more than one Sachverhalt. And the liquid can be des- cribed in some exact symbolic language by a state—description formed by the conjunction of some atomic sentences of the language. If we take this conjunctive statement to be true, we can think of it as asserting a composite, non—atomic fact. Hence it seems compatible with Wittgenstein's assump- tions to say that facts Egg consist of more than one Sachverhalt. Now according to proposition 2.05, the Sachverhalte which exist determine those which do 223 exist, even though their existence is possible. We might explain this passage by reference to Carnap's state—description model again. We said that a basic pair of a language consists of an atomic sentence together with its negation. Only one member of a basic pair can occur in any state—description, and therefore 103 the selection of one member of a basic pair automatically excludes the other member. Hence, which member is selected for _inclusion in a state-description determines which member is excluded: whether the atomic proposition itself or its negation. Thus, for the sake of the argument, let us assume that my typing here is a Sachverhalt. The fact that I am typing is a constituent of the world; the state— description describing the world at this point must include my act of typing. The fact that I am typing automatically excludes my doing anything else at the moment: washing dishes, playing the piano, watching television, etc. Thus this fact determines that other, possible states of affairs do not exist, even though their possibility is not excluded. In this sense, then, what Sachverhalte there are determines that other Sachverhalte do not exiSt. They are possible, but not actual. The introduction of the concept of nonexistent Sachverhalt, however, immediately raises some problems. In the Notebooks and in "Notes on Logic" Wittgenstein introduces the concept of the negative fact. It is re-introduced into the Tractatus, specifically in the following passage: (2.06) The existence and non-existence of states of affairs (Sachverhalte) is reality. (We also call the existence of states of affairs a positive fact, and their non- existence a negative fact.) It is (as it happens) a negative fact that I am not now washing dishes. Thus the proposition which asserts the ... . l.- ‘l r 1 vi. .2 . E . «as ..Inkr ._ ass. .. Inn-1?. |,l.ll. V "t 4A «.1! -\¢ p.- sn.‘ N.\ k ; ..rd. "V tan ..~.. ., Lt 10A negation of the sentence 'I am now washing dishes' will be true. Negative facts correspond to true negated atomic sentences, and the only proviso laid down by Wittgenstein in "Notes on Logic" is that in order to understand the sense of a negated sentence we must also understand the sense of the un-negated version. Something like this seems to be assumed in the Tractatus. Now we have said that an atomic sentence asserts the existence of a Sachverhalt. What does a negated atomic sentence do? We seem to be driven to the following conclu- sion: that negated atomic sentences deny the existence of a certain Sachverhalt. How then does this consideration connect with the notion of a negative fact? Apparently the connection is as follows: let us take the letter 'P', calling it for the moment an atomic sentence. Let 'P' be interpreted as 'Smucker is now watching television'. As it happens, 'P' is false. Then 'nbt-P' is not, for it is a truth—function of an atomic proposition, obtained by apply- ing the operation of negation to 'P' as its base. Now atomic sentences assert the existence of Sachver- thLg, while negated atomic sentences deny the existence of Sachverhalte. Existent Sachverhalte are the only constitu- ents of the world: nonexistent Sachverhalte are not "part of" the world, not constituents of the actual world in any way. But if a negative fact is a fact, it must somehow be part of the world, a constituent of it. In order for a com- plete description of the world to be possible, we must _a: I’ll. r. " 105 include negative facts in our state—description. Therefore we cannot argue that, as a matter of stipulative definition, the term 'negative fact' is to be intensionally identical with the term 'non—existent Sachverhalt'. What are we to say then? It might be possible to F attempt the following definition: Df. 'Negative fact' for 'Fact that a Sachverhalt does not exist'. This seems the only possible course of interpretation, for it appears that Wittgenstein wishes to include negative facts in any description of the world. A negative fact is asserted by the denial of an atomic sentence, which is tantamount to the denial of the existence of a Sachverhalt. Hence it appears again that we cannot identify the notion of negative fact with that of Sachverhalt, but must say this: negated atomic propositions do not assert the existence of a Sachver- halt, but rather assert the fact that a certain Sachverhalt does not exist. Whence it seems that negative facts are not Sachverhalte themselves. And this conclusion seems consis— tent with our supposition that only atomic sentences do assert Sachverhalte. We have thus far treated the problems raised by Wittgenstein's use of the term Sachverhalt in the context of Carnap's theory of state-descriptions. The theory seems to be a very efficient way of explicating these problems, par- ticularly with respect to clarification of notions such as 106 logical space, the independence of Sachverhalte, and the nature of facts, so far as these are discussed in the Tractatus. ihe notion of the atomic sentence, so central to the theory of state-descriptions, occurs also in the Tractatus. The atomic sentence, or "elementary proposition" (Elementarsatz) .- _— .3". 1 as Wittgenstein terms it, is the central concept of the Tractatus' theory of the perspicuous language, and we shall subject this concept to intensive scrutiny throughout the ensuing chapters. EJ Q. Objects (Gegenstande) One more concept in the ladder-language metaphysics needs to be introduced: namely, the concept of the Gegenstand, or the object. We have already introduced this concept in— formally in connection with the nature of the atomic sen— tence as it occurs in state-descriptions. We described an atomic sentence as consisting of a predicate letter with any number of places for individual constants. For the purposes of the state—description model, we said that the constants designate "objects," but we left the nature of the objects unspecified. And yet, the notion of an object is perhaps the most central notion of the ladder-language metaphysics. Let us introduce this topic in somewhat more detail by quoting the following propositions of the Tractatus: (2.01) A state of affairs (a state of things) is a combination of objects (things). 107 (2.011) It is essential to things that they should be possible constituents of states of affairs (Sachverhalte). Proposition 2.01 serves to introduce the objects as those entities which compose Sachverhalte. When we come to objects in the analysis of a state of affairs, we have, as it were, hit rock bottom. The objects are the most fundamental con- stituents of the world, and analysis of a situation can pro— ceed no further than to discover the objects, and to describe both the objects and the manner of their combination in a Sachverhalt. Sachverhalte, then, are combinations (Verbin- dungen) of objects. Notice that, in the German text, the words Qigg (thing) and Gegenstand (object) seem to be used interchangeably. It does not seem that Wittgenstein is arguing for the synonymity of Qing and Gegenstand in this or any other context in the Tractatus.’ Objects are things, to be sure. They are the basic things of the world, but Wittgenstein seems to be saying that there are some things that are not objects. A defense of this position must make use of the fol- lowing proposition of the Tractatus, one of the most impor- tant in the entire work: (2.02) Objects are simple (Gegenstande sind einfach). For this context, let us interpret the difficult word "simple” as meaning 'cannot be further analyzed'. Here the impossi— bility is not merely factual, in the sense that it is impossi— ble for me to run from here to New York and back in five 108 The impossibility of further analyzing objects is seconds. logical. The way in which Wittgenstein uses the term 'object' precludes even the logical possibility of further analyzing them, as we shall show both here and in Chapter IV. “1 Photice, however, that in proposition 2.01 objects are pre— sented as things. Yet most things are further analyzable, 5J1 the sense of being composite. My body, my car, this Iuouse, are all composite, even though we can call them all "thingsfl' Things, then, whether they be simple or composite, must occur in Sachverhalte. This is in fact what proposition 2.011 says: that it is essential to things, whether simple or ccnnposite, that they must be possible constituents of Statems of affairs. It is logically necessary that things Shoulxi occur in states of affairs. But Wittgenstein, in the ladCherm—language of the Tractatus, is talking about two types (H‘Ilcmgical necessity and impossibility. Suffice it to say here triat logical impossibility and necessity of the first kind. ceuq be represented by a truth-functional language which deselfitues Sachverhalte as they occur in logical space. This type (Df‘ necessity is represented by tautologous or contradic— tory mOllecular sentences of the perspicuous language, and concerfiiss the simultaneous existence and nonexistence of §gghf Eggflflldigg. For example, suppose that 'P' is an elementary proposifltjmmldescribing a Sachverhalt: the contradiction '— (P & -—P)' asserts that P cannot simultaneously exist and 109 not exist. Suppose that 'P' and 'Q' describe distince Sachverhalte: then the sentence '-(P & (Q & -P))' is a tautology asserting that the existence of P is incompatible with the simultaneous existence of Q and —P, where '-P' asserts a negative fact. But in 2.01 we are dealing with quite a different matter: that of the combination of things (or objects, if they are simple) into Sachverhalte. And here we are dealing with single Sachverhalte and the conditions under which they exist or fail to exist. This is the second sort of logical necessity and impossibility which Wittgenstein discusses, and this kind cannot be asserted in the perspicuous language, as Wittgenstein argues. In 2.01, we are dealing with the form of Sachverhalte, and Wittgen— stein will argue that this is something that cannot even be discussed in the perspicuous language. The necessity that things be combined in the Sachverhalte, and not exist on their own, is a necessity of the second kind. (2.012) In logic nothing is accidental: if a thing can occur in a state of affairs, the possibility of the state of affairs must be written into the thing itself. (2.0121) It would seem to be a sort of accident, if it turned out that a situation would fit a thing that could already exist on its own. The question might be asked concerning why Wittgenstein be— lieves that the occurrence of a thing in a Sachverhalt is a matter of logical necessity. What does logic have to do with it? Here again, we refer to the perspicuous language. In a I'Iu -' llO language of this kind, there seems to be implicit in the language a set of formation rules, rules which determine what string of symbols constitutes a sentence of that language and what does not. We are here dealing with the way in which the language is formed, and the language reflects the nature of the world. It is constructed in just that way. Once we de- cide how we are to put the language together, then certain things follow as a matter of logical necessity. But it is not the sort of necessity which can be represented by tauto- logies and contradictions in that language. It is a necessity which has to do with the construction of the language itself. Similarly, we seem to have here a necessity dealing with the structure, the construction, of Sachverhalte. And this can- not be represented by contradictions and tautologies of the language. Indeed, the formation rules of a language have to do with the form of the sentences of the language, and so cannot be regarded as part of the language. Likewise, asser- tions about the nature of Sachverhalte cannot be represented in the perspicuous language. In this sense it would be "accidental” if the thing in question could exist apart from some occurrence in a state of affairs, a Sachverhalt. We are dealing with the form of the Sachverhalt and the form of the thing in propositions 2.012 and 2.0121, although Wittgenstein is not telling us so. Let us examine proposition 2.0121 again, this time in the light of the German text: 111 (2.0121) Es erscheine gleichsam als Zufall, wenn dem Ding, das allein fur sich bestehen konnte, nachtraglish eine Sachlage passen wurde. Let us translate this as follows: “2.0121) It would seem, as it were, to be an accident, if a thing which could exist by itself (allein fur sich——alone for itself) could fit (passer-- be convenient for, be correspondent to, be harmonious with) a situation afterward (nachtraglich). TTuis is very rough, but my purpose is to exhibit the ambig— llity of the German. The meaning of 'gleichsam' in this pro- ‘position is not 'a kind of' or 'a sort of' accident, as it appmflis in the English text, but rather is: "as it were," 'Hsomewhat." The point is, that accidents concerning the Stxructure of Sachverhalte and the nature of the objects com- pCNsing them simply don't happen. We are, as we said above, dealing with the form of the object and of the Sachverhalt. But the notion of form in the Tractatus is extremely digfficult to explicate, simply because the term is always useed as a surrogate for another term, whose meaning is not eXFDIained to us: 'possibility'. (2..01U) The possibility of its occurring in states of affairs is the form of the object. If fixt is difficult to explicate the notion of possibility, it will. be difficult to explicate that of form. But we have al- reads; laid the groundwork for a treatment of the concept of DOSSibility: 112 (2.012lb) If things can occur in states of affairs, this possibility must be in them from the very beginning. (Nothing in the province of logic can be merely—possible. Logic deals with every possibility, and all possibilities are its facts.) If I can imagine objects combined in states of affairs, I cannot imagine them excluded from the possibility of such combinations. Sewreral comments are in order on this extremely important prnoposition: in the first line of the above quotation, the vuard 'possibility' occurs. This is not in the German text. The German says: (2.012lb) Wenn die Dinge in Sachverhalten vorkommen konnen, so muss dies schon in ihnen liegen. (2.012lb) If things can occur in states of affairs, this must lie in them already. 'Phossibility' does not occur in the German text, to be sure, bllt it nonetheless seems consistent with the German to include firms word in the translation. The question then arises con- cexrrdng what sense of ’possibility' is being treated in 2.0121. 153 it the sort of possibility indicated by the truth-table EVEiluation of a molecular sentence of the perspicuous language, in 1Nhich the evaluation shows the proposition to be contin- gerrt? The answer here is clearly no, for the sort of possi— bilifity discussed here pertains to individual atomic sen— tencnes and to the Sachverhalte corresponding to them. And more particularly, we speak of objects which occur in Sachver— EfilEfi: and of possibilities pertaining to the objects. 113 What, then, precisely, do we mean by the form of an object? Wittgenstein links the concept of the form of an object with the notion of possibility, as we might expect: (2.01U1) The possibility of its occurring in states of affairs is the form of an object. Agzxin: this is not the sort of possibility which can be ex— hitlited by a truth—table evaluation of molecular propositions, irl which we are evaluating the possibility of the simultan- ecnis occurrence and non—occurrence of Sachverhalte in logical .space. We are talking about possibilities inherent in the gflgject itself for occurring in certain Sachverhalte. Speaking of possibilities inherent in the object it- SEfilf suggests that Wittgenstein is here introducing the rIOtion of the essence or nature of an object. And indeed, tflis is precisely what he is doing. (2.0123) If I know an object I also know all its possible occurrences in states of affairs. (Every one of these possibilities must be part of the nature of the object.) A new possibility cannot be discovered later. Ob;jects have essences, or natures. The nature of an object is constituted by the possibilities inhering in it for com- biruation into Schverhalte. Hence, according to 2.0123, if we Eire to know an object, we must know its nature, and this natture is constituted by the possibilities of combination With other objects in a certain range of Sachverhalte. Wittgenstein's language throughout the first few paEES of the Tractatus suggests that the essence of most llu objects does not allow a given object to combine in all possible states of affairs. Indeed, there is a limited range of Sachverhalte in which an object can occur; this is the case, at least, for most objects. And that range of Sachverhalte is delimited by the internal nature of the ob- ject. The object has certain internal properties which 1* determine the range of possibilities of occurrence in Sggh— verhalte. And this conjecture about Wittgenstein's meaning ; here is strongly supported by the following passage from the f ' L Tractatus: (2.01231) If I am to know an object, though I need not know its external properties, I must know all its internal properties. If this passage is correlated with the preceding one, 2.0123, we have the statement that the internal properties of the object, while not expressible in the perspicuous language, are what determine the range of the object's posSible occur— rences in Sachverhalte. We remember that the object must occur in some Sachverhalt or other. This is of the essence of the object, and it is what constitutes the form of the object. But these two passages also suggest that what parti- 'cular Sachverhalt the object is occurring in is more or less accidental. It is not a matter of logical necessity that the object occur in this particular Sachverhalt. We might there— fore regard Wittgenstein as saying that an external property of an object is the set of objects it happens to be con— figured with at a particular point in the history of the 115 world. It is, in short, its occurrence in a particular Sachverhalt. If the object is to occur in this Sachverhalt, its internal nature, its essence, must allow it to do so. gut: that it does occur in this Sachverhalt is accidental, since it could just as well have occurred in some other Sachverhalt in which its essence allows it to occur. What this says, then, about the knowledge of an ob- ject is that we need not know which Sachverhalt the object happens to be configured in at a given point in the world's history in order to know the object. But we do have to know the range of possibilities of its occurrence in Sachverhalte; and this is apparently the same as knowing the object's essence. It appears, too, that the form of an object and its essence are the same, given the way in which Wittgenstein uses the terms. The phrasing of proposition 2.01ul (quoted on p. 113) suggests that the possibility of the object's occurring in Sachverhalte is identical with its form. And this seems to accord with what Wittgenstein says in 2.0123 about the possibilities of the object's occurrence in Sach- verhalte being part of the nature of the object. There have been several attempts to clarify the notion of the form of an object by means of set—theoretical techni— ques. One such attempt is Black's.23 Wittgenstein, says Black, is thinking of the "power" or disposition of individual 23Max Black, g Companion to Wittgenstein's Tractatus (Ithaca, N. Y.,.l96U), pp. 55-56. 116 objects to combine in producing Sachverhalte when he uses the phrase "logical form of an object." Suppose a certain object, which we designate by the symbol 'x'. And suppose that this object has a disposition to combine with the ob— jects which we designate by the set of symbols 'xl', 'x2', , 'zn'. The resulting set with the elements 'x', 'zl', . . . , 'zn' is at least among the elements of a cer- tain Sachverhalt, according to Black. Following Black, let us call the new set a combination. Now let us define the domain of object x as follows: a set Dx is said to be the domain of x if it consists of all the combinations in which x occurs. The object x has the same form as y, according to Black, just in case the domain of x can be changed to the domain D of y by replacing x wherever it occurs in a combina- tion by y, and vice versa. Now, in an atomic sentence in which the 'x' occurs, if 'x', 'y', and each 'zi' are names of objects, if the names of objects x and y are interchange— able in that atomic sentence, so that the result of the interchange preserves the truth-value of the original state- ment, then the objects x and y are of the same logical form. But Black then incomprehensibly goes on to identify the form of an object as the class of objects isomorphic with that object.2u This is incomprehensible because the statement that the form of an object is the class of objects isomorphic to it is based on a confusion about the nature of isomorphism. 21‘Ibid., p. 56. 117 Black seems to regard isomorphism, in this context, as a relation between an individual object and a set of objects. Isomorphism, however, is a relation between sets, and an individual object (considered apart from an occurrence in a Sachverhalt) is not a set. We might try to repair Black's formulation, so that it presents what he seems to mean, in the following way: consider an actual Sachverhalt, and let us say that 'x' names an object occurring in that Sachverhalt. Then, if our reconstruction of Black's argument is correct, the form of object x is the set of combinations which are isomorphic to the combination in which x actually occurs. Or alternatively, the form of x is the set of combinations in which x can be interchanged with some other constituent object in each such combination. It is an ingenious and interesting argument, but it may be doubted whether this is Wittgenstein's idea when he speaks of the form of an object. If Wittgenstein says in proposition 2.01u1 that the form of the object is the possi- bility of its occurring in Sachverhalte, then the question of the isomorphism of combinations to the one in which x actually occurs becomes essentially irrelevant. The isomor- phisnlrequirement would seem to be tantamount to saying that all Sachverhalte in range of x's possible occurrence should lmave precisely the same number of objects, and should have jpreCisely the same structure. As Wittgenstein says in the following propositions: W'H's 118 (2.03) In a state of affairs objects fit into one another like the links of a chain. (2.031) In a state of affairs objects stand in a determinate relation to one another. (2.032) The determinate way in which the objects are connected with one another is the struc- ture of the state of affairs. Given this definition of structure, the requirement of isomor- phism of°combinations in Sachverhalte seems overly strict. For there is no suggestion in the text, so far as I can see, that the range of an object's possible occurrence in Sach— verhalte must be composed of Sachverhalte of identical struc— ture. Hence we conclude that Black's requirement of isomor— phism is too strict, and not indicated by the text. However, the discussion does prepare the way for Wittgenstein's discussion of the form of a Sachverhalt, a different order of form altogether from the form of an object. The relevant propositions of the Tractatus are 2.032 and 2.02, the latter being the shortest proposition of the Tractatus. We have already discussed the proposition: "Objects are simple" in some detail, but a further proposition becomes relevant: (2.033) Form is the possibility of structure. From the context it is clear that Wittgenstein is speaking of the form of a Sachverhalt rather than the form of an ob— ject. Objects, by their very nature, cannot have structure. Objects, according to 2.02, are simple, and structure is to be found only in complex entities. Such, according to the 119 ladder language of the Tractatus, are the Sachverhalte. Hence when we are speaking of the form of an object, we are refer- ring to an internal property of an object, a property which it has regardless of its actual combination with other objects in a particular Sachverhalt. And since objects are structure- less, in the sense of 2.033, we must be talking about a dif— ferent sort of form. And yet 2.033 refers again to possibility as determining the form of a Sachverhalt, and thus the mys— .rqP-umnfi'?‘ " '. fl terious notion of possibility again makes its appearance in the Tract atus . How might we speak of possibility with respect to Sachverhalte? Let us consider an actual Sachverhalt first, by way of trying to answer this question. An actual Sachver- halt is composed of objects in some sort of configuration, some sort of combination. Wittgenstein seems to use these words interchangeably.25 From 2.032 we find that the deter— minate way in which the objects are connected is the struc- ture of the Sachverhalt. Hence the existent Sachverhalt is a combination of objects with a definite structure, a definite and determinate way in which they are combined. What about a nonexistent but possible Sachverhalt? Wittgenstein seems to suggest that other Sachverhalte are possible, which have ‘the same form as the actual one. I supposedly can imagine (other Sachverhalte of the same form as this one which, none— tflieless, do not exist. And Wittgenstein adds to this con— .jecture: 25cf. 2.01 and 2.0272. 120 (2.022) It is obvious that an imagined world, however different it may be from the real one, must have something——a form—~in common with it. What is this mysterious form, then, which Sachverhalte must have in common in order to be imagined? Let us suppose two Sachverhalte, say 81 and S2, and let us conjecture con- cerning the meaning of the sentence '81 has the same form 22 82'. Now in 2.033 Wittgenstein says that form is the possi— bility of structure; and this suggests that S1 and S2 have the same form if the possibilities for their having a cer— tain determinate structure are exactly the same. To put it in an Aristotelian fashion: S1 and S2 will have the same form if their structure is identical but their "matter" or "content" are different. Hence Sl will have the same form as S2 just in case, assuming that S1 and S2 are distinct Sachverhalte, the objects constituting Sl are all different fronlthose constituting S2, but S1 and S2 are structurally identical, or isomorphic. This suggests that if S1 and S2 are cfi‘the same form, their constituent objects will be ccnifigured in precisely the same way. 1 No suggestion here is given concerning what the ob— jeacts are, how they are configured in Sachverhalte, whether we: can observe such configuration, or how we are to apply true scheme of analysis given in the first few pages of the Tfiéactatus. This is in part what makes the Tractatus diffi— CLth. One may, for instance, ask the question: are the otnjects spatial objects? Are they things which are situatxgd 121 in physical space, and hence can be observed? Or are they very much like the monads of Leibniz, which are not observ— able, but are much more like force fields than physical objects? We may give a preliminary answer here, subject to r further confirmation: it is quite possible that Wittgen— stein did have in mind things which were situated in physical space when he wrote the Tractatus. But in view of proposi— tion 2.02, which merely says: "Objects are simple," this seems somewhat unlikely. Certainly the objects have to be simple, or they would not be the ultimate constituents of Sachverhalte, and so of the world. Hence it seems likely that what more nearly fits the concept of the object as pre— sented in the ladder—language of the Tractatus is the Leib— nizian monad. But many questions remain unanswered: for example, does Wittgenstein conceive of the objects as parti— culars only, or are universals included among the objects? But the differences between Wittgenstein's objects and Leib— niz's monads are many and varied, and we shall deal with them in Chapter IV. Why do we not deal with them here? Because, as stated 11] the Introduction, we are at a loss to determine the ulti— Inate commitments of the perspicuous language of the Tractatus initil we examine that.language, to determine its basic pro— perties, to determine what a sentence of the perspicuous language looks like, what sort of variables and constants 122 occur in a basic sentence of that language. It is my con- jecture that the ladder language provides a clue to just such a determination of the nature of the perspicuous lan— guage. And hence it has been necessary first informally to determine the meaning of such terms as 'Sachverhalt', 'Tatsache' (fact), and 'Gegenstand' (object). For without an informal preparation such as we have presented in this chapter, the ensuing theory of language and meaning devel— oped in the ladder language is unintelligible. It is always frustrating to attempt to provide analyses of basic concepts in the ladder language, simply because such concepts illu— mine each other. The theory of objects, facts, Sachverhalte and forms in the ladder language is necessary as a propaedutie to the understanding of the so-called "picture" theory of meaning. And the situation exists in reverse: the "picture" theory of meaning, to which we shall shortly turn, illumi— nates the nature of the entities of the ladder language. For this reason the preceding discussion does not claim to be exhaustive or ultimately adequate, but preliminary only. It is preliminary to a discussion of the picture theory of 1 meaning, a theory which applies, not to the ladder language to which it is exposited, but to the perspicuous language whose nature is discussed in the later sections of the Trac- Efiggs. Once the picture theory is discussed, we can refer back to the topics discussed in this chapter. And so, to the Iaicture theory of meaning we now turn. THOUGHTS AND PROPOSITIONS: THE PICTURE THEOTY A. Pictures and Possibilities in Logical SpKCQ The theory of meaning discussed in this chapter has perhaps occasioned more controversy than any other doctrine of the Tractatus. It is clearly presented in outline, but many of the details of the theory are vague indeed. The motivations which led Wittgenstein to construct the picture theory of meaning are many, but among the major ones are attempts to answer the following questions: (1) How can Frege's theory of sense and reference be reconstructed so that certain difficulties in it can be eliminated? (2) How is it possible for us to understand a false declarative sentence? (3) How is it possible for us to understand a declarative sentence which we have never seen written nor heard uttered before? (A) What is the minimum set of con— ditions which, when fulfilled, make it possible for s to understand any sentence, true or false? The metaphysical system developed in the ladder language propositions num— bered 1 through 2.063 is constructed as a partial answer to the questions listed above. The other part of the answer is developed in the picture theory of meaning, for which the 123 1.4' " 12A metaphysics is preparatory. And hence in this chapter we focus on the declarative sentence (or, as fears and MacGuin- ness translate the German 'Sgtg',”proposition") and its relation to the world, where the term 'world' is understood as developed in the introductory metaphysical passages of the Tractatus. [- The picture theory of meaning is rather abruptly introduced by the following proposition of the Tractatus: (2.1) We picture facts to ourselves. 1 11‘ The German text has: fir machen uns Wilder der Tatsachen.” A more literal translation of this proposition than that given in the Pears—MacGuinness translation might be: We make pictures of facts for ourselves, or as the Ogden-Ramsay "We make for ourselves pictures of translation has it: "1 _ . . , . . ,. , . ,, facts. What is immediately noticed is hittgensteln s failure to say anything about the picturing of things: facts are pictured, not things. Also immediately noticeable is the J V parallelism with the associated proposition 1.1, which state: that the world is the totality of facts, not things. From this proposition, plus proposition 2.1, we infer that for Wittgenstein what is pictured is the world, since the world is the totality of facts. And from 2.0M, whicn says "The totality of existing states of affairs (Sachverhalte) is the world," we conclude at least that pictures depict Sach— verhalte. The minimum conclusion, for now, is that pictures 1Ludwig Wittgenstein, Tractatus Legion—Philosophicus (London, 1922), tr. C. K. Ogden and F. P. Ramsay. 125 depict existing Sachverhalte. We shall leave open, for now, the point that pictures can also depict Sachverhalte which do not exist, but are nonetheless possible. Now in physical space, things are arranged in such— and-s ch a way, a determinate way, and that they are so arranged is a fact. Are we then committed to the assertion 4'. that things are somehow constitutive of facts, even though facts themselves are not things? Wittgenstein, as we have seen, explicitly asserts that objects are constitutive of facts, for actual Sachverhalte are formed by the actual configuration of objects. What, then, is the relation be— tween Wittgenstein's use of the terms 'thing' and 'fact'? 6 We have already answered this in Chapter II.‘ In the first few propositions of the Tractatus, Wittgenstein seems to be using 'object' and 'thing' interchangeably. But as always in the Tractatus, matters are not so easy as that. Our ana— lysis of these first few passages indicates that while each object can be regarded as a thing, the reverse is not true: there are many things that are not objects. The distin- guishing characteristic of an object is that it is simple, whereas things located in space and time are analyzable according to some scheme or other. Objects then emerge as very special kinds of things. They are the elements of all states of affairs, and thus are elements of all facts. Objects, says Wittgenstein, are constitutive of facts. 2Ibid., p. 99. 126 But this raises an acute problem: objects are things, and yet they are constitutive of facts, which are non—things. Objects occur in Sachverhalte, and therefore in facts. Their configuration produces Sachverhalte, as 2.0272 asserts. But then we have something of a problem: if a Sachverhalt is not a thing, how can things be constitutive of it? How can a non— thing be constituted by a structure of things? Consider an automobile, which, we will agree, is a thing. Its constitu— ents are things too, and these things are arranged in certain patterns. Their arrangement constituted the car. So the car i not merely the totality of the things which constitute it, 0'1 but is also the result of these things being arranged in a certain structural pattern. But we can presumably also regard the car s being a fact. The car's existence is a fact. Apparently the car's constituents are facts as well. So we have one and the same entity being regarded from two different points of View: as fact and as thing. It appears that, whether we regard a physical entity such as a car as a fact or a thing depends on the point of view which we take regarding it. This use of the term 'point of view' is extremely vague, and yet it may well be fruitful. What, we may ask, is the difference between regarding an entity as a fact and as a thing? Clearly Wittgenstein means to draw a sharp dis- tinction between fact and thing, and yet what is the differ— ence? The Tractatus appears to suggest the following distinction, unconvincing as it may first seem: whenever we 127 peggard a car (or any other physical object) as a thing, we are; not genuinely interested in the analysis of its struc- tuice. We are interested primarily in using it, transporting it from place to place, helping with errands; we are simply rwegyarding it as a unity, and are not particularly interested iri its structure. Regarding a thing as a thing is not a InaILter of theoretical interest, since we are not interested 1r1 the analysis of a thing. But if we change our point of view, we turn the thing irito a fact. We have changed our interests, and are now iriterested in its structure. In short, we relate the distinc— tixan between thing and fact to our interest in the entity. EhJen a room can, from this point of view, be regarded in EEither light. A room is an enclosure, and if we are not par— ticularly interested in how things are arranged in it, we are nOt interested in its factuality. We turn our attention to ttiis factuality when we begin to look at the arrangement of tlie terms in it, possibly with a view to redecorating it, or Eiinmly changing the position of a few books or of the bed MIith respect to the window. If this is so, then we still 1“lave a situation in which an entity is viewed under two FNDssible aspects. The mere manipulation of an entity (say, tfle carrying of it from place to place) gives it its aspect 855 a thing. The turning of our interest toward its structure, hOWever, gives it its aspect as a fact. If this is a possible interpretation of the contrast 1r1 the Tractatus between an entity conceived as a thing and an entity conceived as a fact, then this suggests some inter- est;ing interpretations of the notion of simplicity, a notion vflai_ch will have many implications for its application to the piczture theory. What is simple may not be a matter which is fi.Xf3d once for all, but may be relative to the particular iriteerests which we bring to any analysis which we might per- karnn What I am suggesting is that the position implied by truis interpretation of the ladder language of the Tractatus aruj that explicitly stated in the Philosophical Investigations ‘_V-"A_' 3*. .‘ ' - arms far closer than might be realized. In an extraordinary I>aissage in that work, Wittgenstein discuss s the notion of Simplicity which he supposedly used in the Tractatus: But what are the simple constituent parts of which reality is composed?——What are the simple constituent parts of a chair?——The bits of wood of which it is made? Or the molecules, or the atoms?-—"Simple” means: not composite. And here the point is: in what sense 'composite'? It makes no sense at all to speak absolutely of the 'simple parts of a chair'.3 (#U7) If I tell someone without any further ex- planation: "What I see before me now is composite", he will have the right to ask: "What do you mean by 'composite'? For there are all sorts of things that that can mean!"—— The question ”Is what you see composite?" makes good sense if it is already established what kind of complexity-~that is, which par— ticular use of the word-—is in question. (#u7) We use the word "composite" (and therefore the word "simple") in an enormous number of 3Ludwig Wittgenstein, Philosophical Investigations (New York, 1968), third edition, tr. G. F M. Anscombe. _J. Eussages from his work appear in the text, referred to by SeC‘tion numbers . 129 different and differently related ways. . . . To the philosophical question: ”Is the visual image of this tree composite, and what are its component parts?" the correct answer is: "That depends on what you understand by 'composite'." (And that is of course not an answer but a rejection of the question.) (#H?) What this passage seems to say is, among other things, tfldeit the concept of complexity or simplicity which we may 118(3 is dependent on the particular purpose at hand; it is deypendent on the type of analysis we wish to carry out. TWiere is no sense in asking, apart from a particular purpose Wliich we may have in mind, what the meaning of the word 'ssimple' is. The sense of the words 'simple' and 'complex' Ckepends on the purpose of the analysis. With respect to a 813ecial analysis, then, one might say that ye decide what is ESimple and what is complex. This is not by any means to say tfldat the question of what is simple and complex has an arbi— Tlrary answer. The answer depends on what sort of analysis VVe wish to carry out. The later Wittgenstein accuses the earlier Wittgen— Estein of the Tractatus of raising this question apart from Euay particular analysis of some phenomenon or other. And it 1&3 very true——distressingly so——that the Tractatus leaves Cuben the question of how an analysis is to be carried out. E)Ir‘esumably the question of the actual kinds of analysis of f‘acts and Sachverhalte is a factual question to be decided by liiter investigators, for as Wittgenstein says in the Author's I)I‘eface to the Tractatus, "Mogen Andere kommen und es besser 130 H machen." But the very open-endedness of the Tractatus on this point, I Wjuld submit, constitutes the only possibility of its applicability. And I would also argue that this open- endedness concerning the nature of the objects and the pro- cess of analysis of Sachverhalte that discovers the objects, constitutes the only possibility for the applicability of E? the picture theory of meaning to actual cases. These considerations are directly related to the point stated above, that entities, according to the ladder- é 14‘. language of the Tractatus, can be conceived under two aspects: as facts, and as things. We maintained that hgw we regard them depends on the particular purposes we have in mind when we approach these entities. A car can be regarded as a fact, gag as a thing. A room can be regarded both as fact and as thing. The same applies to pictures, a point to be con- sidered in a discussion of the picture theory of meaning as it is developed in the Tractatus. We can therefore begin by repeating what is implied by Wittgenstein's actual assertions: that we picture facts, not things. That is, we picture entities conceived as facts, not conceived as things. And this is the most critical ini- tial distinction to be made in a discussion of the picture theory. The problem now is to determine the mechanics of the picture, and the relation which it has.to the fact (or the Sachverhalte) depicted. The following propositions become relevant here. U Tractatus, pp. cit., p. U. 131 (2.11) A picture presents a situation (Sachlage) in logical space, the existence and non— existence of states of affairs (Sachverhalte). (2.13) In a picture the objects have the elements of the picture corresponding to them. (2.131) In a picture the elements of a picture are the representatives of the objects. "F (2.1M) What constitutes a picture is that its ele- ments are related to one another in a deter- minate way. We are discussing here the general notion of a picture; later, we shall have occasion to discuss various 9. applications of it to particular cases. A picture, according to Wittgenstein, is something which presents the existence and nonexistence of Sachverhalte. There is no mention in the Tractatus of any necessity that the picture should present a fact, or existing Sachverhalte, for the picture can depict Sachverhalte whether they are existent or nonexistent. If the Sachverhalte which the picture presents do not exist, the picture is no less a picture for all that. For now, we notice that according to the text of the Tractatus a picture presents situations Sachlagen) in logi- cal space, and we must decide here what Wittgenstein means by the word 'Sachlage'. Apparently there is no necessity that a picture should present only a Sachverhalt, a state of affairs which is "atomic," having no causal connection with any other situations. A Sachlage may consist of several Sachverhalte, several atomic states of affairs, which happen to coexist in some region of logical space. At the same time, it appears that the term 'Sachlage' and the term 'fact' _______.hd__ 132 are not coextensive, since there seems to be no necessity that a picture should present an actual situation in order that we should be able to understand it. The meaning of Sachlage seems to be this: whereas an existing Sachverhalt, or a collection of them, seems to be a fact, a Sachla. consist either of existent or nonexistent Sachverhalte or both. This room is a wva as it now stands. But this room would also be a Sachlage if it differed in only one respect: say, that the walls should be a light blue instead of white as they are. Or let us take the picture hanging on the wall, which presents a Sachlage. The Sachlage presented by the picture is a woodlot located a few miles north of Bluffton, Ohio. The painting was made by my grandfather on the spot, and therefore the painting is a depiction of an actual scene. If one stands where the easel was while the picture was being painted, one will see the same Tatsache, or fact, that my grandfather saw while painting. There are trees in the background, and far in the background there is a low hill which is sharp ridged, having a copse of birch trees growing on it. Toward the bottom of the picture there is a woodland path, winding through a floor of wildflowers. In the near foreground there is a red—headed woodpecker clinging to a stump, hammering at the bark. This was the Tatsache as my grandfather painted it. But it is quite probable that, while the picture was true to the fact as it was depicted, the picture no longer presents a fact, but a Sachlage. The woodlot is as it was then, ..I. an“- .. . ' D except for one detail of the picture: the woodpecker is pro— bably not on the tree stump. In short, the scene depicted by the painting differs in that one respect from the fact. The painting presents a situation, as it did when my grand- father painted it. But while a situation is still presented by the painting, there are aspects of the situation (in our language, Sachverhalte) which are no longer actual. A Sachlage, then, is a state of the world, usually part of the world, which need not consist entirely of actual (or, equivalently, existent) Sachverhalte. A situation differs from a fact in that one or more of the Sachverhalte constituent of the situation may not exist, while a fact must consist of existent Sachverhalte. Thus a picture can present a situation, iKPrhaps an imaginary situation (in which case none of the Sachverhalte which allegedly constitute the Sachlage exist), and in spite of the situation's being imaginary, we can still understand the picture, knowing what the picture is attempt- ing to present. Pictures, then, present Sachlagen in logical space. And according to the interpretation of logical space which we superimposed on Carnap's state-description model, logical space consists of indefinitely many "independent components of description," or "logical dimensions." Each dimension of logical space, we said, can be filled by a Sachverhalt des- cribed by one member of a basic pair. A state—description then consists of a conjunction of sentences, each of which is drawn from every basic pair of the language. Which facts, 13A both negative and positive, actually fill every dimension of logical space is described by a state-description of that language. And in this model we can say that a Sachlage is described by some segment of that conjunction. To describe a situation, however, we must be able to analyze it into a set of component Sachverhalte each of which is isolable from the others, and such that the description of each of these components plus their mode of composition constitutes a com- plete description of that situation. What this suggests is that in order to construct a state-description, we have to be able to determine how things actually stand in the segment of logical space we are examin- ing. For we wish every constituent statement in the state- description to be true; in case we are trying to describe the world (the totality of facts). Thus presumably we have to know how to determine the truth or falsity of this con— stituent atomic statements or their negations. Consider an atomic statement of Carnap's language, say 'R(a,b)'. Let us interpret this, for the moment, as 'object a is to the right of b'. If we know which objects are named by the letters 'a' and 'b', it seems quite simple: we examine the segment of logical space with which we are concerned, and if object a does lie to the right of b, then 'R(a,b)' will be true, and '-R(a,b)' will be false. This does assume that the objects are identifiable entities. Since Wittgenstein presents no doctrine concerning the observability and identifiability of the objects, we are faced with a problem. And if further we 135 are told that the objects are simple, the problem is com— pounded. For it is difficult to determine just what an absolutely simple object would look like. It is at this point that our considerations of the problem of simplicity earlier in this chapter become relevant. ions states that our decision C1“ For the Philosophical Investiga concerning which entities are simple (and therefore, which entities are to be counted as objects) depends on the purpose of the analysis, and what sort of analysis we wish to carry out. If we are to carry out an actual analysis of a situa- tion, we must (if we apply the position of the Investigations on simplicity to the Tractatus) determine which entities in the situation are not going to be analyzed further. The de— cision concerning which entities are objects and which are formed by the configuration of objects rests with those who actually perform the analysis. Let us return to the picture on the wall of this room. What are the objects in the picture? Tiis depends on how we wish to perform the analysis. We might count the trees de— picted in the scene as the objects. Or if the situation we wish to analyze is part of the picture, we might want to count the woodpecker as being one constituent of the scene, [the stump as the other. In such a case we would have a Sachverhalt depicted as consisting of the bird resting on the stump. Or we might wish to take the woodpecker as the gggh— verhalt to be examined, and take the various depicted parts of the woodpecker as the objects constituting the Sachverhalt. 136 The wings are white, the underparts of the bird are black, and the head is red. Each of these then becomes an object, la the context 9: this analysis, and each object has some quality or other which distinguishes it from its fellows in the configuration. If this is so, then what emerges is this conclusion: the elements of the picture are simple relative to the par- ticular analysis we wish to carry out. And this seems to imply that, in order to carry out an actual analysis of any situation, depicted or otherwise, we must be able to observe the situation and determine what its elements are. It is then that we can begin to construct atomic sentences which describe the situation being analyzed. But another conclusion emerges, perhaps more start- ling: what counts as a particular and what counts as a universal again depends on the sort of analysis we wish to make. We may take the bird, for example, as a particular, and note that it has the characteristic, the external pPOP“ erty, of being a woodpecker. It is also a term in a rela- tion, the other term being the stump, and the relation is the external relation of being 93 the stump. But if we wish to examine the bird depicted in the painting, we take the configuration of the colors, and describe the configuration. The bird then becomes the result of the way in which these "objects" are configured. Here, then, the colors are the particulars, and the quality of being a bird is produced by the configuration of these particulars. -n “A." 137 Thus what we are saying is that what is particular or universal is a question which can be decided only with reference to the given situation. Consider how our inter- pretation of the Tractatus links up with Russell's conception of atomic facts. Suppose that we are examining a situation, and want to know which facts are atomic and which are compo- site in that situation. Suppose, that is, that we are ana- lyzing the situation, and are trying to reduce it to its constituents, each of which is independent of all the other constituent atomic facts. Now do we know when we have arrived at atomic facts? And the answer is: when the terms of the relations in these facts are determined to be parti- 5 culars. But this merely shifts the difficulty to the term 'particular', and we have not determined what an atomic fact is until we can determine what a particular is. Russell's answer is that we cannot determine whether a given entity is or is not a particular until we have de— cided, g priori, what a particular is. And he says explic— itly: "These terms which come into atomic facts I define as 1 'particulars'.’ And thus we get the following definition: Df. 'Particular' for 'Term of a relation in atomic facts'. Apparently a definition is all that is available to us. In fact this is a stipulative definition, and this is the g priori decision required of us. Once, however, we have made 5Russell, Logic and Knowledgg, 9p. cit., p. 139. 6Ibid., p. 199. was 138 such a decision, we can begin to determine which entities satisfy this definition, and this is an expirical matter. So far as the identification of atomic facts is concerned, the matter might be put as follows: if a sentence of the form 'F(x1,x2,...,xn) is true, then the corresponding fact is atomic. But note what Russell is saying: the determination of which entities in a situation constitute terms of an atomic fact is an empirical matter. We determine what counts as a particular by examining the entity in question, just as I determine that the cover of this book is white by looking at it. But according to the Wittgenstein of the Investiga— tions, this determination of the ontological status of an entity is a matter of decision. And we shall decide what counts as a term of a relation in an atomic fact (or in the Tractatus' terminology, a Sachverhalt) only by reference to the analysis which we wish to perform. According to the interpretation we are making of the applicability of the program of the Tractatus, what counts as a particular is a Sachverhalt (i.e., what counts as an object) is not something fixed once for all, but is determined according to the pur- poses at hand. In a sense, what Russell is saying does jibe with the interpretation we are adopting: once we have deter- mined what i t count as a term of a relation, then, the determination of what is an object in a given Sachverhalt is an empirical matter. But first we must make the decision. 139 The mere definition of the term 'particular' which Russell gives is not enough for an actual analysis. One might also re—emphasize that what is to count as a Sachverhalt in a region of logical space is also a matter‘ of decision, in essentially the same sense in which it is a matter of decision what counts as an object, a simple entity. Once this point is established, however, we can say that Sachverhalte are presented by pictures; what the picture presents is a region of logical space containing a set of Sachverhalte. According to our discussion of the term Sach— lage, there appears to be no necessity that each picture must present one and only one Sachverhalt. The picture pre- sents a set of (allegedly) existing Sachverhalte, and by presenting these Sachverhalte it excludes those which it does not represent. We know by looking at the picture, and without having to compare it with any situation, that it ex— cludes many other Sachverhalte, simply by not presenting them. Let us attempt to translate this into the state-des— cription model of logical space. In the picture discussed 'above, a woodpecker clings to a log. If this is a Sachver- halt presented by the picture (and for our present purposes there is no reason why it should not be), then the Sachlage excluded by this aspect of the picture is that of the bird not sitting on the stump. Thus, for each Sachverhalt pre- sented in the picture, there is another excluded from the picture. In a state—description of the situation presented 1A0 by the picture, the atomic sentence describing the bird clinging to the stump would occur as one of the conjuncts. Its negation would then be excluded from the description. Thus the selection of a member of a basic pair of the lan- guage describing the situation automatically excludes the selection of the other member of the basic pair. And this, it seems to me, is the sense of the following proposition of the Tractatus, already quoted: 241/ A). .‘ - . - (2.05) The totality of the existing states of affairs also determines which states of affairs do not exist. In a state-description of the situation presented by the pic— ture, the conjuncts each describe a Sachverhalt; if a Sach— verhalt is presented by the picture as existing, it is des- cribed by an atomic sentence, the unnegated member of some basic pair in the language. On the other hand, a more com— plete description of the situation presented might include assertions to the affect that certain Sachverhalte do not exist (e.g., that the woodpecker is not standing on the limb of a tree). In such a case, a "negative fact” is described by the negative member of a basic pair. Thus a state-des— cription of the situation presented by a picture would con~ stitute a compendium of all relevant information about the situation. The form of a picture, then, is: this is how things stand (in this region of logical space). And the picture, if it were a proposition, would assert that they do so stand, lUl and that they stand in no other way. This is precisely what a state—description of that segment of logical space would assert, a point which will come to have great significance. This interpretation requires that the picture should be understood as depicting what it does before we can say that it fails to depict correctly. We have, that is, to understand r- what the picture depicts; we have to know what is the case if the picture does depict the scene correctly in order to under- stand it. And only if we understand the picture in this e sense of "understand" can we say that the picture depicts the scene correctly or incorrectly. It is well to note at this point that propositions 2.13 and 2.131 both mention the correspondence between "objects" and the elements of the picture. Let us look again at 2.131: (2.131) In a picture the elements of the picture are the representatives (Vertreter) of the objects. The elements of the picture "represent" or "stand for" the objects in the depicted situation, or the elements of the situation. Now there are two ways in which we can consider a picture, just as there are two ways in which we can conceive of an entity: as a thing and as a fact. In proposition 2.1Ul, Wittgenstein says simply: (2.1Ul) A picture is a fact. That is, a picture has a certain structure: its elements are 1A2 related to one another in a determinate way. Hence, con- sidered as a structure which depicts a situation, a picture is a fact. But a picture is also a thing: it may be a photograph, in which case it is a piece of chemically treated paper with lighter or darker shades of silver iodide on its glossy side. It may be a painting, in which case it is prob— ably a canvas contained in a frame, which can be carried from place to place. Considered as a thing, the picture has ’QAf'k -.i’ certain blobs of paint of various lighter or darker shades and colors. Rut considered as a fact, the blobs of paint or shadings in the silver iodide emulsion stand in various re— lations to one another. They have a structure, and their structure becomes important when we consider the picture as a fact. The elements of the painting on the wall of this room are trees, flowers, a stump, a woodpecker, a rill in the background, and they form a structure. It is this struc— ture that makes the whole into a picture. And once we have this structure, then the elements of the picture represent the elements of the situation, and they stand in the same relation to one another that the elements of the situation stand in. This, at any rate, is what the picture "claims." The following proposition of the Tractatus consti- tutes additional comment on and confirmation of the above conjectures about the nature of a picture. (2.1“) What constitutes a picture is that its elements are related to one another in a determinate way. 1A3 We noted that pictures depict situations, not things. A situation, we decided, can be a Sachverhalt or a collection of Sachverhalte. But situations that differ from the facts in one or more details can be imagined; hence we allowed non—existent Sachverhalte to constitute situations. Now what constitutes a Sachverhalt is the determinate way in which its elements are'configured with one another. And proposi— tion 2.032 says that the determinate way in which objects are 131.1 . configured in a Sachverhalt is the structure of that Sachver- ~ 0 A‘A-“ - halt. Or, we could paraphrase 2.1M and say of Sachverhalte that what constitutes them is that their elements are related in a determinate way. There is thus at least a parallel between Sachverhalte and pictures, for pictures also, accord— ing to 2.14, are constituted by the relation of elements to one another in the picture. And this leads to the following proposition, which introduces one of the central features of the picture theory of meaning: (2.1Ul) A picture is a fact. What we have, therefore, is a parallelism of struc- ture between a picture (a fact) and the situation which it represents; 2.1Al, which asserts that a picture is a fact, is meant as a comment on 2.1“, which asserts that a picture is constituted by the relation of its elements . . . when that picture is considered as a fact, rather than as a thing. This leads directly into the following proposition, for which the way has already been well prepared; and let us give the German text first: lb“ (2.15) Dass sich die Elemente des Bildes in bestimmter Art und Weise zu einander verhalten, stellt vor, dass sich die Sachen so zu einander verhalten. Dieser Zusammenhang der Elemente des Bildes heisse seine Struktur und ihre Moglichkeit seine Form der Abbildung. Let us now, departing from the Pears and MacGuinnes trans- lation, translate this passage as follows: (2.15) That the elements of the picture stand to one another in a certain manner repre— sents that matters stand in that way to one another. This connection (Zusammenhang) of the ? elements of the picture shall be called l its structure, and its (the structure's) possibility its (the picture's) form of depiction. ‘t... .1! 3 The "Sachen" or "matters" which stand in a determinate rela— tion to one another may or may not be the objects or Gegenstande whose configuration constitutes the Sachverhalte. Whether or not they are depends on the purpose to which we wish to put our analysis. But this much is clear: that whatever we choose to be the elements of the situation de— picted will also be the elements of the picture, simply be- cause we make it so. Thus the correspondence between the elements of the picture and the elements of the depicted situation will be determined by our purposes. The elements of the scene depicted, then, are in some sort of spatial re— lation to one another. It is this configuration which a spatial picture depicts. But the picture has a structure: its elements are configured in a determinate way, and it is this which makes the picture a fact. 1&5 But proposition 2.15 introduces a peculiarly diffi— cult term: "Form der Abbildung" (form of depiction, or "pictorial form" in the Pears and MacGuinness translation). 2.151 is a comment on this proposition: (2.151) Pictorial form is the possibility that things are related to one another in the same way as the elements of the picture. There is a parallel to this passage which occurs earlier in the Tractatus, already introduced: (2.033) Form is the possibility of structure. The structure of a Sachverhalt, according to 2.032, is the determinate way in which the objects composing the Sachverhalt are configured. And the form of the Sachverhalt is the possi— bility of its structure. In Chapter II we discussed the notion of two or more Sachverhalte having the same form, and decided that sameness of form meant that the different ob— jects constituting the Sachverhalte nonetheless form the same structure: they are structurally identical or isomor— phic. Note again that Wittgenstein defines 'form' in terms of possibility, and leaves the difficult notion of possibility undefined and unexplained. We have taken the less difficult route of explaining the notion of form in terms of two §§£fl‘ verhalte, say S and S having the same form. Thus we 1 2’ 'C‘ explain form by explaining the meaning of the sentence 01 has the same form as 82'. If Sachverhalte have a structure, so too do Sachlagen or situations. We can speak of an actual Sachlage as being 1A6 composed of Sachverhalte selected from a region of logical space. The Sachverhalte composing an actual Sachlage (and therefore, composing a fact) individually have structures, and "The structure of a fact consists of the structures of states of affairs (Sachverhalte)" (2.034). A Sachlage con— sisting of actual Sachverhalte is the totality of the struc— 1 tures of the constituent Sachverhalte. But we also speak of possible Sachlagen as well as a possible but nonactual Sachverhalte. We spoke of a Sachlage which is possible but nonactual as consisting of one or more nonactual Sachverhalte. This room, for example, (a Sachlage) actually has white walls. But a world can be imagined in which the walls are blue, although every other state of affairs in the room remains the same as it actually is. This would be a Sachlaze differ— ing from the present actual one in exactly one respect: the color of its walls. Likewise, a picture "presents a situa- tion in logical space." (2.11) We may conjecture as we did above7 that the picture depicts what it does because there is some sort of structural identity between the picture (con— sidered as a fact) and the situation which it depicts. But what might we say now concerning the notion of pictorial form? At this point we can at least say this: that two pictures have the same pictorial form if, and only if, the situations which they depict are structurally identi— cal, or isomorphic. It follows that the elements of the 1U7 pictures which have the same pictorial form are structurally identical. The elements of the picture, then, have the same structure as the elements of the depicted situation. And this is what makes it a picture. This is the considera- tion which leads Wittgenstein to introduce the closely re- lated notion of the abbildende Beziehung, the pictorial i relationship. Says Wittgenstein: (2.1513) 80 a picture, conceived in this way,8 also includes the pictorial relationship, which makes it into a picture. (2.151“) The pictorial relationship consists of the correlations of the picture's elements with things. (2.1515) These correlations are, as it were, the feelers of the picture's elements, with which the picture touches reality. The pictorial relationship, then, is the relationship con— sisting of the correlation of the picture's elements with the elements of the depicted situation. Without this rela- tionship, there would be no picture. Let us explore further the question of how it is possible for a picture to depict a situation. Wittgenstein explicitly answers this question by the following proposi- tions of the Tractatus: (2.16) If a fact is to be a picture, it must 'have something in common with what it depicts. (2.161) There must be something identical in a picture and what it depicts, to enable the one to be a picture of the other at all. 8 i.e., as a configuration of elements which form a structure. 1&8 (2.17) What a picture must have in common with reality, in order to be able to depict it—- correctly or incorrectly—-is its pictorial form. We agreed that a picture is a fact, and that it depicts what it does through the correlation of the elements of the pic— ture with the elements of the situation. The picture de— nwfln‘ alt ‘R' picts what it does because it shares a determinate arrange— ment of its elements with the determinate arrangement of the elements of the corresponding situation. And this is to say that the two correlated complex entities (the picture—fact and the situation depicted) share their pictorial form; their elements are arranged in the same way. Immediately a question arises. Suppose that I wish to paint a picture of Santa Claus holding some elves on his lap in front of his workshop at the North Pole. Does the fact that I can paint such a picture imply that the situation depicted exists? And Wittgenstein answers here: not at all! In this world there is no such situation, to be sure. In this case the picture is false, or incorrect: (2.21) A picture agrees with reality or fails to agree; it is correct or incorrect, true or false. (2.22) What a picture represents it represents independently of its truth or falsity, by means of its pictorial form. A false picture, such as the picture of Santa Claus, does present a situation which is not real. Yet we understand the picture, and can identify its central figure as Santa Claus. How is this possible? 1A9 We can at least say this: that we have seen pictures of Santa Claus before. The elements of the picture (the large splash of red below a white, semi—triangular beard, the mouth, the nose, the red cap, the brown boots, the wide girth) correspond to similar configurations of elements which we have seen depicted before in other pictures. Such pic- tures share their pictorial form with the picture at hand. But still, all such pictures are false, and yet we can under- stand them, we recognize what they present. It is clear from ; this illustration of a picture that we do not ordinarily need to know the correctness or incorrectness of a picture in order to understand it. The picture ”asserts" a certain situation to obtain, and we have good reason to believe that it does not obtain. The understanding of a picture, there- fore, is a matter which is independent of its truth or falsity. How can a depicted situation, however, have some— thing in common with a non—existent situation? How can a false picture present something which we can understand? To answer this, Wittgenstein introduces the notion of logical form, particularly as applied to the notion of a picture. We said that, according to proposition 2.17, a picture must have something in common with what it presents: and that must be its representational or pictorial form. The possibility must exist that the elements of the picture are related in the same way as the elements of the situation depicted. The form of a particular situation is the 150 possibility that elements can be related to one another in the way in which they actually are. But what is logical form? Wittgenstein says in the following proposition. (2.18) What any picture, or whatever form, must have in common with reality, in order to be able to depict it--correctly or incorrectly—— in any way at all, is logical form, i.e., the form of reality. We have already encountered the term 'reality' (Wirklichkeit) in proposition 2.17. The term is introduced earlier, how- ever, in proposition 2.06, which we have already quoted: (2.06) The existence and nonexistence of states of affairs is reality. (We also call the existence of states of affairs a positive fact, and their non- existence a negative fact.) Reality is the totality of existent Sachverhalte and nonexist— ent but possible ones. Let us try to explicate this para— doxical statement. If we refer to a language in which state- descriptions are constructible, we can say this: that reality is represented by all atomic sentences constructible in the language, together with their negations. No one sen- tence, however long, of the language can truly assert every— thing there is to assert about reality, because a conjunction consisting of all atomic sentences in the language pigs their negations would be inconsistent. But as Wittgenstein uses the term 'reality', its meaning is closely related to the meaning of the term 'logical space'. But each dimension of logical space is "filled" with a Sachverhalt described by one member of each basic pair of the language in question. 151 Reality would be given by that conjunction plus a conjunction consisting of the counterparts of each member of the original conjunction. Reality thus cannot be completely described, since to speak metaphorically, reality extends exactly twice as far as logical space does. What, then, is the form of reality? Since Wittgen- r, stein uses the term in his discussion of what a picture is, ‘ we have to give some sort of answer to this; but it is an extremely difficult question to answer. Reality, according ‘ “ . I .v-a to 2.06 is the existence and nonexistence of Sachverhalte. What is the form of reality? In other words, what is "logical form," since the term is introduced in proposition 2.18 as coextensive with 'form of reality'? Our characterization of this term must be made rather lamely, since Wittgenstein seems to give us no means of characterizing it. But in the Trgg— tatus, the notion of form is generally linked with the notion of possibility. Thus our rather weak explanation of the term 'form of reality' is simply this: the term 'form of reality' means 'the possibility that Sachverhalte either exist or do not exist'. And, given the tools handed us by the Tractatus' ladder language, this weak and vague characterization of this important notion seems to be about the best which we can hope for. But in a sense, as we have repeatedly urged, the ladder language amounts to no more than such weak and vague characterizations. Presumably, according to Wittgenstein, we use the ladder language to climb up to a plateau of 152 intuition of what the central notions of the Tractatus really mean. And then we throw it away. And so, our notion of logical form reduces to something equally vague: logical form is the form of everything there is, and everything that there isn't, but can be! So: reality does include the existence of Santa F‘ Claus and his little helpers, although the world does not. Since logical form includes the possibility that Santa and his helpers exist, and have the characteristics usually 9’ ascribed to them, all that the picture need include, all that ' it need have in common with reality in order to depict some "region" of it, is the form of that reality: i.e., the possibility that that Sachlage which is depicted should exist. A picture, in short, can depict anything whose existence is logically possible. And it is the mere logical possibility of Santa that makes his depiction possible. And Wittgenstein further buttresses this interpreta— tion by saying: (2.201) A picture depicts reality by representing a possibility of existence and nonexistence of states of affairs. What is possible can be portrayed; the existence of Santa Claus, however unhappily improbable, is possible because his existence is part of reality, though not part of the world. Given this background, we may quote the following passage: (2.181) A picture whose pictorial form is logical form is called a logical picture. 153 It becomes clear from the context that 'logical form' is more general a term than 'pictorial form'; we might regard pic- torial form as the logical form of a picture. And this logical form is what the picture must have in common with the situation which it depicts. We have been discussing the picture-in-general, but V- we have been limiting the details of the discussion to such pictures as paintings, photographs, portraits, and the like. The major general point of the discussion is that there are E Ff other kinds of pictures. We have been discussing spatial pictures, which are entities existing as things in physical space. We have, however, also been discussing pictures as facts, determinate arrangements of elements; and it is the picture in this sense—-as a fact-—that holds our interest here. In this connection, Wittgenstein says: (2.182) Every picture is at the same time (auch) a logical one. (On the other hand, not every picture is, for example, a spatial one.) Taken together with proposition 2.181, this proposition sug- gests the direction which the discussion of propositions will take in the Tractatus. Every spatial picture is a logical one, because it has logical form, and shares this form with everything it depicts. Pictorial form is logical form, for it can depict the existence and nonexistence of Sachverhalte in logical space. Which means that a picture, no matter of what type, has logical form. Wittgenstein, as can be seen from 2.181 and 2.182, regards it as perfectly impossible that 15“ there are non—spatial pictures. Indeed, he will insist on this possibility, for this possibility is the whole point of his general discussion of pictures. Proposition 2.18 is the point at which Wittgenstein generalizes the concept of pic— ture, and begins to speak of logical pictures, no longer limiting his discussion to spatial ones alone. Logical but non—spatial pictures have the same function as logico— spatial ones: ‘WQA‘.A3‘ ‘~ - (2.19) Logical pictures can depict the world. In other words, the possibility exists that a picture, of whatever type, (logico-spatial or merely logical) depicts Sachverhalte which exist. And this feature of pictures makes the notion of picture applicable to topics which would ordi- narily be though to fall outside it. Wittgenstein applies this notion to the thought and the proposition, and it is this which constitutes one of the original features of the Trag- tgtgs. For by means of the picture theory of propositions and their meaning it will be possible to characterize the ontological character of the basic entities of the metaphy— sics. g. The Sense pf a Picture We have established that Wittgenstein believes a pic- ture, of whatever type, capable of depicting a situation (or Sachverhalt); this applies to spatial and non-spatial pictures both. In his words: 155 (2.201) A picture depicts reality by representing a possibility of existence and nonexistence of states of affairs. (2.202) A picture represents a possible situation in logical space. Notice that the situation which the picture depicts does not have to exist. A picture can depict a completely imaginary situation as well as an actual one, as we saw in the example of the picture of Santa Claus. We may say that the imaginary situation is possible, in the sense that reality (Wirklich- kgit, in the technical use in which Wittgenstein applies it) includes it. We know that an imaginary situation is one that does not exist, and that a picture which depicts such a situa— tion is strictly speaking incorrect or false. Yet, a picture gag represent an imaginary situation; a picture represents a possible existence of Sachverhalte, and what the picture has in common with the possible situation is logical form. The logical form of a picture, we said, is called its pictorial and the picture need not represent an actual situation in order for us to understand it: (2.22) What a picture represents it represents independently of its truth or falsity, by means of its pictorial form. Given this background, Wittgenstein goes on to intro- duce an extremely important term, a term which we have al— ready encountered in our discussion of the early writings and of Frege's theory of meaning: (2.221) What a picture represents is its sense. 156 (2.222) The agreement or disagreement of its sense with reality constitutes its truth or falsity. (2.223) In order to tell whether a picture is true or false we must compare it with reality. (2.22“) It is impossible to tell from the picture alone whether it is true or false. 3% (2.225) There are no pictures that are true t a priori. These passages are difficult primarily because of the diffi— culties encountered in the use of the term 'reality' here. thxnn We said that reality (Wirklichkeit) includes the existence and nonexistence of Sachverhalte. Thus reality includes all that is possible, and this includes nonexistent Sachverhalte. How, then, do we compare what a picture represents (namely, its sense or Sinn) with reality? Reality includes the total range of existent and nonexistent Sachverhalte. If the Sachverhalte exist, then there is an actual configuration of constituent objects; hence to compare a picture with reality is, in part, to inspect the world and determine whether or not there are any configurations of objects which correspond to the way in which the elements of the picture are configured. In short, we inspect the segment of reality which consists of existing Sachverhalte. If we find no Sachverhalte whose elements (constituent objects) correspond to the elements of the picture, then there is no need to look further. For since we cannot genuinely "inspect" the segment of reality consisting of nonexistent Sachverhalte, 157 it would not be worthwhile to try to look there for a corres- pondence; one cannot inspect something that does not exist. The nub of the matter at hand, then, comes to be this: if we inspect the world (the totality of facts, i.e., existing Sachverhalte) in order to find some situation Fa corresponding to the situation presented by the picture, and find no such situation in the world, we conclude that the picture is false. But this still does not mean that we can- Va‘muz ~ . ‘b not understand the picture, for the picture does present something that is possible. (2.201) A picture depicts reality by repre— senting a possibility of existence and non—existence of states of affairs. (2.202) A picture represents a possible situation in logical space. What a picture represents, then, is its sense, according to proposition 2.221. And thus the sense of a picture is a possible situation in logical space. The sense of a picture is what it depicts. We understand what the picture presents (precisely because the picture has a form in common with the situation presented. Because picture and situation have a common form, we could recognize the situation presented by the picture by noting that the elements of the situation are configured in precisely the same way as these of the picture. We recognize the correspondence. Notice certain similarities between the conception of £5122 or sense of a sentence presented here, and that of Frege. 3339 Proposition, so that argument goes, can be understood only 158 if one understands its sense. To Frege, we understand the proposition if we grasp its Sinn, and the understanding of the proposition does not depend on our knowing its Pedeutung, i.e., its reference, the True or the False. In order to know the Bedeutung of a proposition, we must know its Sinn; with— out knowledge of Sign, we certainly cannot know whether or not the proposition is true. A simple illustration will suffice. Suppose that we consider the following English sentence: (1) Mao Tse—Tung is eating Chinese food. I do not know whether or not this statement is true, but I know what would be the case if it were true. I grasp the sense of this proposition, and although (in Frege's terms) I do not know its reference, it is not necessary to do that in order to understand it. Similarly for Wittgenstein's treatment of pictures. If I were shown a painting of Mao Tse—Tung dining on eggrolls and fried shrimp, I would not know whether or not the picture depicts an actual situation, i.e., is a true picture. But I understand it; I understand the sense of the picture, and I therefore know what to do in order to find out whether it is true or false. Thus far, Frege and Wittgenstein agree in this respect concerning Sign. But consider the following sentence: (2) Mao Tse-Tung jrfan junggwo fan. If we were to ask ourselves whether this is true or false, we would be at a loss. Unless we know Chinese there is no way to determine the truth—value of this assertion. In 159 Frege's terms, we do not know the Sinn of the sentence, and thus we do not know how to go about determining its Bedeutung. It is not until we are told that (2) is the Chinese transla- tion of (1) that we grasp its sense. Presumably Chinese and English differ primarily, not in the fact that one makes better sense than the other, but in that the conventions for F the mediation of sense differ between the two languages. Once we learn enough of the conventions of the Chinese lan- guage for expressing sense, we understand (2), and we can then determine its Redeutung. I How do we apply this to Wittgenstein's treatment of pictures? This is not a particularly easy question to answer. But even so, there seems a way to apply the foreign—language problem to Wittgenstein's picture theory. Suppose I painted a picture and brought it to you, saying "This is a picture of Mao Tse-Tung eating Chinese food." Suppose, however, that it does not give you that impressiOn at all, but rather it consists of an apparently senseless group of symbols. You therefore protest that you do not understand the picture. But suppose that I inform you that I have painted the pic- ture in such a way that there is a way of translating the symbols in the picture into a more conventional representa- tional form. What I might do in such a case is give you rules for translation of the symbols into a more familiar form. If I followed my own rules exactly in producing the painting, you could, using those rules, reconstruct the pic- ture into such a form as would be more familiar to you. The 160 original ideographic picture would then be seen to represent the same situation as the more familiar one, and one would in that case be said to grasp the sense, the Sign, of the picture. Thus far, then, there seems to be agreement between Wittgenstein and Frege concerning the grasping of the sense F? of a picture in the former case, and a statement in the latter. But there is disagreement too, and not only in the fact that Wittgenstein constructs a different metaphysics ‘P‘"! l' J. _ ‘ from Frege's. For Wittgenstein, a statement does not have Bedeutung. A statement does not denote anything at all, and this is probably the main difference between Wittgenstein's and Frege's theory of propositions. We shall be concerned to develop this difference further, in the later pages of this chapter. It is at this point that Wittgenstein introduces the central notion of the thought (Gedanke). (3) A logical picture of facts is a thought. A thought is as much a picture of a fact as a spatial picture is. Since a thought is a picture, we can think a thought and understand its sense without knowing whether or not it is true. And Wittgenstein will wish to argue that the thought has sense in precisely the same way in which a picture has sense. Thoughts have elements, and so do pictures; and there is a correlation between the elements of the thought and the situation thought about, just as there is between the ele— ments of the picture and the situation pictured. 161 The question arises concerning whether there are any limitations on what is thinkable. And Wittgenstein answers: (3.001) 'A state of affairs is thinkable': what this means is that we can picture it to ourselves. This does not tell us what is thinkable, but it does say that if a Sachverhalt is thinkable, a picture can be made of it. A picture can be made of any situation that is logically possible. A situation that can be pictured (and thought, \F'Mi I; I .- according to proposition (3)) is part of reality. The situa- tion that can be pictured is either a part of reality con— sisting of existent Sachverhalte or a part of reality which consists of nonexistent Sachverhalte. But, according to Wittgenstein's use of the term Wirklichkeit, any situation that is a part of reality is logically possible. It has a logical form, and to say that anything has logical form is to say that it is a possible part of reality; for Wittgenstein has already said that the form of reality and logical form are one and the same. And we established that, while the notion of logical form as it is used in the Tractatus is not easily characterized, we Egg characterize it as "the possi— bility of existence and nonexistence of Sachverhalte." This can only mean that everything that exists has logical form, and conforms to whatever conditions logical form lays down. What these conditions are is not explicitly specified by Wittgenstein, but it is possible that, given the assump— tions presented in the ladder language, it is impossible to specify completely such conditions guage. 162 even in that lan- Certainly any proposition that tried to do so would be senseless (Sinnlos), simply because the notion of logical form is presupposed in the notion of sense. It would have been difficult for Wittgenstein to imagine how the conditions of logical form could be met to describe logical form and Such a proposition, to speak "outside" and be logic by any proposition attempting the conditions laid down by it. metaphorically, would have to this itself is senseless. Thus any situation which is possible will ipso facto be part of reality, though it might not be part of the world. And thus thought can be of anything in reality, because thought can be of anything that is logically possible, that obeys the unformulable laws of logical form. For example, we might say that we cannot think of round squares or three- cornered circles; such figures are not possible because we can predict that any propositions attempting to assert some- thing about them would be self-contradictory, contrary to the laws of logic. This seems to be very much like what Wittgen- stein is saying in proposition 3.02 where he maintains that "what is thinkable is possible too." And: Thought can never be of anything illogical, since, if it were, we should have to think illogically. (3.03) We cannot think illogically because, since a logical picture of facts is a thought (3), and a thought must have sense, the thought must have some correlation with possibilities 163 of existence and nonexistence of Sachverhalte. And these possibilities are part of reality, which has a certain form; and that form is the possibility of existence and nonexistence of Sachverhalte. Thus form is explained in terms of an un— explained notion again: that of possibility. Apparently it is left to our intuition to determine what that term means. Wittgenstein, for the reasons argued on the previous page, will not allow us to formulate the "laws of possibility." Hence anything that falls outside the realm of possibility is E':F Anti. ' -I literally unthinkable. So we arrive at the following minimal pronouncement: 'what is thinkable is determined by what is possible. What can be thought must share a form-—logical form--with a possi— ble situation. And what "falls outside" logical form is logically impossible. Thus it is logically impossible for a round square to exist, and logically impossible for a picture to be made of it. The concept 'round' and the concept 'square' logically exclude one another. By the laws of reality (which are never formulated by Wittgenstein) the entities which exemplify these concepts mgst exist in differ- ent regions of logical space. Thus 'Object X is round' implies 'not-(Object X is square)’. To assert that an object should be round and square simultaneously is to assert a sentence and its negation simultaneously. Logical form, then, does not allow us to think a situation and whatever excludes that situation simultaneously. .A fact which is pictured by the thought cannot be 16A simultaneously positive and negative. And this sort of im- possibility does seem to be the only sort which is recognized by Wittgenstein: logically impossible situations cannot exist; they cannot be a part of reality. Wittgenstein says as much: (3.0321) Though a state of affairs that would contravene the laws of physics can be represented by us spatially, one that would contravene the laws of geometry cannot. And further he says: (3.05) A priori knowledge that a thought was true would be possible only if its truth were recognizable from the thought itself (without anything to compare it with). The same thing, presumably, is true of a priori falsity; if a thought is a priori false, we must be able to recognize it from the thought alone, not needing anything to compare the thought with. One important consequence of this discussion of a priori truth and a priori falsity is that no g priori thought can be a picture of anything. Wittgenstein asserts that we cannot know whether or not a picture is true unless we com- pare it with reality. We must be able in principle to com- pare a picture with what it depicts in order to determine whether or not it is true. But there are no pictures (of any kind) which are true (or false) a priori; this much is estab— liShed. For the truth of an g priori true thought can be determined only by inspection of the thought itself, and this -..-“-1.” .nl' n1!’ 165 certainly is not true of a thought which is only contingently true. A thought is contingently true if we can compare it with some actual configuration of objects occurring in some region of logical space. This certainly follows from proposi— tion 3.05. We have established that, for Wittgenstein, the rela- tion of the thought to reality is essentially the same as was determined for pictures in the earlier discussion. But there still remains the question of the application of the theory developed in the Tractatus to some actual process of analysis of reality. Writing to Russell from his prison camp at Cassino in 1919, Wittgenstein answered a number of questions which Russell put to him after having read the manuscript of the Tractatus: ". . . But a Gedanke is a Tatsache: what are its constituents and components, and what is their relation to those of the pictured Tatsache?" I don't know what the constituents of the thought are, but I do know that it must have such constituents which correspond to the words of Language. Again the kind of relation of the constituents of the thought and of the pictured fact is irrelevant. It would be a matter of psychology to find out.9 According to Wittgenstein, we know (apparently a priori, by some unexplained process) that a thought is composed of elements, and that these elements must have some relation to reality. Apparently Wittgenstein regards both the nature of these constituents and their relation to reality as something 9Notebooks, 92. cit., p. 129. 166 which must be determined by scientific investigation. The phrase "determined by scientific investigation" is somewhat ambiguous. There are two possible meanings here: (1) that what is to count as an object (or constituent, or element) is to be determined by pragmatic reasons of convenience: we count as an ”object" or "element" whatever best suits the type of analysis we are carrying out. This is the position which we have been taking in this chapter. Or, (2) what is to count as an object depends on the results of scientific research: what is an object is a question to be answered by scientific research, just as the question: what causes tuberculosis? is answered by the discovery of a certain spirochete bacterium in the sputum of tubercular patients. It is unfortunate for our conception of the program of the Tractatus that Wittgenstein seems to mean (2): that the discovery of the nature of the objects is a matter for em- pirical research. But it is equally unfortunate, I think, for the program of the Tractatus. The question of what the objects are does not seem to me to be a problem for empirical research to discover, simply because, if the Tractatus' pro- gram is to be applied, we must be able to specify in advance of any specific analysis what the objects are. 'Specify' here does not mean 'discover'; it means 'stipulate'. We have taken the position of the Investigations that what counts as simple depends on the purpose of the analysis. And yet, what we take as simple does not necessarily have much to do with what Wittgenstein conceives the thought to be. All we know l67 is that thought consists in a set of elements standing in various relations to each other, and that baa the elements are related to one another determines what the thought will be. The question of aha: the elements are does not enter into the discussion in the Tractatus: only that there are elements. Notice, however, the relation between Wittgenstein's conception of the thought and that of Frege. For Frege, we recall, the thought is not to be identified with the subject process of the thinking of it. The thought, for Frege, is E322 is thought, something which can be thought by several persons. This apparently coincides with Wittgenstein's insistence that the thought is a picture; there is no hint that there is anything subjective in the thought, but as in Frege's work it is conceived as an "objective content."10 Granted, ES produce the picture, and it may be that we differ from one another in the accidental details of the production. But what is essential to the thought—picture is the correla— tion of the elements of the thought which the elements of the situation which is thought. The central point of the Tractatus about thought is that a thought is a picture: more specifically, a logical and non—spatial picture of both posi- tive and negative facts. And it is this picturehood which Wittgenstein uses to connect the discussion of the representa- tion of reality to the problem of the meaning of the proposi- tion. To this discussion we now turn. 168 Q. The Proposition (Satz) aa a Picture Insofar as pictures represent anything, and insofar as thoughts are about anything, they have sense. Wittgenstein now expands the notion of sense, and extends it to sentences (§a£aa). The discussion of pictures and thoughts is, in fact, preparatory to the introduction of his theory of sen- tential meaning. The latter topic is introduced by the following proposition of the Tractatus: (3.1) i In a proposition (Satz) a thought finds an expression that can be perceived by the senses. Throughout their translation of the Tractatus, Pears and MacGuinness translate the German '§§£§' as 'proposition'. 'gaaa' is ambiguous between 'proposition' and 'sentence', but in the case of proposition 3.1, the only possible interpreta— tion of that word is that of 'declarative sentence'. A de- clarative sentence is a symbol, and a symbol is something which is perceived by the senses. How the word 'proposition' might be understood in the context of the Tractatus, however, is something of a mystery. In their translation Pears and MacGuinness make use of the word 'proposition' as we noted, but these seem to be no real indication that this word ever means anything in the English text but 'declarative sentence'. A Saga then becomes a physical object (considered as a thing) or a physical process (as in the speaking of a declarative sentence). 169 Suppose, however, we adopt Leonard's interpretation of a proposition as a logically possible state of affairs.11 On Leonard's terms, the difference between a declarative sentence and a proposition seems to vanish, given Wittgen— stein's subsequent discussion of the nature of the §§£E° Let us see why; consider the following two propositions of the Tractatus: (3.1“) What constitutes a propositional sign is that in it its elements (the words) stand in a determinate relation to one another. (3.1A1) A propositional sign is a fact. Now in any Sachverhalt, there is a certain arrangement of elements; indeed, as we Saw, the Sachverhalt is constituted by the way in which its elements are arranged. Proposition 3.141 is a comment on 3.1“, and indeed seems to follow from it. Sachverhalte all have structures. The structure of a fact, says Wittgenstein, consists of the structure of Sach— verhalte. Hence all facts have a certain structure as well. Now since, according to 3.141, a propositional sign (aaaa) is a fact, all such signs have a certain structure. Hence too a Saga is a logically possible state of affairs (indeed, an actual one). This is precisely Leonard's definition of 'proposition', and this suggests that in the context of the Tractatus, the meanings of 'sentence' and 'proposition' come to coincide. Hence in the perspicuous language the question 11Henry S. Leonard, Principles 9f Reasoniag (New York, 1967), p. A7. 170 of how to translate 'Sagaf, according to this argument, be— comes otiose. We may, perhaps, adopt another interpretation of the term 'proposition': we might identify it with the "meaning" that the sentence expresses. But it is quite unclear how to interpret this, unless we identify the "meaning" of the sentence with its Slag, its sense. What a picture represents is its sense, and this is true of Satze as well; so the pro- position expressed by the Saga comes to be the situation which it describes. This seems to be more in the keeping with Leonard's intention in Principles afi Reasoning, but then the job to be done by 'propositon' has already been pre—empted by '§lflfl'° So in both the first case and in this one, 'proposi— tion' seems to be out of a job, if it is to mean something different from 'declarative sentence' in Wittgenstein's usage of the term. And yet there does appear to be some distinction made between proposition and propositional sign, between what is expressed and the vehicle for its expression. This considera- tion is brought out in the following passage from the Tractatus: (3.12) I call the sign with which we express a thought a propositional sign.—-And a pro- position is a propositional sign in its projective relation to the world. When an image is projected on a screen, say by a slide pro- jector, we might say that each point on the slide can be correlated with each point on the projected image. The set 171 of points on each image can therefore be brought into one-to- one correlation with each other. And this notion of pro— jection is ideally suited to Wittgenstein's discussion here; for we have already had considerable discussion of the correlation of the elements of a thought (or picture) with the elements of the situation depicted or thought of. What Wittgenstein seems to be saying in 3.12 is that a proposi- tional sign is "projected" into a segment of reality, and that the "image" of the proposition is to be found in reality. The image may not match anything in the world (in which case the prOposition is false), or it may be found to correspond to an actual situation. In the latter case, the proposition is said to be true; but we cannot determine this by examining the projected "image" alone, but by examining the world. If it is meaningful to speak this way, then to say that a pro- position is true is to say that the elements of the proposi— tion are found to be configured or combined in the same way as the elements of the actual situation are combined. We find an actual combination of elements or objects, and we determine that, in the case of a true proposition, there is a one-to-one correspondence between the ”image" projected by the proposition and the actual situation. The "image" of the proposition in its projective relation to the world is its sense. And thus a distinction between propositional sign and proposition is warrented by Wittgenstein's discus— sion in the ladder language of the Tractatus. 172 The propositional sign, then, is constituted in pre- cisely the same way as a picture or thought with a sense is, as 3.1M and 3.1Ul (quoted on p. 169) tell us. A proposi- tional sign is a fact, because what constitutes an actual situation (and therefore a fact) is that in its constituent Sachverhalte the elements of those Sachverhalte are configured in a determinate way. A situation has a structure, and in particular an actual situation has a structure. The same thing is true of a propositional sign. A propositional sign is a fact, an actual situation, and it is a structure of ele- ments; the structure consists in the elements being arranged or configured in a determinate way. As Wittgenstein puts it: (3.1Ul) A proposition is not a medley (Gemisch-- "mixture" or ”conglomeration") of words.-— (Just as a theme in music is not a medley of notes) A proposition is articulated. (3.1A2) Only facts can express a sense, a set of names cannot. A proposition, therefore, can express a sense in the following way:' a proposition is a fact, because it is a structure consisting of elements. This is true of all facts, not merely propositions alone. But a mere set of names, a mere set of elements in no particular order and no particular configuration can express nothing. For a structure is a very particular, determinate order of elements, and this is pre- cisely what a propositional sign is. No mere jumble of words can express anything . . . the expression "Radio, Oh! land, over table the, Ab!" expresses nothing, for the words (the 173 elements of the eXpression) are in no particular grammatical order. Indeed, inspection of this expression shows that the words are such that, even if we were to try to put the ex~ pression into (English) grammatical order, we would fail: the words do not go together. Some elements cannot exist in combination with one another, and no amount of trial and error can get them into any particular order, so that a sense is expressed. In a proposition with a sense, the words fall into a grammatical order, an order determined by that lan— guage's rules of grammar. The above expression is a mere jumble of words, and nothing can be expressed. But we have been speaking vaguely about "words" and "names" as being the elements of a propositional sign. On this conception, then, any proposition with a sense is some linear order of words the order of whose occurrence in the propositional sign is determined by the language's rules of grammar. It is one extraordinary feature of Wittgenstein's. theory of propositions that this need not be so: (3.1U31) The essence of a propositional sign is very clearly seen if we imagine one composed of spatial objects (such as tables, chairs, and books) instead of written signs. Then the spatial arrangement of these things will express the sense of the proposition. (3.1U32) Instead of "The complex sign 'aRb' says that a stands in the relation R to b," we ought to put, "That 'a' stands to 'b' in a certain rela- tion says that aRb'." These two propositions of the ladder language have occasioned considerable discussion and disagreement concerning their 17A meaning. They are, in fact, extremely important in the under— standing of what Wittgenstein is trying to do with the pic- ture theory of meaning. Proposition 3.1U32 is particularly difficult, and it will provide the focus of our discussion of the topic of Chapter IV; but it is perhaps not quite so diffi— cult to interpret if it is regarded as an expansion of 3.1A3l. We said that the propositional sign is constituted by a determinate arrangement of the elements of the proposition. The elements would not have to be marks on paper or sounds, but everyday objects such as articles of clothing or furniture which are put into some sort of determinate arrangement. I could, for example, use the pack of cigarettes and the ashtray before me to express the idea of Socrates speaking to Plato. I could, for instance, place the pack on top of the ashtray to indicate the relation of 'talking to'. I could use the pack to stand for Socrates, and the ashtray to stand for Plato. If I wished to indicate Plato talking to Socrates, I could use the pack and the ashtray to stand for the same individuals, but put the ashtray on top of the pack. Thus the relation is expressed by the arrangement of the elements of the representing situation, gag ay one of Eaa elements. There is no element in this ashtray-pack situation which represents the relation of speaking Ea. As in the pre— vious discussion, a sense is expressed by a conventional zarrangement of the elements. The arrangement, the configura- tion of the elements is the vehicle for the expression of sense. And in general, we can say: that the pack of 175 cigarettes is on top of the ashtray says that Socrates is speaking to Plato. Or, as in proposition 3.1U32: Instead of, "The complex sign 'aRb' says that a stands in the relation of R to b," we ought to put "That 'a' stands in a cer- tain relation to 'b' says that aRb.” (Emphasis added) Notice Wittgenstein's extremely judicious and careful employ- ment of the use-mention-distinction. The distinction is employed here with good reason: Wittgenstein here gives us the first indication of the form which propositions of the perspicuous language might take. It begins to appear that relational predicates and monadic predicates do gag occur in that language. Let us examine the two bottom lines of the above quotation. The symbols "a" and "b" are names Of names, and 3.1A32 says that the arrangement of the names 'a' and 'b' is the expressive factor in the proposition. What, then, is the role of 'aRb'? We can conjecture that 'aRb' is not part of the perspicuous language, but is rather an aa gag explanatory device which is part of the ladder language. The situation represented by the arrangement of elements 'a' and 'b' is some hypothetical, unspecified situa— tion which is, for present purposes, expressed by 'aRb': . . e.g., Socrates talking with Plato. What, then, are the elements of a proposition? 4e have already surreptitiously given the answer. We know that, in order to be a picture, a proposition must be articulated into elements, and that this element must be brought into 176 some sort of correlation with the elements of the pictured situation. Hence, says Wittgenstein, (3.2) In a proposition a thought can be expressed in such a way that the elements of the propositional sign correspond to the objects of the thought. (3.201) I call such elements 'simple signs' and such a proposition 'completely analyzed'. (3.202) The simple signs employed in propositions are called names. (3.203) A name means an object. The objects is its meaning. There is an interesting parallel with Russell's thought ex— pressed in the above four propositions of the Tractatus. In an early work, The Principles of Mathematics, Russell intro- duces the proper name as being that unit of language which names things; and in that work he says: Here proper names are to be understood in a somewhat wider sense than is usual, and things also are to be understood as embracing all particular points and instants, and man other entities not commonly called things.1 The quotation above suggests that names refer to particulars and particulars only, and this interpretation is further buttressed by Russell's introduction, in the same passage from which the above excerpt was taken, of the notion of the concept. The concept is something which is indicated by 13 all other words which are not names. And this suggests 12Bertrand Russell, Principles 23 Mathematics (New York, 196“), p. AA. 13Ibid., p. uu. 177 that for Russell, as for Frege, the concept is predicative, that concepts are indicated by adjectives and other devices that indicate universals. Things, then, are indicated by names and concepts by whatever is not a name. Concepts, then, cannot be referred to by proper names. And it appears that Russell's use of 'thing' is very close to Frege's use of 'object', that which is indicated by the subject-term of a proposition. It is perhaps not accidental that Wittgen— stein uses 'thing' and 'object' interchangeably in the early passages of the Tractatus, as if he were quite well aware of the precedent established by Frege and Russell. As a prelimi— nary interpretation of the Tractatus, we may say'that ex- pressions for concepts (universals) do not appear in the expressions of the perspicuous language of that work, and that the only way in which one can represent concepts is through the arrangement of names: each of which names a thing, or a particular. Wittgenstein appears to be following Russell in his use of 'thing' and Frege in his use of 'object'. Russell's views on this subject did not change materially between 1900 (when the Principles was written) and 1918 (when the lectures entitled "The Philosophy of Logical Atomism" were given). As he says in those lectures, The only kind of word that is theoretically capable of standingufor a particular is a proper name . . . And he goes on to give the definitions to which we have zalready alluded: A 1 Logical Atomism, ap. cit., p. 200. 178 15 (Df.) 'Proper names' for 'words for particulars'. The use of proper names is the only way in which particulars can be discussed at all; and Russell goes on to make the following interesting statement: How are you to express in words an atomic proposition? An atomic proposition is one which does mention actual particulars, not merely describe them, but actually name them, and you can only name them by means of names. 16 It is well to remember What we asserted in Chapters I and II: that Russell himself states that the lectures on logical atomism "are very largely concerned with explaining certain ideas which I learnt from my friend and former pupil Ludwig Wittgenstein."17 It is at least reasonable to conjecture here that Russell is reproducing in these lectures actual statements concerning the objects of proper names which Wittgenstein made to him. If so, this throws considerable light on the central problem of this essay: a problem which we shall explicitly discuss in the next chapter. This much now, however: the preceding discussion suggests that uni— versals cannot be named in Wittgenstein's perspicuous lan— guage, but instead must be indicated by the way in which Imames in the sentences of the perspicuous language are related tx) one another. From the evidence of Frege and Russell, we may take ii: that in Wittgenstein's scheme, names designate particulars lSIbid., p. 200. 17Ibid., p. 177. 16Ibid., p. 200. 179 only. And in the four propositions of the ladder language presented above (p. 176), we have the kernel of Wittgenstein's theory of analysis. Sachverhalte are analyzable into simple elements, termed objects. Propositions are analyzable finally into simple signs, called names. The names are called simple signs because Wittgenstein designates them as the ultimate endpoint of analysis; no part of a name has meaning, for if it did, the sign would not be simple accord— ing to the definition of a sign's simplicity. And again this view of simple symbols finds corroboration and support in Russell's lectures on logical atomism: he says there, ”A 'simple' symbol is a symbol whose parts are not symbols."18 One may ask: what counts as a "part" of a symbol? We may say this: that a simple symbol, when written down, describes a certain geometrical shape. For example, the letter 'c', which might, in the perspicuous language, be a simple symbol, describes a sort of curve. If 'c' is to be identified as a simple symbol, then we cannot say that the small geometrical curve described by 'c' can be divided into segments in such a way that these segments themselves have some sort of signi- ficance. If 'c' is a simple symbol, then the entire geometri— cal figure described by 'c' is the entity which has signifi- cance. Likewise for all other written symbols. Continuing this line of thought, suppose that the word 'chair' is regarded as a simple symbol in the context of a particular 180 analysis, and suppose that this word is spoken. As with most English words, the word 'chair' is phonemically complex; and if we are to regard 'chair' as a simple symbol, then we are saying that the entire phonemic complex 'chair' is to be regarded as the symbol, and that no phonemic component of the sound is a symbol. Consider further Frege's treatment of compound proper names, and in this connection let us look at the following statement: 'The man who discovered the elliptic form of the planetary orbits died in misery'. We have slightly changed Frege's example for our own pur- poses, but the point which we are trying to make is essen-~ tially the same. Let us consider the first clause of the sentence: 'The man who discovered the elliptic form of the planetary orbits'. This would ordinarily be termed a definite description, but it does, in Frege's terms, refer to an object. Now in Wittgenstein's terms, anything which designates an object must be a proper name. But while the above sentence does not have the form of a name (though it designates the same object as the appropriate proper name . . namely, Johannes Kepler), it does refer to an object, arni in Wittgenstein's terms it is a simple symbol: its con— sflxituent parts, the words, do not independently have meaning. hkitice that, for Frege, the phrase 'The man who discovered tkma elliptic form of the planetary orbits' does not express a tfliought. A phrase which designates an object does not 181 express a thought, and likewise with Wittgenstein. Insofar as a symbol only designates an object, a thought is not expressed, whether that symbol consists of several elements or only one. A thought can be expressed in Wittgenstein's system 225$ by propositions, not by names in isolation. The object then, says Wittgenstein, is the name's meaning. A name is attached to an object, and this is the only way in which a name can have significance. The English word 'meaning' is the Pears and MacGuinness rendering of the German 'Bedeutung' in the original text. Whenever Wittgen— stein discusses the meaning of a name, the word 'Bedeutung' always occurs in the text. The word 'Sinn' does not occur there. We can see this from the following proposition of the Tractatus (3.3) Only propositions have sense (Sinn); only in the context of a proposition does a name have meaning (Bedeutung). This proposition has strong affinities with a dictum of Frege in the latter's Grundlagen der Arithmetik. In that work, Frege enunciates three fundamental principles which guide the entire discussion concerning the construction of sentences in some system of arithmetic. One of these princi— ples is expressed as follows: "Never to ask for the meaning of a word in isolation, but only in the context of a proposi— "18 tion. The reasoning behind this seems to be as follows: 18Gottlog Frege, Foundations of Arithmetic (New York, 1960), tr. J. L. Austin, p. xxii. 182 a proposition, for Frege, expresses a Gedanke, and the words which compose the proposition have their function solely as constituents of the proposition. But further, a word may have different shades of meaning in different propositions, and if the word is ambiguous, different meanings entirely. Thus, for example, it makes no sense to ask for the meaning of the word 'cardinal' without reference to the context of that word's occurrenCe in the proposition. Its occurrence in a proposition makes the meaning clear; but apart from its occurrence in that proposition, the reference (Bedeutung) of the word is unclear. But for Frege, one can speak of the ging and EEQEB? tung of both names and propositions. The above-quoted pro— position of the Tractatus (3.3) allows only propositions to have Sinn, and only names to have Bedeutung. There is a divergence here from the theory of Frege; and herein we have some indication of why the simple constituents of Sachverhalte are called objects. To see_this, let us refer again to Frege's discussion of the relation of concept and object. An object is anything which can be referred to by either a phrase or word preceded by a definite article, or by a name. Thus, we remember, 'Venus' is a proper name, which names an object, the plant Venus. 'The morning star' is an expression which also refers to an object, also the planet Venus. We saw that 'Venus' and 'the morning star' are expressions which liave the same reference; they differ, however, in their sense. Propositions also have both sense and reference, for Frege. 183 As in the case of names, propositions refer to-their Bedeutung and express a thought, i.e., their sense. With Wittgenstein, the situation is different. Wittgenstein will not countenance the idea that propositions designate a truth-value (which is an object). Wittgenstein does retain the Fregean idea that an object is designated by a name or a description, but re- jects the position that propositions name an object of any kind. Objects, he says, can only be named, not described. On the other hand, Sachverhalte cannot be named, but only described; and it is the function of propositions to describe (not name!) Sachervalte. This position of Wittgenstein with regard to the nameability of situations is enunciated in the Tractatus: ”Situations," he says, "can be described but not given names." (3.1UM) A situation is after all a complex entity, and properly speaking a name cannot refer to anything which we determine to be simple. For Frege, too, a situation cannot be an object; but then, truth-values are not situa- tions. Frege did not claim that propositions named situa- tions, but either of two objects: the True and the False. The idea, then, that propositions name truth-value is summarily rejected by Wittgenstein; but it is not yet clear why Wittgenstein does not regard truth—values as objects. One can only say here that for Wittgenstein objects function purely as constituents of situations, of Sachverhalte. And it is difficult to imagine a situation in which the True and the False were among the objects configured in that Sachver— halt. This at least appears to be consonant with l8” Wittgenstein's expressed reasoning. For Wittgenstein, then, names cannot convey a thought; only propositions can. A name can only designate an object, and the True and the False are not among the objects to be found in Sachverhalte occurring in any region of logical space. Thus, many of the features of Frege's theory of meaning are incorporated into Wittgen- stein's scheme, while others are rejected. Wittgenstein and Frege share at least the concern that a proposition should have a definite sense; there can be no question about any indistinctness of sense, for otherwise we would not know how to compare the proposition with reality. A proposition must have a definite sense; and if it doesn't, then in Wittgen- stein's terms we would be forced to make arbitrary decisions concerning how we are to find in reality a situation with which to compare such a proposition. To understand the sense of a proposition, says Wittgenstein, is to know what is the case if the proposition is true. And if the sense of the proposition were indistinct, there would be circumstances in which it would not be possible to know whether or not the proposition were true. It is this requirement which Wittgen— stein has in mind when he says: (3.23) The requirement that simple signs be possible is the requirement that sense be determinate. (3.25) A proposition has one and only one complete analysis. We infer from this pronouncement that any analysis of a proposition which might be undertaken will end in the same 185 set of names in the same arrangement. And there is a corres- ponding proposition for Sachverhalte: a Sachverhalt can have one and only one complete analysis. And this means that Sachverhalte and atomic propositions (which were introduced in our discussion of the picture theory (Chapter II) will be structurally identical. Indeed, this is the central thesis of the picture theory of meaning. Because the structural identity between atomic pro- positions and Sachverhalte is so central, the discussion has centered on the presentation of situations by pictures, thoughts, and propositions. Much of the terminology which Wittgenstein uses in his presentation of the Tractatus' theory of meaning is taken directly from Frege: Sinn, Bedeu- tugg, Gedanke, the theory of names, the problem of the definiteness of sense, and the expression of a thought by a proposition. But Wittgenstein found what he considered weak- nesses in Frege's theory, and in particular he was perturbed by the notion that a proposition could be a name of anything. Thus, certain Fregean doctrines are retained, and certain of them are rejected. The notion of object is retained, for example, but the discussion of what an object is independently of the expression which names it is different. Further, the subject—predicate form of propositions is dropped by Wittgen- stein, so that the notion of what an object is becomes fur— ther modified. In short, Wittgenstein draws most of the vocabulary for his treatment of the picture theory of meaning 186 from Frege, but makes a number of profound changes in the meaning of those terms. Just how profound these changes are is a problem which will occupy us in the next chapter, and here we come to the question of the ontological commitments of the Trag— tatus. We have already expressed our belief that the ob- jects are particulars, that in Fregean terms, the concept is dependent for its very existence on the objects. And while Frege's distinction between concept and object is retained, we shall see that the relation between them changes at Witt- genstein's hands. To make a further study of this question then, we will begin to look closely at the nature of the perspicuous language of the Tractatus, to determine what its commitments are. The discussion of the picture theory of meaning was preparatory to this central topic, but indis- pensable, since we needed to establish the connection between the picture—proposition and what is pictured. We shall see that only propositions are formulated in the perspicuous lan- guage are pictures, properly speaking; for none of the "pro- positions" of the ladder—language is a picture of anything. So the central topic of the ensuing chapter will be the perspicuous language of the Tractatus, and the form which the sentences of that language take. To this discussion, then, we now turn. CHAPTER IV ATOMIC PROPOSITIONS AND THE ONTOLOGICAL STATUS OF OBJECTS A. Introduction The picture theory of meaning is exposited in the ladder language of the Tractatus, and from Wittgenstein's pronouncements concerning the ladder language it seems clear that, since the propositions of the ladder language do not have sense, none of those propositions are logical pictures. Pictures, says Wittgenstein, have sense, and the sense of any picture is what it represents (2.221). What it represents is a possible situation in logical space (2.202). Since the propositions of the ladder language represent no such situations in logical space, it follows that they are literally sense—less. The picture theory of Ineaning as developed in the Tractatus, is therefore to be applied to the perspicuous language, and this language is to be constructed in such a way that its propositions are ilogical pictures of possible situations in logical space. It is this feature of the recommended language which led us tC) give a fairly detailed discussion of the picture theory ir1 the preceding chapter. 187 188 We assume further that enough information is given in the ladder language to allow us to determine the form which sentences of the perspicuous language take. Through— out this essay this has been a guiding assumption, for we have claimed that the form of the atomic sentences of the perspicuous language can be exhibited, given the information contained in the propositions of the ladder language. But this also is problematic, and one of our concerns in this chapter will be to raise and discuss some of the problems connected with the actual construction of such sentences. And here the material from the two preceding chapters becomes relevant, for in the Tractatus the metaphysics of the ladder language and the picture theory are inseparable. In this connection we have already established that the ladder language demands a correspondence between the elements of the picture-proposition, and the elements of the situation pictured. We have already established, in the discussion of the notion of logical space in Chapter II, that Sachverhalte are correlated with atomic propositions (or as the German text of the Tractatus has it, Elementarsatge). 'The structural identity of the propositions of the perspi— (NJOUS language with the Sachverhalte is the feature of the Ixicture theory which concerns us here, for if the prOpositions are pictures, then from observation of the elements of those gxictures, we should be able to determine the nature of the eelenmnts of the pictured Sachverhalte. 189 It is here that the question arises concerning which criterion of ontological commitment we are to attempt to apply in determining the commitments of the perspicuous lan- guage. And the further question arises: why does Quine himself insist on a criterion for ontological commitment? Essentially, the motivation is this: that unless we know with some degree of precision What sorts of entities a man assumes in his discourse, we really do not know, literally, what he is talking about. And for Quine, to say that en- tities X are assumed in one's discourse is to say that we know how X's are referred to. Does one use names to refer to them? If so, then either the names refer to some entities in one's assumed universe of discourse, in such a way that those entities are irreducible to others; or, one must show how to paraphrase the names in such a way that the entities putatively referred to by the names are reduced to others which one's ontology assumes to be irreducible. The further question then arises concerning how this is done. The means for effecting this, for both Quine and Wittgenstein, is Russell's theory of descriptions, briefly discussed in Chapter I. If we limit our ontology to actual, physical entities, then the question arises concerning how we are to explain reference, in ordinary language, to such "possible but nonactual" entities such as Pegasus or Santa Claus. The Russell theory of descriptions provides an ana— lysis of'such reference, showing that we do not need to posit the "subsistence” of entities such as Pegasus, or the 1'!- 190 existence of entities such as the Pegasus-idea in order to explain the meaningfulness of such terms as 'Pegasus'. The theory provides a means of paraphrasing such names in such a way as to eliminate the necessity of positing arcane enti— ties. The supposed name is replaced by a description; hence, e.g., 'Pegasus' is replaced by 'the winged horse captured by Bellerophon' in whatever sentence in which 'Pegasus' occurs. By means of Russell's theory, the sentence is paraphrased in such a way that it is broken down into constituent clauses which can be examined for their truth—value. The theory then provides for the reduction of sentences about questionable entities to quantified sentences whose bound variables range over the entities which are assumed by one's ontology. According to Quine, the major mistake of MCX and others like him is that they confuse the meaning of a word with what it refers to.1 Thus arose the problem of deter- mining the nature of the objects referred to by the putative name, for if the objects did not in some sense have being, the names referring to them would have no meaning. But this could hardly satisfy those with tastes for sparser ontolo- gies. Hence Russell's theory of descriptions comes as a major aid for theorists which strong ontological consciences; no longer is it necessary to posit a realm of subsistent, possible-but-nonactual entities in order that names should have meaning. The ontology which is assumed by theorists 1W. V. O. Quine, "On What There Is," in From a Logical Point of View (New York, 1961), 2nd edition, p. 9. 191 thesdmmmscan thus be made explicit through the appli- afikmcfilmmmll's theory of descriptions, and for Quine OasisomeOr importance. For, he says, One's ontology is basic to the mmmmtual scheme by which he interprets Mlemperiences, even the most common- ;flam>ones. Judged within some particular (mnmmtual scheme——and how else is judgment mmsflde?—van ontological statement goes wiHmut saying, standing in no need of justification at all.2 an Mum sort of statement is an ontological state- nmnt? Wermw agree with Quine that an "ontological statement" stamxsthecnmology (i.e., the kinds of entities assumed) which:h3basic to some conceptual system. Thus, an "ontolo— gicalsflmmement” might take the following form: "For the purposes of the conceptual scheme I am adopting, I assume the following kinds of entities to exist . . . " If this is the form of an ontological statement, then one cannot say that such a statement belongs to a conceptual system, but is basic:txa it. And to say that a statement "belongs to" a concmnitual.53chene is to say that it is made on the assumption that: cerfixairi‘types of entities exist. Hence if we assume tjmat 'theare~ arm? unactualized possible entities, and also pro- erties and Classes and other abstract objects, our factual atements made within such a conceptual system will appear rflcecilyr ciii‘ferrent from factual statements made within a nceptual scheme which assumes that only physical objects I; 2Ibid., p.lm 192 exmt. Ifweassume the latter type of scheme, we then find oummlwm Mndened with the necessity of paraphrasing sen- tamesih much terms for classes and properties occur into emflvahfim mnmences in which such terms do not occur. Sudia scheme for paraphrasis is provided by Russell's thmnw ofckscriptions. A name referring to an entity whose exhfienceis suspect (within some conceptual scheme) is trmnflateiinto a description and substituted in place of the anNS occurrence in some statement. The resulting :flxmement:k3then translated via the apparatus provided by Russell into a statement in which bound variables occur. It is Quine's thesis that all singular terms are eliminable in this way, and Quine has presented an apparatus which can do just this.3 It is here that the question of ontological commitment arises, particularly in the case of supposed names which refer to questionable entities. Descriptions are ‘paraphrmmxni into sentences containing bound variables, and it if; the bijujing of variables which involves us in ontological comnflinnentxs. And given the non-combinatorial logic of the Prdjicigxia Akithematica, we can "read off" the commitments of tkma ccnicepnnial system in question simply by noting which tuqaes; of“ vaifiiables are bound. If so—called individual varia— tiles; arwe tnaurui, then the only commitment of which we can ccniviwct ‘true tflaeorist is a commitment to particular entities (e.g. , physical objects). But if variables for properties BVJ. ‘V}. O. Quine, Methods f Logic 193 Qweficflm wniables) are bound by quantifiers, then the thandstis amvicted of commitment to the existence of properties at leeust. It thuine's thesis that this is the only way in mnehtmacaninvolve ourselves in explicit ontological com- mflmmnts. he cannot, he says, determine ontological commitments from the use of names: . For we can repudiate their namehood 5N;the drop of a hat unless the assumption of acxmwesponding entity can be spotted in the things we affirm in terms of bound varia- bles. Names, in fact, are altogether irrele- vant to the ontological issue Whatever we say with the help of names can be said in a language which shuns the use of names altogether. To be assumed as an entity is, purely and simply, t8 be reckoned as the value of a variable. Names can be eliminated by an adaptation of Russell's theory And this is what makes of descriptions, as Quine has shown. names, i11Iiolxi‘between individual substanCes, to a proposition in which a predicate is attributed to a subject. And further, each predicate that ever might be lChBeITtruand Russell, A Critical Exposition p: the Ediilcxsogflxy (of lbeibniz (London, 1953), p. 9- 211 athdhfledtozasubject is, in Leibniz's words, "comprised hitherwthniof the subject."11 Hence whenever we make atruejudgmmt,twe are explicating what is already con— mnnedin Unanotion of a subject. Further, says Russell, snmakingcfi‘the individual.snfln3tance: {I When main; preniicatst c1u1 be zittrdJNJteol to mu>and the same subject, while this :nmject cannot be made the predicate of znw other subject, then the subject in quafijon is called an individual substance. Itis in Unaconcept of, e.g., Arnold Schoenberg, that he F‘h'magq‘g'Ji 41'. _t ' should have written the Gurrelieder; hence when we assert the proposition: "Arnold Schoenberg wrote the Gurrelieder," we are simply making explicit something which was already contained in the notion of the individual substance: Arnold Schoenberg. It is this consideration which forms the basis of Leibniz's principle that all true judgments are, in the final analysis, analytic. It is apparent from this discussion that, in a sub- ject-pmmxticate proposition, whenever the subject-term refers to an (flijectrvuiich cannot be a quality, and whenever that subjerfia-teivn cannot be predicated of any other subject, the subject refers to an individual substance. And it is this consideration which forms the basis of Leibniz's version of tflde gxrirnciFXIe ()f the identity of indiscernibles. Here is Leibniz's statement of the principle: lJTQUCfteci in Philosophy pf Leibniz, Ibid., p. 205. 12Ibi6., p.1d 212 I hmer from that principle (of sufficient among other consequences, that there absolute beings, 13 reason) arermt in nature two real, hflimmrnible from each other . . And again: Itis always necessary that, besides the diffinence of time and place, there should be aiinternal principle of distinction, and thmnm there be several things of the same speckm, it is none the less true that there arermne perfectly similar: thus, though (fine and place (i.e., relation to the ex- temwflj help us to distinguish things which by themselves we do not well distinguish, things are n8 e the less distinguishable in l. themselves.1 _.._.1" .t"‘.q And finally: Things which are different must differ in some way, or have in themselves some assign- able diversity . . . 15 All these passages have in common the assumption that it is of individual substances which bear qualities. We must be able to distinguish individual substances from one another. Propositions about individual substances all have a subject- predicmflxe form; and to say that each substance can be dis- tinguiskmxi from all others is to say that we can assert at least cums trans proposition about it in which a predicate is attritnrted tn) the subject—term which cannot be attributed to euxy CHflser*:3ubject-term. If, putatively, we have two substances, but cannot find any quality in which they differ, then there is no sense in treating these substances as separate entities. 13M°3 p- 219- lBIbid., p. 220. luIbid. , p. 220. 213 Thusleibniz's assumption is that in any simple sub- and that all sanme‘wmreinhere infinitely many qualities, Umsecnmlfifles (or as Leibniz calls them, "predicates") are This certainly intnhmiC‘mithe nature of that substance. haszwlanahnnm in Wittgenstein's system, where in proposi- 5-. an! .al' -.. ll timiELOl23MUttgenstein asserts that to know the nature of micmject,cwm must know the range of possibilities of its ocmnuenceznwithe nature of the object are one and the {hm Leibniz makes a move which Wittgenstein does not: 5-9 same. fbr Leibniz, any true judgment about a substance is analytic in the sense that in making the judgment we are merely ex- plicating something already contained in the notion of that In the ultimate analysis (which only God can substance. For Wittgen- perform), all true propositions are analytic. this is not so, since all true propositions are either stein, tautologous (in which case they are not elementary) or contingently true (in which case they can be either elemen- tary or composite). ’The (Lifference appears in the following circumstance: when Leibniz speaks of substance, he means individual sub- not do this; the objects But;ldittgenstein does "iJidiJnidual substances," but are collectively spo- We are told that stance. are not ken of as the the configuration of objects produces states of affairs We are told further, that the objects are "substance of the world." (Sachverhalte). unchanging and subsistent (taken individually), but that 21“ their configuratior1 is \vhai; ctmuagew: arki is inst hale. Scnne— imw,in mmm mmpecified sense, the objects are "independent” aunties,jhithe sense tduat an Cmnfiect caritexist, lunzxwhat .H:is,haveéinature, independentl\ of its actual inclusion inrymm Sadnmrhalt or other. But a Sachverhalt comes into iming only when certain gmmkaats are cxnxfigurei ill a deteiu- minate way. We seem, iii:nuort, tc>kmive h€l€?71 new'\nersion ofl'il_'.. "aura?!“ _ F ‘ cfi’the obi<flstinction between substance and accident: a‘b— stance write identified with the objects which are found in configuration, silliflwe accident can be lxhlflfilfled with the Sachverhalt puwyiucenitn/ those cflgjects iriijr t confdiyira- ti on . Thus in Wittgenstein there is no question of our speaking of one individual substance (a "monai”) in which qualities inhere. The substance is identifialle with the objects in the configuration, and the accident is identi- fiable with tfiue structure which those obiects form in that 1 conffiéyiraticwi. The difference is extremely important. For, (3 we inive semn1, elementary propositions (Whicfi describe .Sachveriwalte) cysnsist of names in configuration. ‘3 schenmz,‘what;kyecomes ofsnflflect, and what bwcmmzth‘tnw prewiicatme? It Lueems that in Wittgenstein's scheme the dis- :iructicni varnishens, or is at any rate so radically reinter— Iwateci as ‘to toe linrecognizable. Since the Sarpverhalte are >rnmni bjr tkme ccaniguration of objects, a pluraligz of<flr— b'.—..-...- ...—.--- Ctxs, :it :is ‘veafiy (Hificult to indicate one of them as 215 Sachverhalt. And there is equal {wing Uwasubstance of‘tflna occurring (fiffhndty hidetermining which one of the names in Uwaelamwmary proposition describing the Sachverhalt is to mnmt astflm subject. All of which is to repeat that to have been eliminated by theznmflect-predicate form seene Wittgenstein so far as cmwmaletely enui”1zed e;;mmmHAiny pro- 5‘5 positions are concerwuai. This position of Wittgenstein has the following interesting consequence: if the objects are parziculars ," are names of i! (Hay, and hence the nam s referring to them a- particulars, there seems to be no predicate—expressions occurring in the elementary propositions. if so, the ques- tion arises concerning how it is possible, given this scheme in which elementary propositions consist entirely of names Sachverhalte. ,he arsJer to in configuration, to represent this already has been suggested: that the wav in which the -. __a . . . .. .16, names are configured is Significant. Copi has suggested that the arrangement of the nam s in an elementary tion is just as significant, or can be just as significant, as the nmnwe conventional device of allowing capital lette1s to stauui for’IDredicates in a formula of first-order logic. On the Stunmosition, then, it is not necessary that predi- should have to occur in the elementary proposi~ cate letters tions (if trma'Tractatus. The significance of this is that if 16 . fl . n . _o , -_-‘ . IIrvaaig Copi, Objects, Properties, and Beiat in? the CRractxatus," Mind, N. 8., vol. 67, no. 266, Apri 1958, pp. lh5-165. 216 prmficaualemmrs do not occur in elementary propositions, Hwy dudomfly cannot name any entities. Butthis interpretation of the Tractatus, espoused asit baby and, raises certain problems. The propositions whidibearrmmt clearly on this point are the following: (2.0231) lhe substance cn‘iflne world £§g1(niLy deter— f“ ndne a form, and not any material properties. For it is only by means of propositions that neterial properties are represented—-only by the configuration of objects that they are produced. . Tr; ‘. W4 . (3.1432) Instead of 'The complex sign "aRb” says that a stands to b in the relation R', we ought to put, 'That "a" stands to "b” in a certain rela- tion says that aRb'. We have already quoted these propositions in a different con- text. Wittgenstein's careful employment of the use—mention device seems significant, for the proposition (3.1U32) says that the spatial arrangement of the names in the elementary propositicni ts significant. The name 'a', standing in a certairliflelation to 'b', represents that a certain relation (here Iwnyresented.in the ladder language by 'aRb') holds There may, in fact, be more objects 'aRb', between two objects. in tflae canfiéyiration represented (unperspicuously) by btu: if‘swo, thirther analysis of the state of affairs repre- senqtexi by" 'affia' will discover that. Proposition 2.0231 says tkuat Inatmerijal Iaroperties are produced by the configuration of‘ otnjecrts.. IIt is not clear from this passage (or any other passage in the Tractatus) what Wittgenstein means by a "material property." But the context at least suggests that 217 anmtmflalgnpperty is identifiable with an "external pro— H agnpperty which is not part of the nature of an perty, from the accidental fact that an object object, but res1fi1ts is mwmigned in a particular Sachverhalt. should we be reluctant to identify a Why, then, mfierialgnpperty with an ”empirical" property, such as that oftxflng nah or having a certain weight? The reluctance is if the objects taken severally in configuration due to this: then how are we to determine which object 1E.» ‘ -. fills. form Sachverhalte, This is a serious in the configuration has the property? problem in the Tractatus, for it points up again how Witt— genstein has radically reinterpreted the notion of substance. We have suggested that the conventional notation Of the so far Principia Mathematica will not work for Wittgenstein, as genuine elementary propositions are concerned. Thus, if our interpretation of the notion of elementary proposition in the Tractatus is correct, there will be no occurrences of 'F(x)' or 'F(a)'. We will not be able to such notations as attatfiieaxactly one property to exactly one identifiable ob- ject; euui in this circumstance lies the main difference betwemni Leitniiz's concept of substance and Wittgenstein's. It may seem that the most we can say about the scheme pre— sented in the Tractatus is that to attribute a property to an object is simply to say that that object occurs in a particular Sachwnhafiz Ehit ‘this has the peculiar consequence that all ob— jects occurring in one Sachverhalt have exactly the same 218 pmxmrtygahd hence, by Wittgenstein's statement of the prhufiplecfl‘the identity of indiscernibles, the objects This unwanted wilee huflstinguishable from one another. unweqwmum must be explained in terms of the metaphysics oftme Tmumatus's ladder language; and the only explana- thxiwhidiseems consistent with 2.0233 is this: that cmjects:hizisachverhalt differ from one another in that l to all other objects 7 Uu9relations which each object bears Hence in the Sachverhalt are different for each object. the only way in which we can describe an object in such a way that its difference from the other objects is repre— sented is to represent (in an elementary proposition) that the object bears such—and-such relations to all the others in the configuration. But this presupposes that there is. some way of singling out a certain object in an elementary proposition, and making the name of that object the "sub— ject" of the proposition. If this cannot be done at all, tfimnq Wittgenstein's statement of the principle of the and objects identiigr<3f indiscernibles cannot be applied, occurwfixug in a Sachverhalt cannot be distinguished from one another. Thtus the issue of the nature 0 f substance in the and the closely related issue of the nature of Tractatus, leads us directly to the problem of relations the objects, .Sacflrvezflialtxa (and according to 2.0231, "material proper- ties") are produced by objects being configured in a certain bvay'. {To ssajr that objects are configured in a Sachverhalt 219 is Misaytmat they bear certain relations to one another. Tosaytmatrmhes are configured in elementary propositions is mnsathat these names bear certain spatial relations tocme mkmher. And the way in which these names are con— Iigurmi(i.e., the determinate way in which they are re- lated)is significant, because the configuration represents Hence the fluastrucmue of the corresponding Sachverhalt. problmncn‘relations in the Tractatus and the problem of since the relations holding among properties are identical, (according to proposi- the objects produce these properties tion 2.0231). Proposition 3.1432 appears to give us the key to the along with the fol— problem of relations in the Tractatus, lowing proposition: (2.03) In a state of affairs (Sachverhalt) objects fit into one another (hangen ineinander) like the links of a chain. Copi runs argued that this proposition provides Wittgenstein with a way out of Bradley's infinite regress.17 Copi's argunmnfi:.is based on a construal of the form of elementary prmnmosititnus which is quite similar to ourS° namely, that Iwalatitnr- and.predicate-variables have been eliminated from elementary propositions, their use being taken over by the deixerndjiatea arrangement of the names Copi argues, as we have, that the arrangement of names in an elementary l7Copi, op. cit., pp. 157-158. 220 gubpmfitimican be significant. Which arrangements are sigflfimnm is a matter to be settled by the establishment ofcmnvmujcns for the construction of elementary proposi- thxm, forthe relations between the names do not have to picmue imwdcally the relations among the objects. That such amxmgements can be significant is illustrated sur- Eh pnfisinghrin elementary mathematics An example which Copi j 'x' and usesvHJl suffice here: consider any two variables '1 In elementary algebra these variables can be combined 1 e.g., ; 'y'. in several ways, to form significant arrangements: we can write 'sy', 'yx', 'xy', 'yx', 'yx', 'sy’, all of which are significant given the conventions established for And there seems no reason why we elementary algebra. The the scheme of the Tractatus. cannot do the same for arrangement allows us to represent how the objects of the pictured Sachverhalt "fit into" one another (or, as the German text says: "hang in" one another) like the links on a chain. But how does proposition 2.03 bear on the question of relations with respect to Bradley's problem? Let us determflmue first what Bradley has to say. So far as Brad- ley”:3gprmfl)len1with relations is concerned, we are ultimately of course, in the application of these consid— interested, theory of relations as developed erations to Wittgenstein's 221 hitheiramEtus. Copi's thesis, in particular, is that the Thacmfimsgnbvides us with an answer to the dilemma of Brmfley mirelations. Let us first review the difficulty. Afimr having rejected the distinction between primary mkisecomflnv qualities, Bradley turns to the distinction 1 betwami"substantive" and adjective,’ or more accurately, 'Hflhg muiquality. The world, according to Bradley, divides into things and their*cphalities. The substantive and adjective is a time- honoured distinction and arrangement of E; facts, with a View to understand them and to arrive at reality.l The problem is to attack this distinction, showing that it cannot, any more than other time-honored distinctions, form the basis for a theory which could discover for us the nature of reality. Bradley proceeds as follows: suppose, he says, a familiar object such as a lump of sugar. It is white, hard and summfiz, having these qualities among others. But now, the fkfithmuing question: suppose that we take the following sentences: (1) Sugar is sweet. (2) Sugar is hard. (3) Sugar is white. What, asks Bradley, does the _i__:_3_ mean in each case? Surely, 118 ssayfr, true "is" cannot mean ”is identical with," for that 19f?. H. Bradley, Appearance and Reality (London, 1962), p. 21. 222 mmldlemitozmsurdity: if it did not, we could say "Sugar isswemf'and”8weet is sugar," using ”sweet” as a substan— tiW?inmutually exclusive: if sugar Ls sweet, it ”0 cmwmm belwnd or white, and so in the other cases. sugar,” fw9says,'fis obviously not mere whiteness, mere hardness, andrmnwesweetness; for its reality lies sorfnow in its 7 0 V O '1 o . o '; 0 unity.”L The trouble is that we cannot flnfl any such unity apart from the existence of these qualities. We might, therefore, try another tack: let us forget, for the moment, about enquiring after a unity which somehow underlies the three qualities, and simply construe the lump of sugar as nothing more than its properties which stand in some relation to one another. But, as Bradley points out, we immediately find ourselves talking about the suger's qual— ities as if the latter were substantives, thing: to which we might predicate other qualities. ihnwnelly, we cannot say such thiruys as "white is sweet," or "sweet is hard.” As Bradley {wits it, "If‘we attempt to identify them, they at . 2 once res1st." l . '\ Btu: if‘ine thus speak of qualities as if they were :substmuqtifines, \Me run into the problem of what to predicate or"thenn. IBrattley suggests that we might predicate relations 3f tflieni, wduaterver:that might mean, for they do stand, ex .—+ 2OIbid., p. 16. 211bid., p. 17. 223 We therefore assert to one another. hypothesi, in relenxion to be in relation with another, say B: one quality, say A, But we have our Ali hisome(unspecified) relation to B. how are we to construe the is? old problem immediiitely: in—relation-to-B?” In such a case, 'in— Can we say ”A is or in construed as a relational grclerty; relation—to-B' is nmre mmfinviparlance, a two-termed or two-place predicate 'in-relation—to—B (A) . But this is collapsed into one: asking whether or Evan . is somewhat misheading, for Bradley is not the 'is' in 'A is in—relation—to—B— construed \ r. can L» C“ as indicating identity. And from this, says Bradley, we nmst "recoil in horror,” we cannot, on pain nf absurdity, identify the subject and the relation. The dilemma seems to be this: If you predicate what is different, you ascribe to the subject what it is “213 and if you predicate what is not different, you say nothing at all.2 We nflgflqt, therefore, attempt another solution. We ’ A hvth term5~ A now asseri.tflus relation to be predicated of We turerefore would have something like A in— ” problem as and B. into a relatixni-to I3. But we run immediately it: tflie former one, continuous with indeed, difficult as A and B, taken each this relation, you are But if you mean are so re- Fcn°, if you mean that severally, even 'have' asserting what is false. ttuat IX and B in such a relation liateci, you appear to mean nothing.¢~ 22.1.9151» 13. 17. 251mm, p. 17'. _ ..q’ ALL—”1 n1 r- -..-7”“ 22M imit:h;essentially tine same gnwflilem as luafore. thzztill in the compound predicate as We run into this problem by the one construe the 'is;' which indicates llkflltlty. Immingtfim relation an attribute or quality of its relata. Leth therefore try to get out of the problem by chmmpingtfim attempt to attribute relations to one or more firmider our two qualities again, A and B. They terms. stand:hisome sort of relation to one another, and let us schematically, for what it is worth, What call that relation C; 'A C B', or 'c(a, B). we might have something like C is different from of this relation C? says Bradley, it cannot then is the status A and B; hence, on the both of its relata, course, be predicated of either of them. This is, of assumption that the indication of identity is the only however, we 'is'. Given this assumption, that relevant sense of namely, must go on to say something of the relation C: Let us call that it is itself related to its two relata. relatitwilD; hence the situation can be represented schemati— (a,B)). But this same process generates a and the situation then becomes says Bradley, cally: D (C, some- say E, (d,(A,B,)))'. and we find ourselves third relation, 'E (d, The process, thing like involved can be repeated indefinitely, And, he says, there is no way in in a Vicious regress. IMhixfld tC) exdxricate ourselves from this regress given the assumptions from which we started. 1H1e eexistence of this regress leads us therefore to renjecrt tflie riotion that a thing can be construed as the sum 225 of its qualities standing in some relation to one another. The relation, upon analysis, turns out to be illusory; or rather, it turns out to be illusory if properties are to be construed as things which somehow have independent exist- ence. The picture given by such a conception of things is~ that of a group of properties, themselves conceived as substantives, which are somehow clumped together. The pro— blem then becomes that of determining how the "clumping" takes place, what sort of "binding" may be discovered to account for the clumping. And the answer is, according to Bradley, that since the supposition upon which the argument is based is absurd, the argument leads nowhere: except to absurdity. At the time that he wrote Principles 9f Mathematics, Russell felt that he had no choice but to accept the inevit- ability of Bradley's regress: The endless regress is undeniable, if relational propositions are taken to be ultimate, but it is doubtful w ether it formws any logical difficulty.2 For Russell, to take a relational proposition to be ultimate is to construe it in such a way that the proposition 'cannot be analyzed into a subject-predicate form. At any rate, Russell did not regard the regress as vicious since in his riew the meaning of 'aRb' does not contain any additional 'elation of 'a' or 'b' to the relational expression 'R'. fi 2“Bertrand Russell, Principles 9; Mathematics (New York, 19614), p. 99. 226 Apparently, in Russell's view, it is true that the regress occursilwe feel the necessity of an extra relation to relate the original relation B and its relata a and b. But whatever 'aRb' may mean, its meaning does not include the extra relation, and therefore we cannot take that crucial first step into the regress. Since the regress is not in some sense included in the meaning of 'aRb', we are free to ignore it. This, at anyrate seems to have been Russell's position at that time. But the situation may not be all that simple, even given Russell's dismissal of the problem in Principles pf Mathematics. Copi certainly takes Bradley's regress seri- cnmly, since he seems to greet Wittgenstein's "solution" of the problem with relief. Copi's point is this: that if we take such a proposition as 'aRb' (to use the notation occurring in the ladder language), the expression 'R' still occurs as a substantive. And it is precisely this construal cM‘zwaLational symbols as substantives that lands us in the regress. The only way to avoid the regress is t avoid 0 taking that first step of construing relations as substan— tive entities. Wittgenstein, argues Copi, allows us to avoid it by eliminating the relational symbol from elemen— tary propositions. In support of his contention we might again site a passage from the Tractatus: :3. 114) What constitutes a propositional sign is that in it its elements (the words) stand in a determinate relation to each other. 227 No mention is made in this passage of the possibility that the determinate relation spoken of contitutes an additional element of the sentence. The elements are names which stand in a determinate relation; but the relation itself is not a further element. What Copi is saying here is consonant with the posi- E“ tion which we established above. The state of affairs ‘2 correlated with 'aRb' can be expressed in an adequate or perspicuous notation simply by the juxtaposition of names ,1 which stand to one another in various spatial relations. Lg Relational terms are thus eliminated by this notation. Nonetheless, notations such as 'aRb' do occur in the text of the Tractatus. Put this can be explained by reference to questions of convenience of exposition; Witt- genstein often writes elementary propositions in such forms as 'F(a)' or 'aRb'. And on this supposition we can always be sure that these are ultimately translatable into the preferred perspicuous style, in which names (n_g_’p including predicate or relational constants) are in immediate combina- tion, and by which spatial relations among names represent relations among objects. It is true, however, that the interpretation of the elementary proposition which we have been urging is not ithout its difficulties. Consider a Eachverhalt in which ccur the objects named by the following constants: 'a', 'b', c ' , 'd' , 'e ' . Suppose that the elementary prOposition 228 describing this Sachverhalt has the following structure: C say 'abd'. This is written in the "perspicuous" style e suggested. Can we, e.g., write this proposition as 'F(a)'? This would then say that object a has the property F. But this would also put the proposition into a subject-predicate form which is unwanted, and inconsistent with what the Trag— I“: t_at_u_s_has already said. Actually this example shows us the profound extent to which Wittgenstein has rejected the sub- ject—predicate schema. The latter schema, which we pre- ' .V‘fiil‘. _A A vv -- sented as 'F(a)', suggests that there is some way in which we can single out the object and identify it as having the properfigfi} But as we have already urged in our discussion of Witmynmtein's doctrine of substance, there seems no way in which this can be done. In the "perspicuous" notation suggested, there is no conceivable way of singling out the subject and a quality which it might have. There are no ‘privileged objects or names; this seems one clear conse- qumche of‘ifiittgenstein's scheme. This is the primary rea— scnq whyrive tuave presented the sentence 'F(a)' as represent- ing an incomplete analysis of the Sachverhalt in question. This consideration leads us full circle, back to the question of interpreting Wittgenstein's version of the Drinciple of the identity of indiscernibles. Objects must liffer- from one another in some respect, otherwise they are .dentical. And this raises a serious difficulty for the :‘actatus, a difficulty which may be stated simply by asking 229 mefMMMnguestion: how, in what respects, may objects thm~fionmm another? The answer has two parts: (U omens may differ from one another in respect to Hmh°material properties; and an object can have amMmrial property in two ways: (a) the very mmumence of an object in a Sachverhalt constitutes Ffii almmerial property of that object; hence they may ;