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Conversation and Conditionals Again:
Lewis. Jackson and Appiah on Pragmatic Defenses

of the Equivalence Thesis.

by
Carol W. Slater

A THESIS

. . Submitted to
. .Mlchl an State University .
1n partial fu fillment of the requirements
for the degree of

MASTER OF ARTS

Department of Philosophy
1985

ABSTRACT

CONVERSATION AND CONDITIONALS AGAIN:
LEWIS. JACKSON AND APPIAH ON PRAGMATIC DEFENSES
OF THE EQUIVALENCE THESIS.

By
Carol W. Slater

Call the claim that the truth-conditions of the ordinary
indicative conditional are just those of the material conditional
the Equivalence thesis (ET). I argue (1) that ET is appropriately
treated as a theoretical claim which must meet the demands of
observation and logic in company with other associated claims: (2)
that ET thus viewed is a plausible thesis in the context of Lewis'
and Jackson's recent pragmatic accounts of the assertability of
indicative conditionals; and (3) that Appiah's criticisms of these
accounts fall short of supporting his conclusion that there is no
reasonable alternative to a non-truth-conditional semantics of
assertability. A Gricean generalization of Jackson's pragmatic

account is briefly sketched.

ACKNOWLEDGEMENTS

My indebtedness is more than usually deep. That a sabbatical
foray turned into a serious journey is due entirely to the
extraordinary patience and solicitude of Allan Hart. Ronald
Suter's encouragement and guidance had very considerably
illuminated an unfamiliar landscape even before he kindly agreed
to serve on this committee. Barbara Abbott's enthusiastic
attention and thoughtful criticism have been invaluable. most
particularly in helping me negotiate the thornier thickets of
Gricean doctrine. My debt to Herb Hendry. who introduced me to
the puzzles surrounding the Equivalence thesis and acted as
committee chair. goes beyond any possible saying but is. I hope.
displayed in the pages that follow. Any grace they may possess is
a reflection of his skill and kindness.

For technical assistance in producing a non-standard text I
owe thanks to Nancy Michael of the Computer Center of Alma College

and to Susan Dinwoody of the Science Division.

ii

TABLE OF CONTENTS

IntrOdUCtion O O I O O O O O O O O O O O O O 0 O O 0

Chapter 1.

Chapter 2.

Chapter 3.

Chapter 4.

Chapter 5.

Chapter 6.

Footnotes.

Appendix .

ET as a Theoretical Claim . . . . . . . .

Objections and Counterexamples to ET. . .

Grice's Conversationalist Strategy. . . .

Adam's Proposal and Lewis' Theorems . . .

Lewis' Quantified Conversational Approach

JaCkson'B SET 0 O O O O O O O O O O O O O

Appiah's Criticisms . . . . . . . . . . .

iii

10

20

30

44

58

81

91

Introduction

This paper is in the service of two theses. One is a reasonably
uncontroversial methodological principle. the other is a position
rather more beleaguered these days. I shall be arguing. against recent
comment. that there are respectable reasons for continuing to say that
the truth conditions of the ordinary indicative conditional are just
those of the material conditional. This is a claim which Frank Jackson

has dubbed the Equivalence thesis.1

It is the embattled position: in
what follows I shall. for convenience. be calling it ET. Its defense
will involve presentation of evidence in its favor. consideration of
problems involved in its endorsement. and the invocation of some
generally accepted criteria for theory choice which. I shall argue.
count strongly in its favor. Less controversially. I shall be noting
that language has many different functions and that it is helpful to
keep this in mind when we try to find order among our conflicting
linguistic intuitions.

A preliminary glance at the over-all shape of this undertaking may
be helpful. I shall. in what follows. be giving critical attention to
one particular attack on ET--Anthony Appiah's criticisms of recent
attempts by David Lewis and Frank Jackson to defend ET by invoking
rules presumed to govern ordinary discourse. In "Conversation and
Conditionals". (1982).2 and"Lewis on the Material Conditional“.
(1983).3 Appiah tells us that both of these ventures are in pretty bad
shape. One of them has a failing"fatal for a whole class of . . .
[such] approaches;' he is sceptical about the other (Appiah. 1982. p.
327). Appiah concludes from this that we have no choice but to give up
on a truth conditional account of the indicative conditional (which.
for convenience. I shall be symbolizing hereafter as '(p4q)'). It is.
Appiah tells us.

just a prejudice that all interesting semantics is

to be done in terms of truth conditions. . . . We

can explain what people are doing when they utter

conditionals by way of the assertability rule

[(p+q) is assertable when Pr(q/p) is adequately

high]. . . . Why do we not rest content with that?
1

(Appiah. 1982. p. 338)

If Appiah is correct. ET is. of course. untenable. I shall be
arguing that Appiah is not correct but suggesting that his criticism is
nevertheless useful in that it calls attention to canons of theory
choice which are easily lost to view amidst technical discussions of ET
and its problems.

Despite appearances. Appiah's conclusion is not based on the claim
that there is an attractive semantics of assertability close at
hand--which. of course. there is not-~but. rather. on what he takes to
be the unavailability of any reasonable alternative. I think that
Appiah's pessimism is misplaced and that on two quite different scores.
First. he seems convinced that it is only by virtue of a pragmatic
defense that ET has any respectable claim on our credence. I think
this is quite mistaken. that while ET has some well-known counter-
intuitive consequences. there are consequences of rejecting the thesis
that are at least as hard to take. 80 the first thing I shall want to
be arguing is that the claim that (p+q) is true just when (qu) is true
has a good deal more going for it. even in isolation. than Appiah seems
to acknowledge. That ET is a peculiarly fragile thesis is. I think. an
illusion fostered very considerably by a mistaken view of what we have
on our hands in the case of claims about the relationship between
formal logic and natural language. I shall be urging that despite
temptations so to view it. what we have here is not a conflict between
unnatural tidy-making proclivities of formal logicians. on the one
hand. and untrammelled and incorrigible linguistic intuitions. on the
other. Rather. I shall suggest. we confront a tension between two sets
of compelling intuitions. beliefs and inferential practices. What is
at issue. I shall propose. is the goodness of competing theoretical
accounts of these phenomena. I shall be urging that our decision
should. in this case. be guided by the same sorts of considerations
which we take to be relevant in other cases of theory choice.

Secondly. I should like to suggest that even if we grant that a
pragmatic solution to the puzzles raised by endorsement of ET would be
welcome. Appiah is surely prematurely pessimistic about our chances of
working out such a solution. That there is no very simple theory

currently available does not seem to me adequate grounds for concluding

that no satisfactory story is possible. Indeed. given the complex re-
quirements to which our linguistic intuitions must of necessity be
responsive. it would be surprising if a simple theory were available.
I shall urge that the current status of pragmatic theory should
encourage rather than discourage attempts to make use of its resources
and that in conjunction with such a theory ET is a persuasive claim.

Doing this will involve a combination of argument and fairly
straightforward exposition. The main arguments are presented in the
first and last chapters; elsewhere. critical comments are restricted
to the numbered endnotes (as are first citations of sources).
Derivations appear in the Appendix and are indicated by (Appendix).

In Chapter 1. I shall be concerned with establishing that. despite
current unpopularity. ET has considerable plausibility as a theoretical
claim and is by no means susceptible of easy dismissal. Chapter 2
reviews some major challenges to ET. including P.F. Strawson's
consequentialist account of ordinary indicative conditionals and a
variety of more or less well-known counterexamples to ET. Chapter 3
introduces Paul Grice's influential conversationalist defense of ET and
some extensions of this strategy. Chapter 4 takes up a more recent
challenge--Ernest Adams' proposal for a thoroughgoing revision not only
of the semantics of conditionals but of criteria for inference schemes
as well. In this chapter we also confront some unobvious but
far-reaching consequences of endorsing Adams' program. in the form of
Lewis' triviality theorems. Chapter 5 lays out two defenses of ET
intended specifically to counter Adams-~David Lewis' neo-Gricean
quantified conversationalist approach and Frank Jackson's SET. a
proposed augmentation of standard conversationalist theory.

In Chapter 6 we are. at last. ready to look in some detail at
Appiah's objections to these two proposals. I shall be arguing here
that Appiah's criticisms are not persuasive and that they fail to
support his conclusion that we should reject ET and endorse a semantics
of assertability. I propose. instead. that in company with a pragmatic
theory general enough to take into account a variety of functions of

discourse. ET deserves very serious consideration.

Chapter 1.

ET as a Theoretical Claim

There is little doubt that the Equivalence thesis is currently
considered a difficult position to defend. Mackie has characterized it
as a paradoxical view3: Hunter finds it a scandal that what he takes to
be a central. non-truth-functional sense of 'if' " has not yet been
caught in any interpreted formal system with an adequate metatheory.'4
Indeed. belief in the falsity of ET has been described by one writer as

5

something of a philosophical orthodoxy. a view which is supported by

the entry under 'If' in the Encyclopedia of Rhilgggnhy;
Many contemporary philosophers. . . use the locutions
'if p. then q' and 'p only if q' in the sense of 'qu'
and have therefore established a new use for them. . . .
[IJt is important to see that when 'if p. then q' is
used in this way. it does not strictly express a
conditional at all-~or if it does express a conditional.

it is a conditional at the vanishing point.6

In this chapter I shall. therefore. be largely concerned with
clarifying the question of what sort of claim ET is and arguing that.
appropriately viewed. it is a thesis which we have good reason to take
seriously.

Let me begin by saying that it is rather tempting to see the
debate over ET along the lines of some sort of opposition between law
and order. on the one hand. and natural unruliness. on the other.

Even Strawson. whose account of the relationship between natural
language and formal system is full of subtle nuance. occasionally seems
to open the door to some such potentially misleading contrast.7 Formal
logic. Strawson tells us. is characterized by clear. explicit. precise
rules which we deliberately establish in the service of system and
elegance (Strawson. p. 232). Natural language. on the other hand. is
full of complexity and ambiguity; we come upon its rules by reflection
on our practice and such rules are characterized by fluidity and
imprecision in the distinctions they involve (Strawson. p. 231).

4

Systematic simplicity. he tells us.
while admirably exemplified by the truth-functional
system. is exemplified not at all by a veridical account
of the maze of logical uses through which we unhesi-
tatingly thread our way in our daily employment of the
customarily related conjunctions (Strawson. p. 93).

Thus.
The formal logician. . . might be compared with a man
ostensibly mapping a piece of country of which the main
contours are highly irregular and shifting. . .
[PJassionately addicted to geometry. . . he insists on
using in his drawings only geometrical figures for which
rules of construction can be given; and on using as few
of such rules as he can. Naturally. his maps will never
quite fit (Strawson. p. 58).

It is. I think. important to match Strawson's remarks here with
the targets to which they are germane. Metaphoric contrasts of this
sort are. for example. prophylactic against the temptation first to
substitute the study of formal languages for that of natural ones
(because formal languages reveal their secrets to us more readily) and
then to assmme that what we find out about our formal system must be
true of natural language. There is no doubt that the study of ordinary
speech is. as Strawson insists."more complicated and less tidy than
the study of formal systems.“ and it is equally unarguable that. as the
old joke reminds us. we do not have the luxury of searching only where
the light is best (Strawson. p. 231). Thus. that the truth-conditions
of (qu) are what they are (because of properties of the propositional
calculus) provides. in itself. no warrant whatsoever for the claim that
the truth-conditions of (qu) are the truth-conditions of (p+q). In
this regard. Strawson's picture is helpful.

Moreover. Strawson's imagery reminds us that it is unlikely that
any formal logic will. in and of itself. provide the theoretical
apparatus for explaining everything interesting about competent
participants' ordinary language inferences or their judgments of truth.
just as it is unlikely that any formal grammar. in and of itself. will

provide the theoretical apparatus for predicting everything interesting

about competent speakers' linguistic performances or their judgments of
grammaticality. Because the surface phenomena to which we have access
(and which may. in fact. be the focus of our interest) are generally
the resultant of many different sorts of determinants--limitations of
short term memory as well as grammatical rules. information processing
biases as well as logical structures--we are not going to observe
precisely what the rule set. by itself. might predict. In this sense.
neither the logician's nor the linguist's maps will ever quite fit. and
it is well to be aware of this.

Insofar as they help us to account for what we observe. however.
we may still insist that rules formulated by the logician or the
linguist have a legitimate place as theses in our over-all account of
inferential practice or linguistic performance. To say that such rules
are simpler than the phenomena which we are trying to understand can
thus. in itself. be no objection to the rules but is merely a remark
about the nature of theory. It can hardly count against physics that
the laws of classical mechanics are compellingly tidy whilst my office
is a mess. Strawson is. thus. both helpful and potentially misleading.
I think. when he talks about“the stylized. mechanical neatness of the
logical system'(Strawson. p. 81). We must at least be careful how we
read disclaimers like the following.

It will not do to reproach the logician for his divorce
from linguistic realities. any more than it will do to
reproach the abstract painter for not being a repre-
sentational artist; but one may justly reproach him if
he claims to be a representational artist (Strawson. p.
81).

While there is a sense in which there is. as Strawson tells us. no
way to ”give the exact and systematic logic of expressions of everyday
speech; for these expressions have no exact and systematic logic."
there is also a sense in which exact and systematic rules may quite
reasonably be said to be the rules of ordinary inferential discourse-~a
logical system L is the logic of such discourse just in case L meets
demands of theoretical adequacy in helping us construe such phenomena
as competent speakers' judgments of truth and inferential validity

(Strawson. p. 58).

I shall. therefore. assume in what follows that it can hardly
count against ET as a thesis of our over-all theoretical account of
competent speakers' inferential practices and logical judgments that
the rules of truth-functional logic are clear. economical and elegant
whilst the observable phenomena in this domain are notably complex.

The question to which we must address ourselves is whether ET does what
any acceptable thesis of any good theoretical structure must do--be. in
company with the rest of the structure. useful in construing the

phenomena with which we are concerned.8

What I should like to emphasize here. therefore. is the claim that
ET gives us a good first approximation to the data--it is. in some
central cases. much more consonant with intuition and usage than is its
denial. To deny ET requires us to make some deeply counterintuitive
moves: we must. it would seem. give up either some substantial logical
commitments. some firmly ingrained inferential practices or some very
plausible metalinguistic beliefs.

For the first--that rejection of ET brings in its wake rejection
of some very fundamental logical commitments--Clark offers the
following argument. which he says he owes to Geoffrey Hunter (Clark.
I'Ifs.‘ p. 35). It is. he tells us. intuitively plausible that

(C): If the conjunction p&q entails r. then p entails that if q
then r.

It is also non-controversial that

(M): ((qu)&p) entails q.

But substituting 'qu' for 'p' and 'p' for 'q' in (C). we have it
immediately that

(E): qu entails that if p then q.

To reject (E) would seem to require us to reject either (M)--modus
ponens for the material conditional-~or (C). Nobody seems willing to
abandon the former and. in Clark's words. the latter seems reasonable
until someone produces counter-examples forcing us to abandon it. 9

Since it is generally agreed that anyone who is willing to say
that 'if p then q' is willing to say that (qu). this amounts to
showing that rejection of ET requires rejection of at least one logical
principle to which we are strongly attached.

Ordinary inferential practice would seem to incline us similarly.

Stalnaker's remarks are at least relevant here--the more so. perhaps.
because he has been no friend of ET.
'Either the butler or the gardener did it. There-
fore. if the butler didn't do it. the gardener
did.' This piece of reasoning--call it the direct
argnmgnL--may seem tedious. but it is surely
compelling. Yet if it is a valid inference. then
the indicative conditional conclusion must be
logically equivalent to the truth-functional
conditional.lo
Finally. not only our inferential practices but what might be
termed our metalinguistic (or perhaps metalogical) intuitions would
seem also to side with ET. Competent speakers talking about the truth
of sentences and the validity of inferences seem inclined to endorse
derivations of the following sort.
(1) Let's suppose that we know it is the case that either p
is not true or q is true. ['qu]
(2) Now let's suppose that p is true. [p]
(3) And surely. you'll grant me that that is the same as
saying that p is not not-true? [--p]
(4) So look back at (1). Remember: Either p is not true or q
is true. and so if p is not not-true. . .7 Right! q is
true. [q]
(5) Which means we can say that if p is true then q is true.
[p+q]
(6) And if we consider where we started. we can say that if
it is the case that either p is not true or q is true.
then it is the case that if p is true then q is true.
[If (*qu) then (p+q)111
Once started. it is difficult to see where it is possible to
withhold assent. We thus have our competent speaker endorsing the only
debatable part of the logical equivalence of ‘+' and '3'.12
Let us recall that the point of this all is not to prove that
(p+q) has the same truth-conditions as (qu): it is questionable what
that would mean.13 It is. rather. to suggest that we have strong

intuitions which count in favor of their equivalence and that

abandoning this thesis thus requires either giving up some deeply
rooted practices or coming up with new explanations of why they are
still reasonable. It is only against this background. I think. that it
makes sense to look at the puzzles which endorsement of ET brings in
its wake.

It is to the puzzles associated with ET that we now turn. In the
light of what we have just seen. why is Appiah so ready to give up on
ET? Let us postpone for the moment consideration of the question of
why he thinks the alternative to ET must be a non-truth-conditional
semantics. and simply ask what difficulties appear to bar endorsement
of what would seem. so far. to be a creditable enough thesis. Here. at
least initially. we shall be traversing rather a well-trodden bit of

terrain.

Chapter 2.

Objections and Counterexamples to ET

I shall not review all of the worries which have arisen with
regard to ET but. rather. confine discussion to one branch of what is
rather a ramifying tree. (It is. however. the branch on which Appiah
is sitting.) What we shall note is that in addition to the very
general objection to taking the rules of formal logic--any formal logic
whatsoever--to be the rules of ordinary language. there are other. more
fine-grained. objections which have been raised against the claim that.
in particular. the truth-conditions of (p+q) are those of (qu).

Three sorts of arguments. more or less closely related. have been
made against this thesis. The first. presented most notably by P.F.
Strawson. simply invokes speakers' intuitions that the conditions which
render (qu) true do not guarantee the truth of (p+q). A second
argument relies on speakers' tendency to reject a variety of natural
language arguments which. under ET. would seem to be instances of
deductively valid inference forms. Finally. a third line of argument
calls on speakers' judgments that such logical properties as tauto-
logousness. consistency and equivalence may not survive translation
from formalisms to natural language under the assumption of ET. We
shall consider each of these in turn.

Let us begin with Strawson's well-known objection.

There is a sense. Strawson tells us. in which the logician's rules
can. at least. 'touch ordinary usage at some vital points“ (Strawson.
p. 58). Sentences which play the same role in inferences can be
gathered together as having the same logical form; rules for the
inferences allowable with sentences of such logical form can be drawn
up. It is just this possibility which gives force to his criticism of
ET in particular. Identification of (p+q) with (qu) is not only
misleading. he tells us.--as any such identification of this sort would
have to be--but definitelngzgng. for

the ordinary conjunction. in its standard or primary
use. does not conform to a logical rule which holds for
10

11

the truth-functional constant with which it is
identified. and conversely (Strawson. p. 78).

[OJne of the sufficient conditions of the truth of a
statement of material implication may very well be
fulfilled without the conditions for the truth (or
reasonableness) of the corresponding hypothetical
statement being fulfilled; i.e.. a statement of the form
'qu' does not entail the corresponding statement of the
form 'if p. then a} (Strawson. p. 83).

Specifically. Strawson tells us. for an ordinary English
indicative conditional to be true. there must be grounds for believing
that there is some connection between the truth of its antecedent and
the truth of its consequent. We are entitled to (p+q) when. for
example. this connection is logical or linguistic in nature. (Y): 'If
he is a younger son then he has a brother'. for example. says that 'He
is a younger son but he does not have a brother' is self-contradictory.
That is. to
assert (Y) is to claim that there is a relationship of logical or
linguistic consequence between its constituents. By itself. however.
the logical formulation 'He is a younger son 3 he has a brother' makes
no such claim. To translate (Y) correctly. Strawson counsels. we would
have to represent it formally as

'He is a younger son 3 he has a brother' is logically necessary
(Strawson. pp. 34 ff.).

We are also entitled to (p+q). Strawson tells us. when the connec-
tion which holds between antecedent and consequent is empirical rather
than logical. Not all reasonable inferences are linguistic; a step in
reasoning can be justified."not by linguistic rules but by the way
things habitually happen in the world' (Strawson. p. 37). We may say
such things as 'The butter has been standing on the work surface all
morning. therefore it will spread easily.‘ When we are not sure that
something is true but have reason to believe that from its truth
something else would follow by such a causal connection. we are.
Strawson thinks. also entitled to (p+q): 'If the butter has been

standing on the work surface all morning. then it will spread easily.‘

12

Again. however. this is not what is said by (qu). which simply denies
the conjunction of p and --q.14

This characterization of a very important class of ordinary
'if...then...' statements has been termed the consequentialist position
(Mackie. p. 67). Anne. following Strawson. formulates it as follows.

The most general remark one can make. . . is that what
is stated (granted. supposed. alluded to) in the
if-clause purports to provide a condition of what
follows in the sense that i£,;hg‘hyngthetigal‘is,tzug.
mad.artenahla.thsan9.deaiamldmstitutea
reasonahlainfarancafmthanmtaaia [if-clause].
Thumifanaknewerhadamdmaantathinkthattha
hypotheticalismndartma.nnamldjnstifiahla
m. mmmn. '2. 194'. and supposing it
to be a known fact that 1. one could account for g by
affirming '3. because 9' (Anne. p. 128. my stress).

If (ignoring a certain casualness here with regard to what consti-
tutes an explanation) we accept this claim that a necessary condition
for (p+q) being true. sound or tenable is the existence of a relation
of consequence or causal connection between p and q. then we must
reject ET. for a formula in which '3' is featured never requires such a
relation to hold in order to be true.15

Strawson and others have thus argued from speakers' intuitions
about the conditions under which isolated indicative conditionals are
true or false that there is something more required of us by (p+q) than
by (qu) and that the something more is a matter of causal or
consequential connection. A case against ET has also been argued from
the tendency of competent speakers to jib at certain natural language
arguments involving conditionals despite the fact that translations of
these arguments under the assumption of ET are logically impeccable.
The most notorious case is. of course. that of the so-called fallacies
of material implication. Although an argument from q to (qu) or from
p to (-p=q) is deductively valid. ordinary language reasoning along
these lines is notably unpersuasive: 'I'll ski tomorrow' does not seem
to require us to accept 'Therefore. I'll ski tomorrow if I break.my leg

today' nor does 'I'll have a second cup of tea' appear to entitle us to

13
'Therefore. I'll die if I don't have a second cup of tea.16. 17

Observations of this sort would seem to fly in the face of the
claim that (p+q) and (qu) are true under precisely the same
circumstances. ,

Similarly. it does not seem that a denial of (p+q) is standardly
interpreted truth-functionally as equivalent to p and -q. as ET would
appear to require. Cooper. for example. points out that although
-(p=q) entitles us to p.

It is not the case that if the peace treaty is signed. war

will be avoided
is not normally taken as entitling us to

The peace treaty will be signed.

Moreover. since -(p3q) also entitles us to -q. ET warrants the
inference

It is not the case that if we follow that road we will reach the
city
therefore.

We will not reach the city.
which also seems to be a pretty dubious hypothesis about the conduct of
ordinary discourse. With a bit more ingenuity yet. it can be pointed
out that since -(p=q) entitles us to p. it also entitles us to (-p=r)
for any r. including q. and thus the application of ET to negated
conditionals warrants the inference

It isn't true that if he breaks a mirror he will

have bad luck
therefore.

If he dosn't break a mirror he will have bad luck.

Finally. since -(p=q) entitles us to -q. it also entitles us to (--qu)
for any r. including p. which is to say. it entitles us to (qu). and
hence. under the assumption of ET. we may conclude from

It is not true that if she is over forty she is still young
to

If she is still young she is over forty (Cooper. pp. 197-8).18

That competent speakers do not respond to negated indicative con-

ditionals in the way in which classical logic bids us respond to -(p=q)

14

has seemed to Cooper and others to be important evidence against ET.

Finally. even though we seem to have some idea of what the
extrasystematic analogues of tautology. consistency and equivalence
might be. (to use Haack's handy phrase). these logical properties do
not always survive translations certified by ET. Thus. for example.
(-p=(p=-p) is a tautology and we might thus expect its translation
under ET to seem true under any circumstances (in the same way that
'Either he's coming or he's not coming' cannot be gainsaid). But
competent speakers do not seem to accord such status to. say. 'If she
didn't do it if she did. then she didn't'. As Cooper points out. this
sounds muddled at best(Cooper. p. 203). Similarly. according to formal
logic. the conjunction (qu)&(p=-q) is perfectly licit. We are.
however. made distinctly uneasy by 'If John loses he will try again.
and. if he loses he will not try again'. which sounds somehow
inconsistent or self-contradictory (Cooper. pp. 199-202).

Finally. there is the failure of at least some ordinary indicative
conditionals to withstand transformation into what ought to be their
logical equivalents on the assumption of ET. A speaker who will. for
example. happily endorse 'If Carter wins. it will not be by a large
margin' will predictably not accept what would appear to be the
logically equivalent 'If Carter wins by a large margin. he will not
win'; to say 'Even if it rains it will not pour' does not seem to
commit a speaker to 'If it pours it will not rain'. Such failures of
contraposition would seem. equally. to count against ET.

It was consideration of cases of this sort. Cooper tells us. which
led him to the conclusion that

once one got beyond the simple inference patterns
discussed in logic textbooks. . . .[OJne might almost as
well flip coins as use classical logic to try to predict
which English arguments would seem reasonable and which
not! (Cooper. p. vii)

The advocate of ET has. of course. a response to this which is
both straightforward and time-honored. When somebody says that (p+q)
is not true under circumstances where ET requires it to be true or that
an argument in which (p+q) occurs is not valid even though ET certifies

it as valid. it is possible to reply that the person who offers such

15

objections simply has mistaken beliefs about the truth of the sentence
or the validity of the argument. There is. after all. no a priori
warrant that we are perfect reasoners. accepting all of the genuine
consequences of our beliefs. Indeed. investigation of inferential
errors has become an increasingly popular enterprise among cognitive
psychologists. We have. they tell us. rather a pronounced tendency to
lump together indiscriminately a variety of 'negative' semantic
properties--being untrue. invalid. not universal--into one category and
various 'positive' ones--being true. valid or universal-~into another.
Ascription of one negative (or positive) property is thus likely to
bring in its train ascriptions of other negative (or positive)
properties. (An analogous information-processing bias in person
perception is the familiar 'halo effect'.)

Over forty years ago. Janis and Frick confronted graduate
students with syllogisms such as the following and asked them whether
the conclusions followed logically from the premises.

Many brightly colored snakes are poisonous. The
copperhead snake is not brightly colored. So the

copperhead is not a poisonous snake.

All poisonous things are bitter. Arsenic is not bitter.

Therefore. arsenic is not poisonous.

Some Russians are idealists. All Bolsheviks are
Russians. It follows. therefore. that some Bolsheviks
are idealists.

Janis and Frick also asked the students to indicate. separately.
whether they agreed or disagreed with each conclusion. Not
surprisingly. they found that their participants' errors with regard to
validity were more likely to be consonant with their personal opinions
about truth than contrary to them: they were more likely to evaluate an
invalid conclusion as valid when they agreed with it and to call a
valid conclusion invalid when they disagreed with it than vice-verse.

More recently. Begg and Denny have summarized findings with regard
to syllogistic reasoning as follows.

The first principle. referring to quality. states that

16

whenever the quality of at least one premise is
negative. the quality of the most frequently accepted
conclusion will be negative: when neither premise is
negative. the conclusion will be affirmative. The
second principle. referring to quantity. states that
whenever the quantity of at least one premise is
particular. the quantity of the most frequently accepted
conclusion will be particular: when neither premise is
particular. the conclusion will be universal.19
Thus. the following turn out to be popular errors.

Some M are P.

Some 8 are M.

Therefore.Some S are P.

Some M are P.
Some 8 are not M.
Therefore.Some S are not P.

Johnson-Laird and Steedman found the same sorts of "htmosphere
effect" errors being made in Chicago. New York. Edinburgh. London.
Padua. and Nijmegen.20

Finally. and closest to home. Wason had participants look at cards
with the following symbols on them:

A M 6 3
They were told that each card had a letter on one side. a number on the
other. Their task was to indicate which cards had to be turned over to
determine the truth of the rule 'If there is a vowel on one side. there
is an even number on the other side'. Almost without exception.
participants chose either 'A' or 'A and 6'. 21

In the light of such findings. one might either insist that we
take to heart the fact that there are strong and widespread intuitions
counter to the most unarguable truths of classical logic or one might.
more reasonably. conjecture that there are reasons why people are apt
in some cases simply to be misled about what logically follows from
what. Nor is there any reason why we could not take this view even of
our own judgments and try to tutor our own intuitions to conform more

closely to our best beliefs on the matter.

17

Where ET and intuition part company. then. one response is to say
that intuition is in error. There are two rather closely related
objections to taking this tack which may. I think. be met in much the
same way. First. it may be argued that while such a response might be
appropriate in the case of conflicts between our intuitions and the
deliverances of ET with respect to the validity of more or less
complicated inferences--the sort which. for example. we find ourselves
wanting to cast into logical notation--it is not persuasive when what
we are dealing with are intuitions about the meaning of single. simple
indicative conditionals. Surely. as competent native speakers. we
cannot be wrong about something like that? Secondly. it may be
objected that the errors located by cognitive psychologists are. after
all. only occasional: granted. some errors are much more widespread
than others but not everybody falls into the same trap. Rejection of
the so-called fallacies of material implication. however. is well-nigh
unanimous. Could we all be wrong about that? Does it even make sense
to ask such a question? Both of these objections raise. in slightly
different form. the question of whether ordinary usage might not have a
special claim on our commitments.

I think the most relevant observation here comes from John Austin.
Talking about our ordinary language locutions with regard to actions.
he observed that they might invoke models and noted that

[TJhere is no necessity that the various models used in
creating our vocabulary. . . should all fit together
neatly as parts into one single. total model or

scheme. . . . It is possible. and indeed highly likely
that our assortment of models will include some. or
many. that are overlapping. conflicting. or more
generally simply difipazate.22

First. then. if such local disconnectedness may be presumed to
exist with respect to our model for human action. why not with regard
to our model for the logical relationships involved in the set of basic
connectives? If the meanings of these terms is given by something like
their logical powers. then. to have an inconsistent model would be.
arguably. to be (at the very least) in a position to change one's mind

about what could be true of their powers and. thus. to change one's

18

mind about their meanings. Second. if. as Austin allows. we can make
progress as a community in linguistically encoding more useful
discriminations and generalizations. and developing better models for.
say. human action. why might we not be capable of making progress (all
of us. together) in getting a more consistent model of the logic of our
language? Perhaps. to paraphrase Austin. our ordinary linguistic
intuitions with regard to the relationship between (p+q) and (qu) are
the first word but not the last word.23

There would thus seem to be no reason to object. in principle. to
the claim that even competent speakers' intuitions with regard to the
truth of conditionals or the validity of inferences in which they occur
might be in error.

There is. of course. another. equally time-honored response to
what sound to us like erroneous judgments. Rather than concluding that
our informant is talking about what we are talking about and holding
incorrect views on the subject. we can always decide that there is no
disagreement between us because he or she is making perfectly
defensible claims about something altogether different. As we shall
see. it is possible to claim that when competent speakers tell us.
contrary to the deliverances of formal logic on the assumption of ET.
that an ordinary English indicative conditional is false or an
inference invalid. we may decide that what they are xaa111 referring to
is its unassertability or its failure to preserve assertability. It is
not clear that there is much to be gained by such an exercise in
charity. While it does obviate the necessity for saying that ordinary
speakers are widely mistaken about the truth or falsity of their
utterances. it confronts us instead with the need to see them as
confused about what 'true' and 'false' mean. Moreover. the question of
when we ought to assume differences in belief and when we ought to
assume differences in meaning is itself problematic: it has been denied
that there is. indeed. any fact of the matter to be established in
interesting cases.24

Whichever tack we take. we shall. in any case. need to have a very
persuasive account of how we come to be so systematically misguided in
our intuitions about truth and validity (or so thoroughly confused with

regard to the distinction between truth and assertability) where

19

indicative conditionals are involved. We shall need not only to be
willing to be convinced that we are in error but helped to see how we
got there. To use Rorty's homely example. part of what is involved in
convincing the natives that madness is not the result of demonic
possession is giving them a plausible account of how they came to think
they saw demons.25 Having disposed of the notion that linguistic
intuitions are somehow incorrigible is part of the battle; we still
need an explanation of how they come. in this particular case. to need
such substantial correction. Such an account is. of course. just what
is provided by Grice's well-known conversationalist defense of ET.26

It is to this that we now turn.

Chapter 3.

Grice's Conversationalist Strategy

Grice accepts Strawson's observation that. in standard cases. at
least. we are indeed inclined to feel that (p*q) involves something
over and above the truth of (qu) and. specifically. that (p+q) seems
to commit us to what Grice calls the Indirectness Condition--the claim
that there are non-truth-functional grounds for accepting (qu).27 He
takes his task to be provision of an explanation for this intuition
which does not require endorsement of Strawson's conclusion that (p+q)
and (qu) must. therefore. differ in their truth conditions. Grice's
strategy involves two major moves. First. he develops a general
theoretical distinction between what. on the one hand. a competent
speaker knows to be aaid by the use of an expression and what. on the
other hand. such a speaker will recognize as being implitatad by its
use. For Grice."what is said (in a favored sense of 'say')“ is a
technical term referring to the truth-conditional content of an
utterance.28 He uses 'implicate' in contrast to such logical terms as
'entail' or 'have as a logical consequence' (Levinson. p. 103). Thus.
to distinguish what is (in this special sense) said from what is impli-
cated allows us to see. in general. how an utterance may convey
something which does not affect its truth or falsity.

Next. Grice gives an account of how (p+q). in particular. can come
standardly to implicate the Indirectness Condition. If Grice's pro-
posal is accepted. our sense that (p+q) conveys the claim that there is
a connection between p and q can be acknowledged without our having to
accept a difference in truth conditions between (p+q) and (qu).

To begin with. then. Grice asks us to distinguish between what is
said and what is implicated. When we offer (P): 'She was poor but she
was honest'. for example. our statement requires for its truth only
that she be both poor and honest. That it would not normally be
offered (or accepted) unless we also believed that poverty and honesty
were generally incompatible is. Grice tells us. a matter not of the
truth conditions of (P) but of the implicature conventionally

20

21

associated with 'but': (P) is trna if and only if she is poor and she
is honest.

Implicatures may be of various sorts. according to Grice. On the
one hand. there are entirely arbitrary associations between terms or
locutions and their implicatures just as there are completely arbitrary
associations between terms and the truth-conditions for utterances
involving these terms. (There is. for example. no reason why 'but'
should indicate a presumed incompatibility. beyond the brute fact that
it dgaa). Such cases are called agnxantianal implicatures. On the
other hand. there are cases where we can derive. as it were. what is
implicated from our knowledge of the conventional content of the words
used--what is said and what is conventionally implicated--the context
of use. certain bits of background information and our familiarity with
some very general rules governing (at least certain sorts of)
discourse. Grice calls these rules tanyataatianaleatha and
implicatures in whose derivation they figure essentially are called
tanxataatignal,implicatures.

It is our commitment to construe speakers' contributions as being
in conformity with the requirements of discourse (unless we have clear
signals to the contrary) which gives rise to conversational implica-
tures. Given an utterance. S. we regularly attribute to the speaker
beliefs such that 8 would meet (at least some) such requirements were
the speaker to hold these beliefs. have an intention to convey them and
be in compliance with conversational maxims. The content of these
presumed beliefs constitutes the conversational implicature of S.29

The conversational maxim of Quantity. for example. bids us offer
enough information to be useful to our listener; the maxim of Quality
requires that what we offer be factually satisfactory: the maxim of
Relevance makes a demand which is obvious (albeit difficult to
explicate satisfactorily). The maxim of Manner enjoins such virtues as
clarity. brevity and orderliness. Unless given reason to believe
otherwise. a competent language user expects conversational partners to
be in accordance with these and construes utterances accordingly.

Thus. if to my '18 there any coffee left?' my partner replies 'There's
plenty of cocoa'. I routinely assume that this is a helpful.

informative response and conclude that the coffee is all gone (but that

22

there is plenty of cocoa). Moreover. according to Grice. I am
committed to extending such charity even to what might present
themselves as distinctly deviant utterances--ones which. in his words.
appear to flout conversational maxims. If. in response to my 'What do
you think of Smith's work in philosophy?'. my partner offers the
conspicuously uninformative and irrelevant 'He bakes good bread'. I
ordinarily take myself to be confronted not with trash but with a
puzzle. Was the utterance meant metaphorically? Is my partner in no
position to offer reliably the news that Smith is a competent
philosopher and hence--in accordance with the maxim of Quality and
adherence to something like 'Nil nisi bonum'--offering this skimpy
reply in expectation that I will infer that Smith is ngt notably
competent? Conversational implicatures are often rather drastically
underdetermined by the data; nevertheless. the exploitation of flouted
maxims seems to play a significant role in natural language.

There is one final distinction to be made. When the hearer makes
use. perforce. of information about a specific context of use in
deriving an implicature. the conversational implicature thus generated
is called a pattignlazizad conversational implicature. (The examples
we have just considered are thus both instances of particularized
conversational implicatures.) By contrast. in those cases where the
implicature derives from what we might think of as standing
requirements for information--demands and expectations which. in the
nature of things. quite predictably attach to whole categories of
discourse--the standardly resulting implicature is termed a gangtalizad
conversational implicature.

Grice's example here is the interest we may quite predictably be
assumed to have in the existence of a relationship of ownership between
a person and some object under discussion. It will. for example.
generally matter to an interested listener whether the house out of
which someone stepped was her own or someone else's. To offer 'She
came out of a house'. then. under conditions where it might be possible
reliably to offer 'She came out of her house'. would be. quite
generally. to violate at least a couple of conversational maxims. A
competent speaker might therefore be entitled to conclude that the

potentially useful specification was not given because it could not be

23

offered reliably. Hence. 'She came out of a house' would standardly
implicate that the house was not her own. There is. thus. a whole
range of contexts in which use of the indefinite article carries a
generalized conversational implicature of non-ownership. We do not. in
such cases. have to derive the implicature for each member of the class
but learn it as part of what we know about the use of indefinite
articles and certain categories of situations.

The architecture of Grice's scheme is tidily displayed in the
following figure. adapted from Levinson's text on pragmatics (Levinson.
p. 131).

 

 

 

 

meant
. €238 implicated
[in a fa ored
sense)
' . ‘7?
conventionally non-conventionally
r l .
non-conversationally conversationally
.1
I . j
generally particularly

(It may be wondered what a non-conventional. non-conversational
implicature would be like. It would be a meaning intentionally
conveyed by the speaker by means of mutual knowledge and the hearer's
recognition of the speaker's intention to convey this meaning by means
of the hearer's recognition of such an intention rather than by
conventional encoding in.word or gesture and. in addition. no
conversational maxim would be involved in generating the implicature.
For example. a speaker might non-conventionally. non-conversationally
convey the meaning 'I am finding this party terribly boring' by failing
to hide a yawn which he/she knows his/her listener knows he/she could
very well have hidden had he/she made a bit more effort so to do. If.
on the other hand. both parties share the knowledge that the yawn could
not have been voluntarily masked. it will at most be symptomatic of
boredom without implicating it.)

It is clear that we need some guidance in discriminating among
these kinds of communicational content (Levinson. p. 131). Grice tells
us that there is no knock-down test of whether what we have on our

hands is a conversational implitatnm rather than merely"an element in

24

the conventional meaning of the sentence in question. (Grice. 1978. p.
115). He does. however. offer us what he terms hallmarks
characteristic of conversational implicatures. We have already alluded
to the first of these: conventional aspects of meaning are attached to
terms purely arbitrarily whereas non-conventional aspects are derivable
and. in particular. the derivation of conversational implicatures
essentially involves maxims of conversation (or at any rate. an
over-arching principle of conversational co-operation).

Second. unlike what is conventionally said or implicated.
conversational implicatures can be tantallad. either explicitly. by
some feature of their linguistic context. or implicitly. by some aspect
of the non-linguistic context of discourse. Having answered the query
about Smith's competence as a philosopher by commenting on his
croissants. I may add 'I really don't know anything one way or another
about his work in the field'. thus explicitly cancelling the
particularized conversational implicature that his work is
unsatisfactory. If we happen to be standing on a dark street. knee
deep in fog. when I say. 'She came out of a house.' the generalized
conversational implicature that the individual in question came out of
someone else's house is implicitly cancelled by the situational
context. Cancellability is a second hallmark. then. of conversational
implicatures.

Finally. conversational implicatures are independent of the
precise wording of the utterance in question. With the exception of
those special conversational implicatures which depend upon the manner
in which information is given (e.g.. in violation. say. of maxims
dictating clarity. orderliness. brevity or the like). conversational
implicatures cannot be avoided simply by choosing another turn of
phrase. They are. in Grice's terminology..nanzdsiashahlg (Grice. 1975.
p. 74).

With this in mind. we can consider Grice's conversationalist
defense of ET. The difference between (p+q) and (qu) to which
Strawson draws our attention. Grice argues. is not a difference in what
is said--in.what makes (p+q) true--but. is. rather. a matter of the
existence of a generalized conversational implicature associated (in

the absence of cancelling conditions) with the ordinary English

25

conditional. To substantiate this claim. he first offers evidence that
the Indirectness Condition (hereafter. IC) is. indeed. both cancellable
and non-detachable. He then goes on to show that he can provide a
plausible account of how just such an implicature might come standardly
to be conveyed by the use of (p*q).

The implicit or situational cancellability of IC may be shown.
Grice tells us. by its non-appearance in such contexts as puzzles and
games. where 'If there is an even number on the front of the card then
there is a vowel on the back'. for example. conveys no suggestion
whatsoever of a consequential relationship or connection between the
antecedent and consequent. IC may also be cancelled explicitly. as.
for example. by saying. 'I know just where Smith is and what he is
doing. but all I will tell you is that if he is in the library he is
working' (Grice. Lecture IV. p. 3).

The non-detachability of 10 may be shown by its persistence across
a variety of more or less idiomatic paraphrases--e.g.. the suggestion
of non-truth functional grounds for asserting 'If Smith is in London he
is attending the meeting' is. Grice tells us. present equally when we
say. instead. 'Either Smith is not in London or he is attending the
meeting' (Grice. Lecture IV. pp. 1-2 ). Grice is willing to claim that
even in a recitation of the deliverances of the appropriate truth table
we may still detect the implication (Grice. Lecture IV. p. 2). Both
the cancellability and the non-detachability of IC count toward our
considering it as a conversational implicature of (p+q) rather than as
a feature of what counts toward its truth or falsity. Grice argues.

Finally. we have noted that. on Grice's account. a distinguishing
characteristic of a conversational implicature is the availability of a
functional derivation: we must be able to see how the implication would
be generated. Grice offers two separate accounts of how (qu) could
come to have 10 as a generalized conversational implicature. The first
of these is the better known: Grice characterizes the second as deeper
(Grice. Lecture IV. p. 6). I shall go through both. It may be noted
that the two accounts begin differently. each presenting a distinct
account of how (p+q) might come standardly to implicate the absence of
truth-functional grounds for (qu). The two accounts then converge.

agreeing that given the maxim of Quality. which forbids us to assert

26

anything in the absence of adequate grounds. assertion of (p+q) will
come standardly to implicate the existence of non-truth-functional
grounds for its assertion. which is just to say that it will implicate
IC.

The first way of accounting for the fact that use of (p+q)
implicates a connection between p and q--and. more specifically. a
causal connection between them--goes like this. Suppose that the truth
conditions of (p+q) are. indeed. those of (qu). The conversational
maxims dictate giving one's partner relevant information in as
economical a form as possible. Hence. anyone who had truth-functional
grounds for asserting (p+q)--i.e.. anyone assured either of the falsity
of p or the truth of q--would be better advised to assert whichever of
these was available. Failure to assert either the stronger -p or q
taut tantt would thus come to implicate the speaker's lack of a purely
truth-functional basis for the assertion of (p+q). Offered. then. by a
speaker presumed to be in accordance with the conversational maxim
requiring us not to assert that for which we have inadequate grounds.
(p+q) would be a signal that the speaker had some atha; ground for its
assertion. Whence. to offer (p+q) would be to produce a generalized
conversational implicature of some nonrtruth functional basis for its
assertion--some causal or consequential connection between p and q.
Thus. to offer 'If John is there then Mary is there' is needlessly ver-
bose when we are either sure that John is not there or sure that Mary
is there: in the absence of such assurance. we are entitled to field it
only if we have some other reason to endorse the entire conditional.
The most plausible reason is that we know some causal connection be-
tween John's presence and Mary's such that either John is not there or
John is there and Mary is there. That such a connection exists is.
thus. the implicature standardly conveyed to a competent language user.

Grice offers a second and. he believes. more satisfactory
derivation of the implicature of the existence of such indirect
evidence for (qu) conveyed by use of (p+q). He argues that (qu) is a
logical formula particularly well suited for reasoning from the truth
of p to q--i.e.. for using modus ponens. It seems plausible that the
deployment of a locution which has a particular use--a special matiat

or taiagn‘d'atta--in preference to a logically equivalent expression

27

(especially. perhaps. a more basic one) might come standardly to convey
the conversational implicature that conditions are. indeed. appropriate
for just that use (Grice. Lecture IV. pp. 17 ff). We might thus expect
the choice of (p+q) to have as a generalized conversational implicature
that conditions are appropriate to using modus ponens--that is. (1)
that there is a good chance that p is true. and (2) that we are in the
dark as to the truth of q. (If we are already convinced of the truth
of q. we are hardly in the market for a modus ponens argument and if p
is false. we are in no position to carry it through.) If (1) and (2)
are the case. however. once again we do not have truth-functional
grounds for asserting (p+q) and would thus be in violation of the maxim
of Quality unless we had non-truth-functional grounds for its assertion
--that is. unless we knew of some connection between p and q. Hence.
once again. assertion of (p+q) would be expected quite standardly to
come to convey the implication of IC.

In summary. then. Grice has made a theoretical distinction between
what is required for the truth of an utterance and what is conveyed by
it and he has given reasons why (p+q). in particular. might come
standardly to implicate the existence of uncertainty as to the truth of
both its constituents and. thereby. the existence of some causal or
logical connection between the truth of the antecedent and that of the
consequent. Finally. he has taken pains to provide evidence that what
(p+q) conveys over and above what (qu) requires for its truth is a
conversational implicature and not part of its truth-conditions.
Confronting intuitions that our commitments are greater with respect to
(p+q) than (qu). Grice's answer is thus that there is. indeed. such a
difference but that it is a matter of what is implicated by (p+q)
rather than what its truth-conditions are.

We can. moreover. extend this account to take care of some of the
other counterintuitive consequences of ET which we have noted. A
competent speaker. it would seem. should not only avoid saying what is
false but avoid implicating it as well: an utterance which conveys an
implicature which is not factually satisfactory should be as
inappropriate a contribution to the conversation as one which is
downright false. There should thus be two logically distinct bases for

finding an utterance unassertable (to use the customary term)--either

28

its own factual insufficiency or that of some one of its implicatures
(if any). It is easy to see how these two aspects of assertability
might become confused. A speaker who knew that an utterance S was
somehow suspect might not be clear about whether S was unassertable-
because-false or unassertable-because-conveying-a-false-implicature.
Since the truth of an utterance is. on Grice's account. logically
independent of the truth of its implicatures (if any). there is
possibly a class of utterances which are true but which convey false
implicatures. Such true-but-unassertable utterances are clearly prime
candidates for being (erroneously) evaluated as false.

This account not only explains speakers' intuitions that a
material conditional may be true whilst the corresponding ordinary
English indicative conditional is not. but it also provides a way to
cope with speakers' unwillingness to acknowledge as valid inferences
which ought. under ET. to be so. Thus. confronting the so-called
paradoxes of material implication. the canny conversationalist can
point out that while the truth of q surely guarantees the truth of
(p+q). there is no particular reason to expect it to underwrite its
conversational appropriateness. A speaker who finds a premise
assertable and a conclusion unassertable may quite understandably
mistake this for an argument whose premise is true and whose conclusion
is false and thereby (understandably but erroneously) label the
inference as invalid.

What is more. the conversationalist hypothesis that rejection of a
sentence may be construed as a rejection of its implicature rather than
as an assertion of its negation can also help with the vexing case of
negated conditionals. If an utterance can simultaneously convey two
logically independent claims. 'It is not the case that. . .' (or some
similar locution) might be used with respect to either one of them. It
might thus be used either to negate something said or to reject
something implicated. Given this option. (L) It is not the case that
if he breaks the mirror he will have bad luck. is surely better
understood as an objection to the implicature that there is a causal
connection between breaking a mirror and having bad luck than as a
negation of the conditional. On this reading. (L) does not require us

to endorse 'He will have bad luck' nor 'If he doesn't break a mirror he

29

will have bad luck'. which is just what our competent speaker would
have insisted all along. In the case of negated conditionals. as
Jeffrey and others have pointed out. speakers may best be heard as
committing themselves to less than they appear to be saying (Jeffrey.
1981. p. 79).

It can easily be seen why Mackie has characterized Grice's
proposal as an ingenious and forceful defense against Strawson's
consequentialist claim that (p+q)and (qu) have different truth
conditions (Mackie. p. 77). Currently. however. advocates of ET face
quite another challenge--a proposal by Ernest Adams that we abandon
truth-conditional semantics for conditionals entirely. Interestingly.
Adams also deploys Gricean conversationalist strategies on behalf of
his program. We shall be looking first at Adams' work on the logic of
conditionals and then at two recent responses to it by David Lewis and

Frank Jackson.

Chapter 4.

Adam's Proposal and Lewis' Theorems

On Grice's account. as we have seen. formal logic is a
correct. albeit incomplete. theory of ordinary language reasoning.
Discrepancies between its verdicts and the intuitions of competent
speakers are to be attributed to an understandable but essentially
extralogical disinclination to trade in statements which would
convey misleading implicatures. It is also possible to argue.
however. as Ernest Adams has done. that when we discover competent
language users rejecting inferences certified by formal logic. it
is to the validity of the arguments themselves that we should turn
our attention. Adams claims that various well-known discrepancies
between the deliverances of logic and intuition are. in fact. at-
tributable to misapplications of what he takes to be a very
inadequate theory. 30 What Adams proposes. therefore. is a
wholesale revision of the semantics of standard logic which will
bring the judgments of the logician and the competent speaker into
accord with each other. As we shall see. one cost of achieving
such concordance is abandonment of anything even vaguely
resembling ET.

Adams' proposal has two major components. The first is the
replacement of standard semantic terms--'truth' and 'deductive
validity'--by the analogues 'justifiable assertion' and
'reasonableness of inference'. Justifiability. in turn. is for
Adams a matter of there being adequately high probabilities
associated with statements. The second major component of Adams'
proposal is that the probability to be associated with (p+q) be a

conditional probability.

Pr(q/p) = def. Pr(p&q)/Pr(p).

Let us look at these two prOposals in turn. First. Adams
suggests that we cannot properly evaluate the sorts of arguments
30

31

with which we are concerned in terms of the standard criterion of
deductive validity. He asks us. for example. to consider the
problematic argument

(P) John will arrive on the 10 o'clock plane.

Therefore.
(C) If John does not arrive on the 10 o'clock plane. then he
will arrive on the 11 o'clock plane.31
Is it fallacious?

According to the conversationalist account. as we have seen. the
answer is that the argument is valid but is unlikely to appear so since
it takes us from an assertable premise. (P). to an unassertable
conclusion. (C). (C) is unassertable because. given (P). the speaker is
in a position to offer

(-P) It is not the case that John will not arrive on the 10

o'clock plane
and under these circumstances it is misleading to offer the logically
weaker (C) instead--the listener will standardly conclude both that
there is a significant degree of uncertainty about (-P). which is not
the case. and that there is some causal connection between (-P) and
'John will arrive on the 11 o'clock plane'. which is also not the case.
Our unease. the Gricean theorist would say. is due not to the
invalidity of the inference in question but to our moving from what we
might think of as a 'positively signed' premise to a 'negatively
signed' conclusion.

Adams. however. looks at the case rather differently. Is the
inference warranted?

If we attempt to answer this question by applying the
criterion of validity of formal logic.. . . we must ask:
Is it logically possible for P to be true. but C false?
To attempt to answer this question is to see that
it has no clear answer. The reason is that the term
'true' has no clear ordinary sense as applied to
conditionals. particularly to those whose antecedents
prove to be false. as the antecedent of C must [be] if P
is true. This is not to say that conditional statements

with false antecedents are not sometimes £31124 'true'

32

and sometimes 'false'. but that there are no clear
criteria for the applications of those terms in such
cases. (Adams. 1965. p. 169)

This is. Adams tells us. an empirical claim:
an assertion about the ordinary usage of the terms
'true' and 'false'. . . [which] can be verified. if at
all. only by examining that usage (Adams. 1965. p.
169).32

From Adams' viewpoint. then. we are faced with a problem. In the
absence of criteria for the truth or falsity of such sentences. what we
need. he tells us. is some other way of characterizing the validity of
inferences involving conditionals (Adams. 1965. p. 170). His prOposal is
a rendition for reaeonahleneas of inference:

If an inference is reasonable. it should not be the case
that on some occasion the assertion of its premises
would be justified. but the denial of its conclusion
also [be] justified (Adams.1965. p. 171).

Intuitively. assertions are justified by an appropriately high
probability that a bet on the statement in question would win: denials
are justified by an appropriately high probability that a bet against
the statement would win. In his more recent work on the subject. Adams
offers an alternative pxghahiliatit,agnndnaaa_txitazign:

it should be impossible for the premises of an inference
to be probable while its conclusion is improbable
(Adams. 1975. p.1).

Adams believes that his probabilistic criterion reflects. better
than the classical truth-conditional criterion. both the strategy which
competent speakers actually follow in evaluating arguments in everyday
settings and the strategy which a rational agent ahgnld employ in
reasoning.

The second major issue to which Adam addresses himself is the
nature of the probabilities to be assigned to various sorts of
compounded statements. He agrees with the conventions which are
normally applied except in the case of conditionals. He tells us that
although in the case of many conditional statements

the conditions of settling bets are just as clear as

33

they are on particular non-conditional statements. . .

a bet that 'if p then q' is [in.most cases]
conditiona1--in force only if p proves true. and in that
case winning if q is true. and losing if q is false
(Adams. 1975. p. 175).

Adams therefore takes it to be intuitively plausible that the
probability of an indicative conditional of the form 'if A is the case
then B is' is a conditional probability (Adams. 1975. p.3). He is
prepared to argue that 'appropriateness' considerations--what one nanta
of conditional conclusions--also support this assumption (Adams. 1975.
p. 3).

Taken together. Adams' proposal for a probabilistic criterion of
reasonable inference and his assignment of a conditional probability to
(p+q) yield surprising verdicts about some classically endorsed
inference patterns which involve conditionals.

The easiest way to see this is to present examples. making use of

Adams' informal Venn diagram technique. Consider Figure 1.

 

‘aNNNNr

 

 

 

Figure 1 .

Let the points within the rectangle represent all possible states of
affairs and the subregions A and B represent those subsets of states of
affairs in which statements A and B are true. respectively. Then the
shaded area C represents the subset of possible states of affairs in
which (A & B) is true and so on for various non-conditional statements
compounded from A. B and their negations. Setting the area of the
rectangle equal to l. we may represent the probabilities of such
statements being true by the area of their corresponding subregions.
The probability of a conditional is not. of course. represented by an
area within the rectangle but. rather. by a ratio between such areas.

[TJhe probability of the conditional A+B is identified

in the diagram with the pxgpgztign of subregion.A which

lies inside subregion B. If most of region A lies

34

inside region B. this is interpreted to mean that the
probability of A+B is high. and if most of A lies
outside of B the probability of the conditional is low
. . . [I]f p(A)=O then the probability of A+B is not
defined (Adams. 1975. p. 10).

Such a diagram can be used. Adams tells us. to show that the so-
called fallacies of material implication. for example. represent
inference schemata which do not. in fact. meet the criterion of
probabilistic soundness: we can construct a diagram which shows the
premise as being highly probable and the conclusion as having a

probability of 0.

 

 

15

®

According to Figure 2. while both B and -A are probable. (Afih) has

 

 

 

 

Figure 2.

a probability equal to 0 since none of the subregion A lies within B.
To find an instance of such a probabilistic pattern. Adams tells us. we
need propositions A and B such that

(1) A must be highly improbable;

(2) B must be highly probable:

(3) A must 'probabilistically exclude' B (Adams. 1975. p.11).

One such pair of statements would seem to be those we have already
encountered in Jeffrey's astounding inference.

A = I break my leg today; B = I'll ski tomorrow.

No wonder. Adams would tell us. we reject the argument 'I'll ski
tomorrow. therefore. if I break my leg today I'll ski tomorrow': it is
not rational so to reason.

Having premises of less than total certainty and assigning condi-
tional probabilities to conditional statements. then. can lead to
radical divergence between classical and probabilistic soundness.

Adams explains why this should be so. Let us define the uncertainty of
p as

u(p) = def. 1 - Pr(p)

35

It can be shown that probabilistic soundness parallels deductive
validity neatly just so long as an inference involves nothing but
non-conditional sentences and material conditionals. That is. just as
a deductively valid inference schema cannot take us from true premises
to a false conclusion. so the same pattern. applied to probabilistic
premises. cannot take us from premises of any given degree of
uncertainty to a conclusion whose uncertainty is greater than the sum
of the uncertainty of those premises. As long as we avoid inferences
with very many premises. then. we will not be taken from premises of
high probability to conclusions of low probability. Thus. a deductively
sound pattern will also be a probabilistically sound one.

When. however. we are dealing with a conditional conclusion (p+q)
whose probability is the conditional probability Pr(q/p). the possible
uncertainty of the conclusion relative to that of the premises
increases. This is because the uncertainty of (p+q) so construed will
almost always be greater than that of the corresponding material
conditional.

u(p+q) = u(qu)/Pr(p) (Appendix. a)

Hence. a pattern of inference that would be rational to use with
premises which were certainly true (and which would even be
probabilistically sound on a truth-functional construal of the
probability of (p+q)) can carry us from probable premises to an
improbable (conditional) conclusion. (Under these circumstances we can.
in fact. be taken from premises whose probability is as close as we
wish to l to a conclusion whose probability is as close as we wish to
0.)

Perhaps even more surprisingly. Adams points out that an inference
schema which is both classically and intuitively acceptable may turn
out to be probabilistically unsound. as in the case of contraposition.
Consider Figure 3.

Now take the argument from (B+-A) to (A+-B). Most of B lies
within -A so the premise is probable. None of A lies within -B.
however. so the conclusion is not probable. If A = There will be a
terrible cloudburst and B = It will rain tomorrow. one might well

accept 'If it rains tomorrow there will not be a terrific cloudburst'

36

 

 

B

Figure 3 .

 

 

 

 

but reject 'If there is a terrific cloudburst tomorrow. it will not
rain.' Nevertheless. contraposition is not only a logically impeccable
inference schema but. unlike the so-called fallacies of material
implication. one which figures in ordinary argumentation as well.
At this point. it might appear that Adams has overshot his mark.
It is one thing to field a proposal which shows that inferences
normally rejected by competent speakers are. indeed. unreasonable: it
is quite another to arrive at the conclusion that inference schemata
which are both legitimated by standard logic and routinely applied by
competent speakers fall short of our criterion of rationality. Adams'
response to this is. interestingly. to invoke the Gricean doctrine of
conversational implicature. Although it is possible. as we have seen.
to construct probabilistic counterexamples to widely accepted schemata.
he tells us. the conventions governing their use protect us from
falling into the sorts of error which we have found to be possible.
[I]f one accepts the probabilistic unsoundness of
contraposition he is in a dilemma: what is to be made of
all of the real life reasoning which seems to be of this
form? It is too much to condemn it as irrational

aimplicitet. We will argue . . . that most such
reasoning it rational. only. it is not rational in

virtueofbeinsoftheeontnnooitionform. Where such
inferences are rational it is because further conditions
are satisfied which usually obtain when persons are tgld
propositions of the form B+-A which are not part of the
meaning of the proposition (Adams. 1975. p. 15).
Adams calls such conditions agnditigaa at pattia1.;atianality (Adams.
p. 18). If we figure out the circumstances under which an inference

schema would not lead us astray. then. we should expect to find that

37

there are conversational constraints which ensure that it is used only
under these conditions of rationality. To show that this is. indeed.
the case. Adams shows us. first. when inferences involving conditional
conclusions are. so to speak. safe.
[T]wo rules relating uncertainties of premises to
conclusion uncertainties throw light on partial
rationality conditions. . . (l) The uncertainty of a
factual conclusion of a truth-conditionally sound
inference cannot exceed the sum of the uncertainties of
the premises. whether or not the premises include
conditionals. (2) The uncertainty of an indicative
conditional equals the uncertainty of the corresponding
material conditional divided by the probability of its
antecedent.
[u(A+B) = u(AaB)/p(A)]
Combining these we get: the uncertainty of a conditional
conclusion of a truth-conditionally sound inference
cannot exceed the sum of the uncertainties of the
premises divided by the probability of the conditional's
antecedent. Hence we can say roughly that if a truth-
conditionally sound inference with [a] conditional
conclusion has highly probably premises then its
conclusion must [also] be probable p;gxidad,tha
eonditionalla.anteeedent.ia.not.hixhlx.imazehahle
(Adams. 1975. pp. 18-19).

Thus. in the case of contraposition. the uncertainty of the
conclusion. u(A+-B). cannot be greater than the uncertainty of the
(single) premise. u(B+-A). divided by the probability of A. We will
not go from a probable premise to an improbable conclusion. then.
unless the probability of A is very small. which is to say. unless
p(-A) is large. We are thus reasonably safe (and safely reasonable) so
long as -A is not very probable. But. says Adams.

[I]n the ordinary situation in which a speaker makes an
assertion of the form B+-A . . . it is unusual for -A to
be by itself probable. Possibly it is misleading and in

violation of conversational 'helpfulness maxims' for a

38

speaker to say. e.g. 'if Jones attends the party then
Smith won't' when he also believes 'Smith won't attend
the party'. In such circumstances one feels the 'even
if' locution to be the appr0priate one. as in 'Smith
won't attend the party. even if Jones attends' or 'there
won't be a terrific cloudburst. even it it rains'
(Adams. 1975. p. 21).

Adams thus uses Grice's strategy to support a position which is

diametrically opposed to ET.33

Adams' proposal has been an influential one. It is generally
agreed. even by theorists who otherwise differ in their views. that he
is correct in his hypothesis that the assertability of ordinary English
indicative conditionals can be predicted on the basis of the
conditional probability with which he proposes that they be associated.
Advocates of ET must now contend not only with the objections at which
we have already looked but with what appears to be a complete
alternative to their own program. As we shall see. however. there are
reasons why it is not an unqualifiedly attractive alternative.

Adams observes that his proposal to adopt a criterion of
probabilistic reasonableness and assign the conditional probability
Pr(q/p) to (p+q) is quite controversial at the present juncture--
largely. one suspects. because its implications are radical (Adams.
1975. p. 3). Indeed. Adams has been the first to call attention to the
departures from classical practice demanded by his views. These are of
two sorts. The first (and generally less commented upon) involves
syntactic revisions. the second. semantic ones. Let us look at these in
turn.

First. we may note that. for Adams. a rule of inference is
valid--universally probabilistically sound--if it cannot take us from
probable (justified) premises to an improbable conclusion (one whose
denial is justified). As we have just seen. a given rule may be
probabilistically sound under special circumstances: a truth-
conditionally sound inference is probabilistically sound so long as the
antecedent of its conditional conclusion is not too improbable. for
example. Adams thinks it plausible that recognition that a conclusion's

antecedent is not tag imptghahla may thus standardly function as a

39

'tacit premise' in real life reasoning (Adams. 1975. p. 19.). A
premise of this sort cannot. however. be expressed in the symbolism of
standard logic and therefore cannot figure among its rules. Nor. to
look at the matter from a slightly different angle. can the standards
of correct usage which. on Adams' account. corral everyday inferences
within the bounds of partial rationality (e.g.. the rule that governs
application of 'even if') be represented formally in the notation of
classical logic (Adams. 1965. pp. 191-2). Adams therefore thinks that
systematic analysis of rational inference will require a 'syntactic
generalization' of standard logic (Adams. 1975. p. 19).

The second radical consequence of Adams' proposal is. of course.
its implications for traditional semantics. These go well beyond the
obvious fact that Adams proposes to reject the hegemony of classical
criteria of deductive validity and the use of standard truth conditions
for conditionals. Adams makes clear. to begin with. the futility of
what would seem at first glance to be an attractively moderate response
to his proposal. Looking at the fact that truth-conditional soundness
is closely related to probabilistic soundness in the case of inferences
in which only factual propositions appear. we may imagine that there is
still some way of assigning truth conditions to (p+q) consonant with
Adams proposal which will preserve this neat parallel. Adams throws
cold water on any such hope. It is. he tells us.

hopeless to hunt for the 'right' truth-conditions for
conditionals which can be used in testing the truth
conditional soundness of inferences involving such
propositions. . . .

If the conditional probability measure for
conditionals' probabilities is correct. and given other
standard assumptions of probability theory. there is no
way of attaching dichotomous truth values to
conditionals in such a way that their probabilities will
equal their probabilities of being true (Adams. 1975 p.
5. stress removed).

Adams presents a formal proof to this effect. which has been
helpfully adapted by Carlstrom and Hill in their review of The ngit.gt
Conditionala-34 By showing that there exist two assignments of

4O

probabilities to worlds and of truth values to statements p and q at
those worlds such that the probabilities of (p+q) being true differ
from each other under the two assignments whilst Pr(q/p) does not so
differ. they demonstrate that the conditional probabilities asociated
with the indicative conditional cannot be probabilities of its truth
(Appendix. b).

In another review. Edgington offers a more informal discussion of
the same point.35 Like Adams. she draws our attention to the fact that
we can use areas of a Venn diagram to represent classes of states of
affairs in which simple and truth-functionally compounded statements
are true.

If areas are made proportional to probabilities. the
probabilistic relations between these propositions can
also be read off. But P(A+B) is a tatin: the ratio of a
probability that a state of affairs obtains in which
'A&B' is true. to the probability that one obtains in
which 'A' is true. Thane it no. mh thing as the elaaa
of. atate of affairs in whioh .'.A+B_'. in mm (Edgington.
p. 621. last stress added).

Conditionals. Edgington tells us. are not the agzta of things that
can be true or false.

Some conditionals may have probabilities 1 or 0. but
there is no way of assigning dichotomous truth values to
all conditionals (Edgington. p. 621).

But this finding has consequences that go beyond the
interpretation of inscriptions like Pr(p+q). If we cannot assign
probabilities of truth to (p+q). we cannot assign probabilities of
truth to statements compounded from such conditionals. as. for example.
-(p+q). ((p+q)V((q+r)). (p+(q+r)) and so on. Thus. as Lewis points
out. if we nevertheless

continue to permit unrestricted compounding of sentences
by means of the usual connectives. so that the domain of
our probability functions will be a Boolean algebra (as
is standardly required) . . . we can no longer assume
that these connectives always have their usual truth-

functional interpretations. since truth-functional

41

compounding of non-truth-valued sentences makes no
sense.36

Even Edgington. who is sympathetic to Adams' project. considers
this an area for further work (Edgington. p. 622).

While '(A+B)&(C+D)' can be treated as a double
assertion. and '(A+(B+C))' can usually be acceptably
paraphrased '((A&B)+C)'. there is no obvious treatment
of (i) '-(A+B)'. (ii) '(A+B)V(C+D)' or (iii) '(A+B)+C)'
. . . . Yet. with (i) and (ii). it is obvious what it is
to deny that a conditional is probable (i.e. that a
ratio of probabilities is high). or to say that either
this or that ratio is high (Edgington. p. 621).

Edgington's suggestion here is that

It may be necessary to ascend from merely expressing
probabilities. to making statements about the
probabilities expressed. to reinstate truth values and
give a sense to negation and disjunction. . . .
(Edgington. p. 622).

In the case of (iii). she notes. this will be a challenging
project.

Lewis. on the other hand. pursues the possibility of giving up on
talk of truth entirely. It might seem. he observes. that we could
still develop a semantics without reference to truth were we willing to

replace mention of equivalence. incompatibility. and
necessity. . . by mention of . . .[their syntactic
substitutes]: inter-deducibility. deductive
inconsistency. and deducibility. . . .

In this way we could describe the probability
functions for our language without assuming that all
probabilities of sentences. or even any of them. are
probabilities of truth. We could still hold that
assertability goes in most cases by probability. though
we could no longer restate this as a rule that speakers
should try to tell the truth (Lewis. pp. 135-6).

Even this alternative turns out to be unavailable. however.

Lewis' own proofs show that given standard assumptions about

42

probabilities. probabilities of conditionals cannot be conditional
probabilities for anything like a natural language. Lewis has shown
that if. respecting the usual axioms of probability. we treat '+‘ as a
non-truth functional connective such that Pr(p+q) = Pr(q/p) when Pr(p)
is greater than 0. it will be the case that

(1) whenever Pr(p&q) and Pr(p&-q) are both positive. p and q will
be probabilistically independent;

(2) there cannot be as many as three pairwise incompatible
contingent statements in the language for which '+‘ is a connective
(Appendix. c). Any such language. Lewis suggests. deserves to be
characterized as trivial (Lewis. p. 132). In addition.

(3) the probability function in question can. at most. be
four-valued. and thus is what Lewis calls a trivial probability
function (Lewis. p. 134).

We are thus left with nothing but a truly drastic alternative to
ET: indicative conditionals can only be thought of a

non-truth-valued sentences. governed by a special rule
of assertability that does not involve their nonexistent
probabilities of truth (Lewis. p. 136).
Adams is undeterred by these consequences.
[My] very tentative opinion on the 'right way out' of
the triviality argument is that we should regard the
inapplicability of probability to compounds of
conditionals as a fundamental limitation of probability.
on a par with the inapplicability of truth to simple
conditionals. What is needed at the present stage is
less mathematical theorizing than close examination of
the phenomena of inference involving these problematic
constructions (Adams. 1975. p. 35).

Adams concludes with the conjecture that
an adequate theory will ultimately require just as
radical a departure from the probabilistic 'conceptual
scheme' as this scheme is itself radically different
from the orthodox truth-conditional viewpoint (Adams.
1975. p. 35).

The defense of ET against Adams. then. is a game for high stakes

43

according to participants on both sides of the debate. It is not
surprising that attempts have been made to neutralize this challenge.
Two recent essays in this direction are David Lewis' quantified
conversationalist approach and what Frank Jackson calls SET--ET in
company with a pragmatic theory which goes beyond conversationalist

doctrine. It is to these that we now turn our attention.

Chapter 5.

Lewis' Quantified Conversational Approach and Jackson's SET

Both David Lewis and Frank Jackson offer defenses of ET which.
they believe. can accommodate Adams' observations about the conditions
under which (p+q) is assertable. They are both pragmatic defenses. in
the sense that they invoke speakers' and hearers' knowledge of what is
implicated as well as what is said in order to explain discrepancies
between intuitions about truth and validity of inference. on the one
hand. and the deliverances of formal logic under the assumption of ET.
on the other. It is the presumed deficiencies of these two theories in
particular which lead Appiah to conclude that ET is an untenable
thesis. Let us consider each of them in turn. therefore. before taking
up Appiah's reasons for rejecting them.

First. then. Lewis thinks he can explain why the assertability of
(p+q) tracks the conditional probability (q/p) within a Gricean
framework. What he is proposing. he tells us. is a anantifiad
conversationalist theory. On a Gricean account. the assertability of
(p+q) can be eroded by either one of two factors. First. the
assertability of (p4q) is diminished to the extent that (qu) is
unlikely to be true. Secondly. the assertability of (p+q) is
diminished to the extent that our grounds for believing that (qu) are
purely truth-conditional. (It will be recalled that one of the
generalized conversational implicatures of (p+q) is the existence of
.ngn-truth-functional grounds for believing that (qu).) In particular.
Lewis tells us. assertability is lessened to the extent that our
grounds for believing that (qu) consist very largely in our belief
that -p. Let us call truth on account of a false antecedent 'vacuous
truth' and the probability that a conditional has a false antecedent
the probability of its vacuity. Let us refer to the probability that
the antecedent of a conditional is ngt false the probability of its
non-vacuity. ‘

The assertability of (pxq) should thus be eroded to the extent
that

l) the probability of vacuity. Pr(-p). is high. and.
2) the probability of falsity. Pr(p&-q). is a large fraction
44

45
of the total probability of non-vacuity. Pr(p)-“which is
to say. when the ratio Pr(p&-q)/Pr(p) is high.

Lewis thinks that the product of these two factors is an
appropriate measure of dimunition of assertability (LC. p. 137).
Subtracted from the probability of (qu). then. this product yields the
required resultant measure of the assertability of (p+q). But. Lewis
notes. making conventional assumptions about probability and
simplifying. we find that

Pr(qu) - [Pr(-p)Pr(p&-q)/Pr(p)] = Pr(q/p).

And that. Lewis tells us. is why assertability goes by conditional
probability (Lewis. p. 137).

In favor of his account. Lewis points out that diminished
assertability due to misleading pointlessness is not an ad hoc property
conjured up solely to take care of problems with regard to the
assertability of conditionals but makes sense in the case of negated
conjunctions as well. It is not. for example. appropriate to say
dramatically of a coveted but perfectly edible mushroom 'You won't eat
that one and live!' despite the high probability of truth of the
statement.

Its assertability goes not just by probability but by
the resultant of that and a correction term to take
account of the pointlessness and misleadingness of
denying a conjunction when one believes it false
predominantly because of disbelieving one conjunct
(Lewis. p. 138).

Our unease in the face of such a statement does not tempt us to
hypothesize some special non-truth-functional rule for negated
conjunctions. says Lewis. nor should we be so inclined in the case of
similarly unappealling indicative conditionals. In either case. what
we assert can be true while its assertion is illicitly tricky and. in
either case. this will quite predictably result in a highly
unassertable statement.

Lewis' quantified conversationalist proposal may be thought of as
a neo-Gricean response to Adams. Frank Jackson has more recently
suggested that reliance on conversational maxims alone is insufficient

when we attempt to account for the assertability of various sentences

46
of ordinary English. He proposes what he calls a aapplamahtad
Equixalente thaaia g; fiEI;ran augmented pragmatic theory which. he
thinks. gives a better explanation of discrepancies between linguistic
intuition and the verdicts of logic under the assumption of ET. It is
probably worth noting that what is supplemented in Jackson's scheme is
not ET itself. which is still the claim that the truth-conditions of
(p+q) are just those of (qu). but. rather. the pragmatic theory which
is invoked to explain what might otherwise seem to be discrepant
judgments about truth and validity of inference.

Jackson starts from the assumption that there is a prima facie
case for ET.

The circumstances in which it is natural to assert the
ordinary indicative conditional 'If P then Q' are those
in which it is natural to assert 'Either not P or. P and
Q'. and conversely. . . [TJhe circumstances in which it
is natural to assert 'Not both P and Q' are precisely
those in which it is natural to assert 'Either not P or
not Q'. We explain the latter coincidence of assertion
conditions by a coincidence of truth conditions. Why
not . . . hold that 'If P then Q' has the same truth
conditions as 'Either not P or. P and Q'. . .
[which]--given the standard and widely accepted truth
functional treatments of 'not'. 'or'. and 'and'--amounts
to . . . the thesis that (P+Q) is equivalent to (PDQ)
(Jackson. p. 565).

What we need. says Jackson. is an explanation of deviations from
expectations based on this very plausible hypothesis. His strategy in
providing such an explanation follows the general outlines of the
pragmatic defenses at which we have already looked. Like Grice and
Lewis. Jackson invokes a distinction between truth and assertability
and. like Grice and Lewis. he derives rules of assertability from a
functional analysis of discourse. Unlike Lewis. however. Jackson takes
pains to differentiate his approach from what has become the standard
Gricean strategy--a strategy which. he thinks. has disabling
difficulties. Jackson believes that propriety of assertion cannot be

explained solely by reference to conversational considerations of"high

47
probability. relevance. informativeness. and so on" (Jackson. p. 573).
He tells us that he hopes to fill a gap in the standard way of trying
to eXplain away the so-called paradoxes by taking into account an
additional functional demand on discourse (Jackson. pp. 368-369).
Jackson also prefers to replace talk of conversational implicature by
reference to what is conventionally inditatad or aighallad (Jackson. p.
574).

Let me try to lay out Jackson's arguments as clearly as I can.
Why. to begin with. does Jackson think that the usual conversationalist
explanation will not do? He offers two quite different objections.

The first has to do with the inadequacy of the standard account in
predicting the assertability of various sorts of ordinary sentences.
including indicative conditionals. The second criticism has to do with
the inadequacy of the standard account in explaining our metalinguistic
intuitions with regard to relationships between ordinary language
expressions and logical formalisms. In neither case. says Jackson. can
we make do with conversational maxims alone.

Let us take up the two objections in turn. Jackson points out
that the standard conversationalist explanation of the so-called
paradoxes of assertability invokes only two sorts of conversational
considerations. We are not to say things which will lead our listeners
astray and. within that limitation. we are to offer as much relevant
information as possible. If this is really all that matters. Jackson
notes. we should be able to predict when a relevant and adequately
probable statement will be assertable by reference to the following
simple rule:

(8) Assert the [logically] stronger instead of the [logically]

weaker (Jackson. pp. 566-67).
But. says Jackson. this rule does hat reliably predict assertability.
His suggestion is that it requires supplementation rather than
replacement.

Jackson offers examples of a number of such failures of
prediction. If (8) fully specifies the conditions for assertability of
relevant and adequately probable statements (a proviso we shall simply
understand from here on). we should. for example. never find (p+q)

assertable when -p is highly probable: both statements have just about

48
the same probability and -p is the logically stronger of the two.
Nevertheless. as Jackson points out.

(E) If the sun goes out of existence in ten minutes time. the
earth will be plunged into darkness in about eighteen minutes
time

is highly assertable.

Similarly. if (S) tells us everything we need to know about
assertability. it should never be the case that (p+q) be assertable on
the strength of the very high probability of q alone. Nevertheless.
Jackson says. a speaker convinced that Carter will be reelected no
matter who his opponent may be is entitled to say both 'If Reagan runs.
Carter will be reelected' and 'If Reagan does not run. Carter will be
reelected'.37

A third failure of (S) to predict assertability occurs when we
consider that statements which are logically equivalent (and thus bound
to have the same probability of truth) may not be equally assertable.
Any friend of ET believes that

((-P & (P+R)) and (-P & (P+S)) are logically equivalent.
both being equivalent to -P. But their assertability
can differ sharply. 'The sun will come up tomorrow but
if it doesn't. it won't matter' is highly unassertable.
while 'The sun will come up tomorrow but if it doesn't.
that will be the end of the world' is highly assertable
(Jackson. p. 568).

In particular. all truths of logic are logically equivalent and
their probability of truth is always equal to 1 yet some of them seem
to be assertable under at least some circumstances--'Que sera.
sera'--whereas others seem quite universally unassertable. That truths
of logic are weak as can be does not help us figure out why some of
them are assertable and others are not. says Jackson.38

Jackson's first objection. therefore. is that the standard
conversationalist account does not have the resources to make reliable
predictions about assertability.

Jackson's second objection is of a quite different order. On any
purely conversationalist account. Jackson tells us. the relationship

between the truth of p and the assertability of 'p or q'. on the one

49
hand. must be the same as the relationship between the truth of p and
the assertability of 'If q then p'. on the other. The very same
conversational maxims bridge the gap between truth and assertability in
either case. That the truth of p entitles us to conclude to the truth
of 'p or q' but does not underwrite its assertability should thus be
just as much or as little puzzling to a competent speaker as that the
truth of p entitles us to conclude to 'If q then p' without thereby
rendering thia an appropriate assertion. Our linguistic intuitions
should thus be thoroughly symmetric with regard to the two cases. Yet
we accept with equinamity the equivalence of 'p or q' and 'qu' while
we choke on ET. A consideration of conversational propriety alone.
Jackson concludes. leaves it a mystery why we--who are after all
reasonably normal language users--find it so easy to swallow one thesis
and so hard to swallow the other (Jackson. p. 569).39
In both of these regards. Jackson finds the standard strategy for

dealing with the so-called paradoxes inadequate. Why. then. might we
sometimes be justified in asserting the logically weaker of two
relevant and more or less equiprobable statements? Jackson's answer is
that we often also take into account what he terms the tghuatnaaa of a
claim--the extent to which its probability of truth is high and
undiminished by receipt of athat news. In particular.

If we accept Conditionalization. the plausible thesis

that the impact of new information is given by the

relevant conditional probability. then 'P is robust with

respect to I' will be true just when both Pr(P) and

Pr(P/I) are close and high (Jackson. p. 569).
Jackson takes such robustness to be an important determinant of assert-
ability. Thus. for example. Lewis' 'You won't eat that mushroom and
live' is unassertable. Jackson thinks. not because it is misleading to
field a negated conjunction on the strength of the high probability of
falsity of one conjunct alone (whose negation could thus have been
proffered tant_ggntt) but. rather. because of a failure of robustness.

You take me to be providing information relevant to

mushroom-eating pleasures. and so construct for yourself

the following piece of practical reasoning. I won't eat

that one and live. (Premise supplied by me.) I eat that

50
one. (Premise you can make true.) Therefore. I won't
live. The conclusion is undesirable. hence you are led
to refrain from making the second premise true.

Why were you tricked? The argument is valid. the
premise I supplied does have a high probability. and you
are able to give the second premise a high probability.

But in order to infer the conclusion of a valid argument
all premises need to be highly probable together: and
if you were to make the second premise highly probable.
the first premise (supplied by me) would no longer be
highly probable. In the circumstances you were entitled
to take it that not only was 'You won't eat that one and
live' highly probable. [but that] it was also robust
with respect to 'You eat that one'. My misdeed lay in
asserting something lacking appropriate robustness
(Jackson. p. 572-573).

The difference between a disjunction which is assertable and one
which is not may. similarly. be a matter of robustness. If I read in
the departmental newsletter that. just as I had expected. Mary won the
prize and Margaret did not. it is improper for me to answer a query
with (M) 'Mary or Margaret won the prize'. If. however. still
believing. as before. that Mary is a shoo-in and Margaret a very
unlikely candidate and knowing that they are the only two competitors
whose names begin with 'M'. I catch a glimpse of a memo on the Dean's
desk just long enough to see that the winner's name begins with 'M'. I
may. it seems. appropriately offer (M). But if 'Assert the stronger'
makes (M) unassertable in the first case. why not in the second?
Surely. by my lights. (M) is still only marginally more probable than
'Mary won' and it is logically weaker. Jackson argues that it is the
greater robustness of (M) in the second case that makes it assertable:
were it to turn out that Mary did not win the prize. I would. in the
first case. have to abandon the entire disjunction but not in the
second case. I would merely have to readjust my beliefs about Margaret
(or the selection committee). Jackson tells us that

In general we are happiest asserting disjunctions

which are two-sidedly robust. We most happily

51
assert 'P or Q' when Pr(PVQ). Pr(PVQI-P). and
Pr(PVQl-Q) are all high (Jackson. p. 575).

Jackson's first point. thus. is that robustness is a factor in
determining assertability. His next point is that there will have to
be indications of what might be called the dizgatign of robustness.

Robustness is a relative affair. A highly probable
sentence may be very robust relative to one possible
piece of information and the opposite relative to
another (Jackson. p. 573).

Jackson thinks that there are both implicit. contextual cues to the
direction of robustness and explicit conventional signals. In the case
of the mushroom gathering story. for example. situational factors
suggest to us the sort of reasoning likely to be going on and this. in
turn. determines the direction of the requisite robustness. We can also
find cases in which information about robustness is explicitly signalled
by a word or phrase. For example. 'nevertheless' conventionally signals
the robustness of a claim with respect to what to what has immediately
preceded it. Similarly. the use of 'p a; anynay q' conventionally
indicates what Jackson terms the merely one-sided robustness of a
disjunction. We fly this flag. Jackson says. to avoid misleading our
hearers into assuming the usual two-sided robustness (Jackson. p. 575).

Jackson is careful to note that such conventional signalling does
not invade truth conditions (Jackson. p. 576). The truth-conditions of
'p or anyway q'. he tells us. are just those of 'qu':"'George lives in
Boston or anyway somewhere in New England' is true if and only if either
'George lives in Boston' is true or 'George lives somewhere in New
England' is true"(Jackson. p. 575).

Of most interest to us here is Jackson's claim that certain syntac-
tic constructions also conventionally convey information about
robustness and its direction. We have already seen that he suggests
that using a disjunctive form not only conveys the adequate probability
of the disjunction itself but also (unless cancelled) its robustness
with respect to the negation of each disjunct taken separately.
Jackson's third major claim. then. is the specific hypothesis that

the indicative conditional construction . . . signals

robustness with respect to its antecedent. Hence it is

52

proper to assert (P+Q) when (PDQ) is highly probable and
robust with respect to P. that is. when Pr(PDQ/P) is
also high. But. by analogy with . . . '--or anyway--'.
the truth conditions of (P+Q) are those of (PDQ). . . .

In the widest sense of 'meaning'. (P+Q) and (PDQ)
do not mean the same. But thgit‘ttath.ggnditigna.ata
the game--they agree in sense or literal content. The
extra element is that in using (P+Q) you explicitly
signal the robustness of (PDQ) with respect to P. and
this element affects assertion conditions without af-
fecting truth conditions (Jackson. pp. 576-577. my
stress).

We have such a conventional signalling device. Jackson tells us.
because it is likely to be of interest to us whether a conditional is
robust with regard to its antecedent--this is a requirement for a modus
ponens argument to go through.

Although (PDQ). P. [therefore] Q is certainly valid.
there is a difficulty about using it in practice.
Suppose my evidence makes (PDQ) highly probable but that
I have no evidence concerning P. Q is of interest to
me. so I set about finding evidence for P if I can. The
difficulty is that finding evidence that makes P highly
probable is not enough in itself for me to conclude Q by
.Mgdufi Banana. For the evidence that makes P probable
may make (PDQ) improbable. . . [W]e must distingush the
yalidity of Manna Banana from its utility in a situation
where I know (PDQ) but do not know P (Jackson. p. 577).

Why should we be persuaded by this proposal that the ordinary
indicative conditional construction is. in particular. a conventional
indication of the robustness of the conditional with regard to the
truth of its antecedent? Jackson argues that his theory axplaina
relevant observations about competent speakers' judgments. By this he
means that it predicts speakers' intuitions both about assertability
and about validity of inference.

The first set of observations to which he draws our attention con-

cerns the circumstances under which we are comfortable asserting

53

ordinary indicative conditionals.
Ernest Adams has provided a simple formula governing our
intuitions and the Supplemented Equivalence theory
explains this formula. Adams has shown that the
(intuitively justified) assertability of (P+Q) is given
by Pr(Q/P) = df Pr(PQ)/Pr(P). . . We explain Adams'
thesis as follows. On our theory. the assertability of
(P+Q) will be the product of two factors: the extent to
which Pr(PDQ) is high and the extent to which (PDQ) is
robust with respect to P. But we have from the calculus
[of probability] that Pr(PDQ/P) = Pr(Q/P). and that
Pr(PDQ) > Pr(Q/P). Consequently both conditions are
satisfied to the extent that Pr(Q/P) is high Q.E.D.
(Jackson. p. 580)(Appendix. d).

Jackson also thinks that his theory can go beyond the usual
conversationalist dissolution of what we might think of as the paradox
of dissent from conditionals. We have observed earlier that
disagreement with (p+q) is not normally taken as committing the speaker
to p and -q as ET would seem to dictate and that the standard
conversationalist account of this is that the speaker's dissent is from
what (p+q) implicates rather than from what it says. But. as Jackson
points out. this leaves dissent from conditionals an inexplicably
special case.

Standardly you dissent from an assertion just when its
subjective probability of falsity is high . . . The
probable falsity of what may be signalled by an
assertion is by and large irrelevant. You dissent from
'He is poor but happy' just when it is probable that he
is either not poor or not happy. not when you dissent
from the signalled contrast (Jackson. p. 586).

Why should conditionals be different? Jackson suggests that there
is. in fact. a general rule governing circumstances under which dissent
is appropriately directed at what is signalled rather than at what is
said and that (p+q) falls under this proviso. In general. Jackson
tells us. if S is a statement and C is what is indicated or conveyed

(but not said) by asserting S. then when the truth of C is sufficient

54
for the truth or high probability of S. dissent from S will be taken to
be an objection to C rather than a denial of S.

Jackson offers a non-conditional example. Consider the case
when I say 'The winner of the election for club
president will come from Tom. Dick and Harry'. What I
say counts as true if any one of these three wins. But
you won't dissent only if you think this improbable
. . .[but also] because I left out George. and in your
view George has the best chance after Tom. . . .

The explanation . . . appears to lie in the
peculiarly intimate relationship that obtains . . .
between what is said and what is signalled. . . .[W]hat
is signalled is sufficient for the high probability of
what is said. In saying that the election is out of
Tom. Dick and Harry. I signal that the high probability
for me of the triple disjunction is robust with respect
to the conjunction of the negations of any two of the
disjuncts. . . .This is sufficient (by the calculus) for
the high probability of the disjunction (Jackson. p.
587).

If the general rule Jackson proposes is correct--if the existence
of a close connection between the truth of C and the truth or high
probability of S makes it appropriate to take dissent from S as an
objection to its associated implicature. C.--then dissent from (p+q)
will standardly be heard as an objection to what it conveys rather than
what it says because

What is signalled by the assertion of (PDQ) amounts to
Pr(Q/P) being high. This is sufficient for Pr(PDQ)
being high. So what is signalled is sufficient for the
high probability of what is literally said. . . [and]
dissent from (P+Q) may be prompted by the dissenter
giving a low value to Pr(Q/P) as much as by his giving a
low value to Pr(PDQ) (Jackson. p. 587).

In addition. Jackson thinks his theory explains our discomfort in
asserting '(p+q) and (p+-q)' even though (qu) and (pD-q) can be true

together: if he is correct. we cannot appropriately assert (p+q) unless

55
Pr(q/p) is adequately high and we cannot appropriately assert (p+-q)
unless Pr(-q/p) is adequately high but the axioms of probability
preclude their being adequately high together.

Finally. Jackson invokes his pr0posal to explain why dissent from
(p+q) is often expressed as the assertion of (p+-q). We may dissent
from (p+q) either because Pr(qu) is low or because Pr(q/p) is low. If
Pr(qu) is low. Pr(q/p)) will also be low. Hence. whenever we dissent
from (p+q). Pr(q/p) is low. This. in turn. means that whenever we
dissent from (p+q). Pr(pD-q) and Pr(-q/p) are high and thus that (p+-q)
is assertable. And. says Jackson.

this is just how it turns out in practice. If you
dissent from 'If Fred went. he went by car.' you assent
to 'If Fred went. he did not go by car' (Jackson. p.
588).

One strength of Jackson's pragmatic theory of assertability. then.
is his ability to explain patterns of assent and dissent associated
with conditionals in cases where they depart from expectations based on
ET and standard maxims of conversation alone.

It will be recalled. however. that attacks on ET have involved not
only intuitions about the assertability of particular conditionals
under various circumstances but also the judgments of competent
speakers with regard to the acceptability of arguments in which they
occur. Adams' challenge. in particular. arose initially from his
concern over such things as the so-called paradoxes of material
implication. Jackson thus sets himself to coping with this family of
puzzles as well.

What. for example. can be made of the notorious lack of appeal of
the arguments from either -p or q to (p+q)? It is. says Jackson. easy
enough to explain:

Neither the fact that Pr(-P) is high nor the fact that
Pr(Q) is high is sufficient for Pr(PDQ/P) being high
(Jackson. p. 581).

Jackson also turns his attention to other argument forms which are
truth-conditionally valid but notoriously hard on the nerves. What.
for example. is to be made of supposed failures of contraposition?

The problem is not that it [contraposition] seems

56
invalid stated in symbols: exactly the reverse is the
case. as is evinced by its appearance in Natural
Deduction systems. The problem is rather a certain
class of apparent counterexamples like: 'If George works
hard. he will (still) fail: therefore. if he passes. he
won't have worked hard'. and 'If Carter is reelected. it
won't be by a large margin: therefore if Carter is
reelected by a large margin. he won't be reelected'
(Jackson. p. 581).

We are uneasy with these arguments. Jackson tells us. not because
what was aaid fails to survive contraposition but. rather. because what
was aignallad fails to do so. Our linguistic intuitions. it would
seem. are not discriminating enough to respond to this difference: we
get the same sort of jolt from an argument that carries us from an
assertable premise to an (adequately probable) but unassertable
conclusion as we do from one that carries us from adequately probable
premises to an inadequately probable conclusion. In support of this
interpretation. Jackson offers two sorts of observations.

First. he cites instances where what is implicated by a locution
fails to survive transformation into a logical equivalent without our
feeling that this renders dubious a straightforward truth-functional
interpretation of the ordinary language connective under consideration.

These apparent counterexamples [against contraposition
of (p+q)] are paralleled by ones against the
commutativity of '--or anyway--': for instance. 'It
won't rain or anyway not heavily: therefore. it won't
rain heavily or anyway it won't rain'. Despite this.

. . .[we] give the same truth-conditions to 'P or anyway
Q' as are standardly given to 'P or Q' (Jackson. p.
582).

Similarly. despite the fact that neither 'or at least' nor
'nevertheless' bears up well under commutation. we do not hesitate to
assign standard truth-functional meanings to them as connectives.

Jackson also offers a second sort of evidence in support of his
pragmatic dissolution of so-called failures of transposition. He

points out that it is just the predicted pattern of probabilistically

57
appropriate signalling in the premise and probabilistically
inappropriate signalling in the conclusion which seems to characterize
problem cases in inferences involving conditionals.
Putative counterexamples to Contzapgaitign are all ones
where Pr(qu/p) = Pr(q/p) is high. [making (P+q)
assertable.] and Pr(-qD-p/-q) = Pr(-p/-q) is low [making
(-p+-q) unassertable].

For example. the probability of Carter not being
reelected by a large margin given he is reelected may be
high when the probability of Carter not being reelected
given he is reelected by a large margin is minimal [1].
Accordingly. we can explain our reluctance to assert 'If
Carter is reelected by a large margin. then Carter will
not be reelected' even when we are happy to assert 'If
Carter is reelected. then it will not be by a large
margin' in terms. not of the first being false and the
second true. but in terms of what is signalled by saying
the first being false and what is signalled by saying
the second being true (Jackson. p. 582).40

Jackson has thus supported his proposal by evidence that it
explains speakers' intuitions not only with regard to the assertability
of particular conditionals but also with respect to the validity of
patterns of inference and preservation of extrasystematic analogues of
various logical properties. In each case. he believes he has dealt
with discrepancies between such judgments and the deliverances of
formal logic under the assumption of ET with greater success than could
an orthodox conversationalist.

Both Lewis' and Jackson's proposals are attempts to accommodate
Adams' persuasive thesis that the assertability of (p+q) tracks Pr(q/p)
without giving up ET. Appiah is unpersuaded by either of them. Their
shortcomings. he believes. warrant abandoning the search for a
truth-conditional semantics. In the following chapter we shall look at

his objections.

Chapter 6.

Appiah's Criticisms

Before we pick up Appiah's criticisms of Lewis and Jackson it
will. I think. be useful to review briefly the context in which I have
suggested that they be considered. If I am correct. this is how things
stand. We are considering the claim that the ordinary English
indicative conditional. (p+q). has the same truth conditions as does
the material conditional. (qu). It counts toward our endorsement of
ET that. in company with some auxiliary theoretical considerations. it
enables us successfully to construe the inferential practices and
beliefs of competent language users. This. in turn. is simply to say
that if such an ensemble is sufficiently helpful in making sense of the
phenomena of interest. we may reasonably say that the truth conditions
of the ordinary English conditional at: those of (qu). (What else.
after all. could be meant by such a claim?) To review this is. of
course. just to remind ourselves that every term is a theoretical term.
even the familiar predicates of everyday life. and that theoretical
claims do not meet the world and the demands of logic singly but in
company.

We may remain neutral. if we wish. as between two accounts of
precisely how overall theoretical adequacy is related to the truth of
individual claims: that it is so related follows either from a purely
pragmatic view of truth. on which the two are taken to be the same
thing. or from a correspondence view of truth which allows that
goodness of theory provides us with evidence for the truth of its
tenets. In either case. what we are we are engaged in is the
evaluation of a theoretical framework which includes ET and. in
particular. some auxiliary pragmatic theory. in a context of phenomena
more or less successfully construed within that framework.

Such evaluation. in turn. requires invocation of canons of
rational theory choice. Although we are (to put it mildly) in no
position to lay these out exhaustively. some generally acknowledged
candidates include the past track record of the theory in accounting
for related phenomena. its conceptual economy. its cotenability with
other well-regarded theories in the domain of interest and its promise

58

59
with regard to providing solutions to standing puzzles. Observations
which are inexplicably inconsistent with theoretical prediction and/or
reliance upon clobbered-together 'ad hoc' explanations of such
anomolous cases are generally taken to count against a theory. Last.
but by no means least. it is often urged that the relative
attractiveness of competing theories in these regards also count in
such decisions.

It is. I think. useful to keep this in mind as we look at Anthony
Appiah's criticisms of Lewis' and Jackson's attempts to provide such a
theoretical context for ET. For one thing. this way of looking at what
is going on allows us to bridge the gap between Appiah's catalogue of
supposed deficiencies in Lewis' and Jackson's work. on the one hand.
and his concluding counsel that we bite the bullet with a good grace.
on the other. It is only by assuming that Appiah is inviting us to
assess the relative merits of two competing research programs that his
criticisms could reasonably be seen as relevant to such a conclusion.
This becomes apparent when we note what kind of argument Appiah is
clearly RQL attempting to establish. He is not. for example.
attempting to offer us a demonstration that pragmatic theory is. in
principle. doomed to failure (in the way in which. for example.
Chomsky's followers set themselves to demonstrate the utter
impossibility of accounting for language acquisition with any finite
state theory or in the way in which ethicists have argued against the
possibility of deriving a theory of value from purely naturalistic
considerations). Criticisms of this sort--arguments against the very
possibility of success of some whole category of theory--lead in an
instantly recognizable way to calls to abandon ship. Appiah does not
offer this sort of argument. however. The route to his conclusion
must. therefore. be a different one. It would be uncharitable to
suppose that he envisages himself as persuading us with the induction
that a pragmatic strategy didn't work for Grice nor for Lewis nor for
Jackson so it's not going to work for anybody: more plausibly. we may
suppose that Appiah is simply asking us to choose between Adams'
program and that of the pragmatic defenders of ET on much the same
grounds that we might be asked to choose between any two competing

research programs.41

60

With this in mind. we may proceed to look at the reasons Appiah
offers for urging rejection of the pragmatist program and then go on to
ask whether he has been persuasive on this score.

Let us look first at Appiah's criticisms of Lewis. They fall into
two main parts. Lewis. it will be recalled. wishes to show that the
difference between the probability associated with (p+q) on the
assumption of ET and the conditional probability which gives a measure
of the assertability of (pxq) can be derived from Gricean
conversationalist considerations. Lewis proposes that this difference
--expressed as Pr(-p)Pr(-q/p)--represents a measure of dimunition in
assertability due to the misleading pointlessness of conditionals whose
probability of truth is very largely due to their almost-sure-to-be-
false antecedents. Appiah argues. first. that Lewis' derivation of
this difference from conversationalist considerations is unsatisfactory
and. second. that even if it were.

it would not provide a satisfactory explanation in terms
of conversational implicature and consistent with the
view that conditionals are material conditionals. of the
fact that the conditional has the odd assertibility rule
[Adams proposes] (Appiah. 1983. p. 29).

Appiah's argument against Lewis' derivation is a complicated one.
These are. I think. its major themes. First. Appiah finds in Lewis'
text two different characterizations of the conditions which ought to
lessen the assertability of (p+q).

On one hand he suggests that we ought not to assert the
conditional (ADC) if
a) it is probable hat
b) its probability of truth consists mostly of its
probability of vacuous truth.

(Call this the first approach).
On the other. he suggests that we ought not to assert it if
a) it is probable and
b) the probability P(-A) of vacuity is high. . .and
. . .the probability P(-C&A) of falsity is a large fraction
of the probability P(A) of non-vacuity.

(Call this the second approach) (Appiah. 1983 p.29.

61
Appiah's ellipses).

Appiah argues that these two characterizations lead us to
demonstrably different results. Second. Appiah notes that at least one
plausible representation of the dimunition of assertability called for
by the first of Lewis' readings of Gricean doctrine does not yield the
required difference but. rather. a factor which can be shown to be
unequal to it in all of the cases of interest to us. Thirdly. Appiah
thinks that for the correction factor which Lewis offers to be capable
of representing the relevant Gricean considerations. Lewis must endorse
an untenable combination of views. Finally. Appiah thinks that there
is pervasive difficulty with Lewis' notion of what it means to say that
an agent believes S predominantly because of believing T.

Let me try to prune this a bit.

First. although it takes up considerable of Appiah's attention. I
shall set aside the question of what the proper analysis of the notion
of believing S predominantly because you believe T is (Appiah. 1983. p.
34). It is my impression that explication of Appiah's notion of
analysis would take us a good deal further afield than we want to go.
Moreover. whatever the results which Appiah seeks. the suggestion that
our assessment of a theoretical program must wait on getting straight
about our concepts of causality and explanation seems well worth
resisting.

Secondly. I shall not pursue the question of whether Lewis really
considered the second approach to be an explication of the first in the
sense of being logically equivalent to it or whether (as seems more
likely to me) what Appiah takes to be a second approach is simply
Lewis' elaboration of what he said to begin with. Since the correction
factor which Lewis finally presents includes the term Pr(-q/p). I shall
assume that he was not wedded to a pure vacuity version of the
conditions which diminish assertability. (This seems the more likely
because the maxim of quality is so central to Gricean doctrine that
ignoring the question of falsity would seem curiously uncharacteristic
of any worker within the tradition.)

Appiah's most interesting objection. it seems to me. concerns
Lewis' right to the derivation of the correction factor which he

actually proposes--the one that closes the gap between Pr(qu) and

62
Pr(q/p).
Appiah tells us that the
intuitive Gricean idea of what is wrong with uttering a
material conditional whose antecedent is false is [1]
that the conditional is not only vacuous . . . but [2]
that if it were hat vacuous it would not be true
(Appiah. 1983. p. 32. my stress).
The first of these considerations gives us the first factor in the
correction--Pr(-p)--and to this Appiah raises no objection. What
bothers him is how Lewis gets to represent [2]. the fact that if (qu)
were not vacuous it would be false. by way of the second factor in the
correction--Pr(-q/p). which is to say. by the ratio Pr(-q&p)/Pr(p).
There is now an obvious question: why should the fact
that my P(-C&A)/P(A) is large show that I think the
material conditional would not be true if its antecedent
were true?

The answer must surely be that this ratio is
equivalent to P(-(ADC)/A): and the reason that thia
captures the idea that the conditional would be
disbelieved if the antecedent were believed. . .[must
be] that probabilities should change by
conditionalization. . . .[For if they do.] the agent
would come to believe that the material conditional was
false if he came to believe its antecedent was true just
in case P(-(ADC)/A) is high (Appiah. 1983. p. 33).

But. says Appiah. given Lewis' views about (p+q). he is in trouble
if he tries to derive his correction factor along these lines. More
precisely. if Lewis avails himself of the attractive principle that
beliefs change by conditionalization and continues to maintain that
(p+q) has the truth conditions of the material conditional. he will
find himself in the position of having to come up with an explanation
of our “strong intuition. . . that if someone believes that if A then
C. and comes to believe A (while having no other direct evidence about
C). he will come to believe C.“ For. says Appiah. on Lewis' account.
this intuition will now be incorrect (Appiah. 1982. p. 330).

The reason for this is as follows. If the conditional is a

63

material conditional then a speaker can assign ever so high a
probability to (qu)--and hence to (p+q)--while Pr(q/p) is ever so low.
But if beliefs change by conditionalization. then coming to believe p
will not lead such a speaker to assign a high probability to q. It
follows. says Appiah. that on Lewis' views. ”someone tan believe ADC
and not be so disposed that if he came to have evidence that A he would
come to believe that C"(Appiah. 1982. p.330). And this is a problem
for Lewis. says Appiah. because our intuitions strongly resist such a
possibility.

Anyone who has tried to teach propositional calculus to

an intelligent student knows that it is a hard business

getting people to accept that it is all right to believe

a conditional purely on the grounds that its antecedent

is false or its consequent true (Appiah. 1983. p. 331).

Appiah's first objection to Lewis. then. is that his derivation of
the correction factor is deeply flawed. A dimunition factor based
entirely on considerations of vacuity due to falsity of the antecedent
cannot. by itself. give us the required correction: a factor which can
give us the required correction reflects Gricean doctrine only when it
is interpreted in a way which raises major difficulties for a theorist
of Lewis' persuasion.

Appiah's second criticism of Lewis is that. even were its
derivation to be acceptable. the correction factor would not do what he
claims. Appiah notes that Lewis is relying on something like

(R) Do not utter a sentence 8 in circumstances where.
for some R.

(a) R entails S. and S does not entail R

(b) R is relevant
and (c) R is assertible (Appiah. 1983. p. 332).

This rule. however. adoes too much. . . . (R) rules out not only
the assertion of conditionals with vacuous antecedents. but the
assertion of those with vacuous consequents alsoI (Appiah. 1982. p.
333). Lewis has no explanation. Appiah argues. of

why he does not [also] introduce a factor which
discounts for the unassertibility of a conditional which

should arise when its consequent is believed true (for C

64
[also] entails (ADC)) (Appiah. 1983. p. 35).

Appiah thinks that this problem infects any attempt to account
for the vacuity of the conditional with vacuous antecedent in terms of
a form of the maxim of quantity (Appiah. 1982. p. 334). Not only does
Lewis' argument fail. he thinks. but so must a whole class of
conversationalist defenses.

Although Appiah does not think that Jackson's defense of ET shares
this weakness. he does not find it any more successful. Jackson is not
going to get into the same trouble as Lewis because he is not relying
exclusively on conversational principles to take up the slack between
speakers' intuitions and the deliverances of logic under the assumption
of ET. As Appiah points out. Jackson proposes that the assertability
rule is a aghyantignal and not a conversational constraint (Appiah.
1982. p. 335). There is no demand that conditionals with vacuous
consequents behave in the same way as those with vacuous antecedents:
each is governed by applicable local ordinances rather than both being
constrained by the same general law. Jackson's difficulty. Appiah
argues. is. rather. that his assertability rule dangles free from any
essential connection with the truth conditions he postulates for (p+q).
Not only do the truth conditions of (qu) fail to play any essential
role in explaining the assertability rule of (p+q). but. worse yet.
there is no reason to believe that the truth conditions of (qu) even
are those of (p+q). Appiah argues this by contrasting the case of
(p+q) with that of 'p but q'. a parallel suggested by Jackson.

Jackson tells us. says Appiah. that what is conventionally
signalled by use of the indicative conditional construction bears the
same relationship to the truth-conditions of (qu) as what is
conventionally conveyed by 'but' bears to the truth-conditions of '&'.
Just as an appropriately high probability of the truth of (p&q) is
necessary but not sufficient for the assertability of 'p but q'. so an
appropriately high probability of the truth of (qu) is necessary but
not sufficient for the assertability of (p+q). So far. so good. There
is. also. however. a

striking disanalogy between the two cases. . . .
[T]he meaning of 'but' can be broken up. so to speak.

into two independent components. It must be the case

65
for 'S but R' to be assertible. both that

(a) the speaker believes that S and R. and
that

(b) the speaker believes there is some
conflict between the fact that R
and some prior expectation (Appiah. 1982.
pp. 336-7).

It is perfectly possible for (a) to hold without (b) being the
case and vice-versa. When we look at the ordinary English indicative
conditional. however. we do not find such independence: whenever
Pr(qu/p) is high. so is Pr(qu). Appiah therefore concludes

So far as I can see. the truth conditions on Jackson's
view neither give you the logic of the conditional. nor
play any essential role in explaining the assertibility
rule. In the case of 'but'. the truth conditions seem
to be essential to explaining the assertibility rule.
In the absence of even this role. the truth conditions
are idle machinery (Appiah. 1982. p. 337).

Jackson might contend. Appiah tells us. that truth conditions
really 31: essentially involved in the assertability rule for (p+q)
insofar as

we have a use for a form of words which expresses the
fact that we not only believe the material conditional.
but would continue to do so if we believed its
antecedent true. But the state that we thus express is
.heliexina the material.eonditional_and.heinx.diannaed to
eontinnetodoaoelenifnehelimdtheanteeedent:
and it is not at all clear why we should regard the
truth conditions of the sentence we use to express thia
state as those of the material conditional (Appiah.
1982. p. 337).

That there is zafatanaa to the truth conditions of (qu) in our
explanation of (p+q) should not lead us to conclude that the truth
conditions of (qu) ate those of (p4q). says Appiah (Appiah. 1982. p.
337).

Appiah finds these criticisms sufficient to ask us to abandon

66
pragmatic defenses of ET and take up with Adams' proposal instead.
which is to say. to abandon truth-conditional semantics generally.
Ought we to accept the bid? I have already suggested that I find
Appiah's pessimism with respect to the prospects of pragmatic theory
unwarranted and it is to this that I shall now turn.

Let me begin with what Appiah takes to be the more damaging of his
two major criticisms of the quantified conversationalist approach.

If we cannot account for the vacuity of the conditional
whose antecedent is disbelieved in a way that does not
make the conditional with the vacuous consequent
unacceptable also. Lewis' argument fails (Appiah. 1982.
p. 334).

Lewis himself draws our attention to this issue--a fact which
Appiah gets around to acknowledging in his second article. First.
Lewis thinks that it is just as well that his correction factor does
ngt include an additional dimunition for vacuous consequents because.
as it turns out. conditionals with almost-sure-to-be-true consequents
appear to be quite adequately assertable under at least some
circumstances. ('I'll probably flunk. and it doesn't matter whether I
study; I'll flunk if I do and I'll flunk if I don't.') Why there
should be such asymmetry of assertability. however. strikes Lewis as a
puzzle.

The best I can do to account for the absence of a marked
dimunition in the case of the probable consequent is to
concede that considerations of conversational
pointlessness are not decisive. They create only
tendencies toward diminished assertability. tendencies
that may or may not be conventionally reinforced. In
the case of the improbable antecedent. they are strongly
reinforced. In the case of the probable consequent.
apparently they are not (Lewis. p. 139).

This does not satisfy Appiah. who comments

It is not enough to say simply that conversational
pointlessness is not decisive: in the absence of an
account of what it decisive we do not know why the

assertibility of the conditional goes by the conditional

67
probability (Appiah. 1982. p. 334. my stress).

Clearly. Lewis' case would be stronger if he could suggest the
sort of considerations which might be at work to diminish the corrosive
effect on assertability of almost-sure-to-be-true consequents. One
possibility close at hand is a suggestion by Jackson:

Neither the fact that Pr(-p) is high nor the fact that
Pr(q) is high is sufficient for Pr(qu/p) being high [as
it must be for (p+q) to be assertable]. The reason our
reluctance is less marked in the case of asserting (p+q)
on the basis of our certainty that q [than in the case
of asserting it on the basis of our certainty that 'p].
is that Pr(q) being high together with p and q being
probabilistically independent in sufficient for
Pr(qu/p) being high (Jackson. p. 581).

That is. if Pr(q) = Pr(q/p) and Pr(q) is high. Pr(q/p) is also
high. But Pr(q/p) = Pr(qu/p) and. as we have seen earlier. if
Pr(qu/p) is high. so also is Pr(qu). Hence. if Pr(q) is high and p
and q are probabilistically independent. (p+q) is both highly probable
and robust with regard to p. which is to say. assertable.

Are we entitled thus to augment Lewis' theory with Jackson's? I
cannot see why not. Lewis obviously envisages the Operation of
conversational constraints as only a part of the whole story and
Jackson explicitly offers his hypothesis about robustness to
supplement. not to replace. Gricean doctrines of conversational
implicature. Why could not both sorts of constraints be at work
simultaneously. producing a complex surface texture of differences in
assertability? Moreover. I shall be suggesting shortly that there is a
very natural way of seeing Jackson and Lewis as presenting
complementary aspects of a generalized Gricean doctrine. I tend.
therefore. to side with Lewis in believing that his inability to
explain the asymmetry of assertability between conditionals with
almost-sure-to-be-false antecedents and those with almost-sure-to-be-
true consequents by way of (R) alone is not nearly so fatal a flaw as
Appiah takes it to be.

What of Appiah's other major criticism. that Lewis cannot. without

embarassment. give a properly Gricean gloss to the second component of

68
his correction factor? Appiah's criticism depends on two assumptions.
The first is at least questionable: the second. I have already argued.
is scarcely tenable. For the first. it will undoubtedly have been
remarked that Appiah's derivation of Lewis' difficulties in this regard
depends upon accepting the assumption that to believe that 'if p then
q' is just to believe that (qu). Believing that (qu) is surely a
necessary condition for believing that (p+q). but I am not at all
convinced that it is the same thing. I have at least a suspicion that
individuating beliefs is more complicated than that. Is the belief
that Mary is poor but Mary is honest the same as the belief that Mary
is poor and Mary is honest? What. precisely. does the belief that as a
philosopher Smith is a good pastry chef amount to? And what do I
believe when I believe that Charles has a heart of gold? I do not have
any suggestions as to how we ought to characterize (analyze?) the
belief that 'if p then q' or. more generally. how implicatures are
related to beliefs but I doubt that the matter is as cut and dried as
Appiah's treatment suggests.

Second. even if we accept Appiah's argument that Lewis' derivation
of the second component of the correction factor really does bring him
nose to nose with stubborn intuitions contrary to his commitments. why
ought this to be so daunting? A conversationalist is. after all. in
the business of providing explanations of discrepancies between the
deliverances of logic under the assumption of ET and the linguistic
intuitions of assorted students and colleagues. In this particular
case. Lewis can. once again. appeal to Jackson's doctrine of robustness
and say that the reason we are persuaded that someone who believes if p
then q and comes to believe p will also come to believe q is that under
the conditions where competent speakers offer and accept (p+q). the
applicability of modus ponens is. so to speak. guaranteed. That is
what the constraint on robustness is all about. Appiah can hardly
object to this sort of explanation: we have already seen that Adams.
whose program he recommends to us. has recourse to just such a
conversationalist strategy in explaining why competent speakers
regularly take to be valid inference forms (such as contraposition)
which. on his account. are not probabilistically sound. (That is what

conditions of partial rationality are all about.)

69

It is my impression that Appiah takes the (supposed)
counterintuitive consequences of Lewis' commitments so seriously
because he is assuming that there is something epistemically special
about linguistic intuitions. especially. perhaps. his own. “I cannot
myself find cases. he tells us. where I think it is plausible to
suppose that someone believes that if A then C. where p(C/A) is low.“
(Appiah. 1982. p. 331). This may well be true but I do not see why we
need conclude from it more than that either Appiah's treatment of
believing that 'if p then q' is mistaken or that his linguistic
intuitions have been powerfully shaped by the rules of discourse. In
either case. Appiah's intuitions may be as much evidence for pragmatic
claims as against them. I am therefore inclined to think that if Lewis
really is in any trouble producing prOper Gricean credentials for
Pr(-q/p). it is not nearly so deep as Appiah thinks.

Neither of Appiah's major criticisms of Lewis. then. seems to me
anything like lethal. They do. however. make Jackson's contribution to
the cause seem more important than might originally have appeared to be
the case. We should. therefore. take a careful look at Appiah's
criticisms of his proposal.

Appiah tells us that he is sceptical about Jackson's approach.
Perhaps by this he means that he does not find its difficulties as
flagrant as those he detects in Lewis. Indeed. most of the space
Appiah devotes to Jackson is to an exposition of his proposal rather
than to detailed criticism of it. The criticism Appiah does offer
seems directed primarily at the claim with which Jackson closes his
article.

Why not simply say the following about (P-Q)? We can
distinguish truth conditions from assertion conditions.
The truth conditions for (P+Q) are those of (PDQ)
. . . . And the assertion condition for (P+Q) is that
Pr(Q/P) be high. . . . End of story.

My reason is that conjoining is not explaining.
The problem is to explain one in terms of the other. . .
. I have tried to show how a plausible thesis about
(P+Q)'s truth conditions. namely the Equivalence thesis.

can. in the light of the importance of robustness for

70
assertability. explain tha plausible thesis about
(P+Q)'s assertion condition. namely Adams' thesis
(Jackson. p. 589).

As we have seen. Appiah argues that Jackson has done nothing of
the sort: whereas the truth conditions of (p&q) can be invoked to help
explain the assertability of 'p but q'. the truth conditions of (qu).
he tells us. are not essential to explaining the assertability rule for
(p+q). and hence are idle machinery. Indeed. Appiah sees no reason to
believe that the truth conditions of (qu) are those of (p+q) in the
first place. As we have seen. each of these criticisms involves
contrasting the presumably unproblematic case of 'p but q' with the
supposedly troublesome one of (p+q). In what follows. I shall be
arguing that insofar as Appiah gives us any indication of (1) what must
be the case for truth conditions to figure essentially in an
explanation of assertability conditions. or. (2) what must be the case
for a set of conditions to be the truth conditions for a type of
sentence. he gives us no reason to believe that there is a difference
in principle between the case of 'p but q' and that of (p+q). To be
consistent. Appiah must either reject both accounts or neither.

Appiah's suggestion. it will be recalled. is that the first
difference between the two cases is that we can. so to speak. decompose
the meaning of 'but' into two independent components. whereas

it follows from the assertibility rule. . . algae that
the indicative conditional is assertible only if the
speaker believes the material conditional (Appiah. 1982.
p. 337).

Now this seems to me largely a matter of how you want to give the
assertability rule in each case. If we wish. we may say that for 'p
but q' to be assertable. it must be the case that

(a) the speaker believes that (p&q). and
(b) the speaker believes that the truth of p usually
diminishes the likelihood of the truth of q. and
(c) the speaker believes that (p&q) is robust with regard
to p.
It surely now follows from the assertability rule alone that 'p but q'

is assertable only if the speaker believes that (p&q). if the

71
assertability rule comprises (b) and (c). (If Appiah takes it to
include all the constraints on assertability--(a) and (b) and (c)--the
assertability of 'p but q' will. of course. guarantee that the speaker
believes that (p&q) even in the form which Appiah gives above. But
that would be silly.)

We now have an assertability rule for 'p but q' which is
sufficient to guarantee that the speaker believe that (p&q).
Presumably. Appiah would now find the truth conditions of (p&q)
inessential to explaining the assertability of 'p but q'.

0n the other hand. we may. if we wish. describe the assertability
conditions for (p+q) as follows. It must be the case for (p+q) to be
assertable both that

(a) the speaker believes (qu) to be highly likely. and that

(b) the speaker believes that the probability of (qu) is

substantially undiminished by the truth of p.

Jackson would have no objection at all to treating the two
conceptual components of robustness as distinct. (See. for example. his
comments on p. 569.) Indeed. it is somewhat puzzling why he does not do
so to begin with. We now have (a) and (b) independent of each other
and. presumably. Appiah would now say that there is no greater bar to
our finding the truth conditions of (qu) essential to explaining the
assertability of (p+q) than there is to finding the truth conditions of
(p&q) essential to explaining the assertability of 'p but q'. There is
thus no difference in principle on Appiah's account between the case of
'p but q' and that of (p+q) with regard to the eligibility of their
truth conditions to play what he calls an essential role in explaining
their assertability conditions.

We have. I think. dealt with Appiah's first criticism of
Jackson--that even if the truth conditions of (qu) were those of
(p+q). they could not figure essentially in an explanation of the
assertability rule for (p+q).

Appiah's second criticism is that Jackson has. in fact. no right
to say that the truth-conditions of (qu) ate those of (p*q). 0n
Jackson's account. says Appiah. the state that we express when we
assert (p+q) is

(A): believing the material conditional and being

72
disposed to continue to do so even if we believed
the antecedent (Appiah. 1982. p. 337. stress
removed).
But. Appiah tells us.
it is not at all clear why we should regard the
truth-conditions of the sentence we use to express thia
state as those of the material conditional (Appiah.
1982. p. 337).

It is even less clear (to me. at any rate). what Appiah would take
to be appropriate grounds for making such an ascription. He offers
without apparent objection what he calls the standard account of 'but'.
which has it that the truth conditions of

(BUT) John is coming. but Mary is not
are that John is coming and Mary is not (Appiah. 1982. p. 336).

It would therefore appear that Appiah is willing to countenance
the claim that the truth-conditions of 'p but q' are the same as those
of (p6q). Surely. however. the state that we express by 'p but q' is
something along the lines of

(B): believing (p&q) and believing that q is usually
unlikely given p and being disposed to continue
believing (p&q) even so.

And (B) would seem as readily distinguishable from believing (p&q)
as (A) is from believing (qu). Why does Appiah see a problem in
ascribing one set of truth-conditions but not the other? If there is a
difference in principle between the two cases. Appiah does not tell us
in what it consists. If. on the other hand. Appiah sees no difference
and wishes to resist all such ascriptions of truth-conditions--a
position which he may very well favor--he owes us an account of how he
proposes to deal with the (by now equally standard) arguments for the
distinguishability of assertability and truth conditions. At the very
least. I do not think Appiah gives us grounds for thinking that the
truth-conditions of (qu) are any less plausibly the same as those of
(p+q) than are the truth-conditions of (p&q) the same as those of 'p
but q'.

Even if Appiah is not very forthcoming on the subject. it is. of

course. still the case that we need at least some regulative notions of

73
what ascriptions of truth-conditions require. If the approach which I
have been taking so far is correct. the answer to the question he
raises--why should we take the truth-conditions of (p*q) to be those of
(qu)?--is. as I have suggested earlier. quite simply that this
ascription is the one made by the best available theory in the domain
under consideration. That is. taken together. ET and the premises of
an auxiliary pragmatic theory (along with the odd psychological
proposition or two) provide us with the the best account we have of the
inferential beliefs and practices of competent language users. I have
already presented arguments that this ensemble does. indeed. allow us
to account for a wide range of such phenomena. Two final
considerations remain to be discussed. however. The first is the
question of the status of alternatives to ET-plus-pragmatic theory: the
second is its own prospects for future develoPment. Both of these have
been proposed as legitimate concerns in the context of rational theory
choice. It is to these issues that we now turn.

If. as I have suggested. the acceptability of ET is a matter of
the adequacy of the theoretical ensemble in which it plays a role and
if that. in turn. is to be assessed by the criteria which count in any
decision of this sort. then it becomes relevant not only how well ET at
tie. are doing but also how well their competitors. if any. are faring.
Let us assume that Appiah is correct in assuming that the most
attractive alternative to ET is the claim that conditionals do not have
truth-conditions (and a fortiori do not have those of the material
conditional)--a central tenet of Adams' program. What seems to count
most strongly in favor of this proposal is not any good argument on
Adams' part to this effect--he simply invites the reader to note the
lack of clear criteria for the application of 'true' and 'false' to
conditionals with false antecedents and leaves it at that--but. rather.
the collective force of his arguments that probabilistic soundness is
the appropriate criterion for inference forms and that the measure to
be associated with indicative conditionals in predicting their
assertability is Pr(q/p). Just as ET cannot be evaluated apart from
the theoretical context in which it appears. so the proposal that ET is
untenable is persuasive only to the extent that we find attractive an

entire theoretical framework in which it is ensconced. In either case.

74
what we are doing is addressing a set of claims and a set of successes
and problems.

If Adams' entire program is the relevant competition. then. how
well is it doing? What bears noticing. I think. is the fact that Adams
raises. but does not answer. the question of what a non-truth-
conditional semantics would be like. He makes no bones about this:
what lies ahead. he tells us. is likely to be nothing like what we have
been doing and that is substantially all we know about it. Except that
Adams relishes the prospect and Lewis clearly does not. they would seem
to agree in reporting the current lack of any clear alternative to
traditional semantics. We should. therefore. take seriously. I think.
what Lewis characterizes as an inconclusive objection to endorsing the
hypothesis of the non-truth-conditionality of indicative conditionals.

[It] requires too much of a fresh start. It burdens us
with too much work still to be done. and wastes too much
that has been done already. So far. we have nothing but
a rule of assertability for conditionals with truth-
valued antecedents and consequents. But what about
compound sentences that have such conditionals as
constituents?. . . Either we need new semantic rules

. . . or else we need to explain away all seeming
examples of [such] compound sentences (Lewis. pp.
136-7).

If rationality in theory choice requires us to take into account
the relative strength of competing theories. consensus that there is a
lack of any well worked-out alternative or even a clear indication of
how to get started on one would seem to count strongly in favor of
ET-and-pragmatic theory.

In addition. I think it is also worth at least suggesting that
Jackson's program may have theoretical virtues of which its author does
not himself seem fully to be aware. Seen in a properly general and
Gricean perspective. Jackson's notion of robustness seems capable of
being an element of a much more general pragmatic theory than he
indicates and. thus. of having count in its favor considerations of
breadth and economy for which it might otherwise not receive credit. I

should like rather briefly to sketch such a wider theoretical network.

75

One obvious question with regard to Jackson's notion of robustness
is. of course. whether we can give a general explanation of the
direction in which robustness must hold in particular cases. Jackson
tells us. for example. that (p+q) signals the robustness of (qu) with
regard to p because this is what is required for the very useful modus
ponens argument to go through. He is. however. less forthcoming with
regard to other cases. He tells us. for example. that we most happily
field disjunctions when they are robust with regard to the negation of
each disjunct but gives only the sketchiest of suggestions why
robustness of this particular sort might be demanded. Having proposed
'p or q' and discovered not p. he tells us. we are not pushed to
abandon the disjunction if it is appropriately robust. But why we
should want (need?) to salvage the disjunction?

I think we can. without great difficulty. discern the shape of a
general rule. Jackson himself is on the brink of so doing when.
commenting on Lewis' unassertable (W): You won't eat that mushroom and
live. he points out that (W) is misleading giyan‘tha‘ag;t_g£,lh£atahaa
in nhith it.i§,hgnnfi,tg,he employed. We are instantly put in mind of
Grice's second derivation of the implicature of IC and his proposed
new type of generalized implicature: i.e..

the implicature carried by the employment of certain
forms of expression that those conditions are fulfilled
which would haya to be fulfilled if the form of
expression were being employed for those purposes which
constitute their matiat or raiaon.dletze (Grice. Lecture
IV. p. 17).

Locutions liable to enter into particular sorts of inferential
reasoning--either because of context or because of their form--
implicate. so Grice proposes. that all is well for that sort of
inference. In the mushroom case. it is the likelihood that our
listener will employ taggthat two salient premises to draw a conclusion
which. on this account. mandates the constraint (and thus generates the
implicature) that these premises be cotenable (and makes it illictly
tricky to assert them if they are not). We might want to say that in a
parallel way 'but' and 'nevertheless' conventionally implicate that

both conjuncts of the statements in which they figure are (despite

76

normal expectations to the contrary) available at the same time for
such inferential use: their cotenability has been explicitly and
conventionally underwritten. It might further be suggested that when
we wish to advance a similar guarantee in the case of a state of
affairs which. for all we know. may or may not hold. we use the 'even
if. . .' locution: 'p even if q' implicates the availability of p for
inferential use whether q holds or not. where p would. ordinarily. be
unlikely in the case that q. and thus be assumed to be unavailable.

It does not seem too much to say that Jackson has (quite
independently. to judge by his footnotes and citations) rediscovered
Grice's second sort of conversational constraint and observed an
interesting consequence of it which Grice himself did not notice.
Because language serves to exchange information. we are governed by the
maxims of conversation and. accepting their suzerainty. we derive the
well-known conversational implicatures. Because language also serves
as a structure which facilitates the drawing of inferences. we are
equally bound by another set of constraints which. in their turn. give
rise to additional implicatures. To use (p*q) would. thus. standardly
come to implicate not only IC. as Grice saw. but also the robustness of
(qu) with regard to p. as Jackson shows. (Jackson talks about
'signalling' or 'indicating' rather than implicating. but it is clear
that what we have here may be considered a generalized implicature. It
is. perhaps. not a generalized aghyataatighal implicature in what has
become the standard sense of the term. however.--it does not invoke the
usual conversational maxims--and Jackson's scruples on this score are
certainly understandable in the light of widespread pressure to
assimilate generalized conversational implicatures to conventional
ones.)

We can also come to see. from this perspective. why 'p or q'
implicates. as Jackson tells us. the robustness of the disjunction
symmetrically with respect to the falsity of each disjunct. giving rise
to the sense that it is wrong to offer 'p or q' on the strength of our
certainty that p (or that q) alone. Let me take a moment to lay this
out.

On Grice's view. 'p or q' takes its place beside (the presumably

more basic) 'not both not p and not q' because we find ourselves faced

77
with a particular sort of inferential task--the need to answer various
(affirmatively phrased) wh- questions ('Who killed Cock Robin?') and
the necessity of making do in our planning with interim answers to
such questions ('Well. we have several suspects. . .').

Under such conditions. says Grice. it is more economical
typographically and perhaps in terms of concepts explicitly mentioned.
to use the schema 'p or q' than to use 'It is not the case that both
not p and not q' (Grice. Lecture IV. pp. 14-15). To use 'or' would
thus come standardly to implicate that we are faced with just such a
situation--that is to say. one in which we are unsure of the truth both
of p and of q. Once the disjunction had come to convey this
implicature of uncertainty with respect to both disjuncts. it would be
misleading to field 'p or q' on the basis of certainty that p (alone)
or that q (alone)--that is. on truth-functional grounds alone. If we
are uncertain of the truth of p and uncertain of the truth of q. in
turn. we do not have truth-functional grounds for the disjunction and
hence. to be in accord with the maxim of quality. must have non-truth-
functional grounds for it. We would thus come to see 'p or q' as
capable of surviving the falsity of either one of its disjuncts. which
is to say. as signalling symmetric robustness with regard to the
falsity of each of its disjuncts. (We could equally have derived this
from 'Assert the stronger'. of course.)

Reference to the special use in reasoning for which a locution is
developed and selected can also shed light on a puzzle to which Jackson
calls our attention but which he does not (as far as I can tell) try to
solve--the curious asymmetry between our intuitions with regard to the
equivalence of 'V' and 'or'. on the one hand. and 'D' and 'if. .
.then'. on the other. Grice had already noted its inability to explain
a closely related asymmetry between 'or' and 'if. . . then' as a
shortcoming of his first and better-known account of the derivation of
the implicature of IC conveyed by the indicative conditional.

That the account so far given does not go far enough is
shown by the following objection. “The account you have
so far given could be applied not only to 'if p then q'
but also to 'either p or q'. It would. if accepted.

explain why someone who advances either a conditional or

78
a disjunctive would normally implicate that there are
non-truth-functional grounds for saying what he has
said. But there is an important difference between
conditionals and disjunctives which remains unaccounted
for. namely that whereas there seems to be no general
difficulty in the idea that a disjunctive statement
which has been adxanaad on non-truth-functional grounds
can be tgnfizmed truth-functionally. by establishing one
of the disjuncts. the parallel idea with respect to
conditionals is not acceptable: except perhaps in some
very special cases. we do not regard the mere discovery
that it is not the case that p. or the mere discovery
that q. as confirming a statement that if p then q'

(Grice. Lecture IV. pp. 6-7).

Grice tells us that he prefers his second account of how (p+q)

comes to carry the generalized implicature of IC because it allows him

to account for just this asymmetry. His explanation of the difference

with regard to our intuitions about confirmation in the two cases

invokes the doctrine of the matiat of a locution and goes as follows.

First. Grice suggests that we will be comfortable saying that a

statement has been tanfitmed_when we see that it could. indeed. have

been put to the special use in reasoning for which it was evolved and

selected.

A disjunction. thought of as being put to 'planning'
employment. is regarded as confirmed by establishing
either disjunct: for this. after the planning has been
done. will show that a disjunctive statement has done
its job (we haven't wasted our time) (Grice. Lecture IV.
p. 19).

On the other hand. in the case of a conditional.

[T]o discover that 'qu' has the value TT [i.e.. that
both p and q are true] will show. . . [that] as employed
in MPP either [it] has done its job. or would have done
its job but for the 'accident' that the discovery that p
did not precede the discovery that q. But to discover

that not-p would be to discover that there was no job

79
for it to do. . . and to discover natal: that q. would
leave it open whether there was a job for it to do
(Grice. Lecture IV. p. 19).

Thus. unlike the case of (qu). where we welcome equally as
confirmation either mode of truth-functional validation.

Insofar as 'qu' is put to the employment which is its
talagn dlatte as a form of expression it is clear that
we shall not be interested in some of its [truth-
functional] validation possibilities (Grice. Lecture IV.
p. 18).

Grice has thus given at least a tentative account of the coinci-
dence of truth-functional validation and our intuitions with regard to
confirmation in the case of 'or' and of the discrepancy between them
when it comes to 'if. . .then'. This may. in turn. provide an
explanation for the relative ease with which we accept the equivalence
of 'or' and 'V' and the unease we experience when confronted with ET.

If we consider the standard conversational implicatures, then. as
only one sort of constraint on discourse. generated by only one of the
functions of language. and. with Grice. entertain in addition the
possibility that other functions of language may give rise. just as
systematically. to other sorts of constraints. then Jackson's observa-
tions about robustness reveal themselves as fitting neatly into a more
general pragmatic theory. If we are willing to see a connection even
more generally between the conditions of felicity of speech acts and
their implicatures--between. say. the requirement that the door be
closed for 'Please open the door' to be happily fielded. on the one
hand. and the existence of an implicature that the door is closed
coming standardly to be conveyed by the request. on the other--then we
can set Grice's theory into an even more extensive theoretical frame-
work (Levinson. p. 105). That we can do so redounds to the credit of
the thesis we wish to defend: it shows that it is part and parcel of a
research program which promises to produce a coherent account of more
and more phenomena by way of a nicely delimited set of initial presump-
tions and concepts. That we can extend Jackson's proposal in the
manner I have suggested ought. I think. to lend support to ET in just

the same manner that the explanatory promise of any theoretical

80
ensemble lends plausibility to each of its constituents.

I began this paper with the suggestion that. despite rumors to the
contrary. there are respectable reasons to claim that the truth-
conditions of (p+q) are quite standardly those of (qu). If goodness
of theory counts toward the application of predicates such as 'is true'
and 'has the same truth-conditions as'. then I believe I have made a

case for this suggestion.

FOOTNOTES

Footnotes

Frank Jackson. 'On Assertion and Indicative Conditionals.I
.2hilQfiQRhiQfll.Rfi!ifin. 78(1979). 565-689.

2 Anthony Appiah. uConversation and Conditionals.‘ Philgagphlaal

Quarterly. 129(1982). 327-338.

3 J.L. Mackie. Truth. museum and nausea-t Studies in
Philgfighhital Legit. (Oxford: Clarendon Press. 1973). p. 66.

4 Geoffrey Hunter. New An Introaastion .to the Estatheou of.
Standatd_Eit§t,Qtdat.LQgit. (Berkeley: University of
California Press. 1973). p. xiii.

5 Michael Clark. “Its and Hooks.“ mm. 32(1971). p. 33.

6 Bruce Aune. “If." Ehtytlgpadia‘Qf‘ZhilQthhy. 1968 ed.

7 P.F. Strawson. lnttgdattign.tg,Logital.Ihggty. (London: Methuen

& Co. Ltd.. 1952).

That at least some research programs in philosophy may usefully
be regarded as competing in much the same manner and on very
similar terms as those in science is a major thesis in Harold
I. Brown. Pereeeliona.1heora.and.Qommitment1.1he.New
Philgagphy at fitianta (Chitago: University of Chicago Press.
1977). That the participants in the debate over ET are. in
fact. adducing just the sorts of considerations that normally
count in favor of theories will. I hope. become obvious in
the course of this paper.

9 Michael Clark. 'Ifs and Hooks: A Rejoinder.'.Analyaia. 34(1974).

p. 83.

10 Robert Stalnaker. 'Probability and Conditionals.I in lta. ed.
W.L. Harper. R. Stalnaker. and G. Pearce (Dordrecht: D.
Reidel Pub. Co.. 1981). p. 193.

11 I am indebted to H. Hendry for this.

12 An intuitionist informant would. however. demur at the

translation of 'not' by '-'. since the truth conditions of

intuitionist negation are quite a different matter from those
of classical negation. (See D.C. Makinson. Igpiga in nadatn

Logit. (London: Methuen & Co. Ltd.. 1973). pp. 68-69.) If.

on the other hand. our competent speaker had been impressed

81

82
by Anderson and Belnap rather than by Brouwer and Heyting. we
would have a different objection on our hands. Validity of
inference. we would be informed. requires that premises be
relevant to the conclusion being drawn from them. In
particular. the inference from 'p or q' and 'not p' to 'q'
demands for its validity that the disjuncts be relevant to
each other. Thus. according to the relevance logician. 'or'
has an intensional sense which is not captured by the
classical 'V' with which we have represented it and our
translation fails. (Susan
Haack. Zhilgagphy at Legit. (Cambridge: Cambridge University
Press. 1978). pp. 199-200.)

13 There have been attempts to show that (qu) and (p+q) do stand
in a logical relationship to each other. Paris. for example.
has proposed that they are 'interderivable' (J.A. Faris.

'Interderivability of 'D' and 'If'.‘in‘ngit,and‘£hilgagphyt
fialattad,Beadinga. ed. Gary Iseminger (New York: Appleton-
Century-Crofts. 1968).) Haack summarizes his argument as
follows.
He assumes that a necessary and sufficient
condition for the truth of 'If A then B' is
agnaitign E: there is a set S of true propositions
such that B is derivable from A together with S. If
'ADB' is true. . . there la a set of true
propositions. namely. the set of which 'A+B' is the
sole member. from which. with A. B is derivable: so
E is satisfied. and 'If A then B' is true (Haack.

p. 36. my stress).

Haack observes that there have been various objections raised
against Faris' claim and offers a qualification of her own:
Faris' argument. she tells us. depends heavily on a notion
of 'derivability' which spans natural and formal languages in
a somewhat irregular manner (Haack. p. 36).

14 There is. Strawson believes. no natural language connective

which performs this task. 0n the other hand. it has been

83
observed by Gardiner that if we take the four possible
combinations of truth and falsity for two propositions
pfiq p&-q -p&q -p&-q
There exists in the English language. . . the means
of eliminating every possible subset of
alternatives from this exhaustive list. For
instance. when we say 'not both a and q'. we are
eliminating the first alternative: when we say 'if
.2. then q'. we are eliminating the second
alternative: when we say 'either p or q'. we are
eliminating the first and fourth alternatives: when
we say 'neither 2 nor a}. we are eliminating the
first. second and third alternatives. (W. Lambert
Gardiner. Paythglggyt A Stat; at a fiaatth (Belmont.
Calif.: Brooks/Cole Pub. Co.. 1970). p. 213.)
Gardiner seems to think that 'if. . .then' performs precisely
this task.
15 Although Strawson seems to identify the meaning of (p+q) with
its truth conditions. nothing in the discussion that follows
hinges on such a position. ET is the thesis that the
truth-conditions of (p4q) and (qu) are the same. not that
their meaning is the same. We can remain splendidly neutral
with regard to the tenability of a truth-conditional account
of meaning.
16 Richard Jeffrey. Formal 1.93.113. In 3.9.2.9.: and Limits (New York:
McGraw-Hill Book Company. 1981). p. 76.
17 Similarly. in urging that (qu) does not mean what (p+q)
ordinarily means. Aune not only tells us that
'pDa' means approximately 'not-p or q' or 'not
both R and not-q.' and there is nothing very
conditional about these statements

but goes on to object that
if 'p' is true. then 'tDp} j§_ttne int any '1'
whatsoever. And to argue '1. so 2' amounts to
committing a fallacy of relevance. . . . [T]he

arguments 'The moon is made of green cheese. so

84

Socrates was a philosopher' and 'Socrates was a

philosopher because the moon is made of green

cheese' are both jokes. even though 'Socrates was a

philosopher' is true (Aune. p. 129).
This is pretty confused but one gets the general idea that
what bothers Aune about ET is something along the lines of
the so-called fallacies of material implication.

'8 William 8. Cooper. mum of WW
(Dordrecht: Reidel Publishing Co.. 1978). pp. 197-8.

19 I.L. Janis and F. Frick. “The Relationship Between Attitudes
Toward Conclusions and Errors in Judging Logical Validity of
Syllogisms.‘ 1;,Zapatimantal‘zaythglggy. 33(1943) pp. 73-77;
I. Begg and J.P. Denny. “Empirical Reconsideration of
Atmosphere and Conversion Interpretations of Syllogistic
Reasoning Errors.“ ll,Expazimental.£aythglggy. 81(1969) pp.
351-354 cited in Robert L. 80180. Cognitixe.zaythology (New

York: Harcourt Brace Jovanovich. Inc.. 1979).

20 P.N. Johnson-Laird and M. Steedman. " The Psychology of
Syllogisms.‘ Qggnitiya_£aythglggy. 10 (1978). pp. 64-99.
cited in R.L. Solso. Qggnitiga‘Raythglggy.

21 P.C. Wason.“ Reasoning About a Rule.‘ Quattatly.loutnal at
Egnfilimfininl.£fiy£halnz¥. 20(1968). pp. 273-281. cited in A.L.
Glass. K.J. Holyoak and J.L. Santa. ngnitign (Reading.
Mass.: Addison-Wesley Publishing Co.. 1979). (See also P.C.
Wason and P.N. Johnson-Laird. Bayghglggy‘gt‘naaagning
(Cambridge: Harvard University Press. 1972).) When this task
is presented in workshops on cognition. participants are
apparently inclined to defend their erroneous answers with
considerable persistence even in the face of correction.
(John Furlong. informal communication.)

22 J.L. Austin."A Plea for Excuses.“ in his Rhilgagphlaal Zapata.
ed. J.0. Urmson and G.J. Warnock (Oxford: Oxford University
Press. 2nd ed.). p. 203.

23 It is. of course. important to distinguish between the claim
that we could all be mistaken about some such particular

matter of truth or validity and the claim that we could all

85
be mistaken about almost everything of the sort. As Stanley
Cavell puts it.
The claim that in general we do not require
evidence for statements. . . about what we are
doing or about what we say [does not rest on a
claim that we cannot be wrong] but only that it
would be extraordinary if we were (often).
(“Must We Mean What We Say?‘ in V.C. Chappell. ed...Qrdinarx
Language; m in 21111219211111]. Method ( New York: Dover
Publications. Inc.. 1964. rpt. 1981). pp 87ff.)
24 See. for example. Richard Rorty. “Realism and Reference.‘|
.Moniot. 60(1978). pp. 321-339.
25 Richard Rorty." Mind-Body Identity. Privacy. and Categories.'
am at W. 19(1965). pp. 24-54.
26 Presented in H.P. Grice's William James Lectures. delivered at
Harvard University in 1967.
Part of this series has been published as'I Logic and
Conversation.‘ in Iha Lag t at Qtammat. ed. Donald Davidson
and Gilbert Harman. (Encino. California: Dickenson Publishing
Co.. Inc.. 1975) and as Further Notes on Logic and
Conversation. in syntax.and Semantics. vol. 9. Rtagmatigfi.
ed. Peter Cole (New York: Academic Press. 1978).
27 H.P. Grice. William James Lectures. 1967. duplicated
typescript. Lecture IV. p. 1.
28 Stephen C. Levinson. Etagmatita. (Cambridge: Cambridge
University Press. 1983). p. 97. note.
29 Generation of an implicature also involves mutual knowledge
on the part of conversational partners. As Levinson puts
it.
We can say that S and H mutually tag: 2 iff S
knows p. H knows p. S knows that H knows a. H
knows that S knows that H knows p. and so on.
ad infinitum (Levinson. p. 113).

30 Ernest W. Adams. 1h:.LQxi£.Qf.§QndiLiQnalfi (Dordrecht: Reidel.
1975). p. 31.

31 Ernest Adams. "The Logic of Conditionals.” Inquiry. 8(1965). p-

86

169.

32 I think it is worth noting that Adams' argument here seems to
depend upon the assumption. questioned earlier. that ordinary
usage is the last word on meanings. I have already suggested
that it makes better sense to say of items of ordinary
language what we are inclined to say of more obviously
theoretical terms--that their meaning is given by the network
of beliefs and uses in which they occur. (I had to be told.
for example. that 'odd' and 'even' had application to 0.) If
this is the case. then 'true' and 'false' may quite
reasonably be said to have meanings even in cases where
competent speakers may not acknowledge them.

33 Adams' concern in this regard is understandable. Among the
widely used inference patterns which fail his test for
universal probabilistic soundness are contraposition.
disjunctive syllogism. hypothetical syllogism and
conditionalization. It may be noted in this connection that
he has thus to rely on Gricean considerations of appropriate
usage and the avoidance of misleading assertion quite as
heavily as does any conversationalist advocate of ET. Adams
is frank in acknowledging that there is no obvious way to
determine whether such conversationalist considerations are
more reasonably invoked in favor of his proposal or ET.

How to decide who is right?. . . For now we must

simply adopt a position consonant with our ratio

representation of the probability of a conditional.

. . . Chapter III [on criteria for rational

decision making] attempts to deal with these

matters though even there nothing will be

conclusively settled (Adams. 1975. pp. 20-21).
Those who find conversationalist explanations of purported
failures of classical deductive logic under the assumption of
ET to be disagreeably ad hoc should. I think. pay careful
heed to Adams here.

34 Ian F. Carlstrom and Christopher S. Hill. rev. of Ihfi‘LQle.Qf
flonditionala by Ernest V. Adam. Rhiloaenhx of. Seienee.

87
45(1978). pp. 155-158.

35 Dorothy Edgington. rev. of Ihe‘LQgit‘Qfi‘fignditlgnala by Ernest
W. Adams. Mind. 87(1978). pp. 619-623.

36 David Lewis."Probabilities of Conditionals and Conditional
Probabilities.‘ in lta. ed. W.L. Harper. R. Stalnaker. and G.
Pearce. p. 135.

37 My own linguistic intuitions suggest that a speaker who
actually believed that Carter would win no matter who his
opponent was would be considered distinctly misleading in
asserting 'If Reagan does not run. Carter will be reelected'.
Surely. if I think that Smith is a competent philosopher who
will do well on any topic. it would be misleading to offer
'If we stick to first order logic. Smith will do fine'. It
would. of course. be appropriate to say 'If Reagan runs.
Carter will be reelected and if Reagan does not run. Carter
will be reelected' if the speaker wished to emphasize either
the certainty of 'Reagan will be reelected' or its causal
independence with regard to 'Carter runs'.

38 Jackson seems to be assuming here (and perhaps elsewhere) that
conversational implicatures are derived only from the truth
conditions of what is said. While this may be consonant with
his own endorsement of a truth-conditional account of
meaning. there is no reason to attribute this constraint to
conversationalist theorists generally and good reason not to.
Discussing Gricean implicatures. Levinson. for example. says

Some quite detailed arguments can be given to show
that all but the Manner implicatures must be read
from the level of aemantio.zenxeaentation.
including some specification of lggital.£gtm, They
cannot be read off from uninterpreted surface
structures. nor can they be inferred simply from
the truth conditions of the sentence uttered
(Levinson. p. 123).
Levinson's discussion of the need to go beyond truth
conditions includes the observation that despite the fact

that expressions of the forms (p) and (p & (p+p)) will have

88

the same truth conditions. their instantiations may very well
not convey the same implicature. He asks us to compare. for
example. 'It's done' with 'It's done and if it's done. it's
done'. He observes that

The latter alone has a distinctive implicature.

roughly. . . 'It's no good regretting what has

already happened' (Levinson. p. 124).
Grice suggests that because tautologies are deviant
utterances their assertability will be evaluated in terms of
the appropriateness of their implicatures rather than on the
basis of what is said. While there is no simple explanation
of how implicatures are generated by utterances that flout
the maxims in so wholehearted a manner. we may expect that
their semantic and logical character will play a part in the
process. One possibility that occurs to me is that the very
uninformativeness of truths of logic allows their deployment
to signal that they are not being proferred in the service of
conveying information but. rather. are intended to do
something else. What this something else might be. in turn.
might be a matter of the specific semantic content of the
tautology. It seems. for example. that speakers often field
truths of logic when they want to advise or console their
listener or make salient some shared social standard. E.g..
one way of construing the implicature of 'War is war' might
be 'Stop protesting (grieving. struggling) because there is
no reason to expect things to be any different': one way of
construing the implicature of 'Boys will be boys' might be
'Stop trying to change things; it's o.k. for males to act
that way'. Truths of logic might thus be assertable when
they perform an acceptable normative or solidarity-producing
function. This is at least consistent with the observation
that there is often a somewhat dismissive tone to their
deployment--their use cuts off further debate or discussion
(Levinson. p. 111). (You can't really argue with a Hallmark
greeting card.) It is also consistent with Grice's

observation that irony--a stance implicated. under the right

89
circumstances. by factually unsatisfactory utterances--
conveys not only belief about some object but the speaker's
disapproving attitude toward it. (For a discussion of these
issues. see Grice. 1978 and Levinson. Chapter 3.) In general.
by limiting his discussion to the rule 'Assert the stronger'.
Jackson seems seriously to underestimate the resources of a
standard conversationalist strategy.

39 Curiously. Jackson does not seem to offer a solution to this
puzzle. On the other hand. as we shall see. Grice had
already made a very close pass at it.

40 If all we need to explain our intuition that this is not a
valid inference is the observation that we have an assertable
premise and an unassertable conclusion. it is not instantly
evident why we should prefer Jackson's account over the
Gricean one. Despite the assertability of the premise. the
conclusion
(C) If Carter is reelected by a large margin. then Carter

will not be reelected
is unassertable on standard conversationalist grounds because
it improperly implicates IC--the existence of some causal or
linguistic connection between its antecedent and its
consequent. Not only does 'Carter is reelected by a large
margin' fail to provide grounds for believing 'Carter is not
elected' but it is linguistically incompatible with such a
claim. If it makes us queasy to find ourselves implicating
what is contingently false. we should not be surprised to
discover that implicating what is logically false makes us
pretty seasick. (Cf. 'If today is Monday then tomorrow is
Thursday'.)

41 Other participants in the debate seem to be comporting
themselves in a similar manner. It is not the existence of
knock-down arguments but a judgment of over-all theoretical
promise that seems to be leading Edgington. for example. to
characterize Adams' proposal as hammering nails in the coffin
of material implication theory: both Cooper and L. Jonathan

Cohen complain that Gricean doctrine has been evaluated

90
against a misleadingly restricted range of cases (L.
Jonathan Cohen. "Some Remarks on Grice's Views About the

Logical Particles of Natural Language. in Yehoshua

Bar-Hillel. ed. Rtagmatita of Natntal Language (Dordrecht:
Reidel Publishing Co.. 1971)). Cooper comments. in addition.
on what he takes to be the ad hoc quality of Gricean ex-
planations of supposed paradoxes. One of the more surprising
aspects of the debate over ET is. indeed. how much
disagreement there can be over the relative virtues of
competing approaches. given the very high degree of agreement
over the facts of the case and the relevant formal arguments.
Nobody seems to contest Lewis' triviality findings nor does
anyone deny the awkwardness for ET of speakers' treatment of
negated conditionals: the debate is. rather. over what we
ought to make of all this. Perhaps because of their high
regard for the objectivity and consensus characteristic of
scientific undertakings. debates among philosophers in the
analytic tradition tend to sound a lot like debates among

scientists under similar circumstances.

APPENDIX

Appendix

a. Derivation: u(p+q) = u(qu)/Pr(p)

(1) u(p+q) = 1- Pr(p+q) Definition 'u(p)'
(2) = l- Pr(q/p) Definition 'Pr(p+q)'. (1)
(3) = 1- Rxlhéq) Definition 'Pr(q/p)'. (2)
Pr(p)
(4) = 2:121: Rtlpéal Substitution
Pr(p) Pr(p)
(5) = 21(92- Et(p&q) Simplification
Pr(p)

(6) Pr(p) = Pr(p&q) + Pr(p&-q) Calculus of probability

(7) Pr(p)- Pr(p&q) = Pr(p&-q) (6)

(8) u(p+q) = Etlhé;al Substitution in (5). (7)
Pr(q)

(9) Pr(p&-q) = Pr(-(p3q)) Semantics of '(qu)'

(10) = 1- Pr(qu) Calculus of probability

(11) = u(qu) Definition 'u(qu)'

(12) u(p+q) = alplgl Substitution in (8). (11)
Pr(p)

91

92
b. Here is a paraphrase of the version Hill and Carlstrom present.

Let A. B and (A+B) be statements true at some possible world W1.
Since there is no truth functional connective such that its
probability of truth is p((A&B)/p(A). the truth values of A
and B do not determine the truth of (A+B). Hence. there can
be a world W2 at which A and B are true and (A+B) is true and

a world W3 at which A and B are true but (A+B) is false.

Now consider two assignments of probabilities to worlds. Under
one assignment. it is highly probable that either W1 or W2
will be the case and it is just about as likely that W1 will
be the case as it is that W2 will be the case. Under this
assignment. a sentence true at both worlds has a probability
close to 1 of being true. Hence. under this assignment (A+B)

(A+B) has a probability close to 1 of being true.

Now consider a second assignment of probabilities to worlds. This
one is like the first except that the two worlds under
consideration are now W1 and W3. Under this assignment.
since it is true in only one of the worlds. (A+B) has a

probability of about .5 of being true.

Under both assignments. the probabilities of A and of (A&B) are
just about the same. and thus the conditional probabilities
of (B/A) are also just about the same since Pr(B/A) =
Pr(A&B)/Pr(A).

If the probabilities of truth of (A+B) differ from each other
under the two assignments whilst the conditional
probabilities of (B/A) do not. then the conditional
probabilities associated with (A+B) cannot be its

probabilities of truth.

93

c. This is a version of Lewis' proof that. given the standard axioms
for a probability function. it is only for a trivial language
that there can be a probability function Pr such that for any
statements p and q. Pr(p+q) = Pr(q/p) when Pr(p) is greater
than 0. The basic outline is that provided by Jeffrey
(1981): it is clearer by virtue of suggestions by H. Hendry.

First we list some relevant theorems about conditional probabilities.

Definition. Pr(p+q) = Pr(q/p) if Pr(p) is greater than 0.

(1) Suppose Pr(p) is greater than 0. Then
Pr(q/p) = 1 if p implies q
Pr(q/p) = 0 if p implies -q.

(2) Multiplicative law.
Pr(q&r/p) = Pr(q/p)Pr(r/q&p) if Pr(p&q) is greater
than 0.

(3) Law of compound probability.
Pr(q) = Pr(q/p)Pr(p) + Pr(ql-p)Pr(-p).

(4) Law of successive conditionalization.
If Pr'(r) = Pr(r/p) and Pr"(r) = Pr'(r/q).
then
Pr"(r) = Pr(r/p&q) if Pr(p&q) is greater than 0.
(The result of successive conditionalization on two statements
is the same as that of conditionalizing once on the

conjunction of those statements.)

Now. suppose we take 'if' to be a non-truth-functional connective
(as is. for example. 'because') such that Pr(q if p) =
Pr(q/p) when Pr(p) is greater than 0. Then. interpreting '/'
as 'if'. we could go ahead and iterate '/' as we would any

other connective. producing expressions like 'Pr((q/p)/r)'.

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(This would be the same thing as being willing to write

Pr(r+(p+q)). for example. if we think Pr(p+q) = Pr(q/p).)

If it means anything. Pr((q/p)/r) is the outcome of conditional-

izing twice and so. by (4) above. it is equal to Pr(q/p6r).

And if we can conditionalize twice. then we can invoke (3) and.
substituting q/p for q and q for p. conclude that
Pr(q/p) = Pr((q/p)/q)Pr(q) + Pr((q/p)/-q)Pr(-q).

By (4). Pr((q/p)/q) = Pr(q/(p8q)) and Pr ((q/p)/-q) = Pr(q/(p5-q).
So Pr(q/p) = Pr(q/(p&q))Pr(q) + Pr(q/(p5'q))Pr(-q).

But. by (1). Pr(q/(p&q)) = 1 and Pr(q/(p6-q) = 0.

So Pr(q/p) = 1Pr(q) + 0Pr(-q).

Therefore. Pr(q/p) = Pr(q). which means that p and q are

independent.

Our first finding. then. is that
We can treat '/' as a connective only at the cost of
finding that whenever c(p&q) and c(p&-q) are both
positive. p and q are independent. . . . Then unless c
is so trivial a probability function as to make
practically all statements independent of each other.'/'

is no connective. . . . (Jeffrey. p. 84)

This. in turn. leads to the next trivialization result.
'/' cannot be treated as a connective if c assigns
positive values to even three pairwise unsatisfiable

statements (Jeffrey. p. 85).

Let q. r. s be pairwise incompatible and let p be the disjunction

(qu). Let Pr(q). Pr(r) and Pr(s) each be greater than 0.

(1) By the Kolmogorov axioms. Pr(p) = Pr(q) if p and q are
equivalent. Hence Pr(p&q) = Pr(q).

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(2) We have just seen that '/' cannot be treated as a connective
unless p and q are independent. which is to say. unless
Pr(p&q) = Pr(p)Pr(q). Since. by (1). Pr(p&q) = Pr(q). we may
substitute and say that '/' cannot be treated as a connective

unless Pr(q) = Pr(p)Pr(q).

(3) Which is to say. unless Pr(p) = l. (Dividing both sides by
Pr(q). which we may do since. by hypothesis. Pr(q) is greater
than 00)

(4) Which is to say. unless Pr(-p) = 0. (By the Kolmogorov axiom
which has it that Pr(-p) = 1- Pr(p).)

(5) But this is impossible because. since the three statements
are. by hypothesis. pairwise incompatible. 8 implies -p and if
8 implies -p then (by yet another of the axioms of
probability) Pr(s) must be equal to or less than Pr(-p). If
Pr(s) is equal to or less than 0. it cannot be positive but.

by hypothesis. it it positive.

So the assumption that there are as many as three pairwise
incompatible statements with positive probability leads to a
contradiction if we take '/' to be a connective. Thus. the
only language which could have such a connective would be one
with fewer than three contingent pairwise incompatible
statements. As Lewis notes. we may justly call such a

language a trivial one (Lewis. p. 132).]

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d. We have already shown that u(qu) is generally less than u(p+q).

which is to say that Pr(qu) is generally greater than Pr(pxq).

That Pr((qu)/p) = Pr(q/p) can be shown as follows.

(1) Pr((qu/p)
(2)

Pr((-qu)/p) Definition 'qu'
Pr((-qu)&p/Pr(p) PL

(3)(-qu)&p is logically eqivalent to (p&q) PL

(4) Thus Pr((-qu)&p) = Pr(p&q) (2).(3). Substitution
5AdP = 6: 2.4.31). '
( ) n r((p3q)/p) giégygl ( ) ( ) u stitution
(6) Pr(p&q) = Pr(q/p) Definition. 'Pr(q/p)'

(7) So Pr((qu)/p) = Pr(q/p) (5). (6). Substitution

   

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