ATMOSPHERE AND CONVERSSON ERRORS {N
SYLLOGISTIC REASO-MNG WH‘H CONTEXTUAL
MATERIAL AND THE EFFECT OF DIFFERENTIAL TRAINING

Thesis for the Degree of M. A.
MICHiGAN STATE UNWERSRY
R. PAUL STRAUON '
1967

 

 

   
     

  

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ABSTRACT
ATMOSPHERE AND CONVERSION ERRORS IN
SYLLOGISTIC REASONING WITH CONTEXTUAL
MATERIAL AND THE EFFELT OF DIFFERENTIAL TRAINING

by R. Paul Stratton

Several previous studies have shown that §s untrained in
the use of formal logic accept very predictable erroneous con-
clusions when solving syllogism problems. Two types of logi-
cal Operations have been pr0posed to account for such consistent
behavior. The atmOSphere effect (Woodworth and Sells, 1935;
Sells, 1936) was defined as the influence which the context,
or tone, of a situation has upon the completion of a task. It
was assumed that, if s does not understand, or does not use,
the given logical relationships, the conclusion will be based
upon the structural features of the syllogism, i.e., the
quantifiers and qualifiers. Thus, for like premises a like con-
clusion would be predicted. For unlike premises one negative
premise would predict a negative conclusion, and one particu-
lar premise would predict a particular conclusion.

The converSion hypotheses (Chapman and Chapman, 1959) as-
sume that the logical relationships are understood, with the
exception that an A or Q premise may be invalidly converted.
Thus, after making an invalid conversion, a conclusion will be
deduced by the otherwise valid Operations. This was prOposed
as an alternative eXplanation to the atmosphere hypotheses for
certain items. The predicted responses are the same for those

items.

R. Paul Stratton

Because these contradictory hypotheses predicted erroneous
conclusions equally well for certain syllogisms, Simpson and
Johnson (1966) trained against each error separately. On items
where only the atmOSphere hypotheses predicted the favored
conclusion, the groups receiving anti-atmosphere error train-
ing produced the least number of errors and the greatest num-
ber of correct responses. On the conversion error items the
anti-conversion error training did not influence performance
any more than other training procedures. For untrained gs the
correlation between the number of atmosphere and conversion
errors was only -.12. Several methodological faults in this
experiment, however, indicated the neceSsity of replication.

The present experiment used a transfer-of-training para-
digm to detect changes in performance due to differential
training. The premises of the syllogisms were of neutral emo-
tional content and used unfamiliar, or nonsense, words for
terms. These were included in a paragraph to approximate com-
plex reading material. The pretest and posttest included 12
atmosphere error, 12 conversion error, and 12 determinate
items. §s were assigned randomly to six groups of 40 §s each.
These groups received written instructions against the atmos-
phere, conversion, or equivalence errors. One group received
both anti—atmOSphere and anti—conversion error instructions.
A control group received the introductory paragraph and the
definition of "some" which the training groups had received.
The other control group received no training instructions.

The results indicated that the errors made on syIIOgisms

of contextual material were similiar in kind and amount to

R. Paul Stratton
those made on syllogisms of symbolic or verbal material. A
correlational analysis of the relationships between perfor—
mance on error items indicated a substantial dependence. Both
the number of errors and the number of correct reSponses for
the error items were correlated at a statistically significant
level, i.e., between .347 and .589. This was not predicted
from past research and had particular import since only the
atmosphere hypotheses could predict the errors for both types
of items. On the atmOSphere items no predicted error could
result from an invalid A or Q premise conversion. Partial
correlations showed that these correlations were not due to
a covariance with reading comprehension, numerical ability or
tendency to respond "none of the above" to all items. These
results were interpreted as evidence against the prOposed
conversion error. Other evidence, however, is necessary to
strengthen the generality of this conclusion. Differential
training would have supplied further evidence, but no type
of training instructions produced a significant change in
performance. Possible causes of this and improvements in
this procedure were discussed. Further research in this area

was also suggested.

Approved glam/.1 4 a.

‘5'

Committee ChaJFman

Date Vii/72.11 2/93 A [75/
TV,” / / /

ATMOSPHERE AND CONVERSION ERRORS IN
SYLLOGISTIC REASONING WITH CONTEXTUAL

MATERIAL AND THE EFFECT OF DIFFERENTIAL TRAINING
By

R. Paul Stratton

A THESIS
Submitted to
Michigan State University

in partial fulfillment of the requirements
for the degree of

MASTER OF ARTS
DEPARTMENT OF PSYCHOLOGY

1967

TO KARIN

ii

ACKNOWLEDGMENTS

Dr. Donald M. Johnson's support and assistance in this
endeavor have been invaluable. I wish also to thank Dr.
Terrence M. Allen of the Department of PsycholOgy and Dr.
Herbert E. Hendry of the Department of PhiIOSOphy for reading
and criticizing this manuscript. _To my wife, Karin, I owe
a debt of gratitude for her unending encouragement and under-

standing.

iii

DEDICATION . . .
ACKNOWLEDGMENTS.
LIST OF TABLES .
l.IST OF

INTRODUCTION . .

TABLE OF

APPENDICES . . . . .

Atmosphere hypotheses .
Conversion hypotheses .

Equivalence
The Problem

DJ‘ETHOD o o o o 0
Subjects. .
Materials .
Procedure .

RESULTS. . . . .

DISCUSSION . . .

SUMMARY. . . . .

REFERENCES . . .

APPENDICES . . .

hypothesis

iv

CONTENTS

0 O O O

10.

LIST OF TABLES

Split-half reliability for each scale in the
pretest and posttest . . . . . . . . . . . . .

Means and standard deviations for each treat-
ment group on each scale of the pretest. . . .

Summary of analysis of variance for each pre-
test scale between allgroupS. . . . . . . . .

The percentage of S5 choosing each alternative
on the atmosphere and conversion items for the
prEteSto O O O O O O O O O O O O O O O O O O O

The percentage of Ss choosing each alternative
on the atmOSphere and conversion items for the
DOStteSt O O O O O O O O O O O O O O O O O O O

The product-moment correlations between the
pretest scales and CQT scores for reading and
numerical tests . . . . . . . . . . . . . . .

The product-moment correlations between the
posttest scales and CQT scores for reading
and numerical tests. . . . . . . . . . . . . .

Mean gain scores and standard deviations for
groups 1-6 on each scale . . . . . . . . . . .

Gain score reliability and standard error of
measurement for each scale.. . . . . . . . . .

Summary of the analysis of variance for gain
scores between all groups on each dependent
Variab'e O O O 0 O O O O O 0". O‘O‘O 0'. O O O

Page

24

25

26

28

29

32

33

35

37

37

LIST OF APPENDICES

APPENDIX A O O O O O O O O O O O O O O O O 0

Logical Abilities Test (Pretest). . . .
LOgical Reading Test (Posttest) . . . .

APPENDIX B O O O O O O O O O O 0'. O O O O O

Coversheet instructions for posttest of

Groups 1-4 and 6 . . . . . . . . .
Coversheet instructions for posttest of

Group 5. o o o o o o o o 0
Training instructions for Group
Training instructions for Group
Training instructions for Group
Training instructions for Group
Training instructions for Group

UT-TI‘UHU-‘O

vi

52

53
58

63

INTRODUCTION

The term reasoning has had a history of varied usage and
is used by psychologists today to refer to the solution of
problems by logical Operations. Investigations. of such Oper-
ations have used a wide variety of problems ranging from word
series to algebra problems. Reasoning occurs most obviously,
however, during the solution Of problems of formal lOgic.

The syllogism is such a problem and has received wide accept-
ance as an example of deductive reasoning. A categorical,

or Aristotelian, syllogism is an argument composed of two
categorical premises and a categorical conclusion. These pro-
positions together contain three and only three terms, each
of which is used only twice. A middle term appears in each
premise, and the other term from each premise appears in the
conclusion. Thus, there may exist valid and invalid syllo-
gisms. Traditionally these prOpositions are called the major
and minor premises and the conclusion. Problems of this
nature with more than three terms are called sorites or poly-
syllogisms.

Syllogisms have frequently been used in general intelli-
gence tests, and the ability to solve them has been found to
be influential in other intellectual abilities (Guilford,
1959; Guilford and Merrifield, 1960; Guilford and Hoepfner,

1966). In addition, they have been used in psychological

2

studies of behavioral pathologies (e.g., Arieti, 1955;
Gottesman and Chapman, 1960), of emotion and attitudes (e.g.,
Gorden, 1953; Henle and Michael, 1966), of semantic learn-
ing and structure (Lippman, 1966), of verbally mediated
learning (Frase, 1966), and of problem solving (e.g.,
Moore and Anderson, 1954; Newell, Simon, and Shaw, 1958).

Investigations of problem solving processes, however,
tend to underemphasize the role of reasoning when defined as
the use of logically valid inference patterns. For example,
Bruner, Goodnow and Austin (1956) concluded "much of human
reasoning is supported by a kind of thematic process rather
than by an abstract logic. The principal feature of this
thematic process is its pragmatic rather than its logical
structure (p. 104)." The study of errors in syllogistic
reasoning has yielded an impressive amount of evidence which
would indicate that the logic of reasoning does not corres-
pond tO the psychology of reasoning. Specifically reasoning
can be influenced by structure, attitudes, or emotions (e.g.,
Morgan and Morton, 1944). Unfortunately such a theoretical
question as the presence or absence of valid reasoning pro-
cesses has only been tested by the ability to discriminate
valid and invalid solutions to syllogism problems. Thus, it
becomes an inferred process. If one asserts that errors Of
discrimination in solving such problems can be attributed to
other factors, for example, not understanding the meaning of
"valid," the presence of valid reasoning processes may be

argued for. This is the position taken by Richter (1957),

3

Stewart (1959, 1960), and Henle (1962). The present experiment
will test two hypotheses which are Opposed on this question
and consequently on the proposed sources of error in syllo-
gistic reasoning.

Before further discussion is possible certain terms
must be defined. For a more thorough discussion of the
elements Of formal logic see an introductOry logic text such
as Cohen and Nagel (1934) or COpi (1954).

The categorical propositions of a syllogism are noted

symbolically by the letters A, E, l and 9.

Name Expression Symbol
Universal Affirmative All S's are P's. A
Universal Negative NO S's are P's. E
Particular Affirmative Some S's are P's. 1
Particular Negative Some S's are not P's. Q

The major premise of a syIIOgism states the relation
between the middle term and the predicate of the conclusion.
The relajon between the middle term and the subject of the
conclusion is given by the minor premiSe. The conclusion is
deduced from the major and minor premise relatiOns and is
valid or invalid according to certain formal rules.

To distinguish between the possible relations of the
subject (8) and predicate (P) of the conclusion to the middle
term (M) in the major and minor premises, four figures have
become standard. Note, any of the categorical prOpositions
may be used as major or minor premises or as a conclusion.

Figure I Figure II Figure III Figure Iv

Major premise M-P P-M M-P P-M
Minor premise S-M S-M .-S M—S
Conclusion S-P S-P S-P S-P

4
The mood characterizes a syllogism by denoting the logical
structure with symbols for major premise, minor premise,
and conclusion, in that order, and with the figure. Thus, a
syllogism may be characterized by All figure I. From this
information the syllOgism may be reproduced,in symbollic form,
and the validity or invalidity may be ascertained.

The validity of a syllogism fundamentally depends upon
the possible collateral truth of the premises and conclusion.
A syllogism is valid only when, if the premises are true, the
conclusion would have to be true also, even though the
premises may in fact be false. One of the several methods
Of determining the validity of a syllogism is its conformity
to certain rules of validity as given by Cohen and Nagel
(1934, p. 79):

Rules of quantification

1. NO valid syllogism follows from two particular
premises.

2. If one premise is particular, then the conclusion
must be particular.

Rules of qualification

1. No valid syllogism follows from two negative
premises.

2. If one premise is negative, the conclusion must
be negative.

Rules of distribution1

1. The middle term must be distributed only once
for the syllogism to be valid.

2. A term can be distributed in the conclusion if
and only if it is distributed in its premise.

"Distribution" means that all members of a class which are
designated by a term have been referred to by the prOposition.
A term is distributed if it is the subject of a universal
prOposition or the predicate of a negative prOpositon.

5

That people make errors when working such syllogism
problems is reasonable and not surprising. For this reason
philOSOphers have taught courses in formal logic, and
psychologists have taught their students the principles with
which to logically relate research findings. The errors
made by students when solving syllogisms were first reported
in the psychological literature by Wilkins (1928).

Using undergraduates of Columbia College, she found the
frequency of acceptance of invalid conclusions to syllogisms
Of varied content. The syllogistic fallacies most frequently
accepted were drawing a conclusion from two particular pre-
mises and the undistributed middle term. Others were illicit
major and minor terms and negative conclusion from affirmative
premises. The converse of a proposition was also frequently
accepted as a valid inference. With mood and figure constant
the decending order of content difficulty was: unfamiliar
(long, scientific terms), symbolic, suggestive (false con-

clusions), and familiar content.

Atmosphere hypotheses

To Woodworth and Sells (1935) the syllogism was a "promis-
ing lead in the experimental study of thinking (p. 451)." A
syllogism stated in purely symbolic terms possessed the quali-
ties of nonsense syllables in memory experiments for they
were free from extraneous associations and truth or falsity.
Attempting to discover the psychOIOgical principles involved
in the acceptance of invalid syllogistic inferences, Woodworth

and Sells formulated three sources Of error. Ambiguity of

6
the language Operates especially through the quantifier "some."
By the conventions of formal logic "some" means "some and
perhaps all" or "at least one," precluding the inference
"some X is not Y" from the prOposition "some X is Y." A
principle of caution was formulated to account for the prefer-
ence of a particular conclusion over a universal one.

The "atmosphere" of a syllogism is of principal interest
here since the definition Of "some" and cautious reSponses
may be reasonably well controlled by instructions and test
format. The "atmosphere," or "tone," of a syllOgism may be
universal or particular, and affirmative or negative. Which-
ever it is, it creates a sense of validity for the correspond-
ing conclusion. Thus, the primary atmosphere hypothesis would
predict that, when the two premises are of the same type, a
corresponding conclusion would be preferred. For unlike pre-
mise combinations, two secondary hypotheses were postulated.
(1) A particular premise creates a "some" atmOSphere, even
though the other may be universal. (2) A negative premise
creates a negative atmOSphere, even though the other may be
affirmative.

In summary, the atmOSphere hypotheses predict:

A conclusions for AA premises
conclusions for AE or g; premises

('5'
A conclusions for or ii premises
9 conclusions for I, g9, 19 or 99 premises

’ —

ISIEI

In addition, the principle of caution would predict l and Q
conclusions for AA and g; premises, respectively.
Woodworth and Sells presented data from Wilkins (1928)

which supported these predictions.

7
Sells (1936) describes the atmosphere hypotheses which
predict conclusions to syllOgisms as one specific instance

of an "atmosphere effect" which is akin to a determining

 

tendency, a mental set, or an Einstellunq. It is "a temporary
set of the individual, arising within a situation (e.g., prob-
lem) to complete the task with that one of several alternative
responses (e.g., an inference or judgment) which is most
similiar to the general trend or tone of the whole situation
(e.g., problem) 9. 7." Thus, the atmOSphere effect Operates
in any problem, such as perceptual phenomena or judgment,
where the context or tone Of the situation may influence the
response choice. The syllogism, therefore, was used by Sells
as a preparation to demonstrate the existence of the atmosphere
effect and its interactbn with variables such as age, sex,
and intelligence.

Replicating the results of Wilkins (1928), Sells found
a similiar distribution of formal IOgical fallacies and
found abstract (symbolic) syllogisms to be about 15% more
difficult than concrete (verbal) syllogisms in familiar terms.
In a second eXperiment he used abstract syllogisms in all
combinations of A, E, l and Q premises and conclusions. Sub-
jects (Es) were to respond "absolutely true," "probably true,"
"indeterminate" or "absolutely false." For each pair of pre-
mises he found the percent of the Es who selected ”absolutely
true" and "probably true" to each A, E, l or Q conclusion.
For each such item the response predicted by the atmosphere
hypotheses plus the principle Of caution was chosen by sub-

stantially more Es than other invalid conclusions. Thus, the

8
atmosphere effect plus the principle of caution was interpreted
as explaining the predominant pattern of error responses in
all invalid syllogisms.

Other evidence for the atmosphere effect came from the
distribution of invalid conclusions in other studies. Sells
and Koob (1937) present the materials and method for a class-
room demonstration Of the atmosphere effect in syllogisms
where E supplies his own conclusion. Using these Sells and
Koob Obtained data which demonstrated the atmosphere effect
in self-produced conclusions to syllOgisms.

Morgan and Morton (1944) used abstract and concrete
syllogisms of neutral content in a five-choice multiple-choice
format and found 67% and 60% of the erroneous conclusions
could be predicted by the atmOSphere effect for both abstract
and concrete syllogisms, respectively. If, however, the
syllogisms are of an emotional content, invalid conclusions
were more influenced by congruency with one's own convictions
than by logical structure.

The presence of an atmosphere effect in problems other
than syllogisms has been documented by Hunter (1957a,b). Hunter
(1957 a) used a proportion problem where two terms were
related when the third was held constant. When Es were asked
to produce their own solution, 63% gave a response which was
not determined by the relationships involved but by the formal
structure of the problem. Asked what their first impression
of the solution was, 73% indicated the atmosphere effect pre-
dicted solution. Testing 11- and 16- year olds with simple

three-term series problems, Hunter (1957 b) found 11—year olds

9

based their solutions on structural relationships rather than
IOgical ones, whereas 16-year olds made more articulated
judgments according to the logical structures Of the problems.

Having thus been established and verified, the atmosphere
effect in syllOgistic reasoning has received general accept-
ance. So much so that until 1957 no other explanation Of
errors in syllogistic reasoning had been proposed, and it has
received favorable mention in such well-known texts as Under-
wood (1949), Woodworth and Schlosberg (1956), and Stevens'

Handbook (Miller, 1951).

Conversion hypotheses

Another explanation Of errors in syllogistic reasoning
was prOposed by Chapman and Chapman(1959). After a thorough
re-examination of Sells' (1936) research, Chapman and Chapman
criticized the atmosphere hypotheses on several points: (1)
The secondary atmosphere hypotheses predict a conclusion with
wording oflier than that of either premise, i.e., for a uni-
versal negative and a particular affirmative, a particular
negative is predicted . This is contrary to the basic char-
acter of the atmosphere effect. (2) The principle of caution
is not justified, because it is an artifact Of the true-false
format Sells used. And (3) Sells apparently had not labeled
the mood in the conventional manner, preferring to label it
in terms of premise order rather than in terms of major and
minor premises. Thus, although all of his invalid syllogisms
were invalid, one would not have been able to infer this

from Sells' mood distinctions.

1O

Convinced that they had due cause, Chapman and Chapman
then devised a symbolic test of 42 experimental items of which
there were three syllogisms for each of the 14 premise com-
binations with no logical conclusion in one or more figure,
and of 10 filler items for which a conclusion did follow logi-
cally. The test was of multiple-choice format with alterna-
tives A, E, l, E and "none of these." The instructions defined
the task, the term "some," and the use of "none of these."
The percentage of Es selecting each alternative was presented
as a tabulation of errors to syllogisms for which there were
no valid conclusions. The results were impressive. Accuracy
was low as one would eXpect from a test where 80% Of the answers
were "none of these." For most items a single alternative
was chosen,by the majority of the Es, and that alternative
was preferred regardless of premise order or figure for the
same premise pair. Comparing their results with those pre-
dicted by the atmosphere effect (without the principle Of
caution), 1E and EE premises had a preferred error of E while
the predicted error was 9. Also for E9 premises the E and Q
alternatiVes were preferred almost equally. This they inter-
preted to mean, "the atmosphere predictions are not substant-
iated, we must look for other principles of explanation (p. 224)."

Their alternative explanation incorporated the invalid
conversion of A andggpremises and reasoning by probabilistic
inference. ,Both Wilkins (1928) and Sells (1936) found that
many Es interpreted A and Q prOpOsitions to mean that the
direct converse was true. Thus, from "all X's are Y's" they

inferred "all Y's are X's," and from "some X's are not Y's"

11

they inferred "some Y's are not X's." Whereas E and 1 pro-
positions may validly be converted directly, the valid A
conversion produces a negated subject and predicate, and the
E prOposition cannot be validly converted. Such invalid
conversions are frequently consistent with reality, and, thusly,
could be assumed to be in a person's repertoire Of immediate
inferences. The preferred conclusions of AA, EE, Al, and Ag
premise pairs may be deduced validly if one only assumes an
invalid A and 9 conversion to be valid.

To deduce the remainder of the preferred conclusions the
principle of probabilistic inference was necessary. Since
Es are not told that only strict deductive reasoning is allowed,
they may reason that things that have common prOperties are
probably the same kinds of things. This is a form of reason-
ing by insufficient evidence where the solution is probable,
but one cannot know if it will be true for every instance of
the situation. For example, given "some X's are Y's; some
Z's are Y's" the conclusion that "some X's are Z's is probable
since X and Z share property Y. When the syllOgism is not in
the second or fourth figure, E is assumed to restate a premise
in the converse to make this relationship more apparent.
Taken tOgether these reasoning behaviors Often lead to correct
conclusions in everyday life, but may lead to erroneous con-
clusions which are disallowed by the traditional rules of the
syllOgism. The present experiment will not be directly con-
cerned with probabilistic inference as a source of error.
See Alberoni (1962), Cohen and Nagel (1934) and Henle (1962)

for a more detailed analysis Of subjective probability and

l2

probabilistic inference in reasoning.

Equivalence hypothesis

 

That Es so accept the invalid conversions of A and 9 pre-
mises is well verified by the evidence at hand. That they do
so in the solution of a syllogism problem, however, is Open
to question. An alternative explanation of the acceptance of
A conversions would be an inferred equivalence between the
terms of the prOposition which, then, would allow the conver-
sion to follow logically, if necessary. By inferring an
equivalence between the terms of a prOposition, E would in
effect be asserting that one term is a proper subset of the
other. Thus, the union would include each and every element
Of both sets. Such relationships Often correspond to our
experience of reality, and frequently the c0pula "are" is
used to denote such an equivalence. For example, while "all
right angles are 900 angles," and "all 90°angles are right
angles," are true statements, one does not follow logically
from the other. In fact, the converse of a true A prOposition
is not always true. For example, "all cats are mammals" is
true, but the converse, "all mammals are cats," is not.
Usually the equivalence prOperty of a relationship is deter-
mined by the meaning of the terms themselves, but the verb
"are" can be used as a copula in either case. Where the mean-
ing is indeterminable, however, as in syllogisms using un-
familiar or symbolic terms, one cannot make such distinctions,
and an equivalence relationship may well be asserted. An

unjustified inferred equivalence, called an equiValence error,

13
could account for and predict the errors made in those syllo-
gisms which Chapman and Chapman explain by an A conversion. The
present eXperiment will attempt to test this hypothesis by es-

tablishing the non-equiValence of the terms in the instructions.

The problem

 

It is apparent that the conversion and atmOSphere hypotheses
overlap in the errors they predict. For the AA, AE, Al and Ag
premise pairs both hypotheses predict the same error in the
figures where no valid concluSions are possible. The data
verify the predictability of these errors. These hypotheses
differ, however, upon the prOposed.lOgical Operations involved,
as has been discussed before, and upon the basic assumptions
they engender.

The atmOSphere effect must assume that E does not under-
stand or does not use the information given by the relation-
ships between the terms Of each prOposition. E then relies
on the structural prOperties, the context, of the situation
for information on which to base his conclusion. The conversion
hypotheses, on the other hand, assumes that E does understand
the given relationships to the extent that he accepts the con-
verse Of one premise and with that converse proceeds to a valid
conclusion. Thus, for syllogism problems the conversion hypo-
theses assume the invalid conversion to be the only error that
is necessary to otherwise validly deduce the conclusion.

Were one to follow the procedures suggested by either
hypotheses, a predictable invalid conclusion would be accepted
as valid. A computer following the same instructions would

arrive at the same conclusions. But, since both hypotheses

14

predict the errors equally well in syllogisms with an A or Q
premise and the existence of these errors has been documented,
one must conclude that the method of tallying errors has a
limited utility and a new method Of comparison is necessary.
Were a restricted training procedure to influence the usage
of a particular logical Operation, there would be strong
evidence for the existence of that Operation.

This was the approach taken by Simpson and Johnson (1966).
A symbolic syllogism test was constructed of 12 atmOSphere
items of EE, 99, 11, AE, and E9 premises and 12 conversion
of Ag premises. For the LE premises both A and E conclusions
and for E9 both E and E conclusions were scored as atmosphere
errors. Eleven filler items which had valid conclusions were
used and called determinate items. Group 1 received the anti-
atmosphere instructions which included a verbal description
and a demonstration of the atmosphere error plus practice on
six items not to be used later. Group 2 received the anti—
conversion instructions for invalid A conversions and practice
on prOpositions and their conversion. Group 3 received only
a general warning about the difficulty of the syllOgisms
and the necessity of being careful. Group 4 received the in-
structions of Group 3 and the practice Of Group 1. Group 5
was a control group receiving no practice or anti-error in-
structions.

The results of this experiment indicate the independence
of performance on atmOSphere and conversion error items.
although 60—70% of the predicted errors were made, the corre-

lation between atmosphere and conversion error scores was only

15

-.12. This was interpreted to mean "susceptibility to one
type of error is practically independent of susceptibility
to the other (9. 199)." Training produced similiar results.
The anti-atmOSphere group made more correct reSponses and
less errors than other groups on the atmosphere items. The
' anti-conversion group, however, did not perform as well.
The number of correct responses to conversion items was very
low for every group, and the anti-conversion error group did
not make the least number of errors as eXpected. The differ-
ence between groups for the number of conversion errors was
statistically significant but was attributed to the large
number of errcrsnede by the untrained Group 5. The general
warning and practice group, however, made substantially less
conversion errorsthan any other group. The statistical signi-
ficance Of this was not mentioned and was not possible to
calculate from the data. The procedure may be criticized on
several points: (1) By not using a transfer-of—training para-
digm the results were influenced by initial ability of the
groups. (2) By scoring two alternatives as predicted atmos—
phere errors for the A9 and E9 items, the atmosphere hypo-
theses as stated by Sells (1936) were not accurately tested.
(3) By training only against the invalid A.conversion Es could
not be expected to improve performance on the nine 9-conver-
sion and two determinate items Of the conversion error scale.

Material heretofore unused in syllOgism experiments will
be used in the present experiment. Two premises using unfami-
liar words for terms will be included in a paragraph. An III

figure I example follows (Appendix A includes the remainder

16
of the items used):

As technOIOgy advances and natural petroleum re-
sources become more depleted, the securing of
petroleum from unconventional sources becomes
more imperative. One such source is the
Athabasca tar sands of northern Alberta, Canada.
Since some tar sands are sources of refinable
hydrocarbons, these deposits are worthy of com-
mercial investigation. Some kerogen deposits
are also sources of refinable hydrocarbons.
Therefore:

(1) All kerogen deposits are tar sands.
NO kerogen deposits are tar sands.
Some kerOgen deposits are tar sands.
Some kerogen deposits are not tar sands.
None of the above.

AAAAA
UT 4-‘Ul l\)
VVVV

This is intended to demonstrate the existence of atmos-
phere and conversion erronsin difficult reading material
similiar to that found in textbooks. The recording of reason-
ing errors in contextual material has not been done even
though Wilkins (1928), Sells (1936) and others have used fami-
liar and nonsense verbal material. An example Of such a
syllogism is: "All troubles are insults; All insults are un-
pleasant OCCUWEnceS; Therefore, all troubles are unpleasant
occurrences." Wilkins (1928) found the syllOgisms using
familiar words, symbolic, and unfamiliar words more difficult
in that order. Note, however, that such syllogisms do not
approximate a normal reading task. Similiar materials were
also used in studies of the effect of emotion, attitude, or
bias upon reasoning such as Janis and Frick (1943), Morgan
and Morton (1944), Lefford (1946), Thislewaite (1950), Gordon
(1953) and Henle and Michael (1956). For normative studies,
however, nonsense material is preferred to familiar material
because of its relative freedom from prior knowledge and atti-

tude. After studying the mistakes made in reading paragraphs

17

by elementary school children, Thorndike (1917) concluded

that accurate reading involved the elements characteristic

of reasoning. His Es apparently weighed each element in the
paragraph and their organization relative to each other, se-
lected prOper connotations, and coordinated these many forces
into a final understanding. Thus, he concluded reading appeared
to involve some skill in some type of reasoning. This con-
clusion was was further substantiated by Davis(1942, 1946)
through factor analysis of various reading tests and their
components. He found two prominent factors; word knowledge
and reasoning-in-reading. It is reasonable, then, that errors
found in less complex material should also be found in para-
graphs using unfamiliar terms.

To summarize,the present eXperiment will attempt to re-
plicate the findings of Simpson and Johnson (1966) using con-
textual material and more sensitive design. A pretest and
posttest will determine relative gain after training against
the atmOSphere, conversion, and equivalence errors. Specific
hypotheses to be tested are:

Hypothesis I. On the atmosphere and conversion error
items the largest number of errors will be predicted by the
atmosphere and conversion hypotheses, reSpectively.

Hypothesis II. Performance on the atmOSphere error items
will not be dependent upon performance on the conversion
error items.

Hypothesis III. For groups receiving specific training
instructions against the atmosphere, conversion or equivalence

error a decrease in errors or an increase in correct conclusions

18
will obtain only on error items against which the training

instructions were directed.

METHOD

Subiects

Two hundred and ninety-three college freshmen and SOph-
mores from an introductory psychology class at Michigan State
University served as subjects for this eXperiment.2 Of these
53 were eliminated from the final analysis, because they had
had a course in formal logic, had missed one testing session
or had one incomplete test (i.e., left two or more items blank;
average number of blank items was 7.8 with a range of 2 to 23).
Of the 240 remaining subjects 62 were males and 178 were fe-
males. By serial distribution Of tests Es were assigned with-
out bias to six groups of 40 with 7 to 13 males in each.
Materials

The syllOgisms used were of neutral emotional content
incorporating unfamiliar words for terms. The categorical
prOpositions were in a paragraph of relevant fictional mater-
ial. The premise order was major, then minor. Varying lengths
Of paragraphs and steps to solution were distributed through-
out both test and each scale. Items were in tOpical sequences
up to six items long to increase Es' interest and decrease
difficulty due to novelty of material. It was thought that

reading few tOpics would be less tedious than if each item

2The author wishes to eXpress his appreciation to Dr. Dozier
W. Thornton for his COOperation in securing this sample from

his lecture section.
19

20
introduced a new tOpic or if the tOpic was the same for all
items. Each error scale was represented within every sequence

to randomize any practice or fatigue effects. A, E, A, O,

and "none of the above" conclusions were given in a multiple-
choice format for each item. Answers were recorded on machine
scorable answer sheets, and scratch sheets were collected.

The level of difficulty was ascertained in a pilot study

3

for 84 contextual syllogisms, and a pretest and posttest were

constructed of 36 items each. The atmosphere error scales
consisted of 12 items of EE, E9, 1;, l9 and 99 premise pairs
so that they would provide an index of atmosphere error sus-
ceptibility without confounding conversion errors. That is
to say, no predicted atmOSphere conclusion could be deduced
by an invalid A or 9 premise conversion. The mean percent
predicted response (accounting for correct responses) for the
pretest atmosphse scale was 44.4 and 44.3 for the posttest.
The 12-item conversion error scales consisted of premise pairs
A9 figure I and Iv and 9A figure I and IV. There were three
items in each figure. For the A9 and 9A premise pairs the
atmosphere effect should be the weakest, and the A or 9 in-
valid conversion Operable within the same syllOgism. For the
conversion error scales on the pretest and posttest, the mean
percent predicted response was 39.5 and 40.9, respectively.
Items for the determinate scales had valid conclusions given
and 71.8 and 74.6 mean percent correct responses for the pre-

The author would like to thank Dr. Donald M. Johnson for

having constructed 36 of these items.

21
cent correct responses for the pretest and posttest, respec-
tively. Thus, two tests were constructed of roughly equivalent
difficulty and consisted of three scales of twelve items to
detect any performance change after training. The pretest
and the posttest are included in Appendix A.

Procedure

 

A transfer-of—training paradigm was used to determine
the effect of training on syllogistic reasoning performance.
The pretest was given in a large lecture session. Tests,
scratch sheets, and answer sheets were administered as Es
entered the room and were collected as they left. One week
later the training instructions and posttests were administered
in the same way and in serial group order to 187 of the Es
in discussion sections which contained from 10 to 25 Es each.
The remainder of the Es (53) participated within the next two
weeks on a voluntary basis and were serially assigned to
groups until there were 40 Es in each. No knowledge of the
results were given, and the nature of the experiment was not
revealed other than in the most general of terms. Therefore,
no transfer of information affecting the results was su3pected.
For the pretest and the training plus the posttest 45 minutes
was ample time for completion.

The coversheet instructions for the pretest and the post-
test were identical except for one control group which re-
ceived one part of the instructions as training material. The
nature Of the instructions was the same as used in previous
experiments. The logical task was discussed Specific to the

material and format. Verbal instructions also stressed the

22
necessity of drawing conclusions only from the information
in the paragraph. The definition of "some" was given as
"at least one," and it was stated that "some are not" does
not imply "some are," and vice versa. The use of the alter-
native "none of the above" was also defined.

All groups other than control Group 6 received training
instructions which contained an introductOry and concluding
paragraph intended to establish rapport and interest. The
complete instructions for all groups are included in Appendix
B. Group 1 received anti—atmosphere instruction which included
a description of the error and an AAA figure II symbolic ex-
ample. The anti-conversion instructions of Group 2 consisted
of a description of the error, the syllOgism example of
Group 1, and several examples Of premises which could (E and
A) and could not (A and 9) be directly converted. The train-
ing instructions for Group 3 were a combination of those of
Group 1 and 2. Group 4 received instructions explaining the
error of inferring equivalence from an A premise and how to
restate A, E, A, and 9 premises in terms of sets with elements
which are shared or not. A premises were described as stat-
ing a subset relationship wherein the set denoted by the pre-
dicate was assumed to be larger than, and including, the set
denoted by the subject. Group 5 was to serve as a control
against a Hawthorne effect due to Special treatment or moti-
vating instructions. The same introductory and concluding
training material was given plus an elaboration of the de-
finition of the term "some." Es were advised to interpret

"some A's and 8's" to mean "at least one thing exists which

23

is both A and B." Thus, "some" was given its traditional
meaning of "at least one thing exists which is both A and

B." This eXplanation was excluded from the coversheet ins-
tructions for this group. Group 6 served as a control
receiving only the coversheet instructions. All groups
worked the same syllogisms and had equal time for completion.
Since each group was represented every time the posttest

was given, testing conditions had no differential effect.

The dependent variables were the number of correct and
incorrect answers to each item. A difference score was
calculated by subtracting pretest from posttest scores.
Since less errors on the posttest would give a negative dif-
ference, the constant 25, representing the greatest possible
change in either direction, was added to the difference
scores. Thus, the change in performance after training was
calculated by:

GAIN SCORE = POSTTEST SCORE — PRETEST SCORE + 25.
Following the data collection, the Michigan State University
College Qualification Test (COT) scores were secured for all
but one of the subjects. These include scores for reading,

vocabulary, arithmatic, and information tests.

RESULTS

The Split-half reliability for each test scale was de-
termined by the odd-even method and the Spearman-Brown form-

ula (Guilford, 1965, p. 458). These are given for the pre-

test and posttest in Table 1. The split-half reliability was

estimated to account for varying difficulty over the length

of the test. For the pretest the scores for all Es were used,

for the posttest only the untreated Group 6.

Table 1

Split-Half Reliability for each Scale

 

 

 

 

 

 

 

 

 

in the Pretest (N = 240) and Posttest (n = 40)
Determinate Atmosphere AtmOSphere Conversion Conversion
Correct Error Correct Error Correct
Pretest .61 .65 .76 .73 .68
Posttest .58 .70 .86 .80 .91
There were 62 males and 178 females in the sample. The
point-biserial correlation between sex (female = 1; male = 0)

and pretest scores gave one significant value.

phere error scale the correlation was .172 (p<.05).

biserial

correlation between sex and gain scores only

1 were there any significant relationships.

For the atmos-

For

in

the

Group

A correlation

with the atmosphere error scale of -.407 (p<.01) and with the

atmosphere correct scale of .374 (<.05).

24

25
1TB highest other value was .242. The gain scores of females
for the number of atmosphere errors and correct were 22.90
and 28.17, respectively. For the males these gain scores
were 25.54 and 25. 64, reSpectively. Thus, any change in

performance on atmOSphere items

in Group 1 was due to the
females and such a relationship does not hold for any other
group or dependent variable.

The means (Y's) and standard deviations (S.D.'s) for
each scale of the pretest

is given in Table 2. There is

variation between groups in initial but

performance, the
summary Of the analysis of variance (Winer, 1962, p. 56)
for each scale in Table 3 shows no significant differences

which would systematically Because

influence the results.
for each sample n z 40, the pOpulation variances were

assumed to be homogeneous for each analysis of variance.

Table 2
Means and Standard Deviations for each Treatment

on each Scale of the Pretest

Group

 

 

 

 

 

 

 

 

 

 

Treatment Group

1 2 3 4 5 6

Atmosphere error 4.52 5.15 4.60 5.02 5.48 4.75
2.02 2.04 2.34 2.35 1.91 2.26

Conversion error 5.65 6.78 6.82 6.30 6.75 6.92
2.50 2.85 2.73 2.34 2.87 2.48

AtmOSphere correct 4.02 4.38 4.12 3.88 3.65 4.18
2.57 2.53 3.21 2.94 2.38 2.51

Conversion correct 1.98 1.38 1.42 1.52 1.12 1.58
1.90 1.72 2.02 2.44 1.26 1.72

Determinate correct 8.60 8.95 '8.95 8.62 9.05 9.42
V1.58 1.78 1.77 2.13 1.63 1.80

 

26

Table 3
Summary of the Analysis of Variance

for each Pretest Scale Between all Groups

 

 

Atmos. Conv. Atmos. Conv. Deter.
Source error error correct correct correct

df
MS F ms F vs F. MS F vs F

 

 

Between groups 5 5.20 1.119.40 1.362.60 .36 3.20 .915.80 1.19

Within groups 234 4.67 6.96 7.32 3.53 3.20

 

 

 

 

 

 

 

Hypothesis I

 

Several studies have consistently shown the same preva-
lent errors in syllOgistic reasoning with familiar verbal and
symbolic materials. Thus, it was expected that the same
erroneous alternatives would be chosen in a test of contextual

material. The preferred errors for EE, E9, I, 19, and 99

premise pairs were expected to be those predicted by the at-
mosphere hypotheses and for A9 premise pairs to be those
predicted by the conversion hypotheses. The percent of the
responses to each item on the atmosphere and conversion error
scales is given for the pretest (N = 240) in Table 4 and for
the posttest of Group 6 (n = 40) in Table 5. Blank responses
made some totals less than 100%. The mean percent error on
the pretest for the atmosphere and conversion items is 66.4
and 87.6, respectively, and for the posttest 57.6 and 82.1,
respectively.

For the conversion error items on the pretest and post-

testthermmmer of predicted errors exceeded any other single

27
error alternative on a total of 23 out of 24 items. The Pear-
son chi square (Hayes, 1963, p. 582) of errors on each item
was statistically significant (p<.001). On the pretest 62.1%
of the errors were predicted, and 77.8% were predicted on
the posttest. Random responding on the four error alternatives 9,
would have resulted in 25% of the errors being predicted.
To statisically describe the predictability of this hypothesis
the errors for the twelve items on the pretest and the post-
test were classified as not-predicted or predicted, and a
chi square was calculated with one degree of freedom to test
the theoretical pOpulation ratio of 3 : 1. Since more than
half of the errors were predicted, it is not surprising that
the obtained ratio differed from the theoretical ratio at a
statistically significant point (p<.0001).

On the atmOSphere error items of the pretest and post-
test the predicted error was favored on a total of 18 out of
24 items. On all but one item the Obtained distribution de-
viated from a random distribution at a statistiCally signi-
ficant point (p<.0001) as indicated by chi square. The re-
maining item was statistically significant at the .05 level.
On the pretest 62.0% of the errors were predicted by the at-
mosphere hypotheses, and on the posttest 64.8% were predicted.
As with the conversion hypotheses, the obtained ratio of not-
predicted to predicted errors differed from 3 : 1 (p(.0001)
for the pretest and the posttest as indicated by chi square.

On the basis of this evidence Hypothesis I cannot be

rejected.

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29

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30

Hypothesis II

 

If the performance on one error were independent of per-
formance on the other error, there would be no covariance be-
tween the two variables. This would be true if the correlat-
ion between atmOSphere and conversion items for the error
scores and for the number correct was not statistically differ-
ent from zero. For the pretest and the posttest of Group 6
the distributions for the atmosphere and conversion error
scores were approximately normal. The product-moment cor-
relation between the atmosphere and conversion error scores
for the pretest was .382, and for the posttest was .347 as
shown in Tables 6 and 7. A two-tailed test showed the pre-
test correlation to differ from zero beyond the .01 level
(df = 238), and for the posttest the correlation differed from
zero at the .05 level of confidence (df = 38).

The correlation between the true scores on these tests
would be expected to be higher if the errors of measurement
did not attenuate the degree of correlation; i.e., if the
tests were perfectly reliable (see Table 1 for the test re-
liabilities). To find a truer estimate of the above correla-
tions, a correction for attenuation (Guilford, 1965, p. 486)
was executed, and the true pretest correlation was estimated
at .556 and the true posttest correlation at .463.

To account for any variance due to factors other than
reasoning ability itself the reading and numerical components
were partialed out of the total variance by the method of
partial correlation (Guilford, 1965, p. 340). Guilford,

Kettner, and Christensen (1955) found verbal comprehension

31
and numerical facility and achievement to be factors correlated
with a general reasoning ability, and intuitively reading
comprehensionwmuld play a larger part in performance on reason-
ing tests with complex paragraphs than in performance on
symbolic syllogisms. The CQT scores were secured for each E,
and the reading comprehension (R) and numerical (N) scores
were used to eliminate the effects that these variables had
upon the atmosphere-conversion error correlation. The partial
correlation for the pretest between the atmosphere and conver-
sion errors with the effects of reading comprehension eliminated
is .390 and with the effects of numerical ability eliminated
it is .392. That correlation with both effects partialled out
was .399 which remained statistically significant beyond the
.01 level by a two-tailed test. Partialling out the influence
of reading comprehension in the posttest the atmOSphere-con-
version error correlation became .334. With the influence
of numerical ability removed the correlation was .329 which
remained statistically significant at the .05 level by a two-
tailed test.

Since error scores bear such a strong negative correlation
to their respective correct scores, one would expect that the
number correct would have a covariance at least as large as the
error scores. Were this true it would also be evidence against
the independence of the errors. The distributions for the
number correct on the pretest and posttest scales were not
skewed beyond a value of 1.527 when zero was normal. From
Table 6 the pretest atmosphere-conversion correct product-

moment correlation was .505. From Table 7 that correlation

32
Table 6
Product-Moment Correlations Between the Pretest Scales

and COT Scores for Reading and Numerical Tests (n = 240)

 

 

 

Scales 1. 2. 3. 4. 5. 6. 7.
1. Atmosphere error 1.000
2. Conversion error .382 1.000
3. Atmosphere correct -.674 -.005 1.000
4. Conversion correct -.315 -.370 .505 1.000
5. Determinate correct .031 .367 .255 .075 1.000
6. Determinate "none" P.207 -.199 .165 .139 -.572 1.000
7. COT R L.080 .072 .245 .193 .277 -.150 1.ooo
8. COT N 3.035 .151 .243 .192 .278 -.154 .420

 

 

for the posttest was .589. A tendency to respond to "none of
the above" regardless of content could have made this corre-
lation spuriously high. A partial correlation removing the
covariance due to responding to "none of the above" between
the correct responses of atmosphere and conversion items on
the pretest of_.493 and on the posttest of .579 indicated that
such an influence was small. Any covariance contributed by

a common ability such as reading comprehension or numerical
ability would show itself more in correct reasoning than in-
correct reasoning. Thus, the partial correlations were cal-
culated removing the variance due to reading comprehension
(CQT R), numerical ability (CQT N), and a tendency to respond

with "none of the above." For the pretest this partial corre-

33
Table 7

Product-Moment Correlations
Between the Posttest Scales of Group 6

and CQT Scores for Reading and Numerical Tests (n = 40)

 

 

 

1
Scale 1 1. 2. 3. 4. 5. 6. . 7.

1. Atmosphere error }.000

2. Conversion error .347 1.000

3. AtmOSphere correct F.864 -.224 1.000

4. Conversion correct L.51O -.758 .589 1.000

5. Determinate correct .134 .134 .072 -.070 1.000

6. Determinate "none" -.293 -.304 .141 .194 -.580 1.000

7. CQT R . -.225 -.109 .327 .393 .038 -.161 1.000

8. COT N p.247 -.092 .398 .322 .142 -.005 .297

 

 

lation between number correct on the atmosphere and conversion
items was .447. For the posttest it was .466. Statistically
both correlations remained significant beyond the .01 level

by a two-tailed test.

On the basis Of this evidence Hypothesis II must be re-
jected. Note also in Tables 6 and 7 that the correlation be-
tween atmOSphere errors and conversion correct is high and
negative in both the pretest and posttest. The converse re-
lationship, i.e., between atmosphere correct and conversion

error, is small and not statistically deviant from zero.

34
Hypothesis III

It was expected that anti-error training instructions
would reduce the errors against which the instructions were
directed and not others. Similiarly it was eXpected that the
only increase in the number of correct on error items would
be for the group trained against that specific error. Thus,
the hypothesis tested statistically was that the mean number
of errors (or number correct) was equivalent for each group
on each dependent variable. A gain score was calculated by
subtractjrgthe pretest score from the posttest score and
adding 25, the greatest possible change. Thus, an error (or
number correct) gain score of less than 25 would represent
a decrease in errors (or number correct). A gain score of
more than 25 would represent an increase in errors(or correct
responses).

Table 8 shows the mean gain score and the standard devi-
ation for Groups 1-6 with 40 Es per group. Note the highest
mean for number correct was 27.48 which represented an average
increase in the number of correct responses of 2.48. The
lowest mean for the number of errors was 23.62 which represented
an average decrease in errors of 1.38. The reliability and
standard error of measurement (Thorndike and Hagen, 1961, p. 367)
for each scale is shown in Table 9. These were lower than for
the pretest and posttest separately because of the correlation
between the tests which ranged from .306 to .519 for all groups
(n = 240). Because the number of Es in each group was large

and equal, homogenity of variance was assumed, and a one-way

Mean Gain Scores

for Groups

35

1-6 on each Scale

and Standard Deviations

 

 

 

 

H Group
°Ca|e 1 2 3 4 5 6
Atmosphere error 23.62 23.95 24.25 24.48 23.82 24.72
2.94 2.58 3.10 2.87 2.24 2.88
Conversion error 25.65 25.65 24.32 25.78 26.02 25.70
2.85 3.21 3.06 2.55 2.72 2.62
Atmosphere correct 27.48 26.38 26.80 25.90 27.10 25.92
3006 3,83 3062 2.86 2.23 3047
Conversion correct 26.30 26.18 26.55 25.45 25.68 25.62
2.88 2.26 3.00 2.01 1.42 1.81
Determinatacorrect 24.90 25.60 24.92 25.90 25.75 25.65
2.57 2.07 2.34 2.18 1.58 1.94

 

 

analysis of variance was used to test the

equality of mean

gain scores for all groups on each separate dependent variable.

Table 10 summarizes the analysis for each dependent variable.

The differentiation between means on the conversion error was

the only difference which approached significance. Dunnet's

t-statistic (Winer, 1962, p. 89) was used for a post-mortem

comparison of the mean gain score of each experimental group

with that of the control Group 6 across each independent

variable. Only on the atmOSphere correct scale was there
any difference which was statistically significant; Group 1
made more correct responses on atmosphere items than the un-
trained Group 6, and other groups did not differ from the
2.29, p(.05).

control (t = Worthy ofrpte among these results

was that Group 4 with only training in the definition of "some"

36
did well albeit not significantly better than the control
Group 6. Also Group 3 did not perform better than either
Group 1-0r 2, even though that training incorporated the
instructions of both Group 1 and 2.

The equivalence hypothesis was prOposed to account for
the errors made in the solution Of syllogisms which Chapman
and Chapman (1959) explain by an invalid A premise conversion.
In the present materials these syllogisms were A9 figure I
and 9A figure I. If the training instructions did reduce the
number of errors made on these items the relative gain would
be larger than that for Group 6. On these items 37 more errors
were made on the posttest than on the pretest for Group 4,
and Group 6 had 31 more errors. No significance test was
necessary to see that such training instructions did not

affect that type of error.

37

Table 9

Gain Score Reliability and Standard

 

 

 

 

 

Error of Measurement for each Scale
Atmos. Conv. Atmos. Conv. Deter.
Error Error Correct Correct Correct
Reliability .505 .580 .416 .574 .367
Standard Error 3.43 3.83 6.66 3.23 2.65
Table 10

Summary of the Analysis of Variance for Gain Scores

Between all

Groups on each Dependent Variable

 

 

 

 

Atmos. Conv. Atmos. Conv. Deter.
Source df error error correct correct correct
MS F MS F MS F MS F MS F
Between groups ES 7.00 .90 16.20 2.0116.4O 1.76‘180 1.47'140 1.62
Within groups 234'7{%4 8.09 9.28 5.29 4.57

 

 

 

 

 

 

 

DISCUSSION

Hypothesis I

On the atmOSphere and conversion items the largest number
of errors will be predicted by the atmosphere and conversion
hypotheses, respectively.

The Obtained percentage of errors predicted by the res-
pective hypotheses with contextual material is comparable to
that obtained in other studies incorporating other material.
For contextual material 62 & 65% of the errors on atmOSphere
items were predicted by the atmosphere hypotheses, and 62 &
78% of the errors on conversion items were predicted by the
conversion hypotheses. For symbolic syllogisms of the same
mood the atmosphere items in the studies of Simpson and Johnson
(1966), Chapman and Chapman (1959) and Morgan and Morton (1944)
report the percent of the errors predicted by the atmosphere
hypotheses to be about 70%, 67% and 67%, respectively. On the
conversion items they found the percent Of the errors predicted
by the conversion hypotheses to be about 60%, 78% and 73% res-
pectively. Morgan and Morton (1944) found that for familiar
verbal material about 60% and 67% of the errors were predicted
by the atmosphere and conversion hypotheses, respectively.

The direct implication of this is that the errors found in
syllogistic reasoning with contextual material correSpond with
those found in symbolic and verbal material in both kind and

amount.

38

39

Looking beyond the statistical description, these data
do not agree with the data of Chapman and Chapman (1959) on
those items on which the atmosphere error fails to predict
the favored response. specifically this occurs at least
once with each premise pair used except 1;. In view of the
overall predictability of these errors, this may be interp-
reted as the influence of content upon reasoning. In other
words, peOple reason with the information available. If the
syllogisms are symbolic, the available information is less
than if they were of familiar verbal material, and reasoning
may be based on information about the structure of the syllo-
gism, i.e., quantifiers and qualifiers. Thus, the extent
to which the supposedly meaningless context makes meaningful
informationebout the terms available to the subject, the more
the conclusion will be based on that information and less on
the IOgical structure. Thus, if errors are made, they would
not necessarily be those predicted. This corresponds with
the results of Wilkins (1928) and Morgan and Morton (1944)
where it was found that less errors occurred on familiar ver-
bal than symbolic material, and the most difficult syllOgisms
were those where the correct conclusion was contrary to be-
lief. When knowledge about the terms Of verbal syllogisms
either is not available (unfamiliar terms), or is not relevant
(e.g., "all insults are troubles"), they are slightly more
difficult than symbolic syllOgisms according to the data Of
Wilkins (1928) and Morgan and Morton (1944). Thus, for those

items on which the predicted errors are not favored, it could

40
be that the information available led the subject to other
conclusions.
Hypothesis 11

Performance on the atmosphere error items will not be
dependent upon performance on the conversion error items.

On the baSis of this evidence this hypothesis must be
rejected. Rather than being uncorrelated, there is a sub-
stantial correlation between performance on the conversion
and atmosphere items on both number of errors and number of
correct responses. By partial correlations this was shown
not to be due to any variance shared with reading comprehen-
sion, numerical ability, or tendency to reSpond to "none of
the above" on all items. Aside from the statistically sig-
nificant difference from a value of zero, the amount of var-
iance shared does not exceed 36% This, however, is an im-
pressive amount when it is considered that the items were
designed to be as independent as possible. For the A9 con-
version items invalid conversions of both A and 9 premises
were possible which implied that these items would be the
most susceptible to invalid conversions. Although the 9
conclusion was predicted for the conversion items by the
atmosphere hypotheses, it was suspected that the atmosphere
effect would be quantitatively weakest With A9 premises.

The predicted errors on atmOSphere items could not be deduced
by invalid A or 9 conversions since there were no A premises
and no 9-conversion would yield the predicted conclusion for

any syllogism. The obtained correlations would have been

41
larger if the error scales had been perfectly reliable or if
AE and Al premises were used as conversion items. In addition,
the obtained dependence was replicated in the posttest albeit
with the same subjects.

One aspect of the correlational relationship between
performance on the error items which cannot be readily expé
lained is the high negative relationship between the number
of atmOSphere errors and the number of conversion correct.
This was replicated on the posttest, but the converse relat-
ionship, between the number of conversion errors and the
number of atmOSphere correct, does not Obtain either on the
pretest or the posttest. This relationship between the num-
ber of atmosphere errors and the number of conversion correct
corresponds in direction and magnitude to the negative relat-
ionship between the number of atmOSphere errors and the num-
ber of atmosphere correct. This is interesting, but inexp-
licable, at the moment. Perhaps if a test of syllogistic
reasoning which contained several of all possible indeter-
minate syllogisms were factor analyzed, only one factor would
emerge rather than the prOposed atmOSphere and conversion
error factors. Such an analysis would account for all cor-
relations.

The obtained dependence, of course, is contradictory
to the -.12 correlation between the number of atmosphere
and conversion errors reported by Simpson and Johnson (1966).
This may be resolved, however, by examining their scoring
procedure for atmosphere items. For the A9 and E9 premise
pairs conclusions of A or 9 and of E or 9, reSpectively,

were scored as predicted atmosphere errors. Although this

42
scoring is conSistent with the results of Chapman and Chapman
(1959), it is inconsistent with the predictions of the second-
ary atmOSphere hypotheses which state that a particular premise
creates a "some" atmosphere, eventhough the other may be uni-
versal, and that a negative premise creates a negative atmos-
phere, eventhough the other may be affirmative (Woodworth and
Sells, 1935, p. 453). Thus, the original atmosphere hypothesis
would predict only an 9 conclusion for the E9 and A9 premise
pairs. Since there were four E9 and 19 items, 16 responses
were scored as conversion errors. This would be conducive
to a low negative correlation as obtained. The difficulty
of the conversion items was augmented by the presentation of
eight items of 9A figure IV form in A9 figure I order which
necessitated E manipulating premise order prior to actually
reasoning. This was not true for the atmOSphere items. This
would have enhanced the difference as a random variability
in conversion item performance.

The hypothesis of Chapman and Chapman (1959) would also
predict independence of performance, because the items were
designed so that invalid A or 9 conversions would not yield
a predicted error on the atmOSphere items. On the other
hand, the atmosphere hypotheses do predict the conversion
error responses (A99). The Operation of one invalid reason-
ing process or mechanism is possible considering the degree
of dependence between the error scales. It may, therefore,
be concluded on the basis of this evidence that for this con-
textual material and for this sample of subjects the conver-

sion hypotheses are untenable. Because of these restrictions

43
the generality of this conclusion is Open to question. Further
evidence could be obtained from retesting with symbolic syllo-
gisms or differential training.
Hypothesis III

For groups receiving Specific training instructions against
the atmOSphere, conversion, or equivalence error, a decrease
in errors or an increase in correct conclusions will obtain
only on error items against which the training instructions
were directed.

The analysis of variance tested the hypothesis that the
means of all groups were equal, and the‘ hypothesis could not
be rejected for any dependent variable. This indicates that
no group improved more than any other. Thus, Hypothesis III
must be rejected in view of the present data.

The implications of such a rejection are less meaningful

than had it been rejected only for some variables. Post-mortem

 

t-tests showed there was only one gain in any group which
differed significantly from the control group which had
no training. Since the largest gain in performance was +2.5,
the most attractive explanation is that the failure to differ-
entiate between groups was due to the low gains by all grOUps.
The effect of low gains would have been augmented by the large
within group variance which is usually the case with training
studies.

Explanations for low gains are many, and almost any could
be true in this case. Perhaps effective training was not

possible due to the abstractness of the material or the non-

44
existence of the prOposed atmosphere and conversion error
mechanisms. Because Simpson and Johnson (1966) were able
to reduce atmosphere errors and increase the number of correct
atmosphere reSponses, this possibility may be tentatively
eliminated for the atmosphere error.

Another alternative would suggest that the instructions
were not learned because Es were not attentive to them. Al-
though there can be no direct evidence for this, anyone who
has given tests to undergraduates can vouch for their reluc-
tance to read or observe intructions. In this case the in-
structions were Often longer than two double-Spaced pages,
and everyone had taken a similiar test previously.

Other studies which have trained against errors in rea-
soning have reported appreciable success with various procedures.
Simpson and Johnson (1966) used a 15-minute lecture plus numer-
ous examples and practice to reduce atmosphere errors. Their
failure to substantially reduce conversion errors may be due
to the fact that they trained against an A-conversion and in-
cluded nine items which needed an 9-conversion (9A figure IV).
In fact two conversion items were determinate (9A figure III)
with the predicted error actually being a valid inference.
Henle and Michael (1956) reduced the number of invalid con-
clusions by oral instructions on how to solve syllogisms by
using diagrams, and examples were given. Moore and Andersen
(1954) trained Es in the solution of logic problems in a
sentential calculus with an 80 minute lecture, examples, and

a series of visual aids. Wason (1964) used self-discovery

45
to reduce errors in syllOgisms by allowing a valid inference
to contradict a previously drawn invalid inference. Apparently
improvement is possible with a more substantial training pro-
cedure than was used in this eXperiment. Recommended improve-
ments would be the use Of (1) oral instructions with a quest-
ion and answer period, (2) summary instructions which would
be available to each E, and (3) practice on syllOgisms not to
be used later. Care must be taken, however, to make training
specific to one error, not to identify the syllogisms to be
used later, and to maximize transfer between the instructions
and practice and the problem solving task (Duncan, 1959).
Were such improvements made, it would be eXpected from the
present evidence that the anti-atmosphere error training would
reduce atmosphere and conversion errors, and that the anti-
conversion error training would, either not effectively reduce

conversion errors, or would not do so diffenyitially.

SUMMARY

Several previous studies have shown that Es untrained
in the use of formal logic accept very predictable erroneous
conclusions when solving syllOgism problems. Two types Of
lOgical Operations have been prOposed to account for such
consistent behavior. The atmOSphere effect (Woodworth and
Sells, 1935; Belle, 1936) was defined as the influence which
the context, or tone, of a situation has upon the completion
of a task. It was assumed that, if E does not understand,
or does not use, the given lOgical relationships, the con-
clusion will be based upon the structural features of the
syllogism, i.e., the quantifiers and qualifiers. Thus, for
like premises a like conclusion would be predicted. For un-
like premises one negative premise would predict a negative
conclusion, and one particular premise would predict a par-
ticular conclusion.

The conversion hypotheses (Chapman and Chapman, 1959)
assume that the logical relationships are understood, With
the exception that an A or 9 premise may be invalidly con-
verted. Thus, after making an invalid conversion, a conclu-
sion will be deduced by otherwise valid Operations. This
was prOposed as an alternative eXplanation to the atmOSphere
hypotheses for certain items. The predicted reSponses are

the same for those items.
46

47
Because these contradictory hypotheses predicted erron-

eous conclusions equally well for certain syllogisms, Simpson
and Johnson (1966) trained against each error separately. On
items where only the atmosphere hypotheses predicted the
favored conclusion, the groups receiving anti-atmosphere error
training produced the least number of errors and the greatest
number of correct responses. On the conversion error items
the anti-conversion error training did not influence perform-
ance any more than other training procedures. For untrained
Es the correlation between the number Of atmosphere and con-
version errors was only -.12. Several methodolOgical faults
in this experiment, however, indicated the necessity of rep-
lication.

The present experiment used a transfer-of-training para-
digm to detect changes in performance due to differential
training. The premises of the syllOgisms were of neutral
emotional content and used unfamiliar, or nonsense, words
for terms. These were included in a paragraph to approximate
complex reading material. The pretest and posttest included
12 atmosphere error, 12 conversion error, and 12 determinate
items. Es were assigned randomly to six groups of 40 Es each.
These groups received written instructions against the atmos-
phere, conversion, or equivalence errors. One group received
both anti-atmosphere and anti-conversion error instructions.
A control group received the introductOry paragraph and the
definition of "some" which the training groups had received.

The other control group received no training instructions.

48

The results indicated that the errors made on syllogisms
of contextual material were similiar in kind and amount to
those made on syllOgisms of symbolic or verbal material. A
correlational analysis of the relationships between perform-
ance on error items indicated a substantial dependence. Both
the number of errors and the number of correct responses for
the error items were correlated at a statistically signifi-
cant level, i.e., between .347 and .589. This was not pre-
dicted from past research and had particular import since
only the atmosphere hypotheses could predict the errors for
both types of item. On the atmOSphere items no predicted
error could result from an invalid A or 9 premise conversion.
Partial correlations showed that these correlations were not
due to a covariance with reading comprehension, numerical
ability or tendency to reSpond "none of the above” to all
items. These results were interpreted as evidence against
the proposed conversion error. Other evidence, however, is
necessary to strengthen the generality of this conclusion.
Differential training would have supplied further evidence,
but no type of training instructions produced a significant
change in performance. Possible causes of this and improve-
ments in this procedure were discussed. Future research in

this area was also suggested.

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Bruner, J. 8., Goodnow, J. J., and Austin, G. A. A study 9:
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Chapman, L. J. and Chapman, J. P. Atmosphere effect re-exam—
ined. 9. exg. Psychol., 1959, 58, 220-226..

Cohen, M. R. and Nagel, E. An introduction :2 logic and scien-
tific method. New York: Hartcourt, Brace, & CO., 1934.

 

 

COpi, I. M. Symbolic logic. New York: Macmillan, 1954.

 

Davis, F. B. The factorial composition of two tests of comp-
rehension in reading. 9. 3g. Psychol., 1946, 37, 481-486.

Davis, F. 8. Two new measures of reading ability. 9. _g.
Psychol., 1942, 33, 365-372.

Duncan, C. B. Recent research on human problem solving.
Psychol. Bull., 1959, 56, 397-429.

Frase, L. T. Mediation paradigms and syllogistic reasoning
behavior. Proc. Amer. Psychol. Ass., 1966.

 

 

Gorden, R. L. The effect of attitude toward Russia on logical
reasoning. 9. soc. Psychol. 1953, 37, 103-111.

Gottesman, L. and Chapman, L. J. SyIIOgistic reasoning errors
in schiZOphrenia. 9. consult. Psychol., 1960, 24, 250-5.

Guilford, J. P. Three faces of intellect. Amer. Psychologist,
1959, 14, 469-4790

 

Guilford, J. P. Fundamental statistics in psycholoqy and
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Guilford, J. P. and Hoepfner, R. Structure-of-intellect fac-
tors and their tests. Reports from the psychological
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1966, No. 362

 

49

50

Guilford, J. P., Kettner, N. W., and Christensen. P. R.
A factor-analytic investigation of the factor called
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Guilford, J. P. and Merrifield, P. R. The structure of intel-
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Hayes, W. L. Statistics for psychologists. New York: Holt,
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Henle, M. On the relation between lOgic and thinking. Psychol.
Rev., 1962, 366-378.

Henle, M. and Michael, M. The influence of attitudes on syl-
lOgistic reasoning. E. soc. Psychol., 1956, 44, 115-121.

Hunter, I. M. L. Note on an atmosphere effect in adult reas-
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Hunter, I. M. L. The solving of three-term series problems.
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Janis, I. L. and Frick, F. The relationship between attitudes
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Lefford, A. The influence of emotional subject matter on
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Sells, S. B. The atmOSphere effect: an experimental study of
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Simpson, M. E. and Johnson, D. M. Atmosphere and conversion
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18, 451-4600

APPENDIX A

52

53

IDGICAL ABILITIES TEST

Remove the answer sheet frOm.the test booklet and place (1) your_,
name, (2) your student number, and (3)-the name of the test in the
appropriate places.' Place a "Yes" or a "No" in the place marked '
"Instructor" answering whether or not you have previously had a class

dealing with formal logic.

‘Within this test you will find paragraphs each followed by five
statements. Your task is to read each paragraph carefully, then, if
a conclusion is deducible from.the statements in the paragraph,
select that conclusion from those given and mark that number on your
answer sheet. If no conclusion is logical from the statements in

the paragraph, mark option "5" on your answer sheet.

To avoid confusion the definition of the term "some" is to be
"there exists at least one...." This is to say that you may not
infer "Some.A are not B" from the statement "some A are B." Similarly,

"some A are not B" does not imply "some A are B."

‘Work as fast as you can, but there should be ample time for you to

finish. Be sure to answer every question, even if you have to guess.

- Place no marks on this test booklet. There will be scratch paper

provided.

DO NOT BEGIN UNTIliTOLD TO DO 80.

F _ .-.
In

IDGICAL.ABILITIES TEST

1. There are many species of plants in South.America with beautiful flowers

that are practically unknown in Europe and North.America. Visitors to South.
America are always fascinated by the colorful Hofmeisters, named after the
German explorer who first described them, and the shy shade-loving Helgas,
named after his wife. Hofmeister is best known for his cultivation of the
Stersidas, however. None of the Hofmeisters are Stensidas, to be sure, and
none of the Thorntis are Stersidas, but North.Americans like to photograph
all of them.

'What can be inferred from this paragraph?

All Thorntis are Hofmeisters.

No Thorntis are Hofmeisters.

Some Thorntis are Hofmeisters.
Some Thorntis are not Hofmeisters.
None of the above.

AAAAA
\n two N i--l
vvvvv

The Brazilian.Aloutte has a small flower and an unpleasant scent, but some of
them have edible roots and are sold commercially as Picaros. The Pobrecias
which one sees in the markets also have an unpleasant scent, but nope of the
smaller Pobrecias that grow high up on mountains are Picaros.

Therefore:

(1) All Pobrecias are Alouettes.

(2) No Pbbrecias are Alouettes.

(3) Some Pobrecias are Alouettes.

(4) Some Pobrecias are not.Alouettes.
(5) None of the above.

The delicate Glories of Argentina, which open only in cool weather, are all
Sassoids. Some of the equally delicate Fragilas, found only in damp areas,
are not Glories.

'What can.you infer from these statements?

(1) All Fragilas are Sassoids.

(2) No Fragilas are Sassoids.

(3) Some Fragilas are Sassoids.

(h) Some Fragilas are not Sassoids.
) None of the above.

If you hike along the mountain streams of Equador, you may be lucky enough to
see the large red Fiegantas, some of which are not true Corads. All Corads,
we now know, are Vemordas.

Therefore:

All Vemordas are Fiegantas.

NO Vemordas are Fiegantas.

Some Vemordas are Fiegantas.
Some Vemordas are not Fiegantas.
None of the above.

AAA/\A
U1 :6) N [—1
VVVVV

(over)

54
-2-

In Spring in Chile everyone goes to the fields to pick the huge
golden Cunlas, all of which are Platyphores. Some Monarchs are
Cunlas which can be steeped to make a weak tea.g

Therefore: .

All Monarchs are Platyphores.

No Monarchs are Platyphbres. ' . - .
Some Monarchs are Platyphores.
Some Monarchs are not Platyphores.
None of the above.

(
(
(
(
(

U'l PW TU -‘
VVVVV

In the district of Gruanda in Brazil there is only one tribe
remaining wh' i is virtually untouched by civilisation as we know
it. We shalTT Aem Gruandans for simplicity. Reliable sources
indicate that no fisherman on the Amazon is a Christian. All of
the Gruandans are fisherman who depend on the mighty Amazon for
sustenance.

From these statements you may conclude:
All Gruandans are Christians.

No Gmm‘are Christians. " ’ '

Some Gruandans are Christians.

Some Gruandans are not Christians.

None of the above.

U'l-pkfllU-e

One of the earliest civilizations that we have dependable knowledge

of deveIOped in the fertile valley between the Menoh River, as it

was then called, and the Eurak River. For many years historians
believed that the Menoh people and the Euraki had had little contact
But tablets recently discovered from the Menoh River have established
the custom d’dual citizenship. These tablets demonstrated that

the Euraki feared the river, apparently for religious reasons. Thus,
none of the Euraki were sailors. Also the tablets indicated that
some Menoh were actually Euraki.

Therefore:

All Menohs were sailors.

NO Menohs were sailors. '

Some Menohs were sailors.
Some Menohs were not sailors.
None of the above.

(1
(2
(3
(4
(5

8. Tales that come to us from the classical storytellers frequently

mention the Demeks, the Eosirs, and the Fellutos of the middle

kingkhngdoma The glory of the middle kingdom, only hinted at in the

ruins that survive, was due chiefly to the warlike Demeks, some of

whom were Eosirs. The Felluto tradesmen and sailors carried these
tales throughout the Mediterranean and, because some of the EOSlrs

were Fellutos, many of the tales have survived to this day.

Therefore:

All Fellutos were Demeks.

No Fellutos were Demeks.

Some Fellutos were Demeks.
Some Feluttos were not Demeks.
Nan: nf thp shave-

\AAAA
fl 4—‘U 10 d

9.

10.

-3... .

The Lyd people of this period inhabited the arid coastal plains. Wood was
absent, of course, from these regions and no fishermen in this area were
boatmen. To supplement the frequently low crop yield some Lyds labored

as fishermen.

It follows that:

(1) All Lyds were boatmen.

(2) No Lyds were boatmen.

(3) Some 1.de were boatmen.

()4) Some Lyds were not boatmen.
(5) None of the above.

The limestone monuments Of the early kingdom, crude as they are, show us some
of the forms of worship of the Rizehs, all of whom wore leafy ornaments on
the head and were therefore called Leafmen. The Kephru clan, some of whom
were not Rizehs, apparently did not erect monuments. At least none survived.

Therefore :

(1) All Kephrus were Leafmen.

(2) No Kephrus were Leafnen.

(3) Some Kephrus were Leafmen.

(1.1) Some Kephrus were not Ieafmen.
(5) None of the above.

The Kephrus worship the spirits of the weather. Some phantoms who rule the
‘wind and sky are Ives. Kephrus also believe that some spirits of drought are
not Ives.

From these statements you may conclude:

(1) All spirits of drought are phantoms who rule the wind and sky.
$2; No spirits of drought are phantoms who rule the wind and sky.
Some spirits of drought are phantoms who rule the wind and sky.
(4) Some spirits of drought are not phantoms who rule the wind and sky.
(5) None of the above .-

In the mythical land of Id there dwells the Pygian tribe. These uncivilized
natives care from the highlands of Adda, so all of them are Addans. However,
some Addans are not relatives of neighboring Bydans.

Therefore:

(1) All relatives of the Bydans are Pygians.

(2) NO relatives of the Bydans are Pygians.

(3) Some relatives of the Bydans are Pygians.

(14) Some relatives of the Bydans are not Pygians.
(5) None of the above. .

In investigating the" collapse of rabbits' ears Dr. Thomas found that the body

‘ of a rabbit naturally releases trypsins,none of which are papins, Confusing

to the detection of certain enzymes are those called ficins. No ficins are
papins, because of almost indetectable structural dissimilarities.

Therefore:

(1) All ficins are trypsins.

(2) NO ficins are trypsins.

(3) Some ficins are trypsins.

(14) Some ficins are not trypsins.

(5) None of the above. A -
‘ (over): ,

14.

15.

16.

17.

55
-4-

It has long been known that mania digestion, like that.Of the
other mammals, depends on a complex series of chemical reactions
in the stomach and small intestine. Scientists at the Federal
Institute have analyzed certain steps in the digestive process
and have proven that the glyphase, which is produced first in the
stomach under ordinary conditions, is bectone. This bectone, a
clear tasteless liquid, is the familiar dorol, originally .
synthesized by Professor Dorough, after whom it is named.

What can you infer from this paragraph?
All glypahse is dorol.

No glypahse is dorol.

Some glyphase is dorol.

Some glyphase is not dorol.

None of the above.

uvkxuar-
vvvvv

Precise measurements of the gases generated in the stomach have
disclosed the origins of the Iornygen which makes infants uncom-
fortable after eating. Some of the acid-forming cholibase is
lornygen. And some of the respibase, which appears before

feeding, is not lornygen,and seems to disappear without discomfort.

Therefore:

All respibase is cholibase.

No respibaée is cholibase. ""
Some respibase is cholibase.
Some reSpibase is notcholibase.
5) None of theabove.

vvvv

Plaskol is a complex substance of high concentration that absorbs
large amounts of water. All plaskol is solutin. Some of the epidol
found in the intestinal walls, is plaskol.

Therefore:

All solutin is epidol.

No solutin is epidolé . '

Some solutin is epidol.
Some solutin is not epidol.
None of the abOvee

AAAAA
U1 #U N -*
vvvvv

Three chemical substances of particular importance to human
digestion are turgide, hoximide, and cytol. Some turgide is not
hoximide. All hoximide, however, is cytol.

Therefore:

All cytol is turgide.
Nolnfln12fl3tmmgflkh

Some cytol is turgide.
Some cytol is not turgide.
None of the abOve.

“AAA“
VVVVV

1
2
3
4
5

18.

-5-

In the final stage, many of the complex chemical substances are
eliminated, but the dextrocubes remain. Some dextrocubes are
not aminates, which are highly injurious to the digestive

organs. The leptpcubes also remain, all of which are dextrocubes.

20.

21.

22.

(1) All leptocubes are aminates.

(2) ‘No leptocubes are aminates. '

(3) Some leptocubes are aminates.

(4) Some leptocubes are not aminates.

(5) None of the above.

In the automated army of the future, the ranks and assignments
will be highly specialized around technical skills and accomplish-
ments. No POpguards will be Shootmen, because of the Special

training required. All Citmen, however, will be Popguards with
regular duties and privileges. ' H

Therefore:
(1). All Citmen will be Shootmen.
(2) No Citmen will be Shootm.
(3) Some Citmen will be Shootmen.
(4) Some Citmen will not be Shootmen.
(5) None Of’the above.

In this automated army of the future. some Corpgals will not
be Teengals, depending on the results of medical and psychological
tests. All Groundgals will be Corpgals.

Therefore:

(1) All Groundgals will be Teengals.
(2) No Groundgals will be Teengals.
(3) Some Groundgals will be Teengals.
(4) Some Groundgals will not be Teengals.
(5) NOne of the above.
The elite heros of this army, the Astromen, will need years of
specialized training and some Cellmen will not become Astromen.
All Astromen, of course, will be Gomen.
Therefore: -
(1) All Gomen will be Cellmen.
(2) No Gomen will be‘ Cellmen. ‘ .
(3) _Some Gomen will be Cellmen. .
(4) Some Gomannwill not be Gelflmen.

(5) None of the abOve.

At the top of the command structure of the future army will be
the Omnimen, who have come up from the ranks of the Starmen and
Wingmen. Thes, some Starmen will be Omnimen and some Wingmen will
be Omnimen. ' ~

Therefore: -
All Wingmen will be Starmen.

(1 )

(2) No Wingmen will be Stat-lien. .

(3) Some Wingmen will be Starmen.

(4) Some Wingmen will not be Starmen.
(5) None of the above.

(nunrl

 

. _——H————‘—_——___._—u

23.

56
-6-

The Flygirls in the future ariiv Will be recruited from school, but will
stay in school for preliminary indoctrination. None of the other girls,
called Dropgirls, will be Flygirls. A volunteer group will be trained
for special duties after aptitude tests, and some Ingirls will not be

. ,Flygirls.

2h.

25.

26.

AAA“

VIEW N [-4 '
vvvvv

1

You may conclude from these statements:

“(1) All Ingirls will be Dropgirls.

(2) No Ingirls will be Dropgirls.

(3) Some Ingirls will be Dropgirls.

()4) Some Ingirls will not be Dropgirls.
(5) None of the above.

The forward ranger unit of the future army will include Badman, Whitemen,
and Bluemen, chosen for their physical skill and personality. NO Whitemen
will be Bluemen. But some Redmen will be Whitemen in this unit and have

._.the sane duties and equipment.

. Therefore:

1 ' All Rednen will be Bluemen.

2 NO Redmen will be Blueilen.

3 Selle Redllen will be Bluemen.

ll Some Radnen willnot be Bluemen.
(5) None of tie above.

VV‘W

Although psychologists today seldom.speak of personality types, the
typologies of the 19th century attracted considerable attention among
educated people, at least at the conversational level. According to the
system of Professor Heinroth, Liebogynes are friendly individuals and
Rechtgynes are honest individuals. Hence, some Liebogynes are Rechtgynes.
The good old professor also said that no Rechtgynes could be Unigynes.

Therefore: . ,_
(1) All Liebogynes are Unlgy'nes, .. .-

, (2) No Liebogynes are Unig‘ynes.
.; (3) Some -Liebogyne.s‘~are Unigynes.

()4) Some Liebogynes are not Unignes.
(5) None of the above.

An entertaining book publisled by the Earl of Cobb, which was popular in
Britain in the last century, designates philoprogenitive people as Philos.
Those with a career of premeia are called Prams, and all Prems are Philos.
The Earl himself was a Xanthi and, according to this system, some Xanthi
are not Prams, regardless of what others said at the tine. ~

Therefore, according to this system:

All Xanthi are Philos.

NO Xanthi are Philos.

Some Xanthi are Philos.
”Some Xanthi are not Philos.
None of the above.

27.

28.

29.

30.

[American psychology and psychiatry of this period had an influence

-7-

on the literature of the time. Dr. Young's Dextroverts appeared
in plays and novels, and it was well known, because of'his DCKHJ'aF
lectures, that all Dextroverts are Retroverts, and that some
slocatic people are Dextroverts.

According to Dr. Young, therefore:

All slocatic peOple are Retroverts.

No slocatic people are Retroverts. -‘
Some slocatic peOple are Retroverts.
Some slocatic peOple are not Retroverts.
None of the above.

 

AAAAA
VVVVV

1
2
3
4
5

The McLaughlin International School of Personality, which developed
around the turn of the century, tied personality types to foods.
Corn-growing peOple, with an agricultural type of character and
home life, were called Stalks, and fish-eating peOple, with a
fisherman's personality, were called Lines. Some Stalks were Lines,
however,’for one reason or another. The Hunts, who pursued their
food, were supposed to be smaller and more energetic. Some Hunts
were Stalks.

Within this system, therefore:

All Hunts are Lines.

No Hunts are Lines. ‘

Some Hunts are Lines. ‘

Some Hunts are not lines. !
l

—_—____—.—___—__—.——__

AAAAA
U1 #Ul n) -
vvvvv

None of the above.

Several peoples, though uncivilized by our standards, have a rather
sophisticated tribal structure. One such tribe is the Mandes of
the Bolivian Andes. Men called Execs are all Wormen, who are in
charge of military affairs. Some Wormen, however, are not Poolmen.

Therefore:

All Poolmen are Execs.

No Poolmen are Execs. .
Some Poolmen are Execs.
Some Poolmen are not Execs.
None of the above.

AAAAA
U"! #‘W R) -‘
vvvvv

According to history the Mandes carve stone in sh0ps which are as

distinct if form and function as in the works they produce.

The Studia is a shop composed of men who rough-new the stone.

The men of the Bocci smooth the surface until the product is

ready for the detail work of the Bettegi. Recent investigations,

however, have shown that some Studias are actually Boccis. Whereas
some of the Boccis are not Bettégis as originally hypothesized.

Therefore:
(1) All Bettegis are Studias.
(2) No Bettegis are Studies; . .;;l
(3) Some Bettegis are Studias.
(4) Some Bettegis are not Studies.
(5) None of the above.
-- -- -- -- -- -- (over)

31.

32.

33.

34.

57
-8-

The onward march of intellectual progress is continually changing
the boundaries of knowledge, and consequently the organization of
universities must change as well; One forward-looking institution,

which shall be nameless, is planning for the year 2000 a large
department of Jastrology, and all Inchologists will be-Jastrologists
This will be in the same building with the Kastrology Department,
but some Jastrologists will not be ' ' Kastorians.

Therefore, in this uh iversity:‘
(1) All Kastorians will be Inchologists.
(2) iNo Kastorians will be'Inchologists.'
(3) Some Kastorians will be Inchologists.
(4) Some Kastorians will not be Inchologists.
(5) None of the above.

Because of the p0pu|ation pressures in this new university, all
Beadniks will be enrolled as Fellows, with all the duties and
privileges thereof. An extensive dormitory building program is
projected to take care of the Studniks, and all Studniks will be
Beadniks.

Therefore:

(1) All Studniks will be Fellows.

(2) No Studniks will be Fellows.

(3) Some Studniks will be Fellows.

i3) isms sluinikaeiill not be F9"°ws'

Intramural activities in the new university will be designated as
U, V, and W events in order to accomodate all players. No U-players

will be V-players because of limited facilities and scheduling.
No V-players will be w-players. Computers will schedule playing

r-Theeefore:

(1) All W-players will be U-players.

(2) No W-players will be U-players.

(3) Some W-players will be U-players.

(4) Some W-plagers will not be U-players.

(5) None of the above.

Current deveIOpements in the arts and sciences will eliminate the
arbitrary distinction between university administration and poetry.
A new departeent of Administics will be established. Some Bi050phs
will be Administers, however, because of the nature of their work.

Some Administers will not be Sonneteers because of cultural lag.

Therefore:

All BiOSOphs will be Sonneteers.
No Biosophs will be Sonneteers.
Some BiOSOphSflWill be Sonneteers.

Some BiOSOphs will not be Sonneteers.
None of the above.

AAAAA
U1 #U I'D -‘
vvvvv

35.

36.

-9-

Social events for women students in the university of the future
will be organized by the Dean's office, with the help of the
OO-COED computer, for the widest possible particicipation
consistent with high scholarship. The card sorter will assemble
the punched cards for a group to be called Comikes, which wil I all
be Cojims, admitted to Cojim activities. The mews cards will be
processed in the same way. No Cojims will be Cobills in the newv
system. The computer will see to that.

Therefore:

All Comikes will be Cobills.

No Comikes will be Cobills.

Some Comikes wiH be Cobills.
Some Comikes will not beCobills.
None of the above.

AAAAA
vvvvv

1
2
3
4
5

Nbdern textbooks, adjusted to the progress of technology, are now
being revised for the university of the future. 80 tests can be
quickly obtained by machine some Slidebooks, which include
illustrations for home projectors, are Punchbooks. Lightbooks,
which can be read in the dark, will be widely used, and all
Lightbooks are Slidebooks.

Therefore:

All Lightbooks are Punchbooks.

No Lightbooks are Punchbooks. '

Some Lightbooks are Punchbooks.
Some Lightbooks are not Punchbooks.
None of the above.

1
2
3
4
5

--the end--

1..

58
' LOGICAllREADING TEST

The Pygian tribe lives in the nurthical land of Id. Their favorite sport is
the decathlon which is held on a tribal feast day. The men usually prepare
for months in hopes of achieving the fame due the winner. As in our track
meets there are long-distance runners, all of whom are Longmen. The J-men

Lofficiate, but plainly no Longmen are .J-nen.

What is the correct conclusion from this paragraph?

(1) All long-distance runners are J-men.

(2) No long-distance runners are J-men.

(3) Some long-distance runners. are J-men.‘
(’4) Some long—distance runners are not J-men.
(5) None of the above.

The agricultural characteristics of the Pygians*are also interesting, because
only they have been able to cultivate strains of vegetables in the dense
forests of South.America which are similar to those in North America. Some
of the tubers are Dags, which are similar to our potatoes. Pygian festivals
would not be complete without their favorite beverage, Pbt, which is made
from Oades. Some Oades are tubers, because of their particular character-
istics. . .

Whatucan' be concluded from this paragraph?

(1) All Oades are Bags.

(2) No Oades are Bags.

(3) Some Oades are Dags.

(ll) Some Oades are not Dags. ‘
(5) None of the above.

One fine day a Peace Corps worker entered this peaceful land of Id. His
intentions were to bring happiness and prosperity to these uncivilized
natives. Noticing the happiness that Pot brought, he decided to increase the
crop yield of Oades, its principal constituent. He decided to use a Potite
fertilizer, but some Chlorides, which are especially good for the crops, are
not Potites, so he must be careful. On further reading, however, he found
that no Alkamid fertilizers are Potites. Thus, his decision was made.

Therefore :--»‘

(1) All Alkamids are Chlorides.

(2) No Alkamids are Chlorides.

(3) Some Alkamids are Chlorides.

(14) Some Alkanlids are not Chlorides.
(5) None of the above.

(over)

4. Storytellers of the tribe contribute greatly to the education of the

~tales, for here the military wizardry of one-hundred starving,

-2- 8‘
children as well as to the tribal mythology. In one of their tales i
some fairies who punish naughty children are not ghosts of deceased: ,

'chieftains. These storytellers hasten to add that all ghasts of

deceased chieftains are Shaws, which is important to the prOper
education of these infants.

l
According to this mythology you may conclude:
All Shaws are fairies who punish naughty children. I
No Shaws are fairies who punish naughty chi dren.
Some Shaws are fairies who punish naughty children.
Some Shaws are not fairies who punish naughty children. I

AAAAA
VVVVV

l
2
3
4
5 None of the above.

The Battle of the Zapotec is one of the Pygians' favorite heroic

beleagured men repulsed the thousand-fold forces of the fierce Zapote
Having been routed from their village, the Pygians were trapped in

a canyon with steep cliffs on three sides, precluding any escape.
Destitution then ordered all of the Stickmen to becemetRockmen who
mounted the escarpment and released a horrendous deluge of stones
upon the enemy. Later, it was learned that some Bonen were actually
Stickmen before the battle.

 

 

All Bowmen were Rockmen.
NoIwafllwenafiodmwn.

Some Bowmen were Rockmen.
Some Bowmen were not Reckmen.
None of the above.

AAAAA
U1 #‘Ul ID -‘
vavv

Therefore: 1

Like many children of the forest, the Pygians worship many deities

with equal reverence. All phantoms of the songs of night are

Morgans. Some protectors of family shrines are not phantoms of the

song ef night. i
i

If the above statements were true, you would conclude:

All protectorsedf family shrines are Morgans. .

No protectors of family shrines are Mdrgans. 1

Some protectors of family shrines. are Morgans.

Some protectors of family shrines are not Morgans. 1

None of the above.

During the Renaissance, stonecutters were called Raphs, Michs, or

Vinces according to their demonstrated techniques. Later, during a

period of turbulent wars, all Michs were Vinces because of common

political animosities. Some Vinces, however, were not Raphs due

to their furious incompatability. i
l

AAAAA
Vvvvv

1
2
3
4
5

Therefore:

All Raphs were Michs.

No Raphs were Nfichs.

Some Raphs were Michs.
Some Raphs were not Michs.
None of the aboue.

AAAAA
U‘l pk»! h) -*
vvvvv

8.

9.

10.

59
.. _3_
The tools of these stonecutters were named according to their function.
‘Whereas to the apprentices. all tools were of a distinct immutable classifica-
tion, to the masters all Fents were Groads, because they could be used
equally well in certain situations. No Groads were Lets, however, because

of structural deficiencies}

Therefore :

All Fents were Lets.

No Fents were Lets.

Some Fents were lets.
Some Fents were not Lets.
NOne of the above.

AAA/xix
U'lrw N [—1
vvvvv

0f the Bettegoas of Europe, the Florentine Bettego was by far the most famous.
Most of the masters there were not of the Grannacii, one of the oldest and
largest families in Florence. Due to an ancient papal edict, all Grannacii
were prams in Florence, because of their special qualifications.

Therefore:

(1) All prams were masters.

(2) No prams were masters.

(3) Some prams were masters.

(b) Some prams were not masters.
(5) None of the above.

One of the most promising apprentices of the Florentine Bettego was George
Sabaldi. Being an enthusiastic, aspiring youth, George had his mind set on
carving the best statue of Pan ever produced.. Engaging history as his

guide he found the carving of a Fan was so difficult that many Pans were not
statues to be admired for ages hence.h The fatal blow to his callow character
was his discovery that only some productions cf the greatest sculptors were
of the quality to be admired for ages hence. '

From these statements you may conclude:

(1) All productions of the greatest sculptors were of Pan.

(2) No productions of the greatest sculptors were of Pan.

(3) Some productions of the greatest sculptors were of Pan.

(h) Some productions of the greatest sculptors were not of Pan.
(5) None of the above.

In that day to join silver and gold together into one solid ornament was a
task for the most talented of smiths, who were all village leaders because

of their special importance to the community. ,Some peers were the most
talented smiths.

Therefore:

.All peers were village leaders.

No peers were village leaders.

Some peers were village leaders.
Some pears were not village leaders.
None of the above.

AAAAA
U1 rm m [—1
vvvvv

(over)

12.

13.

1h.

15.

_u-

Today no Florentine copper artifacts are treasured objects because of the
damage done in restoring them. The lost-wax castings, however, are
well-preserved, but some of thanlare not treasured objects.

Therefore, according to this paragraph:
(1) All Florentine lost-wax castings are copper artifacts.
(2) No Florentine lost-wax castings are copper artifacts.
(3) Some Florentine lost—wax castings are copper artifacts.
(h) Some Florentine lostawax castings are not copper artifacts.
(5) None of the above.

As technology advances and natural petroleum resources become more depleted,
the securing of petroleum from.unconventional sources becomes more imperative.
One such source is the Athabasca tar sands of northern Alberta, Canada.

Since some tar sands are sources of refinable hydrocarbons, these deposits

are worthy of commercial investigation. Some Kerogen deposits are also
sources of refinable hydrocarbons.

Therefore:
(1) All kerogen deposits are tar sands.
(2) No kerogen deposits are tar sands.
(3) Some kerogen deposits are tar sands.
(h) Some kerogen deposits are not tar sands.
(5) None of the above.

Geologists have found that all.tar sands are bituminous sands which is impor-
tant for finding oil deposits in.this form. Likewise, some natural asphalt-
sand mixtures are tar sands.

Therefore:
(1) All natural asphalt-sand mixtures are bituminous sands.
(2) No natural asphalt-sand mixtures are bituminous sands.
(3) Some natural asphalt-sand mixtures are bituminous sands
(h) Some natural asphalt-sand mixtures are not bituminous sands.
(5) None of the above.

The tar deposits of Athabasca are all potential sources of petroleum. Contrary
to what was commonly believed prior to the formal investigation, some
ancient gorcidian grove sites are not tar deposits.

Therefore, in this region:
(1) .All ancient gorcidian grove sites are potential sources of petroleum.
(2) No ancient gorcidian grove sites are potential sources of petroleum.
( 3) Some ancient gorcidian grove sites are potential sources of petroleum.
(h) Some ancient gorcidian grove sites are not potential sources of petroleum.
(5) None of the above.

6.

7.

9.

60

-5-
None of the oil shale deposits of the Green River of Colorado have been _
found to be sand asphaltum. In this same region all kerogen deposits are oil
shale deposits.

From this paragraph.you may conclude:

(1) .All Green River kerogen deposits are sand asphaltum.

(2) No Green.River kerogen deposits are sand asphaltum.

(3) Some Green River kerogen deposits are sand asphaltum.

(h) Some Green River kerogen deposits are not sand asphaltum.
(5) None of the above.

In petroleum technology it is commonly known that all bituminous sands are
oil sands. ‘With the aid of high-speed computers and the recent influx of
knowledge in this area, it was deduced that some oil sands are not oil fields
which may be the cause of a depletion of our oil reserves.

If the above statements were correct you.mey conclude:
(1) .All oil fields are bituminous sands.
(2) No oil fields are bitumdnous sands.
(3) Some oil fields are bituminous sands.
(h) Some oil fields are not bituminous sands.
(5) None of the above.

Drs. Thomas and Kellner have found the reversible collapse of rabbits' ears
to be resultant upon injection of certain enzymes. This is surely the most
reliable of biological phenomenon, for with every injection of dizine the
ears of the injected rabbit temporarily collapse. The discovery that some
dizines are protelytic enzymes proved very useful to their research, ‘With
further investigation it was found that some fibrozines are protelytic
enzymes which made the picture somewhat more complete.

Therefore:

1 All fibrozines are dizines.

2 No fibrozines are dizines.-

3 Some fibrozines are dizines.

h Some fibrozines are not dizines.
5) None of the above.

(
(

VVVV

After the failure of the Schwartzman reaction to detect any enzymatic change
in the blood of the injected rabbits, Dr. Kellner intravenously injected
fibrogen, and, after a thorough histological examination, found a
cartilaginous malformation present only in the injected rabbits. This
prompted the conclusion that some glucoids are not fibroids. A few more
experiments made it evident that all fibroids were reactins, and the reactins
were responsible for the observed reaction.

Therefore:

All reactins are glucoids.

No reactins are glucoids.

Some reactins are glucoids.
Some reactins are not glucoids.
None of the above.

AAAAA
\rur-u m H
WVVV

(over)

20.

21.

22.

23.

-5-

Mathematics has become so specialized and SOphisticatad that the
invention of a new mathematical system is relatively common. One
such system is Dr. Mark Carr's system of chimerical geometry. In
this system all gamma figures are Betas, which makes classification
somewhat cumbersome. Unbeknowst to Carr, until after his first
public presentation of this system, some Alpha figures are actually
Gammas because of logical misconceptions.

Therefore, in this system:

All Alpha figures are Betas.

No Alpha figures are Betas.

Some Alpha figures are Betas.
Some Alpha figures are not Betas.
None of the above.

AAAAA
vvvvv

1
2
3
4
5

In Carr's system some plane figures are not Gamma figures, which
has been noted as a misclassification by many. All Zeta figures 1‘
are universally accepted as plane figures.

Therefore:

All Zetas are Gammas.

No Zetas are Gammas.

Some Zetas are Gammas.

Some Zetas are not Gammas.

None of the above.

The Mians are a primative peOple who lived in the southern Andes
around 400 B.C.. According to their religion, all Lynns are pro-
tectors of the home and are offered eels during festive ceremonies.
As if to complicate anthr0p0l0gical research, the Mians maintain
that all spirits inhabiting the tools of the village man are
Lynns as wail.

AAAAA

1
2
3
4
5

According to this religion, you may conclude:

(1) All spirits inhabiting the tools of the village man are pro-

tactors of the home.

(2?) No spirits inhabiting the tools of the village men are protectors of
the home.-

(3) Some spirits inhabiting the tools of the village men are pro-
tectors of the home.

(4) Some Spirits inhabiting the tools of the village men are not
protectors of the home.

(5) None of the above.

Some ghosts who shield the men in battle are Kirbys. In addition
some Kirbys are phantoms who live in the talking cave.

From this you may conclude:

(1) All phantoms who live in the talkingcave are ghosts who
shield the man in battle.

(2?) No phantoms who live in the talkingcave are ghosts who shield the men
in battle.

(3) Some phantoms who live in the talking cave are ghosts who
shield the man in battle.

(4) Some phantoms who liveltn the talking cave are not ghosts who
shield the men in battle.

(5) None of the above.

24.

25.

26.

27.

‘261
-7-

Early in the HOpewall are these natives started-making intricate
decoratiVe jewelry. Some decorative pins were Calima casts.
AnthrOpomorphic figures are also found in these ruins, but some
of them are not Calima casts. :

According to this paragraph you may conclude:

All anthrOpomorphic figures are decorative pins.

No anthrOpomorphic figures are decorative pine.

Some anthropomorphic figures are decorative pins.
Some anthrOpomorphic figures are not decorative pins.
None of the above.

AAAA"

1
2
3
4
5

The ancestors of the Mians lived in the Cobra region of the Andes.
Hera fiura furnaces were most frequently used, and some of'thase
are not terra cotta furnaces. With recent excavations at these "+
sites it has been found that all wind furnaces were fiura furnaces
because of distinct similiarities in structure and mechanics.

Therefore:

All wind furnaces wane tarra cotta furnaces.

N0 wind furnaces were terra WV,“ furnaces.

Some wind furnaces were terra cotta furnaces.

Some wind furnaces were not terra cotta furnaces.

None of the above.

Dr. Barnes of NYU has invented the game of Quasae for students who
want physical activity and have little room. It can be played in a
6 x 10 foot room with ping-pong paddles and a tennis ball. In
such a small room two players cannot avoid physical encounters.
Thus, such encounters are called lets, and all lets are fouls.
Occasionally a player gets hit by a ball, but some hits are not
l.ets. This makes scoring difficult at times. '

AAAAA
UT #U 10 -*
vvvvv

Therefore:

All fouls are hits.

No fouls are hits.

Some fouls are hits.
Some fouls are not hits.
None of the above.

AAA/\A
W #U [U -‘
vvvvv

After watching his students play this game, Dr. Barnes grouped them
according to the tactics used. Such grouping could adequately

be accomplished with A-, B-, and C- types. During the Spring
tournament, however, he found that some A- -typas were undoubtedly
B-types. Watching more closely, he also found that some C-typas
were not B-types because of the number of different strokes used.

Therefore:

All C-typas are A- -types.

.No C- s are A-types.

Some -types are A- -types.
Some C- -types are not A- -types.
None of the above.

AAAAA
U‘l kw l\) -*
vvvvv

28.

29.

30.

31.

-8-

Dr. Barnes' assistant, Jim Elliott, thought good players could be separated
from others by classifying body types. Because of the nature of his

sample, he concluded that no mesomorphs were leptosomes, which agreed witkl
the theory of Kretchmer. He also found that some good players were
mesomorphS.

Therefore:

All good players were leptosomes.

No good players were leptosomes.

Some good players were leptosomes.
Some good players were not leptosomes.
None of the above.

AAA/\f“
U'l Em m H
vvvvv

In the past it has been beneficial to classify people by the values they
hold. In these terms none of the holders of influential primary values are
Echinomorphs. In like manner no Dextromorphs are holders of influential

primary values.

Therefore, in these terms you may conclude:

(1) All Dextromorphs are Echinomorphs.

(2) No Dextromorphs are Echinomorphs.

(3) Some Dextromorphs are Echinomorphs.

(h) Some Dextromorphs are not Echinomorphs.
(5) None of the above.

Some effectors of great personality changes are the terminal values of an
individual. In addition, terminal values are all tertiary ones.

Therefore:

All tertiary values are effectors of great personality changes.

No tertiary values are effectors of great personality changes.

Some tertiary values are effectors of great personality changes.
Some tertiary values are not effectors of great personality changes.
None of the above.

AAAAA
vvvvv

l
2
3
h
S

In this manner some Penses are not holders of tertiary values. Important
to clinical classification is the fact that all schizmogentics are Pansas.

Therefore:

All .schiamogentics are holders of tertiary values.

No schizmogentics are holders of tertiary values.

Some schizmogentics are holders of tertiary values.
Some schizmogentics are not holders of tertiary values.
None of the above.

“AAA/K
U'l E'UJ 1'0 H
vvvvv

32.

33.

34.

35.

62
-9-

Ancient coins have now come under the scrupulous eye of the scientist.
Combining numismatics with archaeology and statistics much can be
learned about a peOple and their times from the coins they used as
legal tender. From the Taxila hoard found in India it was deter—
mined that some Constantinian solidia were what the French numisma-
tists had previously called "sou." All "sou" are known to be
silver-based. This apparently led to the inflation that pracaaded
the Taxila decline.

Therefore:

All Constantinian solidia were silver-based.

No Constantinian solidia were silver-based.

Some Constantinian solidis were silver-based.
Some Constantinian solidia were not silver-based.
None of the above.

AAAAA
vvvvv

1
2
3
4
5

The same hoard gave evidence that some Indian sovereigns weee

anna pieces. With constant handling the faces of these coins were
worn to such an extent that only some of the gold coins were
identifies as annas.

Therefore:

All gold coins in this hoard were Indian sovereigns.

No gold coins of this hoard were Indian sovereigns.

Some gold coins of this hoard were Indian sovereigns.
Some gold coins of this hoard were not Indian soveriegns.
None of the above.

“AAA“

1
2
3
4
5

Accurate models of molecular configurations have been as evasive as
desirable to biochemists. Until recently such models have been
impossible to construct, but with the aid of the computer such
models are being constructed with the "construction and rotation"
technique. It has been found that all cytodenes are gastromas.

The oscillosc0pe screen somehow distorts such pictures, such that
only recently it was found that some gastromes are not myoglobins.

Therefore.

All myoglobins are cytodenes.

No myoslobins are cytodenes.

Some myoglobins are cytodenes.
Some myoglobins are not cytodenes.
None of the above.'

U1 #‘Ul I'D -‘
VVvvv

Although some relationships are relatively easy to establish by

this method, others are very resistant to analysis. One such
example is the chained peptide group which is an element of most
proteins. Once the analysis was complete, it could only be conclude
that some chained peptide groups are not helical. Previously it

was found that some heme groups are not helical.

Therefore:

All heme groups are chained peptide groups.

No heme groups are chained peptide groups.

Some heme groups are chained peptide groups.
Some heme groups are not chained peptide groups.
None of the above.

AAA/NA

1
2
3
4
5

36.

-10-

Important to biochemists is the reactivity of these moiecules.
Determining the reactivity of any molecule, the total energy is
minimized naturally by the particular sequential configuration.
This free energy level also dictates that some active hybrids are
active doublets. Because of their dynamic configurations, all
active doublets are mercurial subunits.

Therefore:

All mercurial subunits are active hybrids.

Ne mercurial subunits are active hybrids.

Some mercurial subunits are active hybrids.
Some mercurial subunits are not active eybrids.
None of the above.

AAAAA
U1 #KN [D -*
vvvvv

APPENDIX B

63

Coversheet instructions for Groups 1-4 and 6

LOGICAL READING TEST

Remove the answer sheet from the test booklet and place (1)
your name, (2) your student number, and (3) the name and form
of the test in the apprOpriate places. Place a "Yes" or a
"No" in the place marked "Instructor" answering whether or

not you have previously had a class dealing with formal logic.
Within this test you will find paragraphs each followed by
five statements. Your task is to read each paragraph care-
fully, than, if a conclusion is deductible from the statements
in the paragraph, select that conclusion from those given and
mark that number on your answer sheet. If no conclusion

is logical from the statements in the paragraph, mark Option

"5" on your answer sheet.

To avoid confusion the definition of the term "some" is to be
"there exists at least one . . .." This is to say that you
may not infer ”some A are not B" from the statement "some A
are 8." Similarly, "some A are not B" does not imply "some

A are 8.

Work as fast as you can, but there should be ample time for
you to finish. Be sure to answer every question, even if you

have to guess.
Place no marks on this test booklet. There will be scratch

paper provided.

DO NOT BEGIN UNTIL TOLD TO DO SO.
64

Coversheet instructions for Group 5

LOGICAL READING TEST

Remove the answer sheet from the test booklet and place (1)
your name, (2) your student number, and (3) the name and form
of the test in the apprOpriate places. Place a "Yes" or a
"No" in the place marked "Instructor" answering whether or

not you have previously had a class dealing with formal logic.

Within this test you will find paragraphs each followed by
five statements. Your task is to read each paragraph care-
fully, than, if a conclusion logically follows from the
statements in the paragraph, select that conclusion from
those given and mark that number on your answer sheet. If
no conclusion logically follows from the statements in the

paragraph, mark Option "5" on your answer sheet.
Work as fast as you can, but there will be ample time for
you to finish. Be sure to answer every question, even if

you must guess.

Place no marks on this test booklet. There will be scratch

paper provided.

DO NOT BEGIN UNTIL TOLD TO DO SO.

65

Training Instructions for Group 1

LOGICAL READING TEST -- Form 1

Over the past few years several people in the PsychOIOgy
Department at MSU have been studying reasoning behavior. These
studies have found that peOple make predictable errors on cer-
tain types of verbal reasoning problems. If you took the Log-
ical Abilities Test, you are already familiar with this type
of problem. This will be an attempt to teach you how to better
think your way through these problems and to eliminate these
common errors. Therefore, if you learn and use these precaut-
ions, you will be batter able to use the information given
in each problem to decide whether or not a conclusion is pos-
sible, and if so which conclusion is the logically correct one.
And it is likely that learning these precautions will eliminate
some of the errors you make in similiar reasoning problems,
such as drawing conclusions from a lab experiment or solving
problems on aptitude tests.

The errors which have been found to be the most common
have been explained by the "atmOSphere error." In solving
verbal problems of this type people are often influenced by
similiarities between the statements from which the conclusion
must be drawn.

For example:

All A's are B's.
All C's are B's.

 

Therefore, all A's are C's.

Stated this way the conclusion does not logically follow from
these statements, but many peOple would conclude that such a
conclusion is correct. This is because these peOple do not
understand the relationships between the A's, B's, and C's
which are dictated by the statements, and they are "solving"
the problem by using the ”all are" silimiaritias between the
statements to infer an ”all are" conclusion which is incorrect
in this example.

Two Statements may contain the same elements of A's, B's,
"are," and "all" but dictate relationships which are entirely
different. In the above example, if "all C's are B's” were
actually "all B's are C's," the conclusion would follow logic-
ally, but, eventhough the elements of the statements are the
same, the relationships which are defined by each are so dif-
ferent that one allows the conclusion to follow logically, and
the other does not. Thus, the possibility of a conclusion
following logically from two statements depends upon the rel-
ationships defined, not necessarily upon the similiarities
between the statements. Remember that, when solving problems
of this type, you must fully understand the logical relation-
ships which are defined by the statements.

If, by using these precautions, you find that none of the
four conclusions follow logically from the paragraph, mark
option "5? meaning "none of the above." This will mean eit-
her (1) you can find no conclusion which follows from the
information given, or (2) you can find a conclusion which dOes
follow, but none of the alternatives accurately states that
conclusion.

Do not be fooled by the errors of naive reasoning which
have just been explained to you.

You are encouraged to refer back to these instructions
while you are taking this test.

When you have finished reading these instructions and
you understand them, go on to the next page....

Training Instructions for Group 2

LOGICAL READING TEST -- Form 2

Over the past few years several peOple in the Psychology
Department at MSU have been studying reasoning behavior. These
studies have found that peOple make predictable errors on cer-
tain types of verbal reasoning problems. If you took the Log-
ical Abilities Test, you are already familiar with this type
of problem. This will be an attempt to teach you how to better
think your way through these problems and to eliminate these
errors. Therefore, if you learn and use these precautions,
you will be better able to use the information given in each
problem to decide whether or not a conclusion is possible, and
if so whiCh alternative is the logically correct one. And it
is likely that learning these precautions will eliminate errors
in similiar reasoning problems, such as drawing conclusions
from a lab experiment or solving reasoning problems on aptit-
ude tests.

The errors which are most common have been explained by
the "conversion error." This is the incorrect conversion of
an "all are" or a "some are not" statement in a problem. The
correct solution for these problems have been determined by
the use of the rules of formal lOgic. Thus, the conversion
of statements must be correct by the rules of formal lOgic,
or the conversion error will be committed. Often the "All
A's are B's" statement is converted erroneously to "All B's
are A's." The correct conversion is "all not B's are not A's?
So, if you see an "all are" statement, make sure you convert
it correctly if you do convert it at all.

67

Unlike the "all are" statement, the "some are not” state-
ments cannot be converted correctly. "Some A's are not B's"
is equivalent only to "some things which are not B's and A's,"
and this is not a conversion. The incorrect conversion which
is usually made is to "some B's are not A's." Remember accord-
ing to the rules of formal logic, which you must use to solve
these problems correctly, "some A's are not B's" is not equi-
valent to "some B's are not A's."

For example:

All A's are B's.
All C's are B's.
Therefore, all A's are C's.

 

As it stands the conclusion does not follow lOgically from the
statements. However, if the conversion error were committed
"all C's are B's" were changed to "all B's are C's" the con-
clusion would follow logically. Avoid this invalid conversion;
it can only lead you to errors in reasonig! Such answers as
above are incorrect by the information given, and are scored

as errors on this test.

It should be added that "all A's are not B's" can be con-
verted to "all B's are not A's," and the statement "some A's
are B's" can be converted to "some B's are A's." These con-
versions are transformations which lead to logically correct
conclusions.

These correct conversions would be obviously correct if
you substituted "cats" for A and "mammals" for B. And it is
equally as obvious that "all cats are mammals" is not the same
as "all mammals are cats." Nor is "some mamals are not cats"
the same as "some cats are not mammals."

If, by using these precautions, you find that none of the
four conclusions follow logically from the paragraph, mark
Option #5, "none of the above.” This will mean either (1) you
can find no conclusion which follows from the information given,
or (2) you can find a conclusion which does follow, but none
of the Options accurately states that conclusion.

Do not be fooled by the errors of naive reasoning which
have just been explained to you.

You are encouraged to refer back to these instructions
while you are taking this test.

When you have finished reading these instructions and you
feel you understand them, you may proceed with the test . . ..

68

Training I Instructions for Group 3

LOGICAL READING TEST--FORM 3

Over the post few years several people in the PsychOIOgy
Department at MSU have been studying reasoning behavior.
These studies have shown that peOple make predictable errors
on certain types of verbal reasoning problems. If you took
the Logical Abilities Test, you are already familiar with this
type Of problem. This will be an attempt to teach you how to
better think your was through these problems and to eliminate
these common errors. Therefore, if you can learn and use
these precautions, you will be better able to use the informa-
tion given in each problem to decide whether or not a conclu-
sion is possible, and if so which conclusion is the lOgically
correct one. And it is likely that learning these precautions
will eliminate some of your errors in reasoning on similiar
problems, such as drawing cOnclusions from a lab eXperiment
or solving reasoning problems on aptitude tests.

The errors which have been found to be most common have
been explained by the atmosphere and conversion errors. In
solving verbal problems of this type peOple are often influenced
by similiarities between the statements from which the conc-
clusion is to be drawn.

For examples:
All A's are B's.
All C's are B's.

 

Therefore, all A's are C's.

Stated this was the conclusion does not logically follow from
these statements, but many peOple would conclude that such a
conclusion is correct. This is because these peOple do not
understand the relationships between the A's, B's, and C's
which are dictated by the statements, and they are ”solving"
the problem by using the "all are" similiarity between the
statements to infer an "all are” conclusion which in this
case is incorrect.

Two statements may contain the same elements of A's,
B's, ”are", and ”all" but dictate relationships which are
entirely different. In the above example, if "all C's are
B's" were actually "B's are C's," the conclusion would fol-
low logically, but, eventhough the elements of the statements
are the same, the relationships which are defined by each
are so different that One allows a logical conclusion to
follow and one does not. Thus, the possibility Of a ConCIusion
following lOgically from two statements depends upon the re
lationships defined, not necessarily upon the similiarities
between the statements. Remember that, when solving problems
of this type, you must fully understand the relationships
which are defined by the statements and base your conclusions
on that. 69

Another error whcih has pervasive influence upon the way
peOple reason is the coversionerror. Thsi is the incorrect
conversion of an "all are" or a "some are not" statement in a
problem. The correct solutions for these problems have been
determined by the use of the rules of formal logic. Thus,
the conversion Of statements must be correct by the rules
of formal logic. Thus, the conversion of statements must be
correct by the rules Of fomal lOgic, of the conversion error
will be committed. Often the "all A's are B's" statement
is converted erroneously to "all B's are A's." The correct
conversion is "nothing which is not also a B can be an A.”
80, if you see and "all are" statement, make sute you convert
it correctly if you do convert it at all.

Unlike the "all are” statement, the "some are not" state-
ments cannot be converted correctly at all. "Some A's are not
B's" is equivalent only to "some things which are not B's are
A's" and this is not a conversion. The incorrect conversion
which is usually made is to "some B's are not A's." Remember
according to the rules of formal logic, which you must use
to solve these problems correctly, "some A's are not B's" is
not equivalent to "some B's are not A's."

For example:

All A's are B's.
All C's are B's.

Therefore, all A's are C's.

 

As it stands the conclusion does not follow logically from the
statements. However, if the conversion error were committed

so that "all C's are B's" were changed to "all B's are C's,”

the conclusion would then follow logically by virtue of that
error. Avoid this invalid conversion; it can lead you only

to errors in reasoning! Such answers as above are incorrect

by the information given, and are scored as errors on this test.

It should be added that "all A's are not B's” can be con-
verted to "all B's are not A's. These conversions are trans-
formations which lead-to lOgically correct conclusions.

These correct conversions would be obviously correct if
you substituted "cats" for A and "mammals" for B. And it is
equally as obvious that "all Cats are mammals" is not the same
as "all mammals are cats." Nor is "some mammals are not cats"
the same as "some cats are nOt mammals."

If, by using these precautions, you find that none of the
four conclusions follow logically from the paragraph, mark
Option #5, "none Of the above." This will mean either (1)
you can find no conclusion which follows from the information
givem, or (2) you can find a conclusion which does follow,
but none of the Options accurately states that conclusion.

Do not be fooled by the errors of naive reasoning which
have been explained to you. 70

You are encouraged to refer back to these instructions
while you are taking this test.

When you have finished reading these instructions and you
feel you understand them, you may proceed with the test. . ..

Training Instructions for Group 4

LOGICAL READING TEST--FORM 4

Over the past few years several peOple in the Psychology
Department at MSU have been studying reasoning behavior. These
studies have shown that peOple make predictable errors on
certain types of verbal reasoning problems. If you took the
Logical Abilities Test, you are already familiar with this
type of problem.. This will be an attempt to teach you how
to better think your way through these problems and to elimin-
ate these common errors. Therefore, if you learn and use these
precautions, you will be better able to use the information
given in each problem to decide whether or not a conclusion
is possible, and if so whiCh conclusion is the logically cor-
rect one. And it is likely that learning these precautions
will eliminate some of your errors in reasoning on similiar
problems, such as drawing conclusions from a lab eerriment
or solving reasoning problems on aptitude tests.

The errors whiCh occur most commonly have been explained
by the attributed eqUivalence between two given sets of elem-
ents. Consider A and B as sets of all possible individual A's
and B's., i.e., consisting of elements A's and B's. If the
statement "all A's are B's" were given, many peOple would
interpret it to mean that the set A was equivalent to set B,
i.e., that they contained the same elements. To be true
every element of set A would have to be an element of set 8,
and vice versa. Although this may be often true in real life,
in the problems which follow you will not be able to judge
the equivalence Of the sets by the meaning of the names invol-
ved, for they will be unfamiliar to you.

Therefore, you must assume for "all A's are B's" that
A is a set of fewer elements than B. I you restated "all A's
are B's" to "all A's are elements of set 8" or to "all A's
are included in the set 8,” the relationships intended would
be as Obvious as if they were stated like "all cats are mam-
mals." Obviously the set "cats" is smaller than the set
"mammals," for each mammal is not a cat.

In this manner, "all A's are B's" becomes "all A's are
elements of set 8."

"No A's are B's" becomes "no A's are elements of set 8."

"Some A's are B's" becomes "some A's are elements of
set S."

71

"Some A's are not B's" becomes "some A's are not elements
of set 8."

It would be to your benefit to actually verbalize these
transformations for the first few problems. Always remember
that the first set will always contain fewer elements than the
other, and in that way they are not equivalent sets.

If, by using these precautions, you find that none of
the four conclusions follow logically from the paragraph, mark
Option #5, "none of the above." This will mean either (1) you
can find no conclusion which follows from the information
given, or (2) you can find a conclusion which does follow,
but none of the Options accurately states that conclusion.

DO not be fooled by the errors Of naive reasoning which
have just been explained to you.

You are encouraged to refer back to these instructions
which you are taking this test.

When you have finished reading these instructiOns and
you feel you understand them, you may proceed with the test....

Training Instructions for Group 5

LOGICAL READING TEST -- Form 5

Over the past few years several peOple in the Psychology
Department at MSU have been studying reasoning behavior. These
studies have shown that peOple make predictable errors on cer-
tain types Of verbal reasoning problems. If you took the
Logical Abilities Test, you are already familiar with this
type of problem. This will be an attempt to teach you how to
bettwe think your way through these problems and to eliminate
these common errors. Therefore, if you learn and use these
precautions, you will be better able to use the information
given in each problem to decide whether or not a conclusion
is possible, and if so which conclusion is the logically
correct one. And it is likely that learning these precautions
will eliminate some errors in reasoning on similiar problems,
such as drawing conclusions from a lab experiment or solving
reasoning problems on aptitude tests.

The errors which most commonly occur have been explained
by the implied inclusion or exclusion of a ”some" statement.
Many peOple regard the statement "some A's are B's" as impl-
ying that ”some A's are not B's." Thisis a common error
which may be eliminated if you define the term "some" to mean
"at least one.” You know about some of the Objects, but any
others which may exist are unknown to you. Thus, you cannot
be certain about their characteristics. Thus, the statement
"some A's are B's" is meant to be interpreted as "at least
one thing exists whiCh is both A and B." Stated this correct
way this statement does not imply "some A's are not B's."

Similiarly the statement, "some A's are not B's" does
not imply "some A's are B's."

72

If, by using these precautions, you find that none of the
four conclusions follow logically from the paragraph, mark
option #5, "none of the above." This will mean either (1) you
can find no conclusion which follows from the information
given, or (2) you can find a conclusion which does follow, but
none Of the Options accurately states that conclusion.

Do not be fooled by the errors of naive reasoning which
have just been explained to you.

You are encouraged to refer back these instructions while
you are taking this test.

When you have finished reading these instructions and
feel you understand them, you may proceed with the test....

73

IES

”Iiljililljlilllllllillill/illl

   

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