Memory& Cognition1978, Vol. 6 (1), 76·83

The effect of figure on syllogistic reasoning

LOUIS S. DICKSTEINWellesley College, Wellesley, Massachusetts 02181

Several investigators of reasoning with abstract categorical syllogisms have noted that thefour figures of the classical syllogism, which vary in the order in which terms occur in the majorand minor premises, resemble the four three-stage mediation paradigms in paired associatelearning. On the basis of the analogy, figure differences have been predicted and some supporthas been obtained for these predictions. The present paper proposes an alternative informationprocessing explanation for figure effects based upon contradictions between the correct con­clusions that follow from forward and backward processing of the premises. This explanation,in contrast to the associative explanation, successfully predicts which premise combinationswill show figure effects as well as the nature of the specific errors which will occur.

In recent years, several investigators have concernedthemselves with the cognitive processes involved inperformance on abstract categorical syllogisms (e.g.,Dickstein, 1975, 1976; Erickson, 1974; Revlis, 1975a,1975b). The general intent of these studies has beento clarify the operations that subjects perform ininterpreting premises, combining information anddrawing conclusions. While the focus of these studieshas been the categorical syllogism, the more generalaim has been to identify processes which might havegenerality beyond the specific deductive reasoningtask. This paper continues the effort to articulate thepsychological bases of performance on logical tasks.

Much empirical research on syllogistic reasoninghas been concerned with factors that contribute todifferences in difficulty among the various syllogisms.For example, it has been found that valid syllogismsare considerably easier than invalid syllogisms(Dickstein, 1975, 1976; Roberge, 1970). Within the classof invalid syllogisms, syllogisms that are susceptibleto the logical errors of illicit conversion of universalaffirmative or particular negative propositions aremore difficult than syllogisms that do not allow sucherrors (Chapman & Chapman, 1959; Dickstein, 1975,1976). This paper is concerned with the role of thefigure of the syllogism as a determinant of difficulty.

A categorical syllogism consists of two premisesfollowed by a conclusion. Both premises and theconclusion make assertions about class relationshipsbetween various terms. Traditionally, the first premiseis the major premise, which makes an assertion aboutthe relation between the middle term (M) and thepredicate (P) (e.g., All Mare P). The second premise

The main ideas in thispaperwere developed while the authorwas on sabbatical leave from Wellesley College at the Institutefor the Study of Intellectual Behavior, University of Colorado.The leave was partially funded by Postdoctoral ResearchFellowship I F32 MH05214·01 to the author from the NationalInstitute of Mental Health under the sponsorship of Lyle E.Bourne, Jr.

76

is the minor premise, which makes an assertion aboutthe relation between the subject (S) and M (e.g., All Sare M). On the basis of the information provided by thetwo premises, the task of the subject is to draw adeductive inference about the relation between Sand P.For a valid syllogism, the conclusion would be apropositional statement about the class relationshipbetween Sand P (e.g., All S are P). For an invalidsyllogism, the correct conclusion would be that novalid propositional conclusion may be drawn aboutthe relationship between Sand P.

In the syllogistic task, there are four kinds ofpropositions that are traditionally represented by letters.These are universal affirmative (A) propositions (e.g.,All Mare P), universal negative (E) propositions (e.g.,No Mare P), particular affirmative (I) propositions(e.g., Some Mare P), and particular negative (0)propositions (e.g., Some M are not P). Since there arefour different kinds of propositional statements that canoccur in both the major and minor premises, there are16 different premise combinations in the syllogistictask.

Syllogisms may also vary with regard to the orderingof the terms in the major and minor premises. Thus,the major premise may be stated with M preceding P,or it may be stated with P preceding M. Similarly,the minor premise may be stated with S preceding M,or it may be stated with M preceding S. The order ofthe terms in the major and minor premises defines thefigure of the syllogism. In Figure 1 the order of theterms for the major and minor premises, respectively,is M-P, S-M; in Figure 2 the order is P-M, S-M; inFigure 3 the order is M-P, M-S; while in Figure 4 theorder is P-M, M-S. The conclusion to be evaluatedin all instances proceeds from S to P. Since there arefour figures with 16 different premise combinationsin each figure, the complete syllogistic task consistsof 64 unique syllogisms. The various kinds of propo­sitions and the various premise orders are summarizedin Table 1.

FIGURE EFFECTS IN SYLLOGISTIC REASONING 77

Table 1Types of Propositions and Orders of Terms

for Categorical SylIogisms~~---~---- ----

The order of the terms in the premises significantlyaffects the meaning of some propositions (A and 0).Thus, the proposition "All Mare P" does not have thesame logical meaning as the proposition "All Pare M."Consequently, a premise combination that yields a validconclusion in one figure may yield a different validconclusion or may be indeterminate in a differentfigure. Of the 64 syllogisms that constitute the task,19 are valid and the remaining 45 are invalid. Thereare four valid syllogisms in Figure 1, four in Figure 2,six in Figure 3, and five in Figure 4.

Several investigators beginning with Frase (1968)have noted that the four figures of the syllogistictask are analogous to the four three-stage mediationparadigms in paired associate learning. Figures 1,2, 3, and 4 resemble forward chaining, stimulusequivalence, response equivalence, and backwardchaining, respectively. On the basis of this analogy,it has been argued that performance should becomeprogressively poorer as one proceeds from Figure 1to Figure 4, and some evidence has been advanced insupport of this prediction. Thus, in the first of twoexperiments reported by Frase (1968), the differencebetween figures approached significance, with subjectsmaking least errors on Figure I syllogisms and mosterrors on Figure 4 syllogisms. In the second experiment,the difference between figures was significant, witherrors increasing from Figure 1 to Figure 4. Theseexperiments, however, used a very limited sample ofthe total set of categorical syllogisms. A subsequentstudy by Roberge (1971) compared figures for the ninedifferent premise combinations that have the samelogically correct conclusion in all four figures. Forthese 36 syllogisms, he found that Figure 4 wassignificantly more difficult than Figures 2 and 3. Morerecently, Erickson (1974) has presented data for the 19valid syllogisms in which the percentages correct are79% for Figure 1, 76% for Figure 2, 59% for Figure 3,and 49% for Figure 4. Although Erickson's (1974)model of syllogistic reasoning is not based upon themediation paradigm analogy, he does note that theseresults parallel those from verbal mediation studies.Further confirmation of the difficulty of Figure 4syllogisms has been reported as an incidental finding

figure 1

M-PS-M

Types of Propositions

A AlI S are PE No S are PI Some S are Po Some S are not P

Orders of Termsfigure 2 Figure 3

P-M M-PS-M M-S

Figure 4P-MM-S

by Kintsch and Monk (1972) in a study of memorythat included meaningful materials presented in asyllogistic structure.

Although the analogy between paired associatesand syllogisms is interesting, it is difficult to regardthe mediation analogy as an adequate explanationfor figure differences. Over the years, a number oftheoretical explanations of reasoning on categoricalsyllogisms have been advanced, including those ofChapman and Chapman (1959), Erickson (1974),Revlis (l975a, 1975b), and Woodworth and Sells(1935). A distinguishing feature of all of theseapproaches has been the presentation of some form ofprocessing model leading to the prediction of specificerrors for particular premise combinations. In contrast,the mediation explanation for figure effects does notprovide a processing model, nor does it predict thespecific errors that will occur in figures that are moredifficult. Since it is well established that errors on thistask are not random (e.g., Dickstein, 1975), themediation analogy appears to be seriously incomplete.

The thesis of the present paper is that it is moreproductive to view syllogistic reasoning as an infor­mation processing activity, in which the subjectinterprets the premises and combines the informationin the premises to arrive at a conclusion, than to viewsubject performance in terms of an associative model.Such an analysis suggests an alternative explanation forfigure effects. As noted above, in the traditionalsyllogism task, propositional conclusions proceed fromS to P, and the subject must decide whether suchconclusions are valid or whether no valid propositionalconclusion may be deduced which proceeds fromS to P. However, just as the information in the premisescan be processed to evaluate conclusions proceedingfrom S to P, the same information can be processedto evaluate conclusions proceeding from P to S. Thelogically correct conclusion regarding the relationfrom S to P is not necessarily correct with regard to therelation from P to S. It is proposed that figure effectsoccur on those syllogisms in which conclusions that arelogically justified from P to S are different fromconclusions that are justified from S to P. Even thoughthe task requires subjects to draw conclusions thatare appropriate from S to P, some subjects will drawconclusions that are appropriate from P to S and thenerroneously apply them to the relation from S to P.It is further proposed that whether the subject processesthe information in the premises in a forward (subjectto predicate) or backward (predicate to subject)direction will be influenced by the direction of theinformation presented in the premises. In Figure 1,both premises proceed in the forward direction, andthere should be little tendency for subjects to processinformation from P to S. In contrast, in Figure 4 bothpremises proceed from P to S and here the tendencyto process information in the backward direction should

78 DICKSTEIN

be maximal. Figures 2 and 3 are intermediate since,in both, one premise proceeds in a forward direction,while one proceeds in a backward direction. Thus,it is hypothesized that for those premise combinationsin which forward and backward processing lead todifferent conclusions, performance will be best onFigure I syllogisms, intermediate on Figures 2 and 3,and poorest on Figure 4. Furthermore, this decrementacross figures in the number of correct conclusionswill be paralleled by an increase in the number of errorsresulting from backward processing.

Among the 64 syllogisms, there are 18 in whichdifferent conclusions are justified from P to S thanfrom S to P. These include eight syllogisms that allowpropositional conclusions from S to P but are invalidfrom P to S. These are syllogisms EI-1, EI·2, EI-3, £14,EA·3, EA4, AO-2, and OA·3. (In these abbreviations,the first letter refers to the kind of proposition in themajor premise, the second letter refers to the kind ofproposition in the minor premise, and the number refersto the figure of the syllogism.) There are also eightsyllogisms that are invalid from S to P but allowpropositional conclusions from P to S. These aresyllogisms IE·1, IE-2, IE·3, IE4,AE·1,AE·3,OA·2,andAO·3. Finally, there are two syllogisms that lead todifferent propositional conclusions from S to P thanfrom P to S. These are AA-1 and AA-4.

Unfortunately, the main hypothesis of the presentstudy cannot be tested with all 18 relevant syllogisms.In order to attribute differences between syllogisms tothe effect of figure, the syllogisms to be comparedmust be equated as to premise combination, logicallycorrect conclusion, and susceptibility to errors thathave been identified in previous research, such as illicitconversion (Chapman & Chapman, 1959). Otherwise,the effect of figure is confounded with the effects ofother variables. This caution has not always beenobserved in previous research. Thus, Erickson (1974)compared figures with regard to valid syllogisms, eventhough different premise combinations are representedin the different figures. More seriously, the figurecomparison which Erickson (1974) presents isconfounded with the effects of illicit conversion. Thereare only four valid syllogisms in which illicit conversionleads to error (AA·3, AA4, EA·3, and EA4) and theseare the most difficult valid syllogisms. Since conversionhas been shown to be a very strong error tendency(Chapman & Chapman, 1959; Dickstein, 1975, 1976),it is more parsimonious to attribute the poorerperformance of subjects on Figures 3 and 4 toconversion than to a vaguely defined figure effect.Furthermore, since there are six valid syllogisms inFigure 3 and only five in Figure 4, the difficultconversion syllogisms constitute a larger proportion ofthe total set for Figure 4, and this can account for thedifference between Figures 3 and 4 reported byErickson (1974).-

After consideration of these requirements, thereare 12 syllogisms in four premise combinations forwhich figure differences may be predicted and tested.Premise combination EI in all four figures leads toa valid 0 conclusion in the forward direction and anon propositional conclusion in the backward direction.Conversely, premise combination IE in all four figuresleads to a non propositional conclusion in the forwarddirection and an 0 conclusion in the backward direction.Premise combination EA in Figures 3 and 4 leads to avalid 0 conclusion in the forward direction and anonpropositional conclusion in the backward direction.Finally, premise combination AE in Figures 1 and3 leads to a nonpropositional conclusion in theforward direction and an 0 conclusion in the backwarddirection.

The present study also provides an opportunity totest the proposal of Revlis (l975b) that subjects have aresponse bias against nonpropositional conclusions.Premise combinations EI and IE are complementarysyllogisms. In both there is one universal negativeproposition and one particular affirmative proposition.However, in the former, forward processing leads to apropositional 0 conclusion and backward processingleads to a nonpropositional conclusion, while in thelatter the reverse is true. If subjects have a bias againstnonpropositional conclusions, then performance shouldbe better on the valid El syllogisms than on the invalidIE syllogisms.

METHOD

Two samples of subjects provided the data of the presentstudy. The first consisted of 22 female undergraduates atWellesley College who had participated in an earlier studyof syllogistic reasoning (Dickstein, 1975) as the standardinstruction group. These subjects completed 64 syllogismsincluding all four figures. Half of the subjects received thesyllogisms in the standard order with the major premise first,while the other half received the reverse order. Since the twoorders of presentation were not significantly different, thedata were combined.

The second sample consisted of 76 female undergraduatesat Wellesley College who participated in the study to meet acourse requirement. These subjects were randomly dividedinto four groups of 19. Each group completed aU the syllogismsfor a single figure, with two presentations of each syllogism,for a total of 32 syllogisms. There were no significant differencesbetween the first and second presentations, and the data werecombined.

All subjects received problem booklets with instructionsthat clarified the rules of the syllogistic task. Subjects were toldthat the word "some" means "at least some" and not "onlysome." In addition, subjects were told that in order to drawa substantive conclusion, the premises had to compel thatconclusion. Each premise combination was followed by fiveresponse alternatives, and the subject was required to selectone of them. The alternatives were: "All S are P," "Some Sare P," "No S are P," "Some S are not P," and "No validconclusion." These alternatives were always presented in thesame order to avoid confusing the subjects. Similarly, the lettersS, M, and P were always used to represent the subject, middleterm, and predicate to avoid confusion. Subjects completed

FIGURE EFFECTS IN SYLLOGISTIC REASONING 79

all of the syllogisms a t a single session and no time limit wasimposed.

RESULTS

The mean number correct and the mean predictederror for each of the 12 syllogisms for Sample 1 andSample 2 are presented in Table 2. Since premisecombinations EI and IE are represented in all fourfigures, analyses of variance were conducted with theseeight syllogisms to test the effects of figure, validity,and any interaction between them.

For the first sample, where a within-subjects designwas utilized, two treatments by treatments by subjectsanalyses of variance (Bruning & Kintz, 1968) wereconducted. One analysis utilized the number of correctresponses as the dependent variable, while the otherutilized the number of the predicted error responsesas the dependent variable. 1 For the correct response,there was a significant effect of figure [F(3,63) = 3.76,p < .05] , with performance on Figure I best, perform­ance on Figures 2 and 3 combined intermediate, andperformance on Figure 4 poorest. There was also asignificant effect of validity [F(1,21) = 5.86. P < .05],with performance on valid premise combination EIsignificantly better than performance on invalidpremise combination IE. The interaction betweenfigure and validity was not significant [F(3,63) = 2.62 J.For the predicted error, there was again a significanteffect of figure [F(3,63) =3.07, P < .05], with theleast error in Figure I, an intermediate amount oferror in Figures 2 and 3 combined, and the greatestamount of error in Figure 4. The effects of validity andthe Figure by Validity interaction were not significant.

For the second sample, where validity was a within­subjects factor while figure was a between -subjects

Table 2Mean Percentage Occurrence of Predicted Error

and Correct Answer-_._---

Sample 1 Sample 2Premise

Combination Error Correct Error Correct

EA-3 0.0 18.2 2.6 23.7EA-4 18.2 27.3 34.2 5.3EI-l 18.2 68.2 7.9 68.4EI-2 13.6 72.7 21.1 57.9EI-3 27.3 54.5 18.4 55.3EI-4 36.4 40.9 50.0 23.7AE-l 0.0 50.0 5.3 36.8AE-3 18.2 18.2 7.9 18.41E-1 9.1 59.1 13.2 68.4IE-2 45.5 31.8 36.8 18.41E-3 40.9 22.7 21.1 39.5IE-4 36.4 36.4 34.2 34.2

Note- The predicted error is "no valid conclusion" for premisecombinations EA and EI and "0" for premise combinationsAE and IE. The correct answer is "0" for premise combinationsEA and EI and "no valid conclusion" for premise combinationsAEand IE.

factor, a two-factor mixed-design (Bruning & Kintz,1968) analysis of variance was utilized. Again, twoanalyses were conducted for the number correct andfor the predicted error. For the correct response, therewas a significant effect of figure [F(3,72) =5.86,P < .01] , with performance on Figure 1 best, perform­ance on Figures 2 and 3 combined intermediate, andperformance on Figure 4 poorest. The effect ofvalidity was not significant [F(1 ,72) =3.58] . However,there was a significant Figure by Validity interaction[F(3,72) = 3.40, P < .05], reflecting the relativelypoor performance of subjects on Figure 4 comparedto the other figures for premise combination EI ascompared with the relatively good performance onFigure I compared to the other figures for premisecombination IE. For the predicted error, there wasagain a significant effect of figure [F(3,72) = 6.00,p < .0 I], with the least error in Figure I, an interme­diate amount of error in Figures 2 and 3 combined,and the greatest amount of error in Figure 4. Theeffects of validity and the Figure by Validity interactionwere not significant.

For premise combinations EA and AE, in whichsyllogisms from only two figures were represented,t tests were conducted for both samples on boththe number of correct responses and the number ofpredicted error responses. For the first sample, forpremise combination EA, the difference betweenFigure 3 and Figure 4 was not significant for the numbercorrect but was significant for the predicted error[t(21) =2.17, P < .05, two-tailed] , with more predictederrors occurring in Figure 4. For premise combinationAE, the difference between Figure 1 and Figure 3was significant for the number correct [t(21) =2.63,p < .02, two-tailed], with more correct responsesin Figure I. There was also a significant differencefor the predicted error [t(21) = 2.17, p<.05, two­tailed l, with more predicted errors occurring inFigure 3.

For the second sample, for premise combinationEA, the difference between Figure 3 and Figure 4approached significance for the number correct[t(36) = 1.79, p < .10, two-tailed], with more correctresponses in Figure 3. For the predicted error, thedifference was significant [t(36) =3.00, p < .01,two-tailed], with more predicted errors in Figure 4.For premise combination AE, the difference betweenFigures I and 3 was not significant for either the numbercorrect or the predicted error.

In addition to the comparisons presented abovein which figure differences are predicted, there are anumber of other comparisons in the total set ofsyllogisms for which the model predicts that there willnot be figure differences because the conclusion tobe drawn is the same for both forward processing andbackward processing. These comparisons involve 13different premise combinations and 44 individualsyllogisms.

80 DICKSTEIN

Table 3Response Distributions for 64 Syllogisms, Sample 1

Note-Numbers indicate percentage of total responses to eachsyllogism. *N refers to "no valid conclusion."

Syllogism A

0.0 4.50.0 22.70.0 13.64.5 13.60.0 50.00.0 4.5

18.2 18.24.5 9.10.0 0.04.5 13.60.0 9.19.1 22.7

86.4 13.690.9 9.163.6 31.868.2 31.8

0.0 0.04.5 0.0

18.2 0.027.3 18.2

0.0 72.74.5 68.20.0 77.34.5 77.3

68.2 18.272.7 13.654.5 27.340.9 36.422.7 54.54.5 72.74.5 86.44.5 77.30.0 27.34.5 27.30.0 0.04.5 4.59.1 59.1

45.5 31.840.9 22.736.4 36.4

4.5 45.50.0 31.80.0 63.60.0 59.1

40.9 54.559.1 40.931.8 68.240.9 59.177.3 22.768.2 22.795.5 4.563.6 36.4

0.0 81.80.0 72.74.5 68.2

18.2 68.240.9 54.536.4 63.650.0 50.031.8 63.627.3 72.713.6 77.313.6 77.39.1 81.8

N*o0.00.0

27.322.7

0.00.00.00.0

100.081.890.968.2

0.00.04.50.00.00.00.00.00.00.00.00.00.00.00.00.04.5

13.60.00.0

72.763.690.990.9

0.00.00.04.5

50.063.436.440.9

4.50.00.00.00.00.00.00.00.0

13.69.14.54.50.00.00.00.09.19.14.5

E

0.00.00.00.0

50.095.563.686.4

0.00.00.00.00.00.00.00.0

100.095.581.854.527.327.322.718.213.613.618.222.718.29.19.1

18.20.00.04.50.0

31.822.736.422.7

0.04.50.00.00.00.00.00.00.09.10.00.0

18.213.618.29.10.00.00.04.50.00.00.04.5

95.577.359.159.1

0.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.04.54.50.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0

AA-lAA-2AA-3AA-4AE-lAE-2AE-3AE-4AI-lAI-2AI-3AI-4AO-lAO-2AO-3AO-4EA-lEA-2EA-3EA-4EE-IEE-2EE-3EE-4EI·IEI-2EI-3EI-4EO-IEO-2EO-3EO-4IA-lIA-2IA-3IA-4IE-IIE-2IE-3IE-4II-III-2II-3II-410-110-210-310-4OA-lOA-2OA-3OA-4OE-lOE-2OE-3OE-401-101-201-301-400-100-200-300-4

DISCUSSION

The largest subset of these syllogisms consists ofseven premise combinations that are invalid in all fourfigures, both in terms of forward processing andbackward processing. These are premise combinationsEE, EO, OE, 00, II, 10, and 01. For the first sample,a treatments by subjects analysis of variance wasconducted based upon the number correct over theseven syllogisms in each figure. Figure differences werenot significant [F(3,63) =1.98] . For the second sample,an analysis of variance for a randomized design wasconducted and, again, figure effects were not significant[F(3,72) = .64] .

In addition to these 28 syllogisms, there are eightother comparisons of pairs of syllogisms in which theconclusions to be drawn from both forward and backwardprocessing are the same. These include four pairs in whichthe same valid propositional conclusion is justified fromboth forward and backward processing (AE-2 and AE4,AI·l and AI·3, IA·3 and IA4, and EA·l and EA-2) andfour invalid pairs in which the correct answer from bothforward and backward processing is that no propositionalconclusion may be drawn (AI-2 and A14, IA-l and IA-2,AO·l and A04, and OA·l and OA4). These comparisonswere analyzed with t tests for related measures for thefirst sample and with t tests for independent groups forthe second sample. As predicted by the model, none ofthe 16 t tests for the two samples was significant. Thehighest t value occurred for the comparison of syllogismsAO-l and AOA in the first sample, and this t reachedonly 1.70. The median t for the 16 separate comparisonswas only .76. Thus, there were no unpredicted figureeffects.

In addition to tests of the particular hypothesesof the study, analyses of variance were conducted totest for the figure effect, based on all 19 valid syllogismsreported by Erickson (1974). For the first sample,performance decreased from Figure 1 to Figure 4,with 90.9%, 88.6%, 62.9%, and 53.6% correct,respectively. This figure effect was highly significant[F(3,63) = 32.52, p<.OOl]. In the second sample,performance also decreased from Figure 1 to Figure 4,with 86.2%, 79.6%, 60.1%, and 45.8% correct,respectively. Again, the effect of figure was highlysignificant [F(3,72) = 17.30, P < .001].

Finally, since there do not appear to be anypresentations of the complete response distributionsfor all 64 syllogisms in the literature, these data arepresented here in their entirety. Table 3 presents thedata for the first sample, in which the same subjectsreceived all 64 syllogisms, and Table 4 presents thedata for the second sample in which each figure wasadministered to a different set of subjects.

The results of the present study indicate that figureis a significant determinant of performance within aspecific subset of syllogisms. Figure effects on the

FIGURE EFFECTS IN SYLLOGISTIC REASONING 81

Table 4Response Distributions for 64 Syllogisms, Sample 2

Note-Numbers indicate percentage of total responses to eachsyllogism. *N refers to "no valid conclusion. ..

number of correct responses have been demonstratedfor premise combinations EI, IE, and AE for Sample 1and for premise combinations EI and IE for Sample 2,with the difference on premise combination EAapproaching significance. Of the 24 relevant syllogismsfor the two samples combined, figure effects havebeen demonstrated for 18, with 2 more approachingsignificance.

These data also support the explanation of figureeffects in terms of backward processing. Thus, figureeffects on the occurrence of the predicted error havebeen demonstrated for premise combinations EI, IE,EA, and AE for Sample 1 and for premise combinationsEI, IE, and EA for Sample 2. Of the 24 relevantsyllogisms for the two samples combined, figure effectshave been demonstrated for 22.

Thus, the decrement in the number of correctresponses across figures is paralleled by an increase inthe occurrence of the error that is predicted on thebasis of backward processing. The more strongly thedirection of the information in the premises promotesbackward processing, the greater the number of errorscorresponding to the valid conclusion for backwardprocessing at the expense of the correct conclusion,based upon forward processing that is required of thesubject.

Additional strong support for the explanation interms of backward processing is provided by the analysesof those premise combinations for which both forwardand backward processing lead to the same conclusions.In all of these instances, there are no significantdifferences between figures. Thus, figure differencesonly occur in those instances where the conclusionsderived from forward and backward processing arediscrepant.

This demonstration of the effects of backwardprocessing provides evidence for a new kind of illicitconversion to supplement the principle of conversionof premises proposed by Chapman and Chapman (1959).In the present instance, the subject is erroneouslyconverting conclusions. Thus, the conclusion "Some Pare not S" is erroneously converted to "Some S are notP." Similarly, the conclusion that no propositionalassertion can be deduced from P to S is erroneouslyconverted into the conclusion that no propositionalassertion can be deduced from S to P.

It is possible to reformulate these error tendenciesin terms of a more general proposition. In all of theinstances in which a subject erroneously converts aproposition, the subject is assuming a symmetricalrelation between the classes represented by the termsof the syllogism. Such a symmetrical relation is lesscomplex than an asymmetrical relation in which theform of the relation proceeding in the forward directionis different from the form of the relation proceedingin the backward direction. Some evidence that thispreference for symmetrical relations is a generaltendency on reasoning tasks is provided by studies

N*

2.621.1

5.35.3

36.82.6

18.42.60.0

10.50.0

23.736.813.218.415.8

0.02.62.6

34.260.571.181.673.7

7.921.118.450.055.363.244.781.623.723.7

5.37.9

68.418.439.534.255.336.863.257.952.639.544.744.728.915.8

0.028.98\.657.952.657.957.934.247.457.960.547.465.865.8

o

2.65.3

28.921.1

5.30.02.65.3

89.563.289.576.3

2.67.9

15.85.32.60.00.05.32.65.30.05.3

10.52.6

13.20.07.9

15.80.05.3

63.244.784.289.5

2.60.02.60.0

31.650.028.939.5

0.07.9

18.47.95.3

13.218.413.20.0

10.57.9

26.37.9

13.215.87.9

13.228.9io.s7.9

E

0.02.60.02.6

52.694.771.189.5

5.35.32.60.02.65.30.05.3

92.192.173.752.634.213.218.421.113.215.813.226.3

7.95.37.95.30.05.30.02.6

13.244.736.83\.65.35.35.30.02.67.92.62.65.37.92.65.3

13.25.3

15.810.50.05.32.62.62.6

10.50.00.0

94.768.465.871.1

0.00.00.00.00.00.02.60.02.60.00.00.00.00.00.02.60.05.30.00.00.02.60.00.02.60.00.00.00.02.62.60.02.60.00.00.00.02.60.00.05.32.60.00.00.00.00.02.62.60.00.00.05.30.02.65.32.60.02.62.6

AA-lAA-2AA-3AA-4AE-lAE-2AE-3AE-4AI-lAI-2AI-3AI-4AO-lAO-2AO-3AO-4EA-IEA-2EA-3EA-4EE-lEE-2EE-3EE-4EI-lEI-2El-3EI-4EO-lEO-2EO-3EO-4IA-lIA-2IA-3IA-4IE-lIE-2IE-3IE-4II-I11-211-311-410-110-210-310-4OA-lOA-2OA-3OA-4OE-lOE-2OE-3OE-401-101-201-301-400-100-200-300-4

Syllogism A

0.02.60.00.05.32.67.92.65.3

21.15.30.0

55.373.765.873.7

5.35.3

23.75.32.65.30.00.0

68.457.955.323.726.315.847.4

7.913.223.7

7.90.0

13.236.821.134.2

7.95.32.62.6

39.542.134.244.760.563.278.950.0

2.626.323.75.3

28.947.431.626.321.113.221.123.7

---------------

82 DICKSTEIN

of conditional reasoning (Wason & Johnson-Laird,1972), in which subjects often erroneously assume thatthe proposition, "If p then q" implies both "If q then p"and "If not p then not q."

The present study also replicates the figure effectbased upon all 19 valid syllogisms reported by Erickson(I974). However, as noted above, the comparison acrossfigures for these syllogisms is confounded due to theunequal distribution of conversion syllogisms acrossfigures. In addition, the difference is partially attributableto the difference across figures on premise combinationEI, which has been demonstrated in the present paperas a function of backward processing. When the fourconversion and four EI syllogisms are removed fromthe set of valid syllogisms, there is no significant figureeffect for the remaining II syllogisms in either sample.

The data of the present study do not support themediation paradigm analogy proposed by Frase (1968).Predictions from the mediation paradigm predict figureeffects on a broader range of syllogisms than thosepredicted by the backward processing explanation.Yet, the only significant differences occur wherepredicted on the basis of backward processing.Furthermore, the backward processing explanationsuccessfully predicts the specific errors which will occur.while the mediation paradigm analogy does not. Thus,the present study supports the greater utility of aninformation processing approach to syllogistic reasoning,as opposed to an associative approach.

The figure differences demonstrated in this studyare not predicted by any of the general modelsthat have been proposed to account for subjectperformance on the syllogistic task. The atmosphereeffect explanation (Woodworth & Sells, 1935) basesits predictions on the kinds of propositions (A, E, I,or 0) that occur in the major and minor premises.Since premise combinations remain the same acrossall four figures, no figure effects are predicted. Chapmanand Chapman (I959) confine their attention to invalidsyllogisms, which they divide into two subsets,conversion syllogisms and probabilistic inferencesyllogisms. However, in both instances, predictionsfor a given premise combination remain the same acrossfigures.

More recently, Erickson (I974) has presented a setof quantitative models for the syllogistic task. For thecomparisons under consideration in this paper, thesemodels do not make differential figure predictionsfor premise combinations IE, EA, and AE. Indeed,in all of these instances, the data from the various figuresare combined and are not reported individually. Theonly premise combination relevant to this paper forwhich Erickson (1974) predicts a figure effect is EI.Here, the models predict that performance will be betteron Figures 1 and 2 than on Figures 3 and 4, and thatthis decrement will be paralleled by an increase inE errors in Figures 3 and 4. Unfortunately, the data

reported by Erickson (1974) do not support thesepredictions. In fact, the percentage correct in thesedata is slightly higher in Figures 3 and 4, while thepercentage of E errors in these figures is slightly lower.While these data are discrepant with the predictionsof Erickson's (1974) models, they do not presentany difficulty for the backward processing explanation.Erickson's (1974) procedure did not provide subjectswith the alternative of a nonpropositional conclusion,and no data are reported for this category. Since thebackward processing explanation predicts that thedecrement in percentage correct across figures forpremise combination EI results from an increase innon propositional conclusions, no figure effect wouldbe expected when this option is ruled out by theprocedure. Thus, Erickson's (I 974) data provideadditional, indirect support for the backward processingexplanation.

Revlis (I 975b) has presented a model whichcombines the principle of conversion proposed byChapman and Chapman (1959) with the principleof feature selection based upon the atmosphereexplanation of Woodworth and Sells (1935). However,again, for the comparisons under consideration inthis paper, no figure differences are predicted. Forvalid premise combination EI, the model predictscorrect performance in all four figures. Thus, themodel fails to predict the substantial frequency ofnon propositional . conclusions demonstrated in thispaper and also fails to predict the significant figuredifferences. For valid premise combination EA inFigures 3 and 4, the model correctly predicts the Eerror based upon conversion, which is the dominanterror in both figures, but fails to predict the significantdifference between figures in nonpropositionalconclusions. For invalid premise combination AE inFigures 1 and 3, the model correctly predicts the Eerror based upon conversion, which is the dominanterror in both figures, but fails to predict the significantdifferences between figures in both the number correctand the number of 0 errors. Finally, for invalid premisecombination IE, the model correctly predicts theoccurrence of 0 errors, as predicted by the backwardprocessing explanation. However, for Revlis (I 975b),this error is due to feature selection based upon theatmosphere of the premises. Since the atmosphere isthe same for all four figures, no figure differences arepredicted. Since the present data clearly demonstratefigure differences in this error, the backward processingexplanation appears to provide a better account ofsubject performance than does the principle of featureselection. It may also be noted that there is otherevidence (e .g., Ceraso & Provitera, 1971; Dickstein,1975) against the utility of a feature selection oratmosphere explanation of subject performance.

In summary, none of the existing models ofsyllogistic reasoning predicts the occurrence of the figure

FIGURE EFFECTS IN SYLLOGISTIC REASONING 83

effects demonstrated in this paper, and thus, none canbe regarded as a fully comprehensive account of subjectperformance on this task. Rather, it appears that anycomplete model will have to incorporate the principleof backward processing as one of its components.

The present study provides partial support for theprediction that performance would be better on validpremise combination EI than on invalid premisecombination IE, based upon the assumption (Revlis,1975b) that subjects have a bias against nonproposi­tional conclusions. This prediction was confirmed forSample I but not for Sample 2. In the second sample,while there was no main effect of validity, there wasa significant interaction between figure and validityfor correct responses. This interaction is difficult toexplain, since it was not accompanied by a significantinteraction for the predicted errors.

Finally, it may be noted that the present study useda multiple choice format, in which the subject wasprovided with four propositional conclusions thatalways went from S to P as well as one nonpropositionalconclusion to choose from. Wason and Johnson-Laird(1972) have noted that such a task involves theevaluation of conclusions by the subject, rather than themore active construction of conclusions. They havesuggested the use of a task in which only the premisesare provided and the subject is free to write anyconclusion. Such a task would seem to have specialutility in future research on the effects of figure, sinceit would provide more direct evidence for the occurrenceof backward processing than is possible with themultiple choice format.

REFERENCES

BRUNING. 1.. & KINTZ. B. Computational handbook of statistics.Glenview. Ill: Scott Foresman. 1968.

CERASO. J .. & PROVITERA. A. Sources of error in syllogisticreasoning. Cognitive Psychology. 1971. 2.400·410.

CHAPMAN. L.. & CHAPMAN. J. Atmosphere effectreexamined. Journal ot' Experimental Psychology. 1959.58. 220·221l.

DICKSTEIN. L. S. Effects of instructions and premise orderon errors in syllogistic reasoning. Journal 0/ Experimental

Psychology. Human Learning and Memory. 1975. 1.376-3~4.

Die KSTEIN. L. S. Differential difficulty of categoricalsyllogisms. Bulletin or the Psychonomic Society. 1976. 8.330-332.

ERICKSON. J. R. A set analysis theory of behavior in formalsyllogistic reasoning tasks. In R. L. Solso (Ed.), Theoriesill cognitive psychology: The Loyola symposium. Hillsdale.N.J: Lawrence Erlbaum , 1974.

FRASE. L. T. Associative factors in syllogistic reasoning.Journal otExperimental Psychology. 1968. 76.407-412.

KINTSCH. W .. & MONK. D. Storage of complex informationin memory: Some implications of the speed with whichinferences can be made. Journal ot' Experimental Psychology.1972. 94. 25-32.

REVLIs. R. Two models of syllogistic reasoning: Featureselection and conversion. Journal of Verbal Learning andVerbal Behavior. 1975. 14. 180-195. (a)

REVLIs. R. Syllogistic reasoning: Logical deductions from acomplex data base. In R. J. Falmagne (Ed.J, Reasoning:Representation and process. Hillsdale, N.J: LawrenceErlbaum, 1975. (b)

ROBERGE. J. A reexamination of the interpretation of errorsin formal syllogistic reasoning. Psychonomic Science,1970. 19.331-333.

ROBERGE, J. Further examination of mediated associationsin deductive reasoning. Journal of ExperimentalPsychology. 1971. 87. 127-129.

WASON. P. C. & JOHNSON-LAIRD. P. N. Psychology ofreasoning: Structure and content. Cambridge: HarvardUniversity Press. 1972.

WOODWORTH. R.. & SELLS. S. An atmosphere effect informal syllogistic reasoning, Journal of ExperimentalPsvchologv, 1935. 18.451-460.

NOTE

1. The number of correct responses and the number ofpredicted errors across figures are not independent analyses,since the number of errors is constrained by the number correct.Both analyses are presented to demonstrate that figuredifferences in performance are reflected in the specific errorspredicted by the hypothesis of backward processing and donot simply represent an increase in incorrect responses of alltypes.

(Received for publication July 14.1977;revision accepted September 22,1977.)