Psychological Review 1969, Vol. 76, No. 4, 387-404 ...clark/1960s/Clark, H.H...Psychological Review...

Psychological Review 1969, Vol. 76, No. 4, 387-404 LINGUISTIC PROCESSES IN DEDUCTIVE REASONING 1 HERBERT H. CLARK* Carnegie-Mellon University The present paper develops a theory to specify in part how a person stores and searches through information retained from sentences. The theory states that (a) functional relations, like the abstract subject-predicate relation which underlies sentences, are more available from memory than other, less basic kinds of information; (6) certain "positive" adjectives, like long, are stored in memory in a less complex and more accessible form than their oppo- sites, like short; and (c) listeners can only retrieve, from memory, informa- tion which is congruent at a deep level to the information they are searching for. The present theory, unlike previous ones, correctly predicts the prin- cipal differences in the solution times of 8 types of two-term series problems and 32 types of three-term series problems (e.g., // John isn't as bad as Pete, and Dick isn't as good as Pete, then who is worst?). It also accounts for previous observations on children solving these problems and explains other phenomena in deductive reasoning. Deductive reasoning has often been stud- ied in particular types of reasoning problems. The strategies suggested for their solution have therefore often been of limited gen- erality : they apply in one kind of problem and that kind alone. The present paper pro- poses, instead, that reasoning is accomplished mainly through certain very general lin- guistic processes, the same mental operations that are used regularly in understanding language. Furthermore, the present paper demonstrates in several experiments that these processes, rather than the strategies proposed in the past, correctly account for the difficulties in a variety of reasoning problems. When a person has comprehended a sen- tence, he is said to "know what it means." It is this knowledge that is at the heart of the theory developed here. The theory spe- cifies in part both the form this knowledge takes in memory and the process by which '•The research reported here was supported in part by United States Public Health Service Re- search Grant MH-07722 from the National Insti- tute of Mental Health. The author wishes to thank many colleagues, especially Daryl J. Bern, Stuart K. Card, Eve V. Clark, and William C. Watt, for their constructive comments on the paper, and Joel Gordon and Stephen H. Ellis for their assistance in running the experiments. 2 Requests for reprints should be sent to Herbert H. Clark, who is now at Stanford University, De- partment of Psychology, Stanford, California 94305. it is later retrieved for other purposes. Knowledge of this kind is presumed to be quite abstract. Thus, to answer a question about the content of a sentence, one must know more than the phonological shape of the sentence: one must have come to an interpretation of it. The distinction here is the same as that in the linguistic concepts of "surface" and "deep" structure (Chom- sky, 1965; Postal, 1964). The surface struc- ture of a sentence is the structure which allows it to take on phonological shape; but it is the more abstract deep structure which is necessary for its interpretation. The abstract entities one is presumed to know after interpreting a sentence, then, are closely related to certain linguistic facts about deep structure and the lexicon. And it is at this abstract level that a search for previous in- formation is carried out. For their study of reasoning, many inves- tigators (Burt, 1919; DeSoto, London, & Handel, 1965; Donaldson, 1963; Handel, DeSoto, & London, 1968; Hunter, 1957; Huttenlocher, 1968) have chosen the so- called three-term series problem, which con- sists of two propositions and a question, e.g., // John is better than Dick, and Pete is worse than Dick, then -who is best? The wording of these problems is critical. In all past stud- ies, for example, the above problem has been easier than the following one: // Dick is worse 387

Transcript of Psychological Review 1969, Vol. 76, No. 4, 387-404 ...clark/1960s/Clark, H.H...Psychological Review...

Page 1: Psychological Review 1969, Vol. 76, No. 4, 387-404 ...clark/1960s/Clark, H.H...Psychological Review 1969, Vol. 76, No. 4, 387-404 LINGUISTIC PROCESSES IN DEDUCTIVE REASONING1 HERBERT

Psychological Review1969, Vol. 76, No. 4, 387-404



Carnegie-Mellon University

The present paper develops a theory to specify in part how a person storesand searches through information retained from sentences. The theory statesthat (a) functional relations, like the abstract subject-predicate relationwhich underlies sentences, are more available from memory than other, lessbasic kinds of information; (6) certain "positive" adjectives, like long, arestored in memory in a less complex and more accessible form than their oppo-sites, like short; and (c) listeners can only retrieve, from memory, informa-tion which is congruent at a deep level to the information they are searchingfor. The present theory, unlike previous ones, correctly predicts the prin-cipal differences in the solution times of 8 types of two-term series problemsand 32 types of three-term series problems (e.g., // John isn't as bad asPete, and Dick isn't as good as Pete, then who is worst?). It also accountsfor previous observations on children solving these problems and explainsother phenomena in deductive reasoning.

Deductive reasoning has often been stud-ied in particular types of reasoning problems.The strategies suggested for their solutionhave therefore often been of limited gen-erality : they apply in one kind of problemand that kind alone. The present paper pro-poses, instead, that reasoning is accomplishedmainly through certain very general lin-guistic processes, the same mental operationsthat are used regularly in understandinglanguage. Furthermore, the present paperdemonstrates in several experiments thatthese processes, rather than the strategiesproposed in the past, correctly account forthe difficulties in a variety of reasoningproblems.

When a person has comprehended a sen-tence, he is said to "know what it means."It is this knowledge that is at the heart ofthe theory developed here. The theory spe-cifies in part both the form this knowledgetakes in memory and the process by which

'•The research reported here was supported inpart by United States Public Health Service Re-search Grant MH-07722 from the National Insti-tute of Mental Health. The author wishes tothank many colleagues, especially Daryl J. Bern,Stuart K. Card, Eve V. Clark, and William C.Watt, for their constructive comments on thepaper, and Joel Gordon and Stephen H. Ellis fortheir assistance in running the experiments.

2 Requests for reprints should be sent to HerbertH. Clark, who is now at Stanford University, De-partment of Psychology, Stanford, California 94305.

it is later retrieved for other purposes.Knowledge of this kind is presumed to bequite abstract. Thus, to answer a questionabout the content of a sentence, one mustknow more than the phonological shape ofthe sentence: one must have come to aninterpretation of it. The distinction hereis the same as that in the linguistic conceptsof "surface" and "deep" structure (Chom-sky, 1965; Postal, 1964). The surface struc-ture of a sentence is the structure whichallows it to take on phonological shape; butit is the more abstract deep structure whichis necessary for its interpretation. Theabstract entities one is presumed to knowafter interpreting a sentence, then, are closelyrelated to certain linguistic facts about deepstructure and the lexicon. And it is at thisabstract level that a search for previous in-formation is carried out.

For their study of reasoning, many inves-tigators (Burt, 1919; DeSoto, London, &Handel, 1965; Donaldson, 1963; Handel,DeSoto, & London, 1968; Hunter, 1957;Huttenlocher, 1968) have chosen the so-called three-term series problem, which con-sists of two propositions and a question, e.g.,// John is better than Dick, and Pete is worsethan Dick, then -who is best? The wordingof these problems is critical. In all past stud-ies, for example, the above problem has beeneasier than the following one: // Dick is worse


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than John, and Dick is better than Pete,then who is best? The difference occurseven though both problems present exactlythe same information, at least superficially.Despite the importance of wording in theseproblems, however, past accounts of reason-ing have neglected to deal directly with thelogically prior process of how the languageof the problems is itself understood. In oneway or another, the past accounts all havethe subjects (5s) solving the problems withsomething less than an abstract interpreta-tion of the propositions. The experiments tobe reported here, then, besides lending sup-port to the present theory, also appear to dis-confirm the earlier explanations. The con-tradictory evidence comes mainly from apreviously untouched set of three-term seriesproblems in which the customary proposi-tions, like John is better than Pete, are re-placed by new ones, like John isn't as badas Pete. Although these two propositionshave a superficially similar appearance andseem almost synonymous, they have radicallydifferent abstract interpretations. Becauseof this property, they allow strong tests ofthe previous theories as well as of the presentone.

The present theory will be formulated asthree principles: two specify what it is thatthe listener knows of a sentence he hasheard and a third specifies how he searcheshis memory for the wanted knowledge.These three principles will then be used asa basis for predicting the relative times ittakes 5"s to solve two-term series problems(e.g., // John is better than Pete, then whois worse?} and three-term series problems.Finally, the theory will be applied to pre-vious data on three-term series problems aswell as to other, less directly related phe-nomena in deductive reasoning.


Principle of the Primacy ofFunctional Relations

Functional relations are the primitive con-ceptual relations out of which sentences areconstructed. Chomsky (1965) lists foursuch relations which he claims are universal:Subject-of, Predicate-of, Direct-object-of,

and Main-verb-of. For example, in bothJohn watched the monkey and The monkeywas watched by John, a listener knows thatJohn, watch, and monkey are in the relationsubject, verb, and direct object: it was Johnwho watched, what John did was watch, andit was the monkey which was watched. Butthe listener also knows that the theme ofthe first sentence—what the sentence is about(Halliday, 1967)—is John, whereas thetheme of the second is the monkey; thisinformation, of a quite different sort, is notto be found in the functional relations thatunderlie a sentence. The principle of theprimacy of functional relations asserts sim-ply that functional relations, like those ofsubject, verb, and direct object, are stored,immediately after comprehension, in a morereadily available form than other kinds ofinformation, like that of theme.

This principle, first proposed by Miller(1962) in the language of an earlier lin-guistic theory, is formally related to twodifferent kinds of information present in thedeep structure of a sentence. In one gen-erative grammar of English (similar toChomsky's, 1965), deep structure, a productgenerated by the rules of the "base compo-nent" of the grammar, consists of (a) so-called base strings, like John Past watch themonkey, which fully specify functional rela-tions, and (b) directions for the eventualtransformation of these strings into a sur-face structure, like the passive The monkeybe + Past watch + en by John. The prin-ciple proposed here specifies that the infor-mation of a is more available than the in-formation of b. Significantly, there is onlya small number of functional relations andpossible base strings—linguists differ as tothe actual number—but there is a greatnumber of transformations available to shapethem into numerous different surface forms.

Miller's (1962) proposal was that a sen-tence is understood and stored in memoryas two kinds of independent information—base strings and transformations. In subse-quent research, Miller and others (Gough,1965, 1966; McMahon, 1963; Mehler, 1963;Miller & McKean, 1964; Savin & Percho-nock, 1965) have concentrated on demon-strating that a sentence requiring more trans-

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formations in mapping deep onto surfacestructure is more complex psychologically,taking more time to understand and morespace in immediate memory. The general-ity of this relationship has recently beenquestioned by Fodor and Garrett (1966)(cf., however, Watt, in press). In con-trast, the emphasis in the present paper ison the importance of the base strings them-selves: they constitute the essential part ofthe interpretation of a sentence and shouldtherefore play an important part wheneverthe interpretation is needed at a later time.Evidence for their importance is found es-pecially in the experiments of McMahon(1963), Clifton, Kurcz, and Jenkins (1965),Clifton and Odom (1966), and Clark andBegun (1968).

Principle of Lexical Marking

According to the principle of lexical mark-ing, the senses of certain "positive" adjec-tives, like good and long, are stored in mem-ory in a less complex form than the sensesof their opposites. This principle is derivedfrom certain linguistic facts relevant to thelexical component of English, that part ofthe grammar which defines the senses ofwords; these words, when inserted in thebase component, give phonological shape tothe abstract characterizations of the base.It is the lexicon that specifies that bird issuperordinate to oriole, that man is ani-mate, that good and bad are antonymous,and so on.

Antonymous adjectives, like good and bad,and long and short, are often found, on closescrutiny, to be asymmetric (Bierwisch, 1967;Greenberg, 1966; Lyons, 1963, 1968; Sapir,1944; Vendler, 1968). The first piece ofevidence for this is that the "positive" mem-ber of many such pairs can be neutralizedin certain contexts. A speaker asking "Howgood is the food ?" can merely be asking foran evaluation of the food. He will be satis-fied whether he is told the food is good orbad. But the speaker asking "How bad isthe food?" is implying something more:rightly or wrongly, he is pronouncing thefood to be bad and is asking about theextent of its badness. Since good can be

neutralized and bad cannot, good is said tobe "unmarked" and bad "marked." Otherunmarked-marked pairs by the same cri-terion are long-short, wide-narrow, andinteresting-uninteresting; in the last pair,the marking is made explicit morphologically.

The second piece of evidence, obviouslyrelated to the first, is that the unmarkedmember of each pair also serves as the nameof the full scale. The names of the good-bad and long-short scales are goodness andlength; badness and shortness name onlyhalf of their respective scales. Also, insentences like The board is six feet long,long names the dimension to be measuredand nothing more; six feet long is exactlyparaphrased by six feet in length. The longin six feet long obviously is in the sameclass with other dimensional names, likewide, deep, thick, and high—other unmarkedadjectives-—and not with its opposite short:the sentence *The board is six feet shorts

is unacceptable to English speakers.In sum, the unmarked adjective has two

senses, but the marked only one. The senseof good in the noncommittal how good? andthat of long in the noncommittal how long?or in six feet long will be called their "nomi-nal" senses, for in these instances only thescale name is indicated. The other sensesof good, bad, long, and short, as in the simpleThis board is long, will be called "contras-tive." Contrastive long and short, for ex-ample, specify length in relation to someimplicit standard and contrast with eachother. One property of nominal and con-trastive senses is that they can occur to-gether, as in The short board is six feet long,although two different contrastive senses(without qualification) cannot, as in theunacceptable *The short board is long. An-other property is that the nominal sense issemantically presupposed in the contrastivesenses. Note that contrastive long and shortmean "much in length" and "little in length";both definitions presume that the measureddimension is length—both presume nominallong. Yet the nominal sense of long carriesno presupposition about comparative length.

8 An asterisk indicates that the following sen-tence is generally unacceptable in English.

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This linguistic evidence suggests thatnominal and contrastive senses of adjectivesought to have different codings in memory(cf. also Clark & Stafford, 1969). The cod-ing difference is formalized in the principleof lexical marking: (a) a nominal sense isstored as one less entity than its corre-sponding contrastive senses, hence (&) thenominal sense is stored and retrieved frommemory more quickly than the contrastivesenses. To indicate this in a notation (seeBierwisch, 1967), nominal good would becoded as [+Evaluative[Polar]], and con-trastive good as [+Evaluative[+Polar]].The semantic feature [+ Evaluative] meansthat an evaluation is being made in bothcases. The lack of a sign before the featurePolar in the nominal case means that theend of the scale is not specified; the plussign in the contrastive case means that thepositive pole of the scale is specified. Theonly sense of bad, similarly, is coded as[+Evaluative[— Polar]]. Stated in termsof this notation, the principle states that[+Evaluative[Polar]] alone is easier tostore and retrieve than the more complex[+Evaluative[ — Polar] ] .

The principle of lexical marking has indi-rect support from several previous studies.Greenberg (1966) and Marshall (1968)proposed that the extra specification of themarked adjective should be more easilydropped than added in free association; thedata they examine support this proposal.Clark and Card (1969) have shown a similarloss of the additional feature in the memoryfor comparative sentences containing an-tonymous adjectives. Both kinds of resultsare consistent with the greater simplicityof the memory coding for unmarked adjec-tives in their nominal sense.

Principle 0} Congruence

Answering a question requires more of alistener than a mere understanding of thequestion itself. He must "search" his mem-ory for the wanted information and formu-late that information in an answer. It isproposed here that his search is guided bythe principle of congruence. What he seeksfrom his previous knowledge is informationcongruent, at the level of functional rela-

tions, with the information asked for in thequestion. He cannot answer the questionuntil he finds congruent information, or un-til he reformulates the question so that heis able to do so.

Application of the Principles toComparative Sentences

The role these three principles play intwo- and three-term series problems de-pends first on the role they play in thesentences that make up these problems. Thesentences of interest are comparative con-structions, such as John is better than Pete,negative equative constructions, such as Johnisn't as bad as Pete, and questions such aswho is best? The three principles will beexamined in turn for their application tothese types of sentences.

Principle of the primacy of functional re-lations. By this principle, the informationmost readily available from an interpretationof a sentence is its underlying functionalrelations. But what are the functional rela-tions in comparative and negative equativeconstructions? Lees (1961), Smith (1961),Huddleston (1967), and Doherty andSchwartz (1967) argue that both types ofconstructions are generated linguisticallyfrom two primitive base strings. UnderlyingJohn is better than Dick are the base strings,John is good and Dick is good. It is here inthe base strings that the subject-predicaterelations of John and good and of Dick andgood are found. The two strings are alsodesignated in the base component as partsof a comparative construction. After thefirst transformations, there is a result thatreads, roughly, John is more good than Dickis good. By a further transformation thelast redundant good is dropped; and finally,more good is changed to better to form Johnis better than Dick is or, simpler still, Johnis better than Dick. Had the two basestrings been the door is wide and the deskis long, the resulting sentence would havebeen The door is wider than the desk islong; in this case, the second adjective couldnot be deleted, since it was not identical tothe first. The positive equative constructionJohn is as good as Dick, as well as the nega-tive John isn't as good as Dick, are derived

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analogously, with as-as in place of more-than,

Comparative sentences then contain,roughly, two kinds of information: (a) thefunctional relations, as in John is bad, and(b) the comparison more than. Applied tothe comparative, the principle of the primacyof functional relations asserts that a is moreavailable than b. In John is worse thanPete, the listener realizes that John and Peteare bad more readily than that John is moreextreme than Pete in badness. To empha-size the functional relations in a convenientnotation, the present paper will representJohn is worse than Pete as (John is bad+;Pete is bad), John isn't as bad as Pete as(John is bad; Pete is bad+~), and who isworst? as (X is bad+ + ). One + is onedegree more extreme than none, and two+'s indicate the most extreme.

An important, but surprising, consequenceof this linguistic analysis is that John isbetter than Pete and Pete is worse thanJohn do not impart the same information,as a logician might suggest. The compre-hension of each sentence brings with it dif-ferent kinds of immediate knowledge. Thisdifference will be shown to affect how wellsomeone can use the knowledge in deductivereasoning.

Principle of lexical marking. This princi-ple asserts that the nominal sense of good—the sense found in noncommittal how good?questions—is stored in a less complex andmore available form than the contrastivesenses of good and bad. But in which senseare we to interpret the goods underlyingJohn is better than Pete and the bads under-lying Pete is worse than John? It will beargued that the goods can be either nominalor contrastive, but the bads must be con-trastive. Evidence for this is found in threekinds of examples which show a parallelbetween comparative sentences and howgood? type questions, whose properties havealready been demonstrated.

First, both How good is John? and Johnis better than Pete are ambiguous. If weknow nothing about John or Pete, both sen-tences would normally be interpreted as im-plying nothing about John or Pete. Butwhen prefaced by I know that John and

Pete are good but, they are no longer non-committal and therefore contain the con-trastive good. Note that How good isJohn?, with a stress on how, is understoodin its contrastive sense. How bad is John?and Pete is worse than John, however, un-ambiguously imply negative evaluations ofPete and John. Second-order comparativequestions show the same neutralization phe-nomenon. How much better is John thanPete? can be noncommittal or positive, butHow much worse is John than Pete? is al-ways negative. Pertinent to this point isDeSoto et al.'s (1965) anecdote about thedisgruntled baseball fan who was watchingtwo baseball greats playing a bad game."I came to see which of you two guys wasbetter," he yelled at one of them. "Instead,I'm seeing which is worse."

Second, unmarked adjectives can be usedin ways that marked adjectives cannot.Consider the following examples, remem-bering that intelligent is unmarked andstupid is marked:

1. This genius is more intelligent thanthat genius.

2. This idiot is more intelligent thanthat idiot.

3. *This genius is stupider than thatgenius.

4. This idiot is stupider than that idiot.

If it is assumed that stupid and intelligentare being used in only their contrastivesenses, then Sentences 2 and 3 should bothbe unacceptable sentences. The reason isthat their respective base strings, *idiots areintelligent and *geniuses are stupid, are un-acceptable. However, Sentence 2 is clearlyacceptable, although Sentence 3 is not (ex-cept in an ironic sense). The intelligentunderlying Sentence 2 must therefore benominal, so that the base string this idiotis intelligent really only means "this idiothas measurable intelligence." Sentence 3remains unacceptable because the markedstupid cannot assume a nominal sense. Thereare four parallel examples of the how intelli-gent? type questions, and of these, the onlyunacceptable one—*How stupid is the gen-ius f—is the counterpart of Sentence 3,

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Third, the parallel between how good?type questions and comparative sentences ismore than superficial, for they both havemuch the same structure. How good isJohn? can be written as John is (how)good, and John is better than Pete as Johnis (more in extent than Pete is good) good(cf. Chomsky, 1965; Doherty & Schwartz,1967). The comparative is a type of quanti-fication on the unadorned adjective, just assix feet is on simple long. The parallel inthe semantic properties of the two is there-fore not surprising. In summary, unmarkedadjectives in comparatives, just as in howgood? type questions, can be interpretedeither nominally or contrastively, whereastheir marked counterparts can only be inter-preted contrastively.

The principle of lexical marking, then,has direct application to sentences that con-tain better, worse, isn't as good as, or isn'tas bad as. From the above, we know thatthe good underlying John is better thanPete can be interpreted either nominally orcontrastively. From the principle of lexicalmarking, however, it follows that since thecontrastive sense takes longer to store andretrieve, this good will usually be inter-preted in its simpler nominal sense. Thebad underlying Dick is worse than Jack, ofcourse, can only be interpreted contrastively.This agrees with intuition, leaving John isbetter than Pete normally noncommittal intone, but Dick is worse than Jack clearlynegative in tone. The principle predicts thatbetter and isn't as good as propositions willbe more quickly registered and retrievedthan worse and isn't as bad as propositions.

Principle of congruence. By this prin-ciple, information cannot be retrieved froma sentence unless it is congruent in its func-tional relations with the information that isbeing sought. This can be illustrated in thefollowing two-term series problem: // Johnis better than Pete, then who is best? (Al-though this question is "bad English" bygrammar school standards, it was used inthe experiments that follow because good,better, and best, and bad, worse, and worst,all have different phonological forms andbecause the three-term series problem usesthe same form of questions; as expected, no

6" objected to it.) The proposition providesthe information, (John is good+; Pete isgood). The question requests an X so that(X is good+ + ) ; that is, it requires a searchfor the term with the most-plussed good.The underlying form of the question is con-gruent with that of the proposition, so thesolution is immediately forthcoming—"Johnis best" or just "John." But when who isbest? is replaced with who is worst?, aquestion requesting information not con-gruent with the proposition's information,then the problem solver will search for themost-plussed bad term and, finding none,implicitly reformulate the question to readwho is least good? So (X is bad+ + ) be-comes (X is good ), in which the min-uses direct the search for the term with theleast-plussed good. In this search, the 5"will find congruent information and willformulate the solution "Pete is worst" or"Pete." The principle of congruence im-plies, then, that retrieving an answer shouldtake less time when propositions and ques-tions are congruent in their base stringsthan when they are incongruent.


Implicit in the previous three principlesis a process by which people solve problemsin deductive reasoning. Its identifiablestages are (a) comprehension of the propo-sitions; (b) comprehension of the question;(c) search for information asked for in thequestion; and (d) construction of an an-swer. The three principles affect the out-come of this process at one or more ofits stages. It is convenient, then, to exam-ine the application of the principles to theprocess as it is supposed to occur in two-term series problems. These problems con-sist of eight types, the ones formed whenone of four simple propositions (A is betterthan B, B is worse than A, A isn't as bad asB, and B isn't as good as A) is each fol-lowed by one of two questions (who is best?and who is worst f ) .

The first two stages—comprehending theproposition and question—entail setting upa representation like (A is good+; B isgood) and (X is good+ + ), by the princi-ple of the primacy of functional relations.

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At these stages and later on, the principleof lexical marking predicts that the base-string pair (A is good+; B is good) shouldbe more quickly registered and retrievedthan (B is bad+ ; A is bad), since the mem-ory coding for bad is more complex thanthat for good. At the third stage, that ofsearching for information asked for in thequestion, 5" carries out the instructions im-plicit in the question. It is at this stage thatthe principle of congruence comes into play.Whenever the question is congruent withthe propostion, 5" should take little time; ifhe needs to reinterpret the question to makeit congruent, he will take more time.

Experiment I: The Two-TermSeries Problem

The four propositions of the two-termseries problems, shown in Table 1, can bematched on superficial or deep structure.Proposition I, A is better than B, has thesame order of terms in surface structure asI', A isn't as bad as B. In both proposi-tions, A is the subject, B is the term in thepredicate, and the relation between the termsmeans "strictly greater in goodness than."But Proposition I does not have the samedeep-structure as T. Proposition I is gen-erated from base strings containing good,as indicated in the "Analysis" column,whereas I' is generated from base stringscontaining bad. In deep structure, Proposi-tion I is like II', B isn't as good as A. Thefour propositions, then, allow an orthogonalcomparison of order in surface structureand of deep structure: pairs I and I', andII and II', have the same order in surfacestructure; pairs I and II', and II and I', aresimilar in deep structure. By the threeprinciples, it is claimed that the solutiontimes of the eight problem types should beaffected mainly by the proposition's—andthe question's—deep structure.

Method. Four examples of each of the eightproblem types were constructed using as termscommon English four-letter men's names, no pairof which occurred together in more than one prob-lem. Each of the 32 problems was typed in onecontinuous line on the middle of a blank IBM cardin the following form: If Pete isn't as bad as John,then who is best? The problems were arranged in



Form of problem

I A better than B

11 B worse than A

I' A not as bad as B

II' B not as good as A


A is good

B is good

A is bad

B is bad

A is bad

B is bad

A is good

B is good

Form ofquestion
















Note.-—Mean time is in seconds.

four blocks of eight, each block containing oneproblem of each type. The order within eachblock was random and different for each 6". Thefirst block was considered practice and was laterdiscarded.

The S, at a signal, turned over a card, read theproblem aloud, and gave an answer as quickly ashe could consistent with high accuracy. He wastimed from the first signal to his answer in hun-dredths of a second. After attempting all 32 prob-lems in this manner, he repeated the procedure,omitting the answer. The time duration on thefirst go-round, minus the time duration on the sec-ond, was taken as the solution time for each of the32 problems; this procedure was meant to correctfor possible differences in the reading times of theproblems.

For each S, the problem of each type with thelongest solution time was taken out and the analy-sis was done on the two remaining ones; this pro-cedure eliminates the effect of the occasional verylong solution time resulting from wandering atten-tion or other extraneous factors. Problems withincorrect answers (6% of the nonpractice prob-lems) were also discarded before analysis. The 205"s were students from an introductory psychologycourse fulfilling a course requirement.

Results. The mean solution times for thetwo-term series problems are shown in Ta-ble 1; arithmetic means were used in placeof the more generally used geometric means,because it was possible here to have null ornegative solution times. The predictions

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made by the foregoing theory are clearlyconfirmed by these solution times.

First, the principle of the primacy offunctional relations predicts that solutiontimes will correlate with underlying, ratherthan superficial, structure. It was foundthat Problem Type I took less time thanII. If this difference had been the resultof the superficial order and meaning of theterms, then I' should take less time than II';but if it had been the result of their differentunderlying base strings, then II' shouldtake less time than I'. The data clearlysupport the second interpretation: I and II'had significantly shorter solution times thanII and I', F = 8.79, df = 1/19, p < .01, andthere was no significant interaction.

The principle of lexical marking predictsthat problems with underlying good willtake less time than those with underlyingbad. This is confirmed by the same evi-dence as above. First, note that the prin-ciple of primacy of functional relations wouldalso have been supported if I and II' hadhad longer solution times than II and I',respectively; support for this principle re-quires only that the two problems with simi-lar deep structure be consistently differentin the same direction from the other twoproblems. But the results are quite spe-cific : overall, the good problems, I and II',took significantly less time than the badones, II and I'. This supports lexical mark-ing.

Finally, the principle of congruence pre-dicts that questions congruent with a propo-sition in their underlying base strings willbe answered more quickly than incongruentquestions. This was supported, F = 11.32,df = 1/19, p < .005, with no other signifi-cant interactions. The question who isbest?, rather than who is worst?, had theshorter solution times for Problem Types Iand IF, built on an underlying good, butthe longer solution times for Problem TypesII and I', built on an underlying bad.

Deep structure was clearly dominant overthe order of terms in surface structure. InTypes I and II, the subject term of theproposition was more quickly retrieved thanthe term in the predicate. But this was nottrue for Types I' and II'. For them, the

terms in the predicate were more quicklyretrieved. Order in surface structure, there-fore, is of no detectable importance in theseproblems.

A final result is that the problems withcomparative propositions were more quicklysolved than those with negative equativepropositions, F = 18.65, df = 1/19, p <.001, with no other significant interactions.There is little doubt that the negative equa-tive is syntactically more complex than thecomparative; in current versions of trans-formational theory, there is at least onemore transformation—the negative—neededin generating the negative equative construc-tion. Conceptually, B isn't as good as Ais the denial of B is as good as A, a. con-struction of the same level of complexity asB is better than A. As one more piece ofsemantic information, denial itself takestime to process (Gough, 1965, 1966; Wason,1961).

Experiment II: The Three-TermSeries Problem

Two-term series problems are, for themost part, trivial to solve. But, as it willbe seen, the principles which explain thedifficulties of these problems also explainmost difficulties of the three-term seriesproblems. There is one additional assump-tion needed to account for the further diffi-culties of storing the information in three-term series problems.

Three-term series problems consist of twopropositions and a question, as in // Johnis better than Pete, and John is worse thanDick, then who is worst? The three terms(John, Pete, and Dick) can be placed inthe same evaluative order in 16 differentproblem types which use better, worse, best,and worst. As shown in Table 2, there arefour basic pairs of propositions, labeled Ithrough IV. Completing the 16 types, thetwo propositions of each pair can occur ineither order, and the question can be eitherwho is best? or who is worst? In addition,16 more problem types are possible whenisn't as bad as is substituted for is betterthan, and isn't as good as for is worse than.These are the four pairs of propositionslabeled I' through IV listed on the right

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Form of problem

A better than BI

B better than C

C worse than BII

B worse than A

A better than BIII

C worse than B

B worse than AIV

B better than C


A is goodB is goodC is good

A is badB is badC is bad

A is goodB is good, badC is bad

A is bad5 is bad, goodC is good

Form of problem

A not as bad as Br

B not as bad as C

C not as good as BII'

B not as good as A

A not as bad as BIII'

C not as good as B

B not as good as AIV

B not as bad as C


A is bad5 is badC is bad

A is good5 is goodC is good

.4 is badB is bad, goodC is good

.4 is goodB is good, badC is bad

of Table 2. Although Problem Types Ithrough IV have been studied before, I'through IV have not. For ease of com-prehension the convention is used that theA term is best, the C term worst, and theB term in the middle.

Like the problems in Table 1, those inTable 2 can be paired for the similarity ofeither superficial order or deep structure.The Roman numerals match the problemtypes for superficial similarity. Types I andI', for example, are identical except for therelational terms, and in both cases the rela-tion term (is better than and isn't as bad as,respectively) means "strictly greater than."The deep structure of each pair, however, isdifferent. Underlying Problem Type I isthe adjective good, and underlying I' is bad.In their underlying base strings (shown inthe "Analysis" column), I and II' are alike,as are II and I', III and IV, and IV andIII'.

The three principles afford a number ofpredictions about the problems with homo-geneous propositions (Types I, II, I', andII'). The problems with good relationalterms (I and II') should, as in the two-term series problems, be easier than thosewith bad (II and I')- Also, a questionwhich is congruent with the information inthe propositions should be easier than anincongruent question: who is best? should

be the easier question for Types I and II',and who is worstf, for Types II and I'.

The predictions for Problem Types III,IV, III', and IV—those with heteroge-neous propositions—are slightly more in-volved. Consider Type III problems, whichcontain the underlying base strings A isgood, B is good, B is bad, and C is bad.The answer to who is best? is A, a termwhich belongs to a base string congruentwith that of the question (X is good+ + ).The answer to who is worst? is C, whichalso fulfills the congruence conditions. TypeIV problems, on the other hand, show com-plete incongruence of the propositions andquestions. A, the answer to who is best?,is part of the base string A is bad, and C,the answer to who is worst?, is part of C isgood. Because of this internal disagree-ment, Type IV problems should be harderthan Type III problems. In their deepstructure, III' is like IV, and IV is likeIII, so, for the same reasons, the internallyincongruent Type III' problems should beharder than the internally congruent TypeIV problems.

Method. Three problems were constructed foreach of the 32 problem types indicated in Table 3.Common four-letter English men's names wereused, such that no pair of them would occur to-gether in more than one problem. Each problem

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was typed on a blank IBM card in the followingform:

If John isn't as good as Pete,And John isn't as bad as Dick,Then who is best?Dick Pete John

In addition, there were eight practice problemseach containing one comparative and one negativeequative proposition. The problems were arrangedin four blocks: the practice problems and then threeblocks of 32, each latter block consisting of one ofeach problem type. Within blocks, the problemswere random and different for each 5". The orderof the names following the question was counter-balanced across the last three blocks and acrossproblem types.

On a signal, 61 turned a problem card face up,read the problem silently to himself, and producedan answer as quickly as he could without sacrificingaccuracy. He was timed from the initial signal tothe answer in hundredths of a second. He solvedthe 104 problems with short breaks between each.Unlike Experiment I, the solution time was takenas the time duration from the signal to the answer;>?s found that reading aloud was very disruptiveon this complex a problem. In the followingresults, then, reading time is confounded with solu-tion time. If anything, this would militate againstthe predicted results in one case, for better is onesyllable longer than worse. Again, the longestsolution time was discarded for each problem typefor each S, and so were the errors (7% of theanswers). The 5s were 13 students fulfilling acourse requirement for introductory psychology.

Results. The geometric mean solutiontimes in Table 3 confirm each of the pre-dictions of the present theory. The resultsthat follow, however, were further substan-tiated in a subsequent variation on thisexperiment (Clark, 1969b), in which 100-5*3 each attempted to solve the 32 problemsgiven here, along with 32 indeterminateproblems, in 10 seconds each. The num-ber of £s failing to solve each problemwithin 10 seconds closely parallels the solu-tion times in Table 3: more 5"s made errorson those problems which in the present ex-periment took more time to solve. Thesignificance level in Clark (1969b) willtherefore be given in brackets for eachdifference that follows.

The principles of the primacy of functionalrelations and of lexical marking predict thatProblem Types I and II' will be solved morequickly, overall, than II and I', respectively.The solution times in Table 3 confirm this

prediction, F = 5.38, df - 1/12, p < .05, [p< .001], with no significant interaction.(The analysis of variance was carried out onthe logarithms of the solution times.) Theprinciples of the primacy of functional rela-tions and of congruence predict that III andIV will be solved more quickly, overall, thanIV and III', respectively. The predictionwas confirmed here too, F = 4.92, df = 1/12,p < .05, [p < .001], with no significant in-teraction. These two principles also predictthat solutions will be faster for ProblemTypes I and II' when the question is who isbest? and for Problem Types II and I' whenthe question is who is worst? The resultssupport this prediction, F = 9.73, df = 1/52,p < .005, [p < .01], with no other significantinteractions. Comparative problems (Ithrough IV) had shorter solution times thannegative equative problems (I' through IV),F = 25.06, df = 1/12, p < .001, [p < .001].Again, all results show the relative import-ance of deep structure over the order ofterms in surface structure.

Order of the Two PropositionsAn additional phenomenon to be explained

is the fact that two homogeneous proposi-tions in one order are easier than the sametwo propositions in the opposite order. Con-sider Problem Types la and Ib in Table 3.In la the terms are arranged in a linearorder. Reading from left to right, one findsA, B, B, C. In Ib the arrangement is non-linear—S, C, A, B. In Types I and II,problems with comparative propositions, thenonlinear order was easier, F = 17.56, df —1/52, p < .001, [p < .001], but in the nega-tive equative Problems I' and II', it was thelinear order that was easier, F = 4.04, df —1/52, p < .05, [/><.01]. Although thisphenomenon remains unexplained by thethree proposed principles, it can be accountedfor by a generalization of some observationsDonaldson (1963) made of children solvingthree-term series problems containing com-parative constructions. Her suggestion forcertain difficulties that the children had hasmerely been generalized here, at the level ofdeep structure, to negative equative proposi-tions as well.

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Form of problem

(a) A better than B ; B better than CI

(b) B better than C; A better than B

(a) C worse than B ; B worse than AII

(b) B worse than A ; C worse than B

(a) A better than B ; C worse than BIII

(b) C worse than B ; A better than B

(a) B worse than A ; B better than CIV

(b) B better than C; B worse than A

(a) A not as bad as B ; B not as bad as Cp

(b) B not as bad as C', A not as bad as B

(a) C not as good as B ; B not as good as AIP

(b) B not as good as A ; C not as good as B

(a) A not as bad as B ; C not as good as BIIP

(b) C not as good as B ; A not as bad as B

(a) B not as good as A ; B not as bad as CIV

(b) B not as bad as C; B not as good as A

Form of question




















































Overall M









Note.—Mean times are in seconds.

It is assumed that 6"s try to compress theinformation of the propositions so that theinformation is easier to handle in memory.The proposition John is better than Billwould be stored, not as the full (John isgood+ ; Bill is good), but as the compressed(John is good+), meaning "John is thebetter one." So when the second propositionis Dick is better than John, the three-termseries is easily constructed: since Dick isbetter than John, who is already the betterone, then Dick is best, John next, and theother one least good. But when the secondproposition is Bill is better than Walt, thereis no obvious series, for the term carried

along—"John is the better one"—does noteven appear in the second proposition. Inthis case, 5" must try to recover the wholefirst proposition or back-track with the infor-mation that "Bill is the better one" to applyit to the first proposition or revert to someother time-consuming strategy. By thisanalysis, the nonlinear U and lib should beeasier, respectively, than the linear la andIla. The data bear out this expectation.In exactly the same way, Bill isn't as good asJohn should be compressed as (John isgood+), which has the meaning "John isthe better one." In such sentences, it is thesecond term, not the first, which is at the

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heart of the compressed version. So, incontrast with the comparative problems, thelinear I'o and Il'a should be easier, respec-tively, than the nonlinear I'b and II'b. Thedata bear out the expectation here also.

Comparatives Other than Better and Worse

Good and bad are only two of the manypossible adjectives available for three-termseries problems. Previous experiments onsuch problems have included better-worse,lighter-darker (DeSoto et al., 1965), more-less, faster-slower, farther-nearer, earlier-later (Handel et al., 1968), happier-sadder,warmer-colder (Hunter, 1957), taller-shorter (Hunter; Huttenlocher, 1968), anddeeper-shallower (see below). Almost allpairs showed asymmetries in difficulty whenused in homogeneous problems of Types Iand II; difficulty for Hunter and Hutten-locher was measured by solution time, andfor DeSoto et al. and Handel et al., by pro-portion of errors made in a fixed interval oftime. Also, in an unpublished pilot study,4

seven SB made 128 judgments each of thetruth or falsity of statements like 18 isn't asyoung an age as 23. These judgments weresignificantly faster for the relations olderthan and isn't as old as than for their oppo-sites (p < .025), and for higher than andisn't as high as than for their opposites (p <.025).

The asymmetries in these pairs of adjec-tives are accounted for by the principle oflexical marking. Problems with the com-paratives of good, much, fast, far, tall, happy,warm, deep, old, and high were solved moreeasily than those with their opposites. Eachof these adjectives is semantically unmarked,so their ease in comprehension is explainedby their simpler semantic code in memory.However, problems with earlier were easierthan those with later, a fact which remainsunexplained by this principle, since bothearly and late are marked by the criteria ofneutralization and nominalization used inthe present theory. In this particular case,there appears to be another type of marked-ness operating, but one which will be pur-

*H. H. Clark and S. H. Ellis. Unpublishedstudy, Carnegie-Mellon University, 1968.

sued no further here. On the other hand,there was one pair—lighter-darker—forwhich no asymmetry could be detected. Butsince neither light nor dark (when used forthe color of hair) neutralizes or doubles asthe scale name, they are both lexicallymarked. The principle of lexical marking iscorrect, therefore, in refusing to predict anasymmetry here.

By the analysis proposed previously, themarking of adjectives is irrelevant for thedifferences between Problem Types III andIV (Table 2 or 3). The other two princi-ples, however, predict III to be easier thanIV, regardless of the antonyms used. Thedata for all 10 previously studied pairs ofcomparatives conform to this prediction.

Solution of Three-Term Series Problemsby Children

Previous investigators interested in the de-velopment of reasoning have studied thesolution of three-term series problems bychildren. Their careful observations, thoughusually more informal in nature, lend con-siderable support to the present theory.

Burt (1919) originally, and later Piaget(1921, 1928), Hunter (1957), Donaldson(1963), and Luria (1966) have all noticedwhat Piaget (1921) called "judgment ofmembership" in the child's interpretation ofcomparative sentences. Piaget (1921), forexample, reports that 9- and 10-year-oldswere unsuccessful in solving the followingType IV problem (from Burt, 1919) :"Edith is fairer than Suzanne; Edith isdarker than Lili. Which of the three has thedarkest hair?" To quote Piaget (1928),

It is as though [the child] reasoned as follows:Edith is fairer than Suzanne so they are both fair,and Edith is darker than Lili so they are both dark.Therefore Lili is dark, Suzanne is fair, and Edithis between the two. In other words, owing to theinterplay of the relations included in the test, thechild, by substituting the judgment of membership(Edith and Suzanne are "fair," etc.) for thejudgment of relation (Edith is "fairer than"Suzanne), comes to a conclusion which is exactlyopposite of ours [p. 87].

This is to say, the children have understoodthe functional relations—the base strings—underlying the propositions, but have not

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grasped the comparative information. De-velopmentally, the ability to judge member-ship in comparative statements arrives earlierthan the ability to judge relations, and thisfact is closely akin to the principle of theprimacy of functional relations.

In solving problems out loud, many chil-dren verbalize the underlying base strings ofcomparative statements directly. For ex-ample, Donaldson (1963) quotes one child assaying, "It says that Dick is shorter thanTom, so Dick is short and Tom is short too."But in the next breath the child said, "AndDick is taller than John so Dick is tall andJohn is short [p. 131]." The child appearsto be vascillating between an interpretationof the base strings alone and an interpreta-tion of the comparative information. Thechild, in the second instance, is stating thecomparative relation in the only terms sheknows how—as the positive adjectives talland short.

The children in Donaldson's (1963)studies often made other errors as a result oftheir comprehension of propositions as basestrings. For example, children were giventhe following Type IV problem: "Dick isshorter than Tom. Dick is taller than John.Which of these three boys is tallest ?" Eventhough the problem explicitly states thatthere are three boys, many children assumedthere were four. They said there were twoDicks—a tall one and a short one—followingthe analysis of the base strings. One girl'ssolution to the above problem was, "ThisDick [second premise] is tallest, John is nexttallest, Tom is third and then it's Dick [firstpremise] [p. 131]." Although Donaldson'sSB made the two-Dick error on ProblemTypes I and II, they did so more often onTypes III and IV, problems which, becausethey describe Dick as both tall and short, en-courage this kind of error. In all, fully 70%of the errors Donaldson observed in childrenon Problem Types I through IV can betraced to the children's selective interpreta-tion of the base strings alone.

Although the principle of congruence isimplicit in some of the above examples ofchildren's reasoning, children often made itexplicit. Given the problem, "Tom is tallerthan Dick, Dick is taller than John. Which

of these three boys is shortest ?" one boy ex-plained, "This means Dick is shorter thanTom, John is shorter than Dick. So thatgives the answer—it's John [Donaldson,1963, p. 121]." When asked why hechanged the lines around, he said, "I thoughtit would help." He, as well as other childrenDonaldson reports, apparently changed thelines around to make them congruent withthe question. In the present study, it hasbeen assumed instead that it is the questionthat is reformulated and that it is done soimplicitly. This assumption was made be-cause the present 5"s seemed to process thequestion after the propositions had been com-prehended and stored. The assumptioncould be reversed, but evidence internal toExperiment II seemed to favor it as it stands.

Finally, there is evidence for the principleof lexical marking in Donaldson's and inDuthie's (1963) protocols. Both experi-menters found that children sometimes mis-interpreted a sentence like "Betty is olderthan May" to mean "May is older thanBetty." For adults this is a contradiction,but for these children, it is not. The firstsentence meant only that Betty is different inage from May and, as a symmetrical relation,it was synonymous with the second sentence.But "Betty is older than May" was alsotaken to mean "Betty is younger than May."Apparently, both young and old are inter-preted in a nominal sense, so that bothsentences can mean, "Betty is different inage from May." Duthie (1963) found chil-dren who made this quite explicit in quanti-fied comparative sentences. When one childwas asked in the middle of a problem how heknew that Tom was four, he replied, "Be-cause it says that Tom is four years youngerthan Dick [p. 237]." Children also madethis mistake in "five years older." BothDonaldson and Duthie argue convincinglythat these errors result, not from misread-ings, but from misinterpretations of the sen-tences in question. This evidence is relatedto some further observations on compara-tives by Donaldson and Wales (in press).They found that young Scottish childrencould use the comparatives of unmarked ad-jectives, like more, bigger, longer, thicker,higher, and taller, earlier and more correctly

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than their marked counterparts, less, wee-er,shorter, thinner, lower, and shorter. Onthis and other evidence, it has been argued(Clark, 1969a) that children develop thesemantically prior nominal sense of adjec-tives in comparisons before they do the con-trastive senses. Thus, children appear toacquire the more primitive underlying en-tities of a comparative before they do themore complex ones: just as they understandfunctional relations before they do compari-sons, they understand nominal senses beforethey do contrastive senses.


Theory of Spatial Paralogic

One theory developed to explain the diffi-culties of three-term series problems wasproposed by DeSoto et al. (1965) as thetheory of "spatial paralogic." This theorystates, simply, that in solving problems ofthis sort a person builds up in his mind aspatial representation of the terms involved.By a principle of directional preference,mental representations are easier to buildfrom top down than from the bottom up.And by a principle of end anchoring, theyare easier to build up from the extremesinward than from the middle outward.These two principles together are meant topredict the relative difficulty of the variousthree-term series problems. The presentdata on negative equative problems, however,appear to disconfirm both principles.

In problems containing good and bad, 5susually visualize the three compared objectswith the best on top and the worst on thebottom (DeSoto et al., 1965). Accordingto directional preference, then, problems likeA is better than B, and B is better than C(Type I problems) should be easier thanones like C is worse than B, and B is worsethan A (Type II problems), because theformer are top-down problems and the latterare bottom-up. This is exactly what wasfound by DeSoto et al. and was further con-firmed in the present Experiment II and inClark (1969b). The crucial comparison ofspatial paralogic and the present theory, how-ever, comes in top-down problems like A

isn't as bad as B, and B isn't as bad as C(Type I' problems) compared to bottom-upones like C isn't as good as B, and B isn'tas good as A (Type II' problems). By De-Soto et al.'s analysis, the former problemsshould be easier than the latter; the presenttheory predicts exactly the reverse. Thedata of Experiment II and of Clark (1969b)clearly support the present theory overspatial paralogic: overall, Type II' problemstook significantly less time to solve thanType I' problems. In more detail, each TypeII' problem can be compared to its respectiveType I' problem in which each adjective isreplaced by its opposite; all four comparisonssupport the present theory and disconfirmthe principle of directional preference.

According to the principle of end anchor-ing, extremes-inward problems should beeasier than middle-outward problems. InA is better than B, and C is worse than B,a Type III problem, the extremes are men-tioned first in both propositions, so it isan extremes-inward problem; similarly, B isworse than A, and B is better than C, a TypeIV problem, is a middle-outward problem.The data of DeSoto et al., as well as those inExperiment II and in Clark (1969b), bearout the prediction that III is easier than IV.But again, there is a crucial comparison ofspatial paralogic and the present theory, andit comes in Problem Types III' and IV.End anchoring predicts that Type III' prob-lems, which mention the extremes first,should be easier than Type IV problems,which mention the middle term first; thepresent theory predicts exactly the opposite.Indeed, Type IV problems were found tobe significantly easier, overall, than Type III'problems both in Experiment II and inClark (1969b); this confirms the presenttheory and disconfirms end anchoring. Thefailure of spatial paralogic comes, apparently,from its assumption that 5s work directlyfrom the linear encoding of terms in surfacestructure, disregarding deep structure perse completely.

A phenomenon that DeSoto et al. were ap-parently the first to notice was that 5s areable to assign nonspatial adjectives to anup-down orientation in a consistent way.Their 5s, for example, almost always placed

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the "better" of two objects on top and theother on bottom; more generally from thepresent point of view, they consistently as-signed the unmarked adjective to the upperposition.

The lexical marking of spatial adjectivessuggests an explanation for these consistentjudgments. It is perhaps not coincidentalthat almost all adjectives which refer to anupward direction are unmarked—high, tall,big, much, large, and so on. When askedto assign good and bad to a spatial represen-tation, 5"s could easily consult their knowl-edge of lexical marking to make a consistentassignment with the unmarked good on top.On the other hand, there is no linguistic basisfor a consistent left-right ordering of theseadjectives; in agreement with this, the left-right assignments in DeSoto et al.'s datawere rarely consistent across 5"s. DeSotoet al. also found one pair that was not con-sistently assigned for the vertical axis—lighter-darker. This is only to be expected,since light and dark are both marked andafford no linguistic basis for any reliableplacement.

One might argue, on the above evidence,that the principle of lexical marking shouldbe replaced by a "principle of spatial assign-ments" rather than the other way around:one adjective is easier than its opposite, notbecause it is unmarked, but because it im-plies the upper position in a spatial represen-tation. The critical test of this weakerproposition of spatial paralogic—one, how-ever, that DeSoto et al. did not make—comesin an examination of deep and shallow. Al-though deep is unmarked, it is assigned tothe lower position in spatial representations.This means that deeper problems (of TypeI) should be easier than shallower problemsby the principle of lexical marking, butharder by the principle of spatial assignment.This was tested on 21 more 5"s by repeatingExperiment II with two changes: (a) onlyProblem Types I, II, III, and IV were used;and (&) the propositions were changed toones like Jack has a deeper well than Dick,and the questions to ones like Whose wellis shallowest? The results clearly supportthe principle of lexical marking over its rival

principle of spatial assignment: overall, TypeI problems with deeper were solved .44 sec-onds faster, F = 11.08, df = 1/20, p < .005,than Type II problems with shallower. Ofthe 10 -9s who claimed they used spatialimagery, eight used a vertical representationand seven of these eight visualized the deep-est object on the bottom.

Theory of Constructing Spatial Images

A close relative of the theory of spatialparalogic is the theory of constructing spatialimages (Huttenlocher, 1968). Like thetheory of spatial paralogic, it posits that ^sarrange mental objects in imaginary spatialarrays to enable them to solve three-termseries problems. The main proposal is analternative explanation for end-anchoring.It rests on the presupposition that arrangingthings mentally should show the same diffi-culties as arranging things physically.

In physical situations, >S"s have difficultiesunder certain instructions in placing a mov-able object, like a block, in relation to afixed one (Huttenlocher, Eisenberg, &Strauss, 1968; Huttenlocher & Strauss,1968). Given the instruction, "Make it sothat the red block is under the blue block,"children find it easy if the red block is inhand and the blue block is fixed, but difficultif the blue block is in hand and the red blockis fixed. To summarize their results, ar-ranging objects from an instruction is easyonly when the movable object is the logicalsubject of a transitive verb or the gram-matical subject of a "relational" sentence.

The imagerial counterparts of these manip-ulations, the theory states, should show thesame difficulties. Consider a Type Ib prob-lem, B is better tlmn C, and A is better thanB. The first proposition fixes the terms Band C in mind, B above C. The third termof this array, A, is now the "movable" termto be placed in relation to B and C. Since Ais the subject of the second proposition, a"relational" sentence, the task is easy and Ibis quickly solved. It is not so easy to solve aType la problem, A is better than B, and Bis better than C. Here A and B are firstfixed in mind with A above B, then the thirdterm, C, is placed in relation to A and B. In

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this case, the "movable" term C is not thesubject of the second proposition, so it ishard to place C in order to solve the prob-lem. Just as Ib should be easier than la, libshould be easier than Ha, Ilia than IVb, andIII6 than IVo. The data in Huttenlocher(1968), the present Experiment II, andClark (1969b) all confirm these predictions.

The critical comparison of Huttenlocher'sspatial image theory and the present one,however, is found in the problems contain-ing isn't as good as and isn't as bad as. Bythe former theory, a Type I'b problem, Bisn't as bad as C, and A isn't as bad as B,like a Type Ib problem, should be easy. InI'b, the third term, A, to be placed relativeto the two fixed terms B and C, is the sub-ject of the second proposition, hence itsplacement is easy. But in I'a, A isn't as badas B, and B isn't as bad as C, as in la, thethird term C is difficult to place since it is thepredicate of the second proposition. By thesame analysis, II'b should be easier than Il'a,III1 a than IV'b, and Ill'b than IV'a. Thepresent theory and analysis predict exactlythe opposite. Compressing information fromthe first proposition for use in the second, asdiscussed above, should make I'a easier thanI'b, and Il'a easier than II'b. Also, by theprinciple of congruence, IV should be easierthan III', overall, rather than the reverse.Each of the four possible comparisons in theresults of Experiment II and Clark (1969b)support the present theory and run counterto the theory of constructing spatial images;the appropriate significance tests have beenpresented previously. Thus the latter theoryis disconfirmed as a general explanation ofreasoning in three-term series problems.

It does not follow from the disconfirmationof these two theories of spatial imagery, ofcourse, that imagery does not occur in solv-ing three-term series problems. It certainlydoes occur, although only 49% of the 5s inClark (1969b) claimed that they used spatialimagery. The only firm conclusion we candraw at this time is that it has not beendemonstrated that the use of spatial imagerydifferentially affects the solution of three-term series problems.


To be of use, the present explanation forcertain processes in deductive reasoning musthave generality. It should not be restrictedto three-term series problems alone or toproblems containing comparative proposi-tions. Several examples of another kind ofreasoning problem will serve to illustrate thewider applicability of the theory proposedhere.

The reasoning problem to be examined re-quires 5s to judge the truth or falsity ofpositive or negative statements. In Wasonand Jones (1963), 5s were presented sen-tences like 29 is not an odd number and wererequired to reply "true" or "false" while theywere timed. In Gough (1965, 1966), 5slistened to sentences like The boy didn't hitthe girl, examined a picture of either a boyhitting a girl or a girl hitting a boy, thenpressed a "true" or "false" button while theywere timed. The main result of interest isthe interaction between the truth and positiv-ity of the sentence: true positive and falsenegative sentences took less time, respec-tively, than false positive and true negativesentences.

When these tasks are viewed as reasoningproblems, the present theory provides at leasta partial explanation for the results. Wasonand Jones' task can be thought of as con-sisting of a proposition and a question. Theproposition is some previously known fact—for example, 29 is an odd number—and thequestion is implicit in the presented sentence,Is it true that 29 is not an odd number?The underlying structure of the propositionis simply (29 is odd), whereas that of thequestion is something like (is it true that (itis false that (29 is o d d ) ) ) . The four truthand positivity questions, then, can be repre-sented as: (a) true positive, (is it true that(29 is odd)) ; (b) false positive, (is it truethat (29 is even)); (c) true negative, (is ittrue that (it is false that (29 is even))); and(d) false negative (is it true that (it is falsethat (29 is odd))). By the principle of con-gruence, 5s will answer more quickly whenthe functional relations underlying these ques-tions are congruent with (29 is odd), thefunctional relations of the proposition. Con-

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gruence is found for a, but not b, so truepositives should take less time than falsepositives. This agrees with the results.Congruence is also found for d, but not c, sofalse negatives should take less time thantrue negatives. This is also supported by theresults. In Wason and Jones' study, 5~s alsomade more errors on true negatives (c) thanon anything else; they gave "false" sooften presumably because a preliminary com-parison showed that the functional relationsof the proposition and question were differ-ent. Cough's (1965, 1966) tasks, analyzedin a similar way, further confirm these pre-dictions; the present explanation, in fact, isessentially the same as one of the alternativeshe offered for his results.

The principle of lexical marking, however,accounts for yet another part of Wason andJones' (1963) and Cough's (1965, 1966)results. The question in the above analysiswas always formulated as (is it true that(such and such is so)). It contained true,not false. The reason, of course, is that trueis unmarked and false marked: is it true? im-plies no presuppositions about the answer—it could be either "true" or "false"—but isit jalse? implies that the answer is expectedto be "false" (cf. also Fillenbaum, 1968).Thus, to answer false questions, -S" must re-formulate his representation in memory toread (if is false that (such and such is so)),before he can give the answer, eliptically,as "false"; true questions are already in thecorrect form. This reformulation shouldtake time, causing false questions to takemore time overall than true questions. Thisprediction is confirmed in Wason (1961),Wason and Jones (1963), and Cough (1965,1966).


In the past, deductive reasoning has oftenbeen studied as if it were an isolated process—even as if it were specific to a certain kindof task, such as the solution of three-termseries problems. The processes described inthe present paper, on the other hand, arequite general. They are not meant to ex-plain the solution of two- and three-termseries problems alone, but to account for cer-

tain linguistic processes in understandingstatements and answering questions whereverthey occur. The most important demonstra-tion here has been that the principal difficul-ties inherent in many reasoning problems arenot due to cognitive processes specific tothese problems, but to the very language inwhich the problems are stated. Linguisticprocesses like these arise in every situation inwhich a problem is stated in linguistic terms.


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(Received August 5, 1968)