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Psychological Review1969, Vol. 76, No. 4, 387-404
LINGUISTIC PROCESSES INDEDUCTIVE REASONING1
HERBERT H. CLARK *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 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 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
387
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388 HERBERT H. CLARK
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.
THE THREE PRINCIPLESPrinciple 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 sentencewhat 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
stringslinguists differ as tothe actual numberbut 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 informationbase 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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LINGUISTIC PROCESSES IN REASONING 38Qformations 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 highother unmarkedadjectives-and
not with its opposite short:the sentence *The board is six feet
shortsis unacceptable to English speakers.
In sum, the unmarked adjective has twosenses, 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 lengthboth
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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390 HERBERT H. CLARK
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} CongruenceAnswering a question requires more of
a
listener 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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LINGUISTIC PROCESSES IN REASONING 391
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 goodthe sense found in noncommittal how
good?questionsis 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 fis
the counterpart of Sentence 3,
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392 HERBERT H. CLARK
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.
Two- AND THREE-TERM SERIES PROBLEMSImplicit in the previous
three principles
is 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 stagescomprehending theproposition and
questionentail 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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LINGUISTIC PROCESSES IN REASONING 393
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'sandthe question'sdeep 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
TABLE 1MEAN TIME TO SOLVE TWO-TERM SERIES PROBLEMS
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
Analysis
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
Best?
.61
1.00
1.73
1.17
Worst?
.68
.62
1.58
1.47
M
.64
.81
1.66
1.32
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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394 HERBERT H. CLARK
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 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
-
402 HERBERT H. CLARK
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.
OTHER KINDS OF REASONINGTo be of use, the present explanation
for
certain 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
factfor example, 29 is an odd numberand 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-
-
LINGUISTIC PROCESSES IN REASONING 403
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
answerit 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).
CONCLUSION
In the past, deductive reasoning has oftenbeen studied as if it
were an isolated processeven 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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