Language and the ability to evaluate contradictions and tautologies

Children were found to experience difficulty evaluating contradictions of the form p 6 -p, and tautologies of the form p v -p. It was hypothesized that (a) the difficulty of these statements was not due solely to the logical words occurring in them, (6) part of the difficulty is due to the fhct that their truth value derives from their linguistic f&-m rather than from empirical considerations, and (c) the ability to examine language in an objective manner, apart from events and objects to which it refers, is necessary but not sufficient for correct evaluation of contradictions and tautologies. The results of two experiments support the hypotheses. During our informal conversations with elementary school children, we found that they had difficulty judging the truth-value of sentences corresponding to simple contradictions and tautologies. Roughly speaking, a tautological sentence is true by virtue of its logical form. A contradictory sentence is false by virtue of its logical form. Children were asked *The authors thank Joanne Duncan of the Llanerch Elementary School, and Mary Ostrum of the Portola Valley Elementary School for their cooperation during this study. We also express our appreciation to Rachel Gelman and Burton Rosner for their careful reading of earlier versions of this manuscript. We thank Barbara Abrahams for administering Experiment 1. The first author was supported by an NSF predoctoral traineeship. The second author was supported by PHS Training Grant No. HD 00337-03 from NICHHD. The research was partially supported by Grant No. NIHHD-MH 04598 to Rachel Gelman. The study was conducted while both authors were at the University of Pennsylvania. Co@tion S(3), pp. 2I3 226 2 14 Daniel N. Osherson and Ellen Markman to say “True”, “False”, or “Can’t tell” in response to statements exemplifying such formulas as p & -p, and p v-p.* To use the tautology p v -p as an example, the children failed to recognize the truth of the statement “Either this chip is red or it is not red” (when the chip in question is entirely of one color). For the most part, the children’s poor performance on tasks such as these did not seem attributable to a misunderstanding of the logical words occurring in them (‘or’, ‘and’, ‘not’). Thus, nontautologous and noncontradictory statements such as “Either this chip is green or it is blue” and “This chip is yellow and it is not red” were readily understood. In addition to the presence of logical words, then, an important variable in these simple problems seemed to be whether the task demanded evaluating a contradiction or a tautology. As a first step towards explaining this phenomenon, notice that no empirical evidence is required to falsify or verify contradictions and tautologies. Instead, sentences corresponding to these kinds of formulas are true or false by virtue of their linguistic form, rather than deriving their truth-value from any extra-linguistic states of affairs. For the remainder of this paper, contradictory and tautological sentences will be called nonempirical, in that their truth value does not depend upon states of the world.** To illustrate the difference between empirical and nonempirical statements, compare the sentence “This chip is green and it is not green” with the sentence “This chip is green and it is not red”. Determining the truth of the latter requires examining the chip in question; determining the truth of the former requires no such examination. This distinction has been the focus of philosophical controversy (Hahn, 1959 ; Quine, 1953), but our interest in it is mainly psychological. In particular, it appeared to us that the children’s difficulty with nonempirical statements stemmed from their failure to appreciate just this distinction. The children indiscriminately sought empirical evidence for both types of sentences. Resisting the tendency to seek empirical support for nonempirical sentences requires an ability to examine the form of the statement itself. This ability in turn presupposes that the child can use language not only as a code for reality but also as an object of thought in its own right. The child must be able to reflect upon his language much as he reflects upon more tangible events; he must be able to regard language independently of the reality it refers to. This amounts to the ability to lookat language rather than through it. That children do have trouble considering language in this objective manner has been documented by Piaget (1929). Although the nature of the child’s trouble is not clear, two findings bear comment. First, it has been shown that young *Throughout this paper, we shall follow standard conventions concerning the interpretation of ‘p’, ‘SC’, ‘v’ and ‘-I. Thus, p and q stand for propositions; & stands for logical conjunction (‘and’); v stands for logical disjunction (‘or’) ; and stands for negation (‘not’). **We have coined the term ‘nonempirical’ rather than relying on the terms ‘analytic’ or ‘logical for three reasons. First, given our theoretical position, stated below, the term ‘nonempirical’ has mnemonic value. Second, we wish to avoid questions concerning the relationship between analytic and logical sentences. Third, psychologists commonly characterize contingent statements that include logical connectives as ‘logical’. Language and the ability to evaluate contradictions and tautologies 21.5 children do not appreciate the arbitrariness of the relation between words and their referents (Piaget, 1929; Vygotsky, 1962). Second, it is well known that children find perceptually immediate events quite compelling (Piaget & Szeminska, 1965; Bruner et al., 1966). It is plausible that they find aspects of linguistic structure less salient. We summarize the above discussion by stating two hypotheses. Hypothesis la: Children tend to treat contradictions and tautologies as empirical statements. Hypothesis lb: Much of the difficulty children experience evaluating nonempirical sentences is due to their nonempirical character, and not merely to the logical words occurring in them. Hypothesis 1 will be called the nonempiricality hypothesis. Hypothesis 2: The ability to examine language objectively is necessary for the ability to correctly evaluate nonempirical statements. Hypothesis 2 will be called the objectivity hypothesis. The converse of Hypothesis 2 that language objectivity is sufficient for evaluating nonempirical statements is not implied in our discussion. Among other requirements, it is obvious that encoding the logical structure of the statement is also necessary for distinguishing nonempirical from empirical statements. For complex contradictions and tautologies the encoding requirement might be formidable. Experiment 1 : The nonempiricality hypothesis Experiment 1 was designed to test the nonempiricality hypotheses la and lb. In order to test Hypothesis la, it is necessary to distinguish subjects who correctly evaluate nonempirical sentences on the basis of linguistic form from subjects who correctly evaluate these sentences by relying on empirical considerations. The latter subjects, right for the wrong reason, do not genuinely comprehend tautologies and contradictions. If a subject recognizes the nonempirical nature of sentences of the form p & -p and p v -p, then withholding the empirical means to judge the truth of p should not interfere with this judgment. Conversely, if we are correct in believing that children tend to treat contradictions and tautologies empirically, then the children should be reluctant to respond either ‘True’ or ‘False’ to statements for which the truth of p cannot be determined (responding ‘Can’t tell’ instead). Accordingly, items based on the forms p v -p and p & -p were constructed so that objects referred to in the proposition p were hidden. Questions in which objects referred to are hidden will be called, barbarously, nonvisible items. Hypothesis 1 b states that much of the difficulty children experience evaluating simple nonempirical sentences is due to the nonempirical character of these sentences, and not simply to the logical words occurring in them. To test this hypothesis we asked children 2 16 Daniel N. Osherson and Ellen Markman to evaluate sentences containing various combinations of the same logical words (i.e., ‘and’, ‘or’, and ‘not’) included in the nonempirical sentences. These control sentences, however, were empirical. If Hypothesis 1 b is true then correct eva!uation of the control sentences should not guarantee success with the nonempirical sentences. Method Subjects: Two classes of second graders, N = 26 (13 males, 13 females) and N = 25 (10 males, 15 females), from a middle class suburban school served as subjects. The mean age for the classes was 7 years, 10 months, and 7 years, 8 months, respectively. No subjects were dropped. Materials: The materials were small plastic poker chips in assorted colors (each chip exemplified only one color). Procedure: Each subject was seen individually for one twenty minute session. The chips were placed between the experimenter and the subject on a table. It was explained that the experimenter would say some things about the chips, and that in each case the subject should indicate whether the experimenter’s statement was true or false. The subject was also given the explicit option of responding ‘Can’t tell’. Every item consisted of a statement about a chip held in the experimenter’s hand. In each case the question pertained to the chip’s color, and was preceded by the interrogative “True, false, or can’t you tell?” For the nonvisible items, the subject was asked to close his eyes while the experimenter selected a chip. This chip was then concealed in the experimenter’s closed hand until after the subject responded. For the remaining items, the chip was continuously in view. In order to minimize the time required for each subject, two distinct but overlapping sets of items were administered, one to each class. Order of presentation of the items was randomized for each subject. Questions were repeated if the subject hesitated or appeared puzzled. Items: The left hand columns of Table 1 provide a description of the items. The description includes (a) the question posed by the experimenter, (b) the color of the chip, if visible, and (c) the correct answer. Items 1 4 are nonempirical; all other items are empirical. These remaining items were designed to assess subjects’ ability to evaluate questions sharing properties of the nonempirical items. These properties include negation, conjunction, disjunction, nonvisibility (items 7, 10, 14, 26) and repetition of a constituent proposition (items 21, 22,33,34). Columns 5 and 6 of Table 1 show which of the two groups of subjects (or both) received a given item. Language and the ability to evaluate contradictions and tautologies 217 Results Hypothesis la: The righthand columns of Table 1 give the percentage of subjects in each group passing the items. Few subjects answered the nonempirical items (1 4) correctly. More importantly, 73% of the mistaken answers to these questions were responses of ‘Can’t tell’. This supports Hypothesis la that children tend to treat contradictions and tautologies as empirical statements; without empirical evidence, the children refused to evaluate them.* The percentage of ‘Can’t tell’ responses to the nonempirical items may even be spuriously low. Items 7 and 10, the simplest, nonvisible, empirical questions, show that the children are in general reluctant to respond ‘Can’t tell’. Only 63% of the subjects did so, even though the ‘Can’t tell’ response seems plainly appropriate in these cases. Moreover, the percent of correct responses (i.e., ‘Can’t tell’) for the more complex nonvisible, empirical items 14 and 26 was slightly lower. ‘Can’t tell’ was almost never given to the visible empirical items. Hypothesis Zb: In general, the nonempirical items were substantially more difficult than their empirical counterparts. This supports Hypothesis 1 b: The children had more difficulty with the nonempirical questions than with empirical questions of comparable logical structure. Items 28 and 30, involving disjunction, are exceptions to this pattern, being at least as difficult as the tautologous items 3 and 4. However, these items have a property not found in the nonempirical items. In each case, a response of ‘True’ was required despite the visibility of a chip whose color matched neither of those mentioned in the question. In marked contrast, items of identical logical structure, but not possessing this feature (items 26, 27, 29, 31, and 32) posed little difficulty. Therefore, we do not consider these exceptional items to infirm Hypothesis lb. Consistent with this interpretation is the fact that there were no such exceptions with respect to contradictions. That is, all of the empirical items involving conjunction were substantially easier than the contradictions.** Experiment 2: The objectivity hypothesis*** Experiment 1 provided evidence supporting the nonempiricality hypothesis. Experiment 2 was designed to test Hypothesis 2 that the ability to examine language objectively is necessary for the ability to correctly evaluate nonempirical statements. *On the other hand, in other experiments we included nonempirical items in which the chip was clearly visible, and thus provided such ‘evidence’. In this situation, children are still unable to appreciate the nonempirical character of these items, and revert to a simple ‘matching’ strategy. Both kinds of nonempirical statements (p v -p and p & -p) were judged as true only when p was true, and judged as false when p was false. **We have conducted three additional studies to test Hypothesis 1. The subjects in these additional experiments ranged in age from 6 years to adulthood. The results are fully comparable to those reported for Experiment 1. **+This experiment is part of a larger study in which the same subjects participated. The data from the larger study are fully consistent with the results reported below. 2 18 Daniel N. Osherson and Ellen Markman Table 1. Items for Experiment I Item Number Question _