Linguistics or psychology: An essay in honour of Ruth Berman Pitt

PSYF 8-547


COGNITIVE PROCESSES OF THE ADOLESCENT:
EDUCATIONAL IMPLICATIONS



TERM PAPER



IF NOT, THEN WHAT?
PROBLEMS IN IDENTIFYING FACTORS IN
PROPOSITIONAL REASONING





Robert K. Philips
29 May 1979


Attempts to describe and explain adolescent reasoning, and to account for age-related changes, presuppose an understanding of the nature of reasoning itself. For verbal propositional reasoning in particular, such attempts presuppose an understanding of the relationships between logic and language, meaning and the structure of language, task comprehension and task execution. It is contended here that these binary relationships are conveniences of linguistic description; their manifold interactions render the characterization of adolescent reasoning an exceedingly difficult task.

Although the type of reasoning utilized in Piagetian tasks may be classified as scientific, (Falmagne, 1975) and therefore different from verbal propositional reasoning, it also suffers from the problems of determining what language indicates. Inhelder and Praget express skepticism over the use of linguistic data as criteria for the evaluation of the nature of' the thinking and reasoning of the adolescent. Yet as Ennis (1975) points out, there is some ambivalence their position. They do give some credence to the hypothetico-deductive nature of "if . . . then" constructions. It is clear then that isolating the influence of language on reasoning, as one aspect of the connection between language and thinking in general, is not merely a "psycholinguistic interprise," it is of importance to all who seek to comprehend adolescent cognitive functioning. The alternative is to be satisfied with the uninstructive statement.


All in all, the subjects' language expresses their
thoughts only in a rough way.

Inhelder and Piaget (1958, p. 279)

Intuitively, one would expect a 'natural logic' (Lakoff, 1972) to make a useful connection between language and reasoning, but it was just one aspect of an esoteric controversy among theoretical linguists. Essentially, this controversy was over the place of "meaning" in the grammar of a language. Maclay notes that successive revisions of the generative transformational grammar have given increasingly greater primacy to semantics. The transformational grammar had accounted for ambiguity in meaning (eating apples . . ., flying planes . . ., etc.) but this was not its primary aim. However, meaning was central for the generative semanticists.

[ T]he main reason for the development of interest in transformational grammar was not that it led to discovery of previously unformulated and unformidable distributional regularities, but primarily that, through the study of distributional regularities, the transformational grammar provided insights into the semantic organization of language and into the relationship between surface forms and their meanings

Lakoff, 1971 (p. 269)

It was demonstrated that the ungrammaticality of certain readings of potentially ambiguous class logical statements precludes the corresponding inferences from being made, enabling Lakoff to conclude that the "rules of grammar, . . . are not distinct from the rules relating the surface forms of English sentences to their corresponding logical forms" (Lakoff, 1972, p. 553). It has been noted that much of the 'empirical' support for generative semantics are isolated instantiations, rather than examples of general linguistic principles (Ortony, 1975). Although Lakoff contends that "generative semantics provides an empirical check on various proposals concerning logical form, and can thus be said to define a branch of logic which be called natural logic" (Lakoff, 1971), it might be just as well be called something else, because the "empirical checks" are not sought in any demonstrable performance. The point is that generative semantics is a theory of linguistic competence, and its psychological validity is not subject to disconfirmation (Ortony, 1975).

One derivative of the transformational grammar, the case grammar (Fillmore, 1971), might not be subject to the criticism of being irrelevant. It has been argued to be structurally similar to early linguistic performance (Edmonds, 1975), and to the acquisition of verb meanings in children from age five (Norman, Gentner and Stevens, 1976). The verb is central in the case grammar, and the sentence is characterized as an event. The other parts of the sentence have a semantic relation to the verb; these are the cases, namely agent, counter-agent, object, result, instrument, source, goal, experiences (Fillmore, 1971). Cases "are of more obvious semantic Land psychological] relevance than are the grammatical relations associated with the distinction between subject and predicate and subject and object" (Lyons, 1977).
Another contribution of influence has been the notion of "invited inference" (Geis and Zwicky, 1971). There are certain conditions under which the meanings of particular connectives
are altered. One such, is the perfect conditional. The "if" connective is transformed from a conditional to a biconditional when the statement is a promise, prediction, threat, law-like statement, conditional command or an counterfactual conditional. [This information should be of interest to those involved in moral judgment research.] An example of a statement inviting an inference is the law-like statement "if iron is heated, it turns red."
There are two extreme views in relation to logical competence (Henle, 1962). The first is that there is an underlying logical competence, but lack of correspondence of performance to the ideal is due largely to misinterpretation prior to logical processing. The second view is that processing is inherently defective. Adherents of the first view will attempt to match performance on a propositional reasoning task to the corresponding truth table. A common task involves inplication. The linguistic form "if . . . then," has usually been taken to correspond to implication:

If p then q (pq, -pq, -p-q)

q / q Modus Ponens
p / pv-p
-p / qv-q
-q / -p Modus Tollens

For the remainder of the discourse, we will rely heavily on the implication table, and on the biconditional:

If and only if p then q (pq,-p-q)

p / q
q/ p
-p/-q
-q/ -p

It has also been claimed that 1defective' truth tables can be computed. In these cases there is the category irrelevant, in addition to true and false. (See Evans and Newstead, 1977.)
The proposal that "if – then" corresponds to varying logical interpretations has been challenged by Braine (1978). The first objection is that a counterfactual conditional, like "if Hitler had had the atomic bomb in 1940, he would have won the war" is claimed to be true under a conditional interpretation. The reason for this is that the antecedent is false. Another objection is that "if p then q," "p only if q," "if not q then not p," are logically equivalent yet when the same content is applied to these forms, different meanings are derived. According to Braine, the differences are due to the element of "directionality" in "if-then," which is not reflected in an implicative interpretation. A third claim is that on syllogistic reasoning problems, a biconditional reading of "if" should not produce any difference in difficulty between Modus Ponens and Modus Tollens, however Modus Tollens is invariably more difficult in practice. Fourthly, the biconditional, conditional and defective truth table interpretations are apparently task-specific.
Braine proceeds to demonstrate how his simplified interpretation of "if" accounts for the four problems. One example is "if p then q, p only if q, if not q then not p," the differences between which he claims "fall out quite naturally." Evidently, he means that q is contingent on p, p contingent on q, and the absence of p is contingent on the absence of q, respectively.
In general he claims that:

[A]lthough a speaker who coins an "if-then" sentence is effectively giving the audience a warranty for concluding q given p, the sentence itself provides no information whatever about the justification for that warranty, for example, the speaker may think that p is a cause of q, that p entails q, that q follows from p with shared assumptions or that there is some correlation of unknown basis between the events. In short, if p then q is inherently non-committal about the basis for the rule it states.

Braine reports supporting data for his claims. In the same context, "only-if" should have the opposite reading from "if-then," so there should be a reversal in difficulty of Modus Tollens in relation to Modus Ponens. This was confirmed.

These are strong claims against an underlying propositional-logical competence. However, one test of the validity of the natural reasoning model would be its accounting for attenuation of differences between child and adult performance, with increasing age. Taplin, Staudenmayer and Taddonio (1974), using abstract content, established a developmental sequence from a conjunctive, through a biconditional to a conditional interpretation for "if . . . then" statements. They attribute the transition to changes in meaning of the connective, because
correspondence is obtained between the performances and possible logical interpretations
Evans and Newstead (1977) using adult subjects, did not detect the total conversion of "p only if q" to "if q then p," contrary to Braine's analysis of these two forms.

Cope (1979), manipulated the size of the set from which Modus Tollens could be computed and demonstrated that when there is a binary restriction on the possible inferences from a 11not q" premise, Modus Tollens was significantly easier than when there was no such restriction. For example, in the binary case consider that there is a universe p1,p2, q1, q2. "If p1 then q1; q2" yields p2 but when the universe is p1,p2,p3, q1, q2, q3, a non-binary case "If p1 then q1, q2" yields p2 or p3. Cope argues that in the non-binary case there was "cognitive overload" since the conclusion was less precise. So logical competence may be masked by task-specific processing load. According to Braine's model, Modus Tollens is always more difficult, requiring more computations than Modus Ponens, irrespective of the context and the strategy of the subject.

In another task with adult subjects Staudenmayer (1975) compared the interpretation of "if . . . then" with "cause" to show "that pragmatic, contextual presuppositions are primary and necessary considerations for understanding how people interpret the complete meaning of a semantic, causal relation and make inferences from implicative statements." It was the intention to give a biconditional or conditional classification. Among the findings was that "cause was interpreted more often as a biconditional than '1if . . then." In addition, a conditional interpretation was given more frequency for "not necessary" pragmatic relations than for "necessary." Staudenmayer claims to have shown that "presupposition about alternative agents can be induced by manipulating the case structure in the sentence." What he means is that if an agent is introduced in an implicative statement a conditional interpretation is more plausible than when there is no agent, in which case a biconditional interpretation is appropriate.
It is recognized that the treatment thus far has been descriptive rather than evaluative. Moreover, most of the research has not been developmental. However, it is evident that applications from linguistic theory can impinge on, if not illuminate the analysis of human reasoning.
Although the "roughness" of the indication that language gives, has not been removed, Moshman (1979) has attempted to make a more explicit link between propositional reasoning performance and scientific reasoning. He contends that there are at least three components of formal-operational thought. Implication, a falsification strategy--the attempt to falsify a hypothesis rather than prove it--and a non-verification insight--recognition that cumulative positive information is insufficient for proof.
Subjects were required to determine which empirical statements proved a hypothesis true, false or were indeterminate. Further, they had to decide whether positive or negative
information would allow falsification, and give an explanation for the decision. For a hypothesis "If a person uses fluoridated toothpaste he will have healthy teeth," an empirical statement would be "Bertie uses fluoridated toothpaste and does not have healthy teeth." For the three measures there was a linear trend in performance from seventh graders to tenth graders to college students. The most corrimon alternative to implication was the biconditional interpretation. Moshman argues that what apparently develops is an asymmetry in thinking, evident in the transition to implication and a change from "a symmetrical conception of truth and falsity to non-verification insight."

Unfortunately there is no visible synthesis in this treatment of language and reasoning: the potential for fusion seems to lie in paradigms manipulating case structures. An assessment of the other'1inference rules," (Braine, 1978) would have to be made, before the suitability of the entire model can be determined. At present however, the proposed rule for "if . . then" probably explains away rather than explains a reasonably consistent trend (Taplin, Standenmayer and Taddonio, 1974).





REFERENCES



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