Abstract
Psychological research on people's understanding of natural language connectives has traditionally used truth table tasks, in which participants evaluate the truth or falsity of a compound sentence given the truth or falsity of its components in the framework of propositional logic. One perplexing result concerned the indicative conditional if A then C which was often evaluated as true when A and C are true, false when A is true and C is false but irrelevant“ (devoid of value) when A is false (whatever the value of C). This was called the “psychological defective table of the conditional.” Here we show that far from being anomalous the “defective” table pattern reveals a coherent semantics for the basic connectives of natural language in a trivalent framework. This was done by establishing participants' truth tables for negation, conjunction, disjunction, conditional, and biconditional, when they were presented with statements that could be certainly true, certainly false, or neither. We review systems of three-valued tables from logic, linguistics, foundations of quantum mechanics, philosophical logic, and artificial intelligence, to see whether one of these systems adequately describes people's interpretations of natural language connectives. We find that de Finetti's (1936/1995) three-valued system is the best approximation to participants' truth tables.
Highlights
THE BAYESIAN APPROACH TO THE PSYCHOLOGY OF REASONINGFrom the beginning of their investigations, and for nearly a century, psychologists studying human deductive reasoning considered bi-valued logic as the sole frame of reference
We review systems of three-valued tables from logic, linguistics, foundations of quantum mechanics, philosophical logic, and artificial intelligence, to see whether one of these systems adequately describes people’s interpretations of natural language connectives
We describe below the three-valued truth tables that define this system, specifying how these values are propagated for the usual connectives
Summary
From the beginning of their investigations, and for nearly a century, psychologists studying human deductive reasoning considered bi-valued logic as the sole frame of reference. Their early inspiration was limited to Aristotelian syllogistic (Binet, 1902; James, 1908) but in the 1950s Piaget adopted propositional logic which he assumed to be the basis of adults’ cognitive functioning (Inhelder and Piaget, 1958). In 1966, Wason observed that when people are required to make judgments about conditionals in terms of true and false, they often produce a table that differs from the material conditional. Psychologists came to call this truth table “defective” to underscore participants’ apparent
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