The collapse illusion effect: A semantic-pragmatic illusion of truth and paradox

Abstract

Two Experiments demonstrate the existence of a “collapse illusion”, in which reasoners evaluate Truthteller-type propositions (“I am telling the truth”) as if they were simply true, whereas Liar-type propositions (“I am lying”) tend to be evaluated as neither true nor false. The second Experiment also demonstrates an individual differences pattern, in which shallow reasoners are more susceptible to the illusion. The collapse illusion is congruent with philosophical semantic truth theories such as Kripke's (1975), and with hypothetical thinking theory's principle of satisficing, but can only be partially accounted for by the model theory principle of truth. Pragmatic effects related to sentence cohesion further reinforce hypothetical thinking theory interpretation of the data, although the illusion and cohesion data could also be accounted for within a modified mental model theory.

Notes

¹It is not merely the inclusion of paradoxical components; had Ben's assertion been “I am a knight” the puzzle would have been soluble. Adam's assertion is a disjunction, and disjunctions are true if one of their constituent propositions is true. This means that if we make the assumption that the second disjunct (Ben is a knight) is true, this makes the whole proposition true, and therefore Adam is a knight. But this only holds when Ben asserts he is a knight.

²By “indeterminate” I refer to any non-classical truth-value. Hence, “True” and “False” are determinate truth-values; “Neither” and “Both” are indeterminate truth-values.

³“Collapse” is a term borrowed from philosophical logic (Rescher, 1969) denoting the conversion of a truth-table with n truth-values to a truth-table with n − 1 truth-values; e.g., a four-valued truth-table to a three-valued truth-table.

⁴Whether extensional or intensional may be moot; see Evans & Over, 2004; Evans, Over, & Handley, in press; but compare Boden, 1988; and Elqayam, in press.

⁵Strictly speaking, in this paradigm “neither” is equivalent to Belnap's B (which means that you know both p and ¬p to be the case), and “both” is equivalent to Belnap's ø or N (which means that you have no definite data on either p or ¬p).