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cryptically, how is everyday narrative logic different from extensional
In everyday "story logic," how "we," the story-tellers, characterize an event or person is crucial. If a man touches his hand to his eyebrow, for example, we may see this as an indication he has a headache. We may also see the gesture as a signal from a baseball coach to the batter. Then again, we may infer that the man is trying to hide his anxiety by appearing nonchalant, that it is simply a habit of his, that he is worried about getting dust in his eye, or indefinitely many other things depending on indefinitely many perspectives we might have and on the indefinitely many human contexts in which we might find ourselves. A similar open-endedness characterizes the use of probability and statistics in surveys and studies.
Furthermore, unlike mathematical logic, story logic does not allow for substitutions. In mathematical contexts, for example, the number 3 can always be substituted for the square root of 9 or the largest whole number smaller than the constant without affecting the truth of the statement in which it appears. By contrast, although Lois Lane knows that Superman can fly, and even though Superman equals Clark Kent, the substitution of one for the other can't be made. Oedipus is attracted to the woman Jocasta, not to the extensionally equivalent person who is his mother. In the impersonal realm of mathematics, one's ignorance or one's attitude toward some entity does not affect the validity of a proof involving it or the allowability of substituting equals for equals.
John Allen Paulos is Professor of mathematics at Temple University adjunct professor of journalism at Columbia University, and author Once Upon a Number.