Seduction 101 for Logicians and Economists

Seduction, whether with an amorous or an acquisitive intent, often follows the same interactive pattern, the hook sometimes being logical, sometimes psychological.

Propositional Logic

One might think this example absurdly unrealistic, but consider the opaqueness of derivatives and other complicated financial instruments. There too, the commitments one unknowingly takes on are invisible and substantial. The seduction scam is child's play compared to securitized mortgages.

Nevertheless, perhaps more typical than the seduction question is the following, which is still a matter of elementary propositional logic. The question: For the following set of premises, determine whether the conclusion below (the part after "Hence") follows from them. (Don't worry about whether the premises are true or false.)

If private sector investment stays the same, then government spending will increase or more unemployment will result. If government spending will not increase, taxes can be cut. If taxes can be cut and private sector investment stays the same, then more unemployment will not result. Hence government spending will increase.

There are, of course, simple techniques for deciding if the conclusion follows from the premises in propositional logic or whether a set of such statements is consistent, but from sad experience and casual observation, I suspect that only a sprinkling of policy-makers know them.

In any case, the real economy is complex, interactive, convoluted and impossible to describe with elementary propositional logic. The logic required is more extensive, involving quantifiers -- words like "all," and "some" and "none."

An adequate description also calls on arithmetic, probability, and statistics, calculus, and differential equations, non-linear dynamics, etc. It's not too surprising that few if any people can assert with much confidence that we should take this economic course rather than that and come to this conclusion rather than another.

There are, however, some conclusions using propositional logic that can be made with the utmost confidence.

Recall the logician/economist riding an elevator who, when the doors open, is asked whether the elevator is going up or down.

He replies, "Yes."

John Allen Paulos, a professor of mathematics at Temple University, is the author of the best-sellers "Innumeracy" and "A Mathematician Reads the Newspaper," as well as "Irreligion: A Mathematician Explains Why The Arguments for God Just Don't Add Up." His "Who's Counting?" column on ABCNews.com appears the first weekend of every month.

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