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Rational Decisions by Ken Binmore

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1

Revealed Preference

1.1 Rationality?

A rational number is the ratio of two whole numbers. The ancients thought that all numbers were rational, but Pythagoras’s theorem shows that the length of the diagonal of a square of unit area is irrational. Tradition holds that the genius who actually made this discovery was drowned, lest he shake the Pythagorean faith in the ineffable nature of number. But nowadays everybody knows that there is nothing irrational about the square root of two, even though we still call it an irrational number.

There is similarly nothing irrational about a philosopher who isn’t a rationalist. Rationalism in philosophy consists of arriving at substantive conclusions without appealing to any data. If you follow the scientific ...

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