Saturday, January 9, 2010

Frege and Obviousness vs. Self-Evidence

In a recent article Shapiro writes"There are obvious propositions, such as 2 + 3 = 5, that are not self-evident. Frege emphasized that to know sums like those, one need not invoke any intuition, Kantian or otherwise, but he insisted that one must reason one’s way to this knowledge."

But in what sense did anyone before Frege "reason their way" to the claim that 2+3=5? From what? The quoted claim seems to have the consequence that either:
a) no one knew any arithmetic before Frege's derivation of arithmetic from logic
b) people before Frege could count as knowing arithmetic because they were unconsciously going through Frege's derivation

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