Re: limitation to induction on finite bounds
From: Aatu Koskensilta (aatu.koskensilta_at_xortec.fi)
Date: 06/15/04
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Date: Tue, 15 Jun 2004 20:34:15 +0300
Saverio Trioni wrote:
>
> Induction is not universal. There are some properties on which you can
> do induction (for instance, x=0, x=x, x is finite, (x+1)+1=x+2 ), other
> on which it does not make a sense to use induction. Logicists call them
> "second order formulas", meaning that they are properties that depend on
> some relation between the *sets* of elements, not only the elements
> themselves.
Induction does hold for second order formulas as they are usually
understood. I don't see what makes you think otherwise.
-- Aatu Koskensilta (aatu.koskensilta@xortec.fi) "Wovon man nicht sprechen kann, daruber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
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