Re: Gödel's system P, Principia Mathematica,

On 2008-01-29, in sci.logic, Rupert wrote:
I think he's just saying, Russell conceded that the logicist project
failed, but you don't need to vindicate logicism to justify
mathematics.

Quite so.

Aatu certainly expressed no view himself about whether the axiom of
reducibility is justified. For all I know he may not think this
question is meaningful, he may be a mathematical antirealist.

Regardless of what stance one takes on mathematical realism, it is
certainly a meaningful question whether the axiom of reducibility is
justified on Russell's conception of propositional functions. As it
happens I think it's not only unjustified but patently false, on most
reasonable reconstructions of that conceptions.

--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.

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