Re: help with Godel's

On 2007-03-27, Herman Jurjus wrote:
Aatu Koskensilta wrote:
There are two distinct issues: whether our conception of naturals is clear,
coherent, sensible and so forth - a philosophical or conceptual question -

Nice trick: call every question you can't answer a 'philosophical
question' (i.e. not mathematics). But aren't the naturals so fundamental
to mathematics that it's very -mathematically- relevant what answer one
gives to this question?

It is relevant to mathematics whether our conception of the naturals is
clear, coherent, sensible and so forth, but that does not make the question
mathematical. In the same vein, whether a proof, in a journal, say, is
elegant, readable, complicated, is not a mathematical question.

Setting aside the silly notion that I call "every question" I can't answer
a 'philosophical question', you might notice that I did answer the question,
stating that there is nothing unclear or muddled in our understanding of the
naturals.

and whether there is a sequence of formulas in the language of arithmetic
satisfying certain syntactic criteria - a mathematical question.

Hmm; i would rather call it a question about Scrabble.

Why?

You draw the distinction line at a remarkable point. Is it entirely
unfair to call it neo-logicistic?

I haven't said anything specific about where I draw the line. It's patently
obvious that the question of the existence of a sequence of certain kind is
a mathematical question just like other questions about existence of finite
graphs having certain properties, questions about twin primes and so on.
There is nothing profound in this observation, and any relation it might
have to logicism espaces me.

--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

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

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