Re: what makes it true?


>>> Outside of *some* formal system, I don't know what 'and so on'
>>> means.

>> You don't? Then I don't see how you can understand anything in
>>mathematics. For example, how can you understand descriptions
>>of formal systems?

>Formal descriptions of formal systems? Via some set theory
>(so I can talk about the set of statements, etc). Informally?
>One step at a time.

> So you can understand formal systems one step at a time? What
>does this mean, specifically?

I can understand, given a formal system, whether I have a well formed
formula, a proof, etc because I can apply whatever rules are given
for forming formulae or for deriving new strings from the ones already
obtained. However, without a set theory, I can't talk about the set of
statements or prove anything about proofs. So my understanding of
formal systems would be purely local if not for some type of set theory.

--Dan Grubb


.

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