Re: WHAT IS THE AIM OF THE PHILOSOPHY ??

I believe the intense effort Russel put in to Prncipia rather killed
his desire to any more serious maths.
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I think that that is rather unkind! The Principia did indeed fail in
its objective, but it opened the way to a much more fundamental
understanding of the nature of mathematics. It was a serious and, at
the time, quite clearly important project. Actually, its failure showed
how important it was, probably more than its success possibly could
have.

It's nice, really, that Russell's paradox turns out not to be
paradoxical at all, as with most paradoxes, it is simply the result of
looking at things the wrong way. This was also an important lesson -
until then, people, Russell in particular, were very gung-ho about
deciding how to characterise sets.

It also has some interesting bearing on platonism. If Russell had
succeeded, it would have been a nicely constructed basis for showing
how arithmetic worked - just what you'd expect if you thought platonism
to be nonsense. As it was, real facts about how mathematics really is
were discovered by Russell - not something he'd have expected, but
something that a plationist certainly would have.

.

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