Do Numbers Exist?

[bennyboy]

Numbers do not exist. They are an invention of man so we could understand and adapt to the world around us.

If they didn't exist, they couldn't be an invention. Inventions exist.

[Angrboda]

I think you need to unpack the predicate "to exist" if you intend to meaningfully answer the question. To my mind, attempting to use a "bog standard" definition of the predicate will only lead to difficulty and error. The more time I spend with philosophical questions, the more inclined I am to agree with Wittgenstein that what many presume are philosophical problems are actually language problems, caused by careless and unthinking use of language. I keep coming to the same conclusion that, in philosophy, you can't truly resolve a question without a comprehensive theory of meaning, or what it means to mean. If you don't have a clear view toward what "to exist" means, how can you hope to fruitfully approach the question?

[LostLocke]

^
While I agree with what you're saying, the biggest problem I have in philosophical discussions is that this is usually the point where it goes off on a 5000 page tangent just to try and define a word or phrase, and never really gets back to the original topic that was brought up in the first place.

[Angrboda]

While I agree with what you're saying, the biggest problem I have in philosophical discussions is that this is usually the point where it goes off on a 5000 page tangent just to try and define a word or phrase, and never really gets back to the original topic that was brought up in the first place.

You didn't notice me volunteering, did you? That tangent is usually as fruitless as the first because people have little idea how to solve that larger problem. Either way, it's a bunch of piss.

[LostLocke]

Lol, amen to that brother.

Oh wait, am I allowed to say "Amen"?

[MindForgedManacle]

I think you need to unpack the predicate "to exist" if you intend to meaningfully answer the question. To my mind, attempting to use a "bog standard" definition of the predicate will only lead to difficulty and error. The more time I spend with philosophical questions, the more inclined I am to agree with Wittgenstein that what many presume are philosophical problems are actually language problems, caused by careless and unthinking use of language. I keep coming to the same conclusion that, in philosophy, you can't truly resolve a question without a comprehensive theory of meaning, or what it means to mean. If you don't have a clear view toward what "to exist" means, how can you hope to fruitfully approach the question?

I too would say I'm quite convinced that Wittgenstein was on to something with his thought that metaphysical problems were only apparent, and brought on by the misapplication of language. Or at least some of them.

So, with regards to the ontology of mathematical 'objects', I don't think that Wittgensteinian path will work unless you assume a phenomenological position that when we say something 'is', we mean it appears to us. By that, I don't merely mean we see it, but rather that we are cognizant of it. I suppose if you take that view, then you could potentially show that this question can be dissolved... maybe.

[Angrboda]

* Angrboda exits, stage left.

[MindForgedManacle]

Darn.

[houseofcantor]

Darn.

Lolz. If there's anything more boring than philosophy, it's mathematical philosophy.

My original confusion with the OP is that when last approached with such a consideration, I was somewhere between Conceptualism and Platonic Realism; and neither Conceptualism nor Intuitionism is mentioned.

(And I hadda go back and look those up. )