(January 4, 2014 at 5:03 pm)rasetsu Wrote: 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.
