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Is it possible to deny the existence of infinities in the real world, by philosophical means only?

If it makes it easier, I'm mainly interested to deny that we can know an infinite amount of things (even if we would live forever), since (and that's what I assume) there are only finitely many?

I don't want to make use of the physical finiteness of the universe. Is it then still possible?

closed as too broad by Hunan Rostomyan, iphigenie, user2953, Lucas, Joseph Weissman Apr 29 '14 at 23:58

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • Whether the universe is infinite or not, the human brain certainly is. We can only have finitely many thoughts in a finite lifetime. Is that the kind of thing you're asking about? If we could live forever then we certainly could know infinitely many things ... 1, 2, 3, 4, 5, ... one each second forever. If I have infinite time I can definitely know infinitely many things. – user4894 Mar 24 '14 at 22:02
  • @user4894 yes that kind. How would you convince yourself about the finiteness of things you could know, when you don't know that your brain is finite. Assume you were born without any senses, but smart enough to come up with something like "I think therefore I am"... – draks ... Mar 24 '14 at 22:07
  • If it takes you a millisecond to have a thought then you can only have 1000 thoughts per second, and you live only a finite number of seconds. If it takes any positive nonzero amount of time to have a thought, the same analysis applies. I'm not sure why this is not obvious. – user4894 Mar 24 '14 at 22:26
  • Just a little note: some philosphers hold that one can conceive that there are infinite numbers, that matter is infinitely divisible, that we actually have infinite chains of justfication in our mind, in some sense. I agree with user4894, but there are those other philosophers. Check out Siders 'Van Inwagen and the possibility of gunk', for example. – Lukas Mar 24 '14 at 22:29
  • @user4894 how do you measure time without senses? – draks ... Mar 24 '14 at 22:29
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Of course, it's legitimate to be philosophically uncommitted about the reality of an infinity of material objects, until a proof is given one way or another. And given that all ontological arguments are suspect, I strongly doubt the possibility of a pure philosophical argument for an infinity of things. There may be scientific arguments for this, which can be believed with more or less degree of certainty. And one might even be able to provide an argument that the concept of an infinity of material objects is inherently inconsistent. That wouldn't need to be an ontological argument, so I suppose such an argument could be attempted, but I doubt there are any good arguments like that.

So from a purely philosophical perspective, I don't think you can make a decision about the real world. From a scientific perspective I think both possibilities are viable.

Now you mention being particularly interested in there being no infinity because we cannot know an infinity of things--but you seem to base this on the assumption that there is no material, or physical, or ontological infinity. But as I've described above, I don't think that's a philosophically proven thesis, so the foundation of that argument may not be sound. But perhaps I misunderstand you when you say "deny that we can know an infinite amount of things ... since ... there are only finitely many".

  • +1 thanks, if you ever find a way to show that the concept of an infinity of material objects is inherently inconsistent, please let me know... – draks ... Mar 27 '14 at 10:46

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