Is finitude possible?

Is finitude possible?
haydar
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Posted Mar 6, 2013 - 11:25 AM:
Subject: Is finitude possible?
Some philosophers and mathematicians believe that an actual infinite is impossible and they have given reasons for this (e.g. Hilbert's hotel & similar paradoxes). Do we have any philosophical proofs that finitude in anyway is impossible? I.e. that there must be an infinite of things that exist?
haydar
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Posted Mar 6, 2013 - 11:41 AM:

I must clarify that I am not talking about the finitude of any one thing but that of reality.
Mystermenace
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Posted Mar 6, 2013 - 1:30 PM:

The universe is composed of things.

A person can think of things.

If a person can think of a thing then a person can think of half of a thing.

A thought is a thing.

If half of a thing is still a thing then a finitude of thoughts is a not a possible limitation.

An infinte number of things can exist.

Occam's Chainsaw
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Posted Mar 6, 2013 - 2:20 PM:

Things like Zeno's paradoxes come to mind. Infinite divisibility of empty space implies at least theoretical infinite divisibility of filled space. By this I mean that if you can divide the distance of space between me and my wall infinitely (which leads Zeno to say that I could never get there), I could just as well divide the space infinitely if my room were full of water. Therefore the water between my wall and I is infinitely divisible. Therefore there is an infinite ammount of parts of this block of water between me and my wall.

To be clear, I am not saying this is necessarily a good proof, just a proof.
jedaisoul
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Posted Mar 6, 2013 - 4:21 PM:

haydar wrote:

Some philosophers and mathematicians believe that an actual infinite is impossible and they have given reasons for this (e.g. Hilbert's hotel & similar paradoxes). Do we have any philosophical proofs that finitude in anyway is impossible? I.e. that there must be an infinite of things that exist?

This is not a philosophic question. Whether the universe is finite or infinite cannot be deduced by philosophic means. The universe came into existence around 14.7 billion years ago, and has been expanding at a finite rate since then. So unless the universe was already infinite, it is and has always been finite. Now measurements of the universe suggest that the universe may indeed be infinite, but it is not conclusively proven to be the case.

Oh, and infinite divisibility is a different issue. Infinite divisibility does not equate to infinite. Finite distances can, in theory, be infinitely divisible, but they are still finite.

Edited by jedaisoul on Mar 6, 2013 - 4:26 PM
andrewk
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Posted Mar 6, 2013 - 4:22 PM:

I like your question. I have often pondered this issue recently.

Like most philosophical things, I very much doubt any proof one way or the other is possible, although there will be proofs about what finitude or infinitude of the universe(s) would entail.

Although I cannot prove anything, it seems to me just totally implausible that there is only a finite set of events, objects or whatever we want to call it. It's like 'if there can be one set of twenty, then why can't there be another set of twenty, the same or perhaps a little different?'

Looking at jedaisoul's post above, I should clarify that I am not talking about the finitude of our own spacetime, which is a question that may one day be answered by scientific means. I am talking about whether there could be an infinite number of spacetimes, or even of other things that are nothing like spacetimes (as in Tegmark's mathematical universe).
Occam's Chainsaw
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Posted Mar 6, 2013 - 5:34 PM:

After a bit of thought, surely there finite must be possible. There are 4 cups in my room. That is a finite set. There may be an infinite number of cups in an infininte nuber of spacetimes, but when I define the set myself as simply the contents of my room, I'm not sure how this specific set cound not be finite.

I guess the idea I would like to present is that infinitude must entail finitudes because anything infinitly big must have parts (although not a finite number of parts) or else it would simple be 1 (which isn't infinite). These infinite number of parts (or subsets) of infinitude necessarily must contain finite parts or sets.

Thought? If this is not clear, I can give a better answer in a couple hours. A bit busy right now.
On Mar 6, 2013 - 5:44 PM, andrewk responded: You lazy sausage. You should take those cups to the kitchen and wash them up.
MIRasskazov
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Posted Mar 6, 2013 - 6:07 PM:

Mystermenace wrote:
The universe is composed of things.

A person can think of things.

If a person can think of a thing then a person can think of half of a thing.

A thought is a thing.

If half of a thing is still a thing then a finitude of thoughts is a not a possible limitation.

An infinte number of things can exist.


If there is a fundamental, indivisible particle (a light photon, e.g.), then wouldn't this refute your point?

Then again, if it takes an infinite amount of energy to accelerate to the speed of light, yet light exists, doesn't that mean infinity exists?

I really don't know where I stand on this.
On Mar 6, 2013 - 7:24 PM, andrewk responded: Photons have no mass, so infinite energy is not reqd. For a particle with mass, inf energy wd be reqd
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Posted Mar 6, 2013 - 8:24 PM:

The concept of infinities is a result of mathematical constructs which ultimately are fine for analyzing aspects of nature but having nothing to do with the actual nature of Nature other than being part of it.

Is there an infinity. No. Time is not divisible nor is space. We only apply these ideas for practical sharing of information. Is there a limit to the Universe. Yes. It is simply all that there is. Can we apply a mathematical number to this concept? No, which is why we use infinity as a place holder.

All one has to do is understand the nature of mathematics the the conceptual problems that mathematics creates go away.
On Mar 6, 2013 - 10:11 PM, jorndoe responded: You haven't supplied any arguments (i.e. only assertions).
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Posted Mar 6, 2013 - 8:31 PM:

Seems to me that in thought, and let's include computation of the electromechanical kind, there is only the finite. Thus irrational numbers such as pi can be conceived, but only some finite approximation can be known or used.

But it is not clear that the world is thus limited, unless physics has gone somewhere without telling me.
On Mar 6, 2013 - 8:34 PM, Csalisbury responded: Set theory makes use of various infinities, no?
On Mar 6, 2013 - 9:42 PM, unenlightened responded: No, concepts of infinity but not actual ones, unless brains are much bigger on the inside...
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