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I'm new to the forum, I'm not a philosophy student, I'm an engineer of sorts. I was struck the other day by a thought after reading several unrelated posts here.

Given that :

1) Infinity exists for all countable items

2) Infinite time must exist

3) the universe is of a finite age

Then : Since our reality is not infinitely old, there must be something other than our reality.

What is wrong with this argument? All I can think of is, that it is also possible that infinite time, though possible, may not exist.

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    "Infinity exists" Why ? – Mauro ALLEGRANZA May 25 '17 at 13:24
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    "Infinite time must exist" On what ground we can assert this ? – Mauro ALLEGRANZA May 25 '17 at 13:24
  • Infinity must exist because otherwise some branches of mathematics wouldn't work, and they provably do. And since time is a countable number, it must therefore have an infinite value. – Richard May 25 '17 at 13:53
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    "time is a countable number" ? time is a physical magnitude (maybe) and countable in math does not mean that infinite. "it must therefore have an infinite value" ? The set of natural numbers is countable infinite but does not have an "infinite value". – Mauro ALLEGRANZA May 25 '17 at 14:32
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    "Infinity must exist because otherwise some branches of mathematics wouldn't work, and they provably do. " this assertion is an open question in the philosophy of mathematics. You can't really claim it definitively out of context because there are hundreds of professional philosophers and mathematicians that would disagree. Just because a branch of mathematics works does not necessarily mean that nature and reality reflect that branch. Think of all of the equations of motion you could make up on the spot, nature does not actually follow those even though they exist mathematically. – Not_Here May 25 '17 at 19:45
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I don't even see how the argument here is supposed to work logically. I wouldn't say that infinity "must exist" otherwise maths wouldn't work. I think this is a common idea to people who are mathematical Platonists, believing that all mathematical objects "exist" in some "other world." I don't think that's a necessarily bad way to talk about it, but it does lead to problems like this which don't even arise outside of that view of mathematics. The invention vs discovery debate in maths is also part of these questions.

I would go more towards the ideas of infinity and the way real and complex analysis deals with it is ingenious, but is an especially good creation. I don't think "infinity" refers to an object like "chair" does. So saying "infinity exists for all countables" is, to me, not really saying anything. What does it mean? If you mean it to say, e.g. that there is no biggest natural number, no biggest rational, etc, that's fine. That's different to imagining this object called infinity which exists in some metaphysical world.

Infinite time must exist - what does that mean? I don't know. Do you mean to say that there is something "out there" which corresponds to that label "infinite time"? Or more that time will keep going?

I don't think it's meaningful to talk about proving infinity exists any more than it is meaningful to be able to prove negative numbers, rationals, complex numbers, etc exist. Would you say that quaternions must exist? Or instead that they're just a useful way of looking at and doing mathematics?

Time being countable and therefore of infinite value? What does that mean? What does it mean to assign a value to time? Countable sets don't necessarily have an infinite number of elements. Also, what does it even mean to say time is a countable set? What are you taking as its elements? Like a set of values for t?

  • Time in our reality is finite, and nobody is to say whether the dimension of our reality we refer to as time will always exist. However since it is possible for the set of numbers 'seconds' to be infinitely large, then there exists in some way, infinite time. Since that doesn't exist in our reality, there must be some other reality. – Richard May 25 '17 at 14:39
  • Consider the way "exists" is used. "Our reality exists"," infinity exists" and "mount everest exists" are all completely different uses of "exist" and their similar form make it look like there is something in common to all three. I think you're going wrong in using the mathematical sense of "exist" to then make a claim about a completely different kind of existence. It's not that I think the answer to your question is yes or no, and I'm saying no, I think the question itself is not meaningful as I don't know what any of the statements is supposed to show or say (apart from point 3). – Franz May 25 '17 at 15:20
  • I accept your point. However I've just thought of another proof that makes them both 'exist' in the same sense. Infinity exists, and infinite time exists for the same reason. There is an uncountable infinity of time between T and T+1. So we know one form of infinity, and infinite time already exists. The question is, does the existence of uncountable infinite time, infer that countably infinite time exists? Is uncountable, and countable infinity the same infinity? – Richard May 25 '17 at 15:29
  • I don't understand what you mean by saying uncountable/countable time exists. What's the difference between countable time existing and countable time not existing? – Franz May 25 '17 at 16:55
  • I mean there are two forms of infinity. The infinity between the number 1 and 2 (so 1.1, 1.01,1.001...infinity) which is called 'uncountable infinity' and countable infinity which is 1,2, 3, 4....infinity. The first form clearly exists in reality. The question is, does that therefore prove that countably infinite time exists, because if it does, then there must be an 'elsewhere'. – Richard May 25 '17 at 16:57
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I don't understand what you mean by the first item, by which I mean that I do understand what 'countable' means but the way that you've used in this sentence suggests that perhaps you might not; try asking a few questions on Math.SE to clear up what conceptual confusions you have on this point.

As for your second item, time is generally understood to potentially infinite in the future and not actually infinite (what would this mean?).

The third item is obviously observationally justifiable given the currently accepted consensus on physical cosmology, but to my mind contra one of Kants antinomies, it is deducible from the second item.

The deduction doesn't follow, since to put it mildly the assumptions are a somewhat incoherent; since you're just making a seemingly logical, but in fact a fairly random list of assertions tied together by portentiously sounding trigger words: time, infinity and reality, why not just assume that there is another reality and be done with it? Its much easier, and saves thinking about it.

  • on reflection..i'm asking where the future is, because it exists but isn't here – Richard Jun 25 '17 at 1:43
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I'm just going to look at your second and third assumptions, because I don't actually understand what you mean by the first assumption.

Assumption 2 can be expressed as "Time has always existed", and the Assumption 3 can be expressed as "The universe has not always existed". From there, it seems to easily follow that the answer to "Are there things that exist outside of the universe?" is "Yes, because we know that time existed even when the universe did not."

Given these two assumptions, it is certain that time exists outside of the universe. I imagine that by making such a claim you are inheriting a lot of ontological baggage that would make you reconsider those assumptions.

  • Ahh.. well... Time as we know it in our universe did not exist before the universe, it was created along with space, about 15bn years ago. According to all current evidence. What I'm arguing is that if infinite time does exist, it doesn't exist in our universe (because our universe is only 15Bn years old), so it must exist elsewhere. – Richard May 25 '17 at 16:15
  • I added nothing to your assumptions. That's just the immediate consequence. If you think it is incorrect, then your assumptions are faulty. – Conner N. Howell May 25 '17 at 16:22
  • I'm not sure what you mean by 'I imagine that by making such a claim....'. What baggage are you referring to? – Richard May 25 '17 at 16:25
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    Asserting the existence of time outside of the universe is likely not falsifiable. – Conner N. Howell May 25 '17 at 16:28
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    The assumptions you made are substantial. A philosopher who wishes to argue for the truth value of any one of them could make a career writing tomes in defense of those assumptions. Your argument is basically "Things in class A exist. Everything we know is in class B. There are things in A that are not in B. Thus, there must be something more than we know." The logic is sound, but the assumptions are tough pills to swallow. – Cort Ammon May 25 '17 at 16:32
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Your argument could be worded a lot better/more carefully, but I don't think it's completely useless so I'll address it and try to make some assumptions about what you're trying to do along the way.

We can all agree that the universe has a finite age. A large portion of your proof then rests on the idea that time goes back infinitely from the present point. You're trying to claim that this must be so because time is countable, i.e. we can use a counter to increase it or decrease.

You're right that we can count time in either direction infinitely, and imagine times that are arbitrarily large or small. For example, the universe is known to be about 14 billion years old, so we can theoretically consider 15 billion years ago, and 16 billion, and so on... However, quite simply, this doesn't in any way prove or give evidence for the claim that these years actually existed. In fact, we can consider two possibilities where this wouldn't be the case

  1. Time is finite: Consider an NBA basketball game, which is is 48 minutes in length if it doesn't go to overtime. The minutes in this game are countable just as they are in reality. As such we can imagine a point in the game where the clock reads -1:00 minutes, -2:00, etc. but that simply doesn't mean that those are valid instances that occurred. Time in this instance is countable, but certainly finite.
  2. Time is infinite to positive infinity, but not negative infinity: What if time is similar to the concept of length? Length is clearly countable, as we can increment as we wish. However, it is only positively infinite. We can imagine (and even mathematically study) something of negative length but it is simply not in line with reality.

So your proof fails at your attempt to claim that time has existed for infinity. In fact, if you study Einstein, Dawkins, etc. you'll find that the opposite is likely true.

However, even if we look past this and allow you to assume that there is no beginning of time, there are further still problems with your argument. I won't disagree that if this is the case that some other reality outside of our current universe must have existed, but this certainly doesn't equate to "other dimensions" currently existing as your title seems to suggest. What if in the past some other universe existed, then with the big bang that universe was destroyed and ours created?

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