Hopefully my last post on infinite regress.

[jumbojak]

I have been doing a lot of research lately into the idea of an infinite temporal
regress and I have reached the conclusion that such a state of affairs is
impossible. Let me be clear that this does not mean I have concluded that a
transcendent being is required to explain the existence of the universe. ( The
fact that time cannot go back forever does not inform us of its origin. )

We should start by first defining what we mean by temporal regress. When
I say that there is a temporal regress, which will henceforth be referred to
simply as regress, I mean to say that any event is preceeded by some sort
of cause in time. A stack of dominoes for example, can be arranged to cascade
one after the other when either end of the stack is disturbed.

In this example the first domino, nudged away from its center of gravity, knocks
down the second domino and starts a chain reaction that ends when no dominoes
are left standing. What we are interested in is whether a first dominoe is
required. To support the conclusion that any regress ( whether it is represented
by dominoes or the events that led to the evolution of our universe ) must
consist of a finite number of steps I will propose the following argument:

  1) It is impossible to create an actual infinite collection by adding items to
     the collection one after the other;

  2) The chain of causal events in our universe happen one after the other;

  3) Therefore the chain of causal events must be finite;

Defense of the first premise rests upon the notion that so long as a collection
can accept another element the collection cannot be said to be infinite. The
function y=x does indeed approach infinity, however whatever value of x we choose
will still result in a finite value for y.

It makes no difference how many times the process is repeated because the very
fact that the process is repeatable means the collection does not contain a
truly infinite number of elements. I suspect that this premise will draw the
most critisism. 

The second premise is, I believe, self evident. We all experience events
happening one after the other every day of our lives. This post was caused by my
curiosity regarding the possiblity of an infinite regress which was caused by
internet debates etc. Perhaps I am mistaken but this certainly seems to be the
case and I think this is the strongest premise of the argument.

Given these two premises, namely that it is impossible to create an actual
infinite and that events happen one after the other, I believe it follows that
the actual number of events must be finite. Such a philosophical conclusion
seems to fit with at least some of the models physicists are using to explain
our existence.

Any thoughts? I would love some feedback, as I have been working this out over
the last few weeks. The ideas may not be rock solid but this does give me strong
reason to think an infinite regress is impossible.

[Genericguy]

Defense of the first premise rests upon the notion that so long as a collection
can accept another element the collection cannot be said to be infinite.

I'm no expert here, but this doesn't make sense to me. Moving forward in time, from the present, or adding "another element to the collection" would lead us to only one "end" of the collection. This, by itself, does not mean another end must exist. Also, if we go forward 2 million years, today would not have been the end, but just a moment within infinity.

[Recusant]

For now, a couple of points regarding what appear to be assumptions that you've made:

What of events which may lie outside of any "chain of causal events." Are you convinced that no such events exist? If so, what reason(s) can you give for positing that no un-caused events exist? If un-caused events do exist, what prevents the existence of an actual infinity of un-caused events? It's true that if such an infinity exists, it isn't really an infinite regress in the classical sense, but that classical sense may be the result of our limited perspective and perception, which has possibly led us to create inaccurate model of the universe. This ties into the next point:

How can you be certain that the human perception of the arrow of time is definitive? Perhaps time as such doesn't even exist. If that's the case, then the question of infinite regress simply becomes irrelevant.

A side question: Do you consider that an infinite future is also impossible?

[xSilverPhinx]

How can you be certain that the human perception of the arrow of time is definitive? Perhaps time as such doesn't even exist. If that's the case, then the question of infinite regress simply becomes irrelevant.

Mind boggling. I wish I knew more physics to better understand these things (or at least live under the illusion that I do). Exciting time for the science now.

[Stevil]

How can you be certain that the human perception of the arrow of time is definitive? Perhaps time as such doesn't even exist. If that's the case, then the question of infinite regress simply becomes irrelevant.

Mind boggling. I wish I knew more physics to better understand these things (or at least live under the illusion that I do). Exciting time for the science now.

Didn't Einstein prove that time is relative? That moving objects perceive time differently to each other. Which is why we all see photons of light as moving at the speed of light.
e.g. if we ourselves are moving at 99.999% of the speed of light in the same direction as a beam of light, we will still see that the light is traveling away from us at the speed of light.

[jumbojak]

Defense of the first premise rests upon the notion that so long as a collection
can accept another element the collection cannot be said to be infinite.

I'm no expert here, but this doesn't make sense to me. Moving forward in time, from the present, or adding "another element to the collection" would lead us to only one "end" of the collection. This, by itself, does not mean another end must exist. Also, if we go forward 2 million years, today would not have been the end, but just a moment within infinity.

I knew this was going to cause the most problems, and I'm not sure how to explain it better than I allready did. Hmm, imagine you were trying to count to infinity. It would seem to me that the only way you could know that you had finished was when you couldn't count any higher, and until that point you would be bound to acknowledge that you had not counted all the way to infinity. Does this explain it any better?

[jumbojak]

For now, a couple of points regarding what appear to be assumptions that you've made:

What of events which may lie outside of any "chain of causal events." Are you convinced that no such events exist? If so, what reason(s) can you give for positing that no un-caused events exist? If un-caused events do exist, what prevents the existence of an actual infinity of un-caused events? It's true that if such an infinity exists, it isn't really an infinite regress in the classical sense, but that classical sense may be the result of our limited perspective and perception, which has possibly led us to create inaccurate model of the universe. This ties into the next point:

How can you be certain that the human perception of the arrow of time is definitive? Perhaps time as such doesn't even exist. If that's the case, then the question of infinite regress simply becomes irrelevant.

A side question: Do you consider that an infinite future is also impossible?

I'm not quite sure what you mean by outside of any chain of events. If you mean an event outside of time, which is what I think you mean by un-caused, I certainly think that events can occour outside of time, however I do not believe that our common sense view of how things happen in time will be of much use to us in that situation. It seems that an event would merely happen, and that perhaps only very simple events could occour.

The idea that a raging tiger could pop into existence at a singularity ( if a singularity is the best explanation for the origin of our universe ) seems quite absurd. The idea that something very simple, like fundamental particles and our four-force laws, seems much more reasonable given the very primitive machinery that would be availible in such a state.

And I don't think that our understanding of the concept of infinity is hindering us in this endeavor.  It is precicely because I realise that we cannot really count to infinity, that I conclude the idea of an actually infinite series of events in time is impossible. You could redefine infinite in some different way I suppose, but that wouldnt be infinity in the sense that I am using the word.

As for the arrow of time, I think that thermodynamics indicates that events happen in a certain direction. We could certainly imagine that a glass of water spontaneously boils when it is put in the freezer, but that isn't what normally happens. Thermofynamics has in intrinsically irreversible nature.
That article could be a little misleading if the last few weeks are any indication. Many scientists and philosophers have adopted the B-Theory of time which treats time as a "static" quantity, with events described in terms of relationships with other events. It's the result of an effort to describe events without making use of tensed verbs, and I have seen a few places where its implications were confused to mean no time. I will try to contact the scientists and inquire more on their specific views.

For the side question, I do think that our future could never actually be considered infinite, even if the universe goes on expanding forever. It would still just be one event happening after another and thus could not actually be infinite.

[jumbojak]

How can you be certain that the human perception of the arrow of time is definitive? Perhaps time as such doesn't even exist. If that's the case, then the question of infinite regress simply becomes irrelevant.

Mind boggling. I wish I knew more physics to better understand these things (or at least live under the illusion that I do). Exciting time for the science now.

Didn't Einstein prove that time is relative? That moving objects perceive time differently to each other. Which is why we all see photons of light as moving at the speed of light.
e.g. if we ourselves are moving at 99.999% of the speed of light in the same direction as a beam of light, we will still see that the light is traveling away from us at the speed of light.

Einstein showed that the laws of physics are the same in all inertial reference frames, but to my understanding this does not mean that time itself is relative. We may experience time differently when we are moving at different velocities relative to on another but this doesn't change the chain of events that led to us moving at that speed. I could be wrong here and admit that I only have a basic understanding of the special theory of relativity.

[Genericguy]

Defense of the first premise rests upon the notion that so long as a collection
can accept another element the collection cannot be said to be infinite.

I'm no expert here, but this doesn't make sense to me. Moving forward in time, from the present, or adding "another element to the collection" would lead us to only one "end" of the collection. This, by itself, does not mean another end must exist. Also, if we go forward 2 million years, today would not have been the end, but just a moment within infinity.

I knew this was going to cause the most problems, and I'm not sure how to explain it better than I allready did. Hmm, imagine you were trying to count to infinity. It would seem to me that the only way you could know that you had finished was when you couldn't count any higher, and until that point you would be bound to acknowledge that you had not counted all the way to infinity. Does this explain it any better?

Infinity doesn't finish. You can't count to infinity, but, for the sake of your counting example, you can count infinitely. I think the concept of the present is throwing you off. In your counting example you have a beginning; when you start counting, and you have an end; the current number you are on. Infinity, in regards to counting, is not a reachable number. It is the never ending process, itself, that gives infinity it's value. Because of this, the actual number we are currently on is irrelevant. The bold statement needs to be changed to something more like the following: It would seem to me that the only way you could know that you are counting, infinitely, is if you are still counting.

[jumbojak]

Defense of the first premise rests upon the notion that so long as a collection
can accept another element the collection cannot be said to be infinite.

I'm no expert here, but this doesn't make sense to me. Moving forward in time, from the present, or adding "another element to the collection" would lead us to only one "end" of the collection. This, by itself, does not mean another end must exist. Also, if we go forward 2 million years, today would not have been the end, but just a moment within infinity.

I knew this was going to cause the most problems, and I'm not sure how to explain it better than I allready did. Hmm, imagine you were trying to count to infinity. It would seem to me that the only way you could know that you had finished was when you couldn't count any higher, and until that point you would be bound to acknowledge that you had not counted all the way to infinity. Does this explain it any better?

Infinity doesn't finish. You can't count to infinity, but, for the sake of your counting example, you can count infinitely. I think the concept of the present is throwing you off. In your counting example you have a beginning; when you start counting, and you have an end; the current number you are on. Infinity, in regards to counting, is not a reachable number. It is the never ending process, itself, that gives infinity it's value. Because of this, the actual number we are currently on is irrelevant. The bold statement needs to be changed to something more like the following: It would seem to me that the only way you could know that you are counting, infinitely, is if you are still counting.

If it's not finished then it's not infinity. You could count towards infinity for as long as you like but the fact remains that you will never actually reach infinity. By counting forever you are creating an indefinite collection that grows each time a new number is counted and tends towards infinity. It is a potentially infinite collection, not an actually infinite collection. If we suppose that an infinite regress has occoured, we must suppose that the number of events is actually infinite , which is impossible because the number of events in time is constantly increasing

Your change in bold could read: It would seem to me that the only way that you could know that you are counting indefinately, is if you are still counting. This is true, but it doesn't change the fact that if you are still counting you have not reached infinity.

[xSilverPhinx]

But infinity isn't even a number, so is counting the right way to even think about trying to reach it? Counting just seems rather misplaced.

[jumbojak]

But infinity isn't even a number, so is counting the right way to even think about trying to reach it? Counting just seems rather misplaced.

I think you are correct in saying that infinity isn't a number. An infinite collection has infinity as one of its properties. For a collection to be actually infinite it would have to be created all at once, and the counting example is designed to demonstrate this, in a round about way. So long as there is room to grow, the collection is not infinite, and so because the chain of temporal events continues to grow that chain cannot be infinite.

[Genericguy]

So long as there is room to grow, the collection is not infinite

You're using it as a number, though. The process of never ending growth is the defining quality of infinite.

[xSilverPhinx]

I'm really not good at maths, so I might be making a total mess here, but what about the common example used to describe infinity, where in a hotel with an infinite amount of rooms will always be able to cram in one more room, thus making infinity equal to infinity plus 1?

Also, there are different types of infinities, and even contained within a finite set. Decimals, for instance, between finite and well defined numbers.

[jumbojak]

So long as there is room to grow, the collection is not infinite

You're using it as a number, though. The process of never ending growth is the defining quality of infinite.

Mabye I wasn't completely clear. Actual infinity is a property of the collection, not a member of the collection itself. The set of natural numbers is most certainly infinite, but the set itself is not growing. Thats the difference between a collection that is actually infinite ( commonly denoted by the Hebrew charachter aleph, which I don't know how to post ) and an indefinite collection that is growing towards infinity. ( commonly denoted by the lemniscate an eight turned on its side ) We could imagine a collection that has nothing to do with numbers:

   x = (a), (aa), (aaa), (aaaa) ..

All we are doing here is adding 'a' to the previous element, and I think it can clearly be seen that such a collection could contain every possible string of the letter 'a'. This actually infinite set could exist if it were created all at once ( and you could say that the thought experiment did create them all at once, at least conceptually ) however you cannot say that by adding new elements to the set we have written down, the firtst three elements of the set, that you have written down every possible string of the letter 'a'.