Proofs... So what?

[Nirvana-Eld]

After some thinking I am willing to accept that there must have been a first cause that initiated the series of events we call existence. I think that this is the underlying substratum of causuality. Here the problem. So what? I do not see the connection from "there must have been a first cause" to "this is a being which we all call God" (quod omnes dicunt Deum). I see the point of the First Cause Idea more as pointing to a natural process, not a Christian God and or the classic "Omnipotent, Omniscient, Omnibenevolent God". There seems to be no connection.

I would like the proponents of the First Cause Argument who believe in the God of the three "O's" to logically make the connection between a process and a God. Civility is a must! I just glanced through a thread by a "killingevolution" ( ) and I would like this thread to be cleaner. 8)

[HughDP]

So if an infinite number of sequential, temporal events need to happen before 'now', we would never have made it to 'now'.

The concept of infinity is always a diffeicult one to deal with.

It certainly is. Our language sometimes seems ill-constructed to deal with it.

My main point is that in a steady state Universe, an infinite amount of time has already happened. This, by definition, means that an infinite amount of temporal events have occurred.

If that is the case, we cannot add any further events. How do we add another event to an infinite number of temporally sequenced events? What does infinity + 1 mean?

The issue here is if the infinite series of prior temporal events is possible (based on your logic that we could never get to 'now'). If not then a steady state Universe is also impossible meaning that there must be a first cause. This is where we argue Kant's First Antimony.

Yes and no. There would have to be a first cause for temporally sequenced events that must be traversed.

Also an additive series of temporal events does not necessarily need to traverse an infinite period of time (as QED points out in his reference to 'Supertasks') as per Xeno's paradoxes.

Yes.

We're now getting into the realms of Kalam Cosmology and the contributions of Kant, Xeno, Craig et al.

There are a number of propositions that eliminate the necessity for First Cause.

(1) What appears to be an inifinite temporally sequenced set could have been 'created in one go'. I'm not totally happy with that phrase as it contains temporalness and the word 'created' itself, but I can't think of how else to word it off hand: imagine something like a rolled up loop of spacetime which unravels and we begin to traverse it.

(2) We may not be traversing the set in additive fashion. 'Now' doesn't add anything to the sequence; we simply traverse a pre-existing sequence.

(3) The concept that the past 'has been', the present 'is' and the future is 'potential' might not be valid. Instead it could merely be an illusion that fits the human understanding. There may be more to this than the wishy-washy its-all-in-the-mind argument it first seems to be.

[Bugmaster]

imagine something like a rolled up loop of spacetime which unravels and we begin to traverse it.

If you want to go that route, you can also imagine that the set of all possible events forms a "circle". There's a finite number of events, but they just keep repeating, so there's no beginning or end. That's another way of getting infinite regress, sort of.

[HughDP]

imagine something like a rolled up loop of spacetime which unravels and we begin to traverse it.

If you want to go that route, you can also imagine that the set of all possible events forms a "circle". There's a finite number of events, but they just keep repeating, so there's no beginning or end. That's another way of getting infinite regress, sort of.

Yes, although I'm not sure that's infinite regress; maybe more like 'finite but unbounded'.

[harvey1]

So if it is absurd to say that there is a lowest computable number (and I agree that it is based on the term meaning computable by a Turing Machine) then surely this backs up BugMaster's original point that there need not be a First Cause?

I don't see how. The reason it is absurd is because of a couple of reasons. For one, there cannot be a complete infinite set of computable numbers. The other reason is that the lowest computable number is itself an uncomputable number.

As for the First Cause argument, no one is saying that this first cause was a physical event occurring in the universe that had no previous cause. The cause is due to some non-physical cause that would force the Turing machine to halt if it encounted it. Namely, a Turing machine would not have an instruction on how to calculate the cause of causation, so it would halt.

[OccamsRazor]

If that is the case, we cannot add any further events. How do we add another event to an infinite number of temporally sequenced events? What does infinity + 1 mean?

I do not see the issue. Why can we not add one to infinity. Infinity + 1 = Infinity. Furthermore aleph-1 > aleph-0 but both values are infinity.
It does not makes sense to say that if we have traversed in infinite set of temporally sequential events we therefore can add no more.

I don't see how. The reason it is absurd is because of a couple of reasons. For one, there cannot be a complete infinite set of computable numbers. The other reason is that the lowest computable number is itself an uncomputable number.

Yes but this surely points to there being no computable first number or by reference to the initial analogy no first cause.

As for the First Cause argument, no one is saying that this first cause was a physical event occurring in the universe that had no previous cause. The cause is due to some non-physical cause that would force the Turing machine to halt if it encounted it. Namely, a Turing machine would not have an instruction on how to calculate the cause of causation, so it would halt.

This appears to be branching into a metaphysical ontology which indescribably breaks the program on your Turing Machine. I can't help but feel you are attempting to shoe-horn in a supernatural first cause.

[HughDP]

If that is the case, we cannot add any further events. How do we add another event to an infinite number of temporally sequenced events? What does infinity + 1 mean?

I do not see the issue. Why can we not add one to infinity. Infinity + 1 = Infinity. Furthermore aleph-1 > aleph-0 but both values are infinity.
It does not makes sense to say that if we have traversed in infinite set of temporally sequential events we therefore can add no more.

How can we ever traverse an infinite set of temporally sequenced events to add 1 to it? You are implying that we can somehow get to the end of this infinite sequence. If the set of temporally sequenced events leading to now was infinite, we could never have traversed them to get here.

This is why I believe that the events leading to now are either finite, were not created in a temporally sequenced (additive) fashion, or it has never been the case that they must all be traversed in order to reach now.

I think my set theory is right in relation to additive infinities, but I'll have a look tomorrow to see if I can find some supporting material.

[harvey1]

I don't see how. The reason it is absurd is because of a couple of reasons. For one, there cannot be a complete infinite set of computable numbers. The other reason is that the lowest computable number is itself an uncomputable number.

Yes but this surely points to there being no computable first number or by reference to the initial analogy no first cause.

Right, there is no lowest computable number if we are talking about a complete infinite set (i.e., all negative integers), in fact the term is meaningless. However, if we are talking about a finite set (e.g., all negative integers greater than -100), then there obviously is a first computable number. In the analogy with a First Cause, it's the latter situation that applies. The lowest computable number is based on computing a finite set and halting at the point when all the members of the finite set have been outputed (i.e., when the final state has been reached).

This appears to be branching into a metaphysical ontology which indescribably breaks the program on your Turing Machine. I can't help but feel you are attempting to shoe-horn in a supernatural first cause.

I don't think so. The algorithm to decipher the first physical cause is the laws of physics, something far from a supernatural first cause. The physics take us to a certain point, and beyond that point the "Turing machine" (i.e., the best physicists that a mind can produce) are not able to compute a physical state prior to this point.

[HughDP]

If that is the case, we cannot add any further events. How do we add another event to an infinite number of temporally sequenced events? What does infinity + 1 mean?

I do not see the issue. Why can we not add one to infinity. Infinity + 1 = Infinity. Furthermore aleph-1 > aleph-0 but both values are infinity.
It does not makes sense to say that if we have traversed in infinite set of temporally sequential events we therefore can add no more.

How can we ever traverse an infinite set of temporally sequenced events to add 1 to it? You are implying that we can somehow get to the end of this infinite sequence. If the set of temporally sequenced events leading to now was infinite, we could never have traversed them to get here.

This is why I believe that the events leading to now are either finite, were not created in a temporally sequenced (additive) fashion, or it has never been the case that they must all be traversed in order to reach now.

I think my set theory is right in relation to additive infinities, but I'll have a look tomorrow to see if I can find some supporting material.

OccamsRazor,

I'll have to concede that your set theory is better than mine because we can add 1 to infinity. It took an obvious example to get it into my thick head: if we record the infinite past moments with, say, negative even numbers and then starting from now we begin recording moments with negative odd numbers, we've successfully added to an infinite set. As the set of negative even numbers is the same size as the set of negative odd numbers, which in turn is the same size as the set of all negative numbers, we're not going to run out.

Now to the next point which relates to the idea of successive additions. The problem I had here was that I didn't see how a temporal infinity could be created by successive additions of a finite time period, but it could be created by an infinity of successive additions. I turned my nose up at this one for the totally unscientific reason of just not feeling comfortable with it (an infinity within an infinity etc.), but it doesn't matter: the idea of creating a temporal succession assumes a starting point from which we are supposed to begin adding moments in order to reach this infinity, and that assumption isn't valid. I still have trouble seeing how an infinite number of moments could be given to start with, but I'll let that go on the grounds that I've already been wrong in a lot of my set theory assumptions.

So if we accept an infinite past and consider the succession of moments that make up all of spacetime, then - even if we break each moment down as being a single movement across the Planck length in the Planck time - everything that could possibly happen has already happened an infinite number of times.

I'm not suggesting that this is a problem, but I'm wondering about the metaphysical implications.

[Bugmaster]

Right, there is no lowest computable number if we are talking about a complete infinite set (i.e., all negative integers), in fact the term is meaningless.

Right, which is exactly the situation with infinite regress. I've never claimed for there to be a lowest computable number, so proving that there isn't one doesn't get you anywhere.

I don't think so. The algorithm to decipher the first physical cause is the laws of physics, something far from a supernatural first cause.

I realize that you think that "physics proves God", but this is irrelevant for now. Remember, my argument is that infinite regress is possible, in principle, not that it actually is taking place.

I don't really see the point of your main counter-argument. You're saying that it's impossible to traverse an infinite set in finite "time" (i.e., a finite number of traversals). You then conclude that an infinite set of events cannot exist. A hidden assumption that you're making is that an infinite set of events must be traversable in finite time. Why is that ? I don't think your assumption is true.

So, basically, why do you feel that the set of events must be traversable in finite time ? After all, the set of integers is not traversable in finite time, and yet it exists (assuming your dualism is true, of course).

[harvey1]

Right, there is no lowest computable number if we are talking about a complete infinite set (i.e., all negative integers), in fact the term is meaningless.

Right, which is exactly the situation with infinite regress. I've never claimed for there to be a lowest computable number, so proving that there isn't one doesn't get you anywhere.

My point, though, is that your analogy of complete infinity of negative integers breaks down since a complete infinite set of causes would need to exist, but it is not possible to compute such a set. So, you cannot use this analogy as it breaks down.

I realize that you think that "physics proves God", but this is irrelevant for now. Remember, my argument is that infinite regress is possible, in principle, not that it actually is taking place.

O.Razor asked how it is possible for there to exist a lowest computable number, and I was showing how physics can stop after arriving at the lowest "computable" cause if the set of computable causes is finite.

I don't really see the point of your main counter-argument. You're saying that it's impossible to traverse an infinite set in finite "time" (i.e., a finite number of traversals).

No, that's not correct. I'm not saying that:

7) Invoking the Axiom of Infinity to advocate that set C exists is begging the question since a complete infinite set of causes, C, does not require a beginning by definition of it being a complete infinite set

I'm saying that you cannot invoke the Axiom of Infinity to advocate that a complete infinite set of causes exist, and therefore you cannot meet this condition for an infinite set:

3) Causes must be actual events that can be referred to as occurring (i.e., if it is logically impossible to reference that event, then it cannot be a cause to an event that you can reference)

You then conclude that an infinite set of events cannot exist.

Again, I've never claimed this. I've claimed that an infinite set of (regressive) causes cannot exist.

A hidden assumption that you're making is that an infinite set of events must be traversable in finite time. Why is that? I don't think your assumption is true.

I don't think that is an assumption of mine. I deny that computable numbers can be computed in finite time without somehow assuming the Axiom of Infinity or a platonic conception of mathematics.

So, basically, why do you feel that the set of events must be traversable in finite time? After all, the set of integers is not traversable in finite time, and yet it exists (assuming your dualism is true, of course).

The set of integers might exist by assuming the Axiom of Infinity and/or a platonic conception of mathematics.