St. Thomas Aquinas & A Beginning-less World

[hatsoff]

Well, that’s precisely why it seems illogical. There’s really no starting point in the succession in order to say where the book actually came from…

The contradiction as I see it is between these two claims:

(1) the book got to “this point” (2) but in order to get to “this point” it had to pass through an infinite series of hands.

To put it another way, that’s as illogical as telling a guy to drive to point X on a never ending road – though telling him he has to make an actual infinite number of pit stops through an infinite number of gas stations – you assure him he will eventually get there.

But he will never get there - not if the distance to point X involves an actual infinite number pit stops through an infinite number of gas stations. For if there’s an actual last pit stop before point X, the number of pit stops would be finite, however unimaginable the total amount may be.

Let’s look again at your analogy. We tell this person to drive to point X. Where is he when we tell him? Let’s call that point W. So, we’re asking him to travel from point W to point X.

Now, in what way do you propose to specify this trek as “never ending”?

But the book could not have gotten to “this point”, or any point for that matter, if it had to go through an infinite series of hands; just like the guy in the above scenario could never get to point X if he had to go through an infinite series of stops.

Maybe that’s what your intuition tells you, but I submit that your intuition is in error in this highly abstract matter.

 

[MindOverMatter]

(emphasis added)

One does not follow from the other.

You are merely asserting a problem, but not really showing that you understand.

I mean no direspect. But let me put this problem another way.

When somebody says that there is an infinite “number” of events in the past, then one is saying that the past is infinite because of the numbers that it contains. But if it is impossible in prinicple to count to an infinite, this means there is no such thing as a number or numbers that are infinite in value, because you can always add a number, you cannot exust or complete numbers. There is no such thing as a number that is infinite.
When you apply this principle to events themselves, one ought to see the impossibility of an infinite regress, because it would mean that all logically possible numbers have been exusted, transversed and transcended, since the past is complete in the sense that it is already actual. If you say that an infinite is simply an ongoing number of events, then what you are really saying is that there is a potential infinite in the past rather then a definite number of events; which is illogical since potential infinites only apply to the future.

 

[j1akey]

MoM, I’m curious to know what you do for a living because I can never understand a thing you say.

 

[hatsoff]

You are merely asserting a problem, but not really showing that you understand.

On the contrary, you are the one making the claim that an infinite past is impossible. I am merely pointing out that you haven’t justified that claim.

I mean no direspect. But let me put this problem another way.

When somebody says that there is an infinite “number” of events in the past, then one is saying that the past is infinite because of the numbers that it contains. But if it is impossible in prinicple to count to an infinite, this means there is no such thing as a number or numbers that are infinite in value, because you can always add a number, you cannot exust or complete numbers. There is no such thing as a number that is infinite.
When you apply this principle to events themselves, one ought to see the impossibility of an infinite regress, because it would mean that all logically possible numbers have been exusted, transversed and transcended, since the past is complete in the sense that it is already actual. If you say that an infinite is simply an ongoing number of events, then what you are really saying is that there is a potential infinite in the past rather then a definite number of events; which is illogical since potential infinites only apply to the future.

You keep saying that it’s “illogical,” and that an infinite past is an “impossibility.” But you haven’t given me any coherent reason to believe you.

What does it mean that all the numbers are exhausted? What numbers? Are you trying to model time on the naturals? The integers? The rationals? The reals? The ordinals? Something else?

 

[MindOverMatter]

You keep saying that it’s “illogical,” and that an infinite past is an “impossibility.” But you haven’t given me any coherent reason to believe you.

I have. I don’t mean to make it difficult. personally i think its very clear.

What does it mean that all the numbers are exhausted? What numbers? Are you trying to model time on the naturals? The integers? The rationals? The reals? The ordinals? Something else?

This is a problem that alot of people seem to be having on this forum. Inorder to understand the truth of my statements, you would have to understand the different levels of abstraction and how they apply to objective reality, or which is justifed in respect of objective events.

If we are moving from the past to the present and then on to the future, and wish to apply an approximate “age” to what we call the universe, then we can apply numbers in terms of objective quantity, since there is an objective quanitity to reality and also in regards to events themselves. In my case, i am talking about plain old addition in correlation to events. I assume that any person who says that there is in fact an infinite number of events in the past, is in fact saying that the **sum total of events is infinite **. I am talking about ontological numbers as dictated by objective events. You, at the very least, are saying that you don’t know that its impossible that there is in fact a infinite regression of objectivly real actual events in the past. If one is saying that it is actually possible, then one is speaking about a definite number of actually real concrete events that represents infinity in the past. I have given my reasons for why i understand this to be impossible in principle.

I guess, if you are serious, you will have to work out for your self which kind of mathematics best represents objective reality and which is just pure abstraction when understood in respect of past events. I am not in the mood for explaining this any further.

 

[hatsoff]

I have. I don’t mean to make it difficult. personally i think its very clear.

I believe I understand your thought processes, here–at least, well enough for our purposes. However, it is my opinion that you have made a crucial error in likening successive addition (or “counting”) to the process of time moving forward.

Successive addition is a binary operation. That means you need to plug a number into your function in order to get out another number. What number are you plugging in? If successive addition is the movement of time, and time is past-infinite, then the only number you can ever plug into a successor function is an infinite number. And of course this renders the analogy rather useless for showing that past-infinite time is impossible.

This is a problem that alot of people seem to be having on this forum. Inorder to understand the truth of my statements, you would have to understand the different levels of abstraction and how they apply to objective reality, or which is justifed in respect of objective events.

If we are moving from the past to the present and then on to the future, and wish to apply an approximate “age” to what we call the universe, then we can apply numbers in terms of objective quantity, since there is an objective quanitity to reality and also in reagrds to events themselves. In my case, i am talking about about plain old addition in correlation to events. I am talking about ontological numbers as dictated by objective events. You, at the very least, are saying that you don’t know that its impossible that there is in fact a infinite regression of objectivly real actual events in the past. If one is saying that it is actually possible, then one is speaking about a definite number of actually real concrete events that represents infinity in the past. I have given my reasons for why i understand this to be impossible in principle.

I guess, if you are serious, you will have to work out for your self which kind of mathematics best represents objective reality and which is just pure abstraction when understood in respect of past events. I am not in the mood for explaining this any further.

This doesn’t answer my question, but okay.

 

[MindOverMatter]

I believe I understand your thought processes, here–at least, well enough for our purposes. However, it is my opinion that you have made a crucial error in likening successive addition (or “counting”) to the process of time moving forward.

Successive addition is a binary operation. That means you need to plug a number into your function in order to get out another number. What number are you plugging in? If successive addition is the movement of time, and time is past-infinite, then the only number you can ever plug into a successor function is an infinite number. And of course this renders the analogy rather useless for showing that past-infinite time is impossible.

There is no logical justification for plugin in an infinite if in principle one cannot make up an infinite with numbers. We are talking about numbers of events. One is saying that the past is infinite because of the number of events it contains which are additional in corelation with events that are going from past to the future.

 

[Ginkgo100]

St. Thomas Aquinas believed that we can’t demonstrate the world had a beginning through reason alone.

Really? I did not know that. Even though I’m a fan of Aquinas, I have not actually read any of his works yet. (Soon to change: I got a book of Aquinas writings from the library just yesterday.)

I tend to side with you: I think we can deduce that the natural world, i.e. the world subject to the law of causality, must have had a beginning. But that requires the existence of a phenomenon independent of the laws of causality, which cannot have had a beginning, having no cause.

The alternative, that this “uncaused cause” had a beginning, requires it to have sprung into existence spontaneously, for no reason at all. (Otherwise, it would not be uncaused.) That cannot happen in a rational universe. I think the first unproven philosophical assumption that must be made is that the universe is consistently rational.

I wrote more about the uncaused cause here: leavethelightson.info/the-uncaused-cause I didn’t address necessary v. contingent existence, though. I think of the uncaused cause as “self-existing.”

 

[hatsoff]

There is no logical justification for plugin in an infinite if in principle one cannot make up an infinite with numbers.

Sure there is.

Suppose we model time discretely, as an infinite chain of equally-spaced (temporally) events. This appears to be how you envision it. So, which numbers are we going to use to model that chain? The natural numbers (hereafter N) have a beginning of sorts–the number 1. But a past-infinite timeline has no such beginning, so N seems inappropriate. How about Z, the set of integers? This will work, since it extends infinitely in both directions.

So, how do we form an infinite chain? A successor function is the way you apparently wish to go. Okay, fine. But wait a minute! Where do we start? If time is past-infinite, there is no beginning from which to begin counting. So let’s pick an arbitrary point on the line. We don’t know which point we’ve picked, so let’s call it n. Now then, as we move along the timeline, we plug n into the successor function, getting n+1, n+2, n+3, and so on.

Now, how many numbers have we skipped by choosing n? Well, we have skipped over all the numbers in Z \ n, \infty). But this is an infinite set! So, if time is past-infinite, we can only start using our successor function by skipping over an infinite number of past events.

And all this assumes time is indeed discrete.

 

[nkbeth]

Disregarding all that actually happens in the world, can we prove by reason alone that the world will have an end?

It seems to me that whether it is time in the past or time in the future, God could if He chose cause existence without end. And in fact our existence is endless into the future, even though the world comes to an end.

There is no “actual” infinity; an infinity of discrete items in your hand. But things can truly be countless, I think. God is not confined to “starting” a world any more than he is to “ending” it. Our desire to get a “final” count does not limit His timeless causality.

 

[j1akey]

nkbeth:

Disregarding all that actually happens in the world, can we prove by reason alone that the world will have an end?

I guess that depends on what reason you’re talking. Based on what we know about stars we know that the sun will eventually in a few billion years run out of fuel and blow up to be a red giant, go nova, and fry the earth to a cinder. Whether the human race lives long enough to see it is another story altogether.

 

[nkbeth]

I guess that depends on what reason you’re talking. Based on what we know about stars we know that the sun will eventually in a few billion years run out of fuel and blow up to be a red giant, go nova, and fry the earth to a cinder. Whether the human race lives long enough to see it is another story altogether.

When I said “Disregarding all that actually happens in the world” I was excluding the kind of things you refer to. Maybe I should have said “universe” instead of “world”.

I was talking about the very idea of the “beginning of time” and the “end of time” (or the beginning or end of any possible world/universe).

And I was talking about God’s relationship to this world; which I see may not influence you since you identify yourself as an atheist.

 

[j1akey]

nkbeth:

When I said “Disregarding all that actually happens in the world” I was excluding the kind of things you refer to. Maybe I should have said “universe” instead of “world”.

I was talking about the very idea of the “beginning of time” and the “end of time” (or the beginning or end of any possible world/universe).

And I was talking about God’s relationship to this world; which I see may not influence you since you identify yourself as an atheist.

The thing with reason basically impossible to exclude what you already know and then try to reason something out while ignoring what has already been discovered. If I lived 1000 years ago and knew nothing about the how nature even worked let alone the complexities of the universe. I would use reason to tell myself that the earth would be around forever because I don’t know any better. I would have no concept of long timescales much beyond my own life of say 30-40 years if I was lucky. Back then the entire universe basically consisted of just our planet. There was no concept of anything beyond it for western civilizations for the most part.