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MindOverMatter
Guest
No there isn’t. There is always a “potentially infinite” number of events in the future. To say that time can be completed, in the sense of saying that there is an ultimate number, is meaningless to me.
I don’t know that eternal life will have anything to do with time. However, even if there is an eternal future, it is not an actual infinite; rather it will simply go on for ever and ever.
Not if you apply it to the past. Possibility implies potentiality in regards to the future. If you apply an actual infinite to the past, you would have to transcend all numbers, or admit that the past is finite. The illusion of plausibility occurs to you because you are counting backwards from the present moment as if to count forwards. You are applying an potential infinite to the past and calling it an actual infinite. And since there is no whole number in past, you have transcended all descriptive numbers to an extent as to make counting meaningless. To be more accurate; the past has already occurred, so all numbers have been counted in-so-far as the past is concerned. But thats the problem; there is no such thing as “all numbers”. There are only potential infinites in regards to numbers. A true infinite is not a number, and so is therefore not a true event.
First of all, you implied in your first post that my arguments were not sufficient in providing a first cause by complaining that atheists can simply say that the world is eternal. Perhaps, i misunderstood, perhaps you were playing; i don’t know. It seems to me that you assumed that i was trying to prove that the universe was not infinite perhaps? Secondly; I’m not sure in what sense Thomas did hold to your position. He certainly seemed to deny mechanical infinites, for the simple fact that he argued for a “sufficient cause”. For instance, the act of **knowing **cannot infinitely regress; otherwise an infinite number of processes would have to be completed before you ever knew anything. Hence, so far as logical necessity will allow, there are only a finite number of processes before we reach the “knower”. As for non-mechanical infinites, Thomas knew of no arguments that could refute it. That doesn’t mean that the concept of an infinite universe is irrefutable. In any case, it seems to me, if i am not mistaken, that Thomas rejected an eternal universe on the basis of faith.
Because a hypothetical eternal life in regards to time, would alway be successive from the beginning.
K
Katholish
Guest
I think you might be missing the point of the current discussion (or tangent of the discussion), which is asking whether or not the material universe could have had an infinite past if God chose to design it that way, or if there is some kind of inherent contradiction in the very notion of an infinite past, and hence it would not have been possible.
Past time has actually happened. There is no “could have been yesterday.”
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Katholish
Guest
MindOverMatter,
Certainly in regards to how God chose to create this universe, He created it with a beginning in time. Thus, indeed St. Thomas rejects the idea that this universe is truly eternal on the grounds of faith (in that it needed to be revealed to know with certainty).
Since Atheists do not accept our basis in revelation, however, I don’t think it possible to disprove an eternal universe, and hence it needs to be clear that St. Thomas’s proof does not require a temporal beginning in order to be valid. The proof would not logically work for an atheist if it is tied to a notion of a first cause in time. It seemed to me that the arguments that had been presenting were tying the two together, hence the reason for my objection.
A potential infinity would mean that something might have boundaries or it might not. Being actually infinite is a quality of a thing, and means it has no boundaries in a certain aspect. If we know for certain that time will not end, then we know it has no final boundary, and is therefore actually infinite, since infinity is a quality of a thing. If we said that time were merely potentially infinite instead of actually infinite, then there woudl exist the possibility of its ending.
Even the existence of matter in Heaven, we can know with certainty that there is time in the afterlife. The fact that eternal life is in time and does not end, means it has no end boundary and is hence an actually infinite thing. It does not potentially have this quality, it actually has the quality.
St. Thomas doesn’t believe an infinite chain of causes is ultimately possible, but he does think that one cause can cause an entire system of infinite causes in time. Causality for Thomas is not chronological, but ultimately exists outside of time, and as such does not need to entire a temporal chain of causes at any given point, but can merely cause the whole from without. In this manner, he thinks it could have been possible for God to create an eternal universe which had no beginning in time, yet still requires an outside First Cause.
Certainly in regards to how God chose to create this universe, He created it with a beginning in time. Thus, indeed St. Thomas rejects the idea that this universe is truly eternal on the grounds of faith (in that it needed to be revealed to know with certainty).
Since Atheists do not accept our basis in revelation, however, I don’t think it possible to disprove an eternal universe, and hence it needs to be clear that St. Thomas’s proof does not require a temporal beginning in order to be valid. The proof would not logically work for an atheist if it is tied to a notion of a first cause in time. It seemed to me that the arguments that had been presenting were tying the two together, hence the reason for my objection.
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MindOverMatter
Guest
A potential infinite is something that can go on forever, but will never exhaust or transcend numbers. And in so far as that is true, the future will always have a finite number.
True.
True.
No. Knowing that time will not end, does not change the fact the the future is finite, and is dependent upon a continuous becoming. It is potentially infinite. A true infinite is perfect; it has no potentiality.
Yes; there is the possibility of its ending. However; this does not contradict ones knowledge that it will not end; just as much as Gods knowledge of my future does not contradict my freewill.
Only God is infinite. A duration of time cannot be successively exhausted in respect of numbers, therefore the future is always potentially infinite. There is always one number succeeding the other. It is countable. But an actual infinite has transcended numbers. It cannot be counted.
Well…for reasons that i mentioned above, including my other posts, i don’t think that it is possible.
If an actually infinite universe were logically meaningful and therefore possible, then yes, God could do this. But an infinite universe is meaningless. It is no wander then that we find ourselves in a universe that started from a big bang.
Yep.
Sorry if this sounds rude, but the notion of an actually infinite and successive universe has been disproved several times over; and if you haven’t grasped the illogicality of it by now, your not likely to any time soon. Lets just agree to disagree.
Nice talking. Peace.
J
JDaniel
Guest
OK, well, I’m sort of looking at it from a logical-scientistic (I know, right!) viewpoint, that the precise first instant just forward (as in maritime stuff) of the BB was the start of time. And, as I said in my OA, unless we know that the energy inside of the singularity was in motion, then there were no physical laws or motion when the singularity was intact.
You say, “Potato,” and, I say, “Potato.”
jd
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MindOverMatter
Guest
Sorry to butt in to your conversation, but does my refutation of an actual infinite in the past make sense to you? It makes sense to me. Perhaps I’m not phrasing it correctly? Some times you can know something but find it difficult to communicate it in to words.
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JDaniel
Guest
Katholish:
We expect that God would not cause a logical contradiction. If there was an infinite past, we would never be able to arrive where we are now. As MoM said, there is no such singular number as “infinite”. (If there is, I’d like to know it - and, so would everyone else.)
“Infinite”, per definitionem, includes in its meaning, “potential”. It cannot mean, “actual”. If it meant “actual” the resultant number would be finite. A logical contradiction.
Definitions:
1.) Finite = any number at all, no matter how large or how small.
2.) Infinite = no number at all, or zero. (We use “zero” as a number, in mathematics, because of its conceptual significance as a place-holder only. I know mathematicians have ascribed other meanings to it, but, anyone can call anything anything they want, but name-calling doesn’t change the nature of a thing.
jd
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JDaniel
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Katholish
Guest
MindOverMatter,
Taking what the Catholic Encyclopedia said (the section JDaniel quoted earlier) to heart, I take infinity to most properly and most commonly refer to material things. Perhaps what you are calling potentially infinite is what I am calling actually infinite. An infinite succession of real things is most properly an “actual infinity” according to the manner in which I have been using it, and I would argue the manner Thomas uses infinity.
newadvent.org/summa/1046.htm
I think I am starting to understand what you mean by actual infinity. I have never once been suggesting that time could “exhaust or transcend” number in the manner that you seem to mean it. The way you mean it, I agree that there could be no such thing as an infinite material thing, or an infinite thing in time. You are defining it in such a way that only the transcendentals such as being, truth, etc. could possibily be “infinite” and ultimately only God could be truly “actually” infinite.
Taking what the Catholic Encyclopedia said (the section JDaniel quoted earlier) to heart, I take infinity to most properly and most commonly refer to material things. Perhaps what you are calling potentially infinite is what I am calling actually infinite. An infinite succession of real things is most properly an “actual infinity” according to the manner in which I have been using it, and I would argue the manner Thomas uses infinity.
I am more than willing to bring this tangent of the discussion to a close. Since we cannot seem to convince each other through argumentation (at least not within a reasonable amount of time) I will make an appeal to authority before concluding. Here is the Question from the Prima Pars that addresses the question. When St. Thomas asserts that belief in the temporal beginning of the universe is a matter of faith and cannot be proven by reason, I tend to think he is correct. If you are so inclined, the first two articles are the most pertinent and make for an interesting read.
newadvent.org/summa/1046.htm
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Katholish
Guest
Never said infinity was a single integer or number. I did say, however, that there can be an infinite series of numbers.
Several things to be said here. If potentiality is included in infinity by definition, then there would be no sense in which God could be called infinite because in God there is no potential at all, rather He is pure Act. Thus, you cannot be correct because surely you would agree that God is rightly called infinite, and futhermore that God is the most “actually” infinite thing there is.
Secondly, I need to again point out the Catholic Encyclopedia which you yourself brought in as an authority. In the article on infinity it says: “the term infinity applies primarily to space and time” yet space and time must always have number, hence the meaning of infinity cannot simply be “no number at all”.
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JDaniel
Guest
MoM:
Either Katholish is having some fun here, or there’s a huge failure to communicate. I think it’s the former. In any event, you are the actually actual actuality and, you are correct.
I know what Katholish is doing, that’s what makes me think he/she is playing with us. He/she is word-playing, slipping words back and forth grammatically, alternating usage between adjective, adverb and noun, to produce a play on words. That’s kind of cool, I think. But, you are right, there cannot be an actually infinite actuality, or, an actually actual infinity. If you contrive the definition too narrowly, all you end up with is muddy water to look through.
From Wikipedia -
“In metaphysics, Aristotle distinguished between actual and potential infinities [citation needed]. An actual infinity is something which is completed and definite and consists of infinitely many elements. A potential infinity is a sequence which is endless. Whereas all the elements of an actually infinite set are assumed to exist together simultaneously, the elements of a potentially infinite sequence exist only consecutively over time” ad infinitum.
and,
*"The **mathematical meaning *of the term “actual” in actual infinity is synonymous with definite, completed, extended or existential[1], but not to be mistaken for physically existing." or, existing, period.
jd
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Katholish
Guest
JDaniel,
I don’t see why you think I might be purposefully equivocating. If you think I am using words differently at different points, please show me. An unintended equivocation is often the source of error and confusion (which is why St. Thomas is constantly making distinctions).
I think I might take issue with one thing from the Wikipedia source you quoted. It says, “An actual infinity is something which is completed and definite.” Saying that something is definite seems to contradict the idea of infinity, unless there is some significant difference between finite and definite that needs to be applied.
MoM and JDaniel,
If we want to agree to use potentially infinite to describe something which is an infinite succession, I am fine with that provided we don’t fall into word play and say that because we call it a potential infinity, there is nothing really infinite about it…yet. In my mind, an infinite succession of points, events, etc, is still rightly called infinite.
I don’t see why you think I might be purposefully equivocating. If you think I am using words differently at different points, please show me. An unintended equivocation is often the source of error and confusion (which is why St. Thomas is constantly making distinctions).
I think I might take issue with one thing from the Wikipedia source you quoted. It says, “An actual infinity is something which is completed and definite.” Saying that something is definite seems to contradict the idea of infinity, unless there is some significant difference between finite and definite that needs to be applied.
MoM and JDaniel,
If we want to agree to use potentially infinite to describe something which is an infinite succession, I am fine with that provided we don’t fall into word play and say that because we call it a potential infinity, there is nothing really infinite about it…yet. In my mind, an infinite succession of points, events, etc, is still rightly called infinite.
J
JDaniel
Guest
But, for all intents and purposes you are when you indicate, by your words, that you do not seem to mean that it is something “dynamic”. You speak of is as if it were a static, singular event. That’s what’s confusing.
As to your second sentence, it would more properly be stated, “numbers in a series ad infinitum”.
You are correct that God is infinite. When we say, “God is infinite”, we mean that in a metaphysical sense. We cannot begin to know what a metaphysical infinite is, except that it equals God.
God is the most actually infinite thing there is, although, you and I cannot understand precisely how He is infinite.
The Encyclopedia is quite correct, IMHO, we usually do tend to apply it to “space and time”. And, because space and time can be said to exist, it can be applied to them with the caveat that time is always marching on and space is always expanding. Again, the word must be understood in the sense that it is dynamic - as, not stopping from growing, expanding, contracting, and so on. In this regard, we are understanding that space and time are relative to physical things, not metaphysical things.
jd
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JDaniel
Guest
Sorry, but it wouldn’t be the first time someone as astute as you used the forum to have some fun.
If you are telling you aren’t, I will retract that statement.Alas, the trials and tribulations of using English for putting ideas into words!
Your words are not interchangeable with existence or reality. You may say anything you want. But, a real infinite succession cannot exist, except, in words. It can’t even be conceived of. All we have is the words.
jd
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Katholish
Guest
JDaniel,
Do you at least admit that a series of events *ad infinitum *is possible, and that this is in fact what the future is/will be?
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JDaniel
Guest
Absolutely, unless God simply allows the universe to become a cold, dead debris pile at 400 below zero. Will there be any causal series once we are in the afterlife? It seems that will be the case.
jd
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Katholish
Guest
But you do not accept that a series of events *ad infinitum *(if those events are in the past) is even theoretically possible, correct? Or have I misunderstood?
D
Dr.Bonnette
Guest
I confess that I have not read every post on this thread, but I have the distinct impression that the argument here is about whether a causal regress can go backward through time infinitely, and that St. Thomas’ prima via and secunda via somehow depend upon such a regress being impossible in order for them to conclude validly to a First Mover and First Cause. If my impression is wrong, please correct me.
If anyone is thinking of a causal regress backward through time in St. Thomas’ arguments, they misunderstand a fundamental element of the Ways. The causal regress described here is atemporal. Cause and effect are always simultaneous. That is why St. Thomas says that to take away the cause is to take away the effect. The causal regress is one in which all causes and effects are simultaneous. It does not go back in time. In fact, the tertia via presupposes an eternal world, based on the argument from Moses Maemonides. In fact, in his De Aeternitate Mundi, St. Thomas argues that it is not logically impossible that the world be eternal, and that the truth that the world had a beginning in time is not a philosophical truth, but an article of Catholic faith. After all, if God exists from all eternity, what is to prevent Him from having been creating the world from all eternity as well?
If you want to see how these arguments are properly framed, I would suggest you find a copy of my own “St. Thomas Aquinas’ Proofs for God’s Existence,” Martinus-Nijhoff, The Hague, 1972. While the book is now available only as a PoD for an outrageous price, it can be found in many libraries today in its original form.
If anyone is thinking of a causal regress backward through time in St. Thomas’ arguments, they misunderstand a fundamental element of the Ways. The causal regress described here is atemporal. Cause and effect are always simultaneous. That is why St. Thomas says that to take away the cause is to take away the effect. The causal regress is one in which all causes and effects are simultaneous. It does not go back in time. In fact, the tertia via presupposes an eternal world, based on the argument from Moses Maemonides. In fact, in his De Aeternitate Mundi, St. Thomas argues that it is not logically impossible that the world be eternal, and that the truth that the world had a beginning in time is not a philosophical truth, but an article of Catholic faith. After all, if God exists from all eternity, what is to prevent Him from having been creating the world from all eternity as well?
If you want to see how these arguments are properly framed, I would suggest you find a copy of my own “St. Thomas Aquinas’ Proofs for God’s Existence,” Martinus-Nijhoff, The Hague, 1972. While the book is now available only as a PoD for an outrageous price, it can be found in many libraries today in its original form.
K
Katholish
Guest
Thank you. That is precisely what I have been trying to argue.
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