I don’t recall saying that the universe had grown infinite from a finite origin (that would imply a beginning.) I have been claiming all along that we observe a finite subset of an infinite set. There has never been a point at which the regression was finite, there was no beginning at all.
TTC:
Nor did I accuse you of that claim. Again, you are being argumentative.
I think what science says about this or that property of space is mostly irrelevant.
On what basis? Or, is this another naked assertion?
Indeed we do not know very well what is outside the edge of our observable universe, what came before the big bang, or what will happen to our universe trillions of years from now.
I agree with the first part of your statement. This “science,” that you are so ready to disparage, says that our universe has about 26 billion years left to wait out entropy. Of course, we won’t be here - at least in our present form - then. But, “trillions of years?”
Unless you would like to cite science as having some empirical evidence that is able to make a positive statement about time, space, etc, then it is all conjecture, scientific or otherwise.
Entropy is mere conjecture then?
We must remember that we are asking the question “Why is infinite regression held to be impossible?” answering “Science suggests x” is not very satisfactory.
Especially, I guess, if one does not like the answer.
We must remember that people were rejecting infinite regressions long before we had modern science, so what were their reasons for doing so? It would seem that an immediate and complete dismissal of infinite regression would require some clear and simple reasoning to do, but so far I have not heard it.
Again, my apologies. Conversing with many on these fora can, and does, give rise to confusions as to what others have said and what one has said to others. I believe that an actual infinite regression is impossible. However, I’m not sure there’s a simple proof for the impossibility of a purely mathematical infinite regression. And, that’s what it would be.
I believe that an infinite regression can be postulated in sheer math. I do not believe it can be successfully postulated of an aggregate of physical, or temporal, exigencies. Physical exigencies are separate things with boundaries. Things consist of either other things, or pieces of a first thing. And temporal exigencies require separation that would otherwise result in contradictions. I believe that there is a smallest actuality that, for all intents and purposes, cannot be sub-divided any further and remain dimensional. ‘Points’ may be said to exist, but may (beyond) equally be said not to exist. Any proposition based on “points” would be irrelevant if they are involved solely for the purpose of asserting an
actual infinity.
But, that’s not the kind of infinite regression that you were talking about. The only kind of infinite regression you could be talking about is an infinite regression of time. Nothing else will satisfy. Time is an essentially subordinated series of “nows,” or “seconds,” or “Planck lengths,” each one dependent upon the previous one as any change is dependent upon a previous state. Besides, “time” has a
reality that is considerably different than the
reality of beings.
St. Thomas says, in the
Summa Theologiae, “This, however, is impossible, since
every kind of multitude must belong to a species of multitude.
Now the species of multitude are to be reckoned by the species of numbers. But no species of number is infinite, for every number is multitude measured by one.” In other words, in either direction, number is multitude measured by
one. In any progression, one more may always be added (or, two, or three, etc.) Likewise, in any regression, number is multitude measured by
one. So, since one may be added to any regression such that no actual number is ever achieved, an infinite regression can never be achieved either. An actualized infinite regression can only be potentially (a tending toward) infinite.
However, I am interested in your idea of God as an Infinite Regression. Care to elaborate? Also, if you have a differing idea of an actual infinity, would care to elaborate on that, too? And, I am interested in your idea of a “finite set” within an “infinite set.”
God bless,
jd
