Sure. Here is how I see it.
First, we demonstrate that infinite regress is incoherent.
1. Infinite Regress is logically incoherent.
Infinite regress would mean that we have completely iterated, one-by-one, through every single item of an infinite series.
If we were to go backwards through each previous item, and there were an infinite number of past items, there would necessarily be some item in the set of previous items that we would never, ever get to. If that were not the case, it would not be infinite. (To put it another way, as we go backwards through the infinite items, there would always be something beyond us. If there is always something beyond us, there is something that is always beyond us.) If there is some supposed prior item in the set of previous items that we could never get to while iterating backwards through all previous items, then, iterating forward from that item to the current item, we would never arrive at the current item for the same reason that going backwards we could never arrive at the earlier item -- namely, the infinite (or unending) number of items in between the two.
To suggest infinite regress is to suggest that the infinite is not infinite, which is logically incoherent.
2. Past time had a beginning
This follows from the impossibility of infinite regress.
3. Temporality is neither permanent nor eternal
This follows from the above.
4. Temporality is caused
If temporality began uncaused, then having nothing, doing nothing to it, something resulted. This is the same as saying 0 + 0 > 0. I call this "Atheist Math". To suggest that 0 + 0 > 0 is to claim that 0 is not 0, which is logically incoherent.
5. The ultimate cause of temporality is an eternal, personal entity
If the cause were inherently temporal rather than eternal, temporality would be a necessary precondition for its existence. It, however, as the ultimate cause of temporality, is a necessary precondition for temporality. If each were a necessary precondition of the other, we would have an infinite regress of necessary preconditions in a circular fashion, which is logically incoherent. Thus, the First Cause is eternal.
Being the ultimate First Cause, it was not forced by a prior cause to cause, rather, it caused on its own. If it caused necessarily (simply because it is), then the results would be co-eternal with it, and they aren't (see item 3 above). Therefore it caused volitionally, or optionally, making it volitional or willful and thus personal.
As a side note, the First Cause does not have to be caused, because it (unlike temporality and temporal events) is necessarily eternal. This is different than saying it has existed for an infinite amount of time, rather, it is to say that it is permanent or timeless.
6. The ultimate first cause of every temporal event is an eternal person.
Everything that happens temporally has a previous cause, since 0 = 0 (see item 4 above). Temporal previous causes can only go back as far as temporality itself, then we must plead eternal causes. Because of the incoherence of infinite regress, there must be a First Cause, and (per item 5 above) it must be personal in addition to being eternal.
7. If there are multiple eternal personal uncaused First Causes, they are perfectly united as One God
If there were multiple personal eternal first causes, and they each had ontologically equivalent authority, and they ever disagreed, then whatever they disagreed upon would both be and not be at the same time and in the same way. This is logically incoherent. Thus, either only one of these persons is ontologically in ultimate authority and therefore there is only one ultimate God, or else all of these persons are in complete and eternal unity of mind, purpose, intent, desire, etc, such that they present a perfectly unified front and are therefore a single united GOD.
Thus, Atheism and polytheism are false because of the impossibility of the contrary.
The way I see it, it's more likely for something complex to exist as a result of gradual change through trial and error. A mind that is capable of thinking and reasoning is pretty complex. To say that something like that would just exist with no previous state sounds absurd to me.
Thank you in advance for taking the time to address my questions.
"[A] Why is the 'ultimate cause of temporality [...] an eternal, personal entity'? [B] Why does this entity need to be personal? [C] And why is it so impossible for the universe itself to exist as an eternal entity?"
Since the universe changes (things move around inside it), it has no permanent state. Either (1) there was no first change or (2) there was. If (1), then infinite regress, which is incoherent. So there was a first change.
Either (1) that change was caused or (2) it wasn't. If (2), the change resulted from nothing. This is the same as claiming that having nothing, doing nothing to it, something resulted: 0 + 0 > 0. So the change was caused.
To avoid infinite regress, there had to be a first cause. [A] This first cause has to be eternal because otherwise it too would need a prior cause.
The first cause acted in a manner that was either (1) voluntary or (2) involuntary. If (2), the first cause was caused to cause, which means it was not the first cause; but it was. So the first cause acted in a voluntary manner. [B] If it has volition, it is personal.
[C] Since the universe has no permanent state, it is not permanent. Yesterday's universe is not the same as today's, so today's universe has not always existed.
Let me know if this isn't clear or if you disagree with my conclusions.
It seems to me that your objection to infinite regression can be solved in the same way as Xeno's paradox: namely, that while a unit (in this case, the existence of the universe throughout time) can be broken up infinitely so that all the pieces can never be named, yet the whole still exists.
I believe that that would then make God a philosophical possibility, but not a philosophical necessity.
(I am a Christian, by the way, but have been having some serious doubts lately, and am trying to approach my questions in a fully logical manner.)
"If you don't believe in infinite regression, how do you deal with the mathematic concept of infinity?"
The existence of an infinite set and the creation of an infinite set through the process of repeated addition are two different concepts. Certainly if there can be no infinite sets, then no infinite set can be created through repeated addition. However, if infinite sets cannot be created through repeated addition, it doesn't seem to follow that infinite sets cannot exist at all.
"It seems to me that your objection to infinite regression can be solved in the same way as Xeno's paradox..."
Quantum Mechanics (QM) seems to insist that in the physical universe there is a smallest possible length (Planck length), meaning that distances cannot actually be divided ad-infinitum. Your objection applies to time rather than space, but QM seems to make the same claim in that realm regarding the Planck time unit, the shortest possible "moment".
However, whether QM really provides an accurate picture of reality or not, Zeno's Paradox, were his claims accurate, would necessitate that everything is everywhere all the time (everything is always zero miles away from everything else), that every number is identical to every other number, that every color is the same, and that every musical note is likewise identical to every other note. These things are not the case, so we know there is some kind of problem with Zeno's claims. QM offers one explanation as to what the problem may be.
"I believe that that would then make God a philosophical possibility, but not a philosophical necessity."
Were infinite regress coherent -- let's say it is for the sake of argument -- that would only render this one argument based on the incoherence of infinite regress fairly worthless. It would not render God Himself unneccessary. Other arguments have been posited that make the claim that God is a philosophical necessity for other reasons (moral argument, transcendental argument, etc).
And again, even if every one of those arguments were demonstrated to be invalid, that still would not conclusively demonstrate that God is not a philosophical necessity. The Christian position must always be that God is philosophically necessary, because He makes it clear that He is (Genesis 1:1; John 1:3; Proverbs 9:10; Revelation 21:6), even if we ourselves can create no intellectual or logical argument that demonstrates this.
"I... have been having some serious doubts lately, and am trying to approach my questions in a fully logical manner."
Logic is a wonderful thing. I have no intent of disparaging it. Our God is fully logical in that His person defines the Law of Identity and His actions make possible the Law of Non-contradiction. God's people are to think logically. The denial of logic is a clear mark of false worldviews. However, logic alone has never forgiven anyone of their sins (James 2:19). At the end of the day, as Ravi Zacharias asks, "what do you do with your guilt"? (Romans 3:23, 6:23)
God bless. You are in my prayers.
And I quote again, from our earlier exchange, the final point:
Temporality did not begin and we have no reason to suggest it did, as it is not an iteration. In fact, it can't have begun or else we would be confronted with an infinite regress of causes which is logically impossible.
Therefore, the nonexistence of temporality is logically impossible, as thoroughly and clearly explained in the above two paragraphs. It's not simply an assertion. I've proven it quite coherently above.
In short - you are mistaken in your line of reasoning, something I pointed out to you years ago in our exchange.
You said you would take some time and pray about what I said, presumably to understand it better. It is unfortunate that to this day, you continue with a false line of reasoning. At the very least, you are misusing the words and are therefore unintelligeble, as you yourself admitted in that earlier exchange:
Your quote: "I would like to point out that even if you could clearly and coherently demonstrate that anything properly called a "cause" (producer, reason, etc) or anything properly called an "effect" (consequence, result, etc) must unquestionably be temporal in nature, or that the causal relationship between the two must necessarily be temporal, all that would serve to do is demonstrate that I have chosen the wrong words for my argument, not that there is anything wrong with the argument itself."
I just read a little bit further where you say:
"4. Temporality is caused
"If temporality began uncaused, then having nothing, doing nothing to it, something resulted."
This one line of argument is so incredibly and sophomorically false ("temporality began uncaused" does not equal "having nothing" or by any stretch of the imagination, logic, or even known science) that I'm already dismayed to think we would get anywhere with any further discussion, except if you were to cross out every single thing you wrote and started from scratch.
but applies equally in Christianity; is some good because god wills it or does god will it because it's good?
Either god decides what's moral arbitrarily,
Or morality is independent of God.
Either God can change moral law on a whim.
Or God's law might to actually be moral.
I've yet to see a compelling argument to disprove polytheism; any argument which purports to proves God's existence supports multiple Gods.
If we suggest multiple perfect Gods agreed on a timeless moral law, it would be both objective and not arbitrary.
Since we are endowed with reason, and if t comes from the Gods, then we can ascertain moral law for ourselves.