Ok, John, I read your First Order argument as well as the Beginningless Time Paradox and Beginningless Cause Paradox. Here’s my initial thoughts:
If I can pick one line from your First Order argument that is the crux of it, it would be this:
Unfortunately, you didn’t really offer any justification beyond this so the reader is left to take it as a brute fact. For many, this would be fine considering many share your sentiment. But if you’re offering this as a response to someone who expressly states that he sees no problem with an infinitely regressive universe, it leaves something wanting. One is not apt to take bald assertions as evidence that one is wrong. So I’ll ask: can you explain why an infinite regress is impossible?
Having said that, you did say this:
Now this is just a trick. You drew the conclusion that without cause A, there could be no effect B, and without B, there could be no C. A series of causes and effects must have a first cause to start the whole chain, you said. The picture you end up planting in the readers mind is that absent cause A, there would be nothing to bring about B. But the picture of an infinite regress of causes is very different. We aren’t absenting anything. Whatever cause your heart desires–A, B, C … X, Y, Z–it’s all there and an infinity of others. There is always a cause A to bring about B. We don’t get to say cause A is the first–you got that right–but not by virtue of an absence of any cause preceding another, but because of a plethora, an infinity, of causes preceding every other. So the reason why your argument about A being required to bring about B, which in turn is required to bring about C, doesn’t carry over to the case of the infinite regression. There being no first cause means something very different in each case.
As to your Beginningless Time Paradox, here’s what I take to be the crux of the argument:
While this is true, it sort of presupposes that the traversing of time began at a certain point. Indeed, if we say time started marching forward at point t0, then how would it arrive at another point t1 an eternity away? You simply switched the roles of the two points in time, t1 being not an eternity away but now, and t0 being not at a certain point in time but an eternity back in time.
But the flaw in this thought experiment lies in the assumption that we can even talk about time beginning to march forward at a certain point. It doesn’t start marching forward, it was always marching forward–for an eternity as a matter of fact–and if it would take an eternity to traverse all of time in order to arrive at now, then we arrive at now because we’ve had an eternity.
^ I’ll take this snippet as summarizing your Beginningless Cause Paradox. Admittedly, I’m not 100% certain how to interpret this, but it sounds like the same argument behind the Beginningless Time Paradox. Instead of talking about having to traverse infinite points in time, here you talk about having to undergo an infinite number of causes. You say that such a chain of causes would have to be exhausted in order to get to now, but since an infinity of such causes could never be done unfolding, neither could they be exhausted. I think the same response I gave to the Beginningless Time Paradox can be given here.
The point for both is that it only seems impossible to traverse an infinity if we imagine starting from somewhere. Yes, if I start from here, I could never reach a point an infinite distance away. But the point of a beginningless universe is that there is no start. Rather, an eternity is already given, and therefore you can talk about being at any point in time just as you can talk about being at any point in space despite space being infinite.