Another thing I picked up from Craig's forum is arguments that infinite causal regresses are impossible. I've heard it elsewhere too, but it's on Craig's forum that I realized just how bad of an argument it is. Specifically, it's usually phrased something like this:

1- If time is boundless in the past, then there is an infinite number of things that must have occurred to get to the present.

2- It is absurd for an infinite duration of time to pass.

3- Thus reductio ad absurdum, it is absurd to say that time is boundless in the past.

I don't like that phrasing. I realized the error when I realized how I might make that argument a tad more formal. I think the following is a fair rephrasing of the argument.

1- It is absurd for an observer to experience a passing of an infinite duration of time.

2- If time is boundless in the past, then there exists a hypothetical observer who experienced an infinite duration of time, namely the hypothetical observer who had to experience everything before the present.

3- Thus reductio ad absurdum, it is absurd to say that time is boundless is in the past.

The mistake is in premise 2. I would argue that we should use the Real number line to model time (ignoring the complications of Relativity for the moment). If time is boundless in the past, and we use Real numbers to model points of time, then there is no hypothetical observer who can experience an "infinite duration" of time. The difference of any two Reals is Real and finite. Any hypothetical observer who has a beginning will only experience finite durations of time (in finite time).

I suppose we could talk about a hypothetical observer in time who always was, is, and will be. Even here, using the model of Real numbers, I don't see how you could show that this observer experienced an "infinite duration" of time. A duration has a start and end. That's what a duration means. For the always-existing observer, we can talk about durations of time it experienced, but we cannot talk about everything it experienced as a "duration" because there is no start and end. In fact, this is the critical flaw of the argument. The critical flaw is that they implicitly assume there exists a first time. They say that there is a first time before all negative Reals, that the hypothetical observer who always-exists experienced the first time, and that allows them to construct a duration of infinite length. To defeat the claim that there is no first time, they implicitly assume a first time.

I think this is intimately tied to Zeno's Paradoxes.

Having just wrote it all out, I'm not sure I'm entirely comfortable with this, because of so much potential for semantic ambiguity. However, I think that if you try to formalize the argument in terms of the Reals, then it falls apart precisely as explained above. Does anyone have any comments? Am I missing anything? I think the definition of the word "duration" is critical. I think it's absurd for an observer to ever get from a point X to a point Y where the distance between the two is infinite. But that's the rub. There are no such points on the Real number line.

Instead, if the premise is changed to "it is absurd for the set of experienced time to be unbounded in the past", then it's just assuming the conclusion, and you don't have an argument, just a rather large and obfuscated begging the question.

PS: I am undecided and ignorant on the topic of whether there was a first time, or whether such a concept is even well defined with all of the possible complications of General Relativity and modern cosmology (because I am largely ignorant of the details).