It seems to me that you-all try to evade the force of the arguments by denying that it is "real" or "possible" or "interesting" to visualise the past as a collection of discrete time intervals. Here are your actual words:
Dan: "The Past" is a concept of convenience. The Infinite can't be carved up that way in reality (it's just us creating arbitrary mathematical sets to help us out).
Diebert: The conception of a past as a collection of discrete time units stretched out is just not very interesting, in case you were talking about that.
Dan: Cause and effect isn't ultimately real, so trying to make metaphysical arguments based on "amounts" of it is entirely worthless.
Robert: As has been said before, trying to divide what isn't possible to divide only leads to confusion.
Do these objections successfully counter the arguments though? Not in the slightest! Let me explain why through an analogy.
We might equally suggest that "The parabolic equation of the path of a projectile is just not 'interesting'; such an equation is merely a 'concept of convenience'; The Infinite can't be represented mathematically 'in reality'; it 'isn't possible' to represent reality via mathematics" - and yet, the fact remains that projectiles
do follow the path described by a parabolic equation, and we can use such an equation to prove that a projectile if fired with a certain amount of force at a certain angle will land in a certain place rather than in another.
In the same way, when we "carve up" time into discrete intervals, we are faithfully observing and representing reality: time really
can be viewed as a sequence of discrete intervals - just watch the hands of a ticking clock! - we create no contradiction or lack of truth, accuracy, faithfulness or fidelity to do so, and, as with the parabolic equation of the path of a projectile, we can use this conceptualisation to prove something: namely, that a beginningless past is not possible, for, as WLC writes in that paper, "If the universe never began to exist, then prior to the present event there have existed an actually infinite number of previous events. Hence, a beginningless series of events in time entails the existence of an actually infinite number of things, namely, past events." (whereas, he has disproved the possibility of an actual infinite).
It is this quote that you will need to argue against, Dan, for this is where WLC establishes that beginninglessness entails an infinite past, and I agree with him, yet you seem to be suggesting that you uphold the former but not the latter... very peculiar.
No
legitimate objection to the quantification of time in this argument has been raised in this thread. You might prefer not to think in those terms, but it is perfectly valid to do so, and even helpful, as the arguments WLC presents demonstrate.
I'd also suggest that the house philosophers equivocate on this point, referring to causes when it suits them and denying the reality of causes when it suits them. A classic example is Kevin in Poison for the Heart, where he does this within separate points in his very own list:
Kevin in PFTH wrote:Firstly, it may be true that all things have causes. But Nature Herself is not a "thing" and therefore cannot be said to have causes. "Things" can only exist for observers, and as we are manifestations of Nature, we cannot stand apart from Her to observe.
Secondly, no law says that all things must have causes. Show me a single cause! Show me where that cause begins and ends - it cannot be done, so why all this talk of "causes".
Thirdly, why create the notion of a "necessary being" at all? Such a being is actually an unnecessary being. Why must things have an ultimate cause? Why can't causes stem back endlessly?
The first and third points entail the existence of causes; the second denies the existence of causes. It's all very pick-and-choose based on what suits the argument.
Cue the GFer response: but these are teachings at different "levels" (of understanding). Be that as it may, the "higher" level of "causes don't really exist because beginnings and ends are arbitrary" doesn't invalidate the perspective of the "lower" level of "we can distinguish causes by specifying a(n arbitrary) beginning and end to them": to differentiate causes in reality in that way does not, as I've pointed out above, lead to any misrepresentation of reality, regardless of how "arbitrary" the choice of beginning and ending is; beginnings and endings
do not impose any unsupportable obligation on reality in the way that, say, a misrepresentative physical law (e.g. a gravitational law of repulsion rather than attraction) would: they are
accurate conceptual mappings of reality as both experience and science bear out.
Robert, you also object that WLC does not define "the universe", whereas it seems to me perfectly obvious, since he includes scientific arguments, that he means the term in the same way that a scientist means the term when proposing a Big Bang. I think he would agree with you that this is "short of the whole story", because, as he argues, something cannot come out of nothing, and the whole point of his argument is to prove the necessity of a timeless Being out of which the "scientific" universe originates. There's no sleight [note the "e"] of hand here. The fact that you see equivocation, I would suggest, is really due to you adopting, and viewing WLC's argument through that lens, this forum's definitions of "finite" (i.e. "less than the Totality") and "infinite" (i.e. "the Totality"), whereas WLC is using the mathematical definitions, and there are no problems when viewing his argument through his own lens.
Jamesh, "tomorrow" has been and gone... oh yes, Dan, we know the drill. ;-)
In any case, this is probably my last post to this thread at least for some time; it's a pretty pointless argument, and I'm happy enough to let my original post and WLC's paper speak for themselves.