Dear Prof Craig,
Thank you very much for your answer to my and my wife's question! (http://www.reasonablefaith.org/site/News2?page=NewsArticle&id=6281 )
We appreciate your hints concerning our first two questions. As for the question 3 (i.e., are there any good reason for (P) as expressed below?), you wrote, „I suppose that what commends P is the inconceivability of making the transition from the first w* series to the second w* series in a series ordered w* + w*." But then you add, „Maybe your question isn't about the possibility of the order type of an infinite series of past events' being something other than w* [...]" That's correct. Even if we suppose that the w* + w* past is inconceivable and impossible, we still have a problem with the premise (P). The premise reads as follows:
(P) If (i) the temporal series of all past events is actually infinite in its duration (as measured by equal temporal intervals), then (ii) there could be some mind/clock/counting machine/computer/angel/god which would SUCCESSIVELY pair all the past equal intervals (say, seconds) to all negative whole numbers in the corresponding order.
The Kalam arguer assumes (P), then he argues from some other premises (including the premise "the pairing should already have finished") to Not-(ii), and finally he derives Not-(i) from Not-(ii) and (P) by modus tollens.
Note that this time we emphasized the successiveness in (P). The reason of this emphasis is also the reason of our remaining worries about (P). Suppose for now: that past is infinite; that the w* + w* past is inconceivable and impossible; that past is of the type w*; that there is one-to-one correspondence between all negative integers and all the past seconds; that one-to-one correspondence obtains with the past comprising all the past seconds, but also with the past comprising all the the past seconds except the last second, with the past comprising all the past seconds except the last second and the semi-final second, etc.
Still, even assuming all of this, maybe one can coherently deny that these one-to-one correspondences can be established/represented by the mind/clock/counting machine/computer/angel/god SUCCESSIVELY.
You seem to deny this alleged coherence. You wrote, „The inconceivability of animating that picture is precisely the point of the defender of the finitude of the past, given the reality of temporal becoming." In other words, you seem to claim that if the past infinite, then there is, e.g., one-to-one correspondence between all negative integers and all the past seconds, SO, this correspondence can be established/represented by the mind SUCCESSIVELY. But, as you argue, it can't, thus the past is not infinite.
Yet the agnostic about in/finitude of the past could doubt the claim that if the correspondence obtains, then it can be represented successively. You reply, „Why couldn't a god who has existed from eternity take note of every event as it has occurred? Indeed, maybe the events just are the counting down from infinity of such a being. If an infinite past would have the order type w*, then I can't see why a co-eternal being couldn't enumerate them as they happen."
But the agnostic could counter: according to the Kalam arguer, infinite past together with (P) and other premises (like „the pairing should have already finished") entails a contradiction: (ii) and Not-(ii), which means that there both could and could not be some mind/clock/counting machine/computer/angel/god which would SUCCESSIVELY pair all the past equal intervals (say, seconds) to all negative whole numbers in the corresponding order. But, the agnostic continues, why should we, in reaction to this contradiction, drop infinite past -- why not deny (P) instead? If one is, like we, unconvinced by other arguments against infinite past (different from the argument from counting down from infinity), he doesn't know how to decide. Could you help? Do you treat this question somewhere in your your books or articles?
Thank you again!
Pavla Vohánková and Vlastimil Vohánka