This is essentially about William Lane Craig's publications on (his version of) the Kalam cosmological argument. Craig is constantly talking about "absurdities" that result from considering infinite quantities. In plain English, that term and its derivatives have very ambiguous and squishy meanings. For instance we might say that "fairies are absurd," by which we mean that we just subjectively find the idea to be ridiculous or silly. But Craig seems to be using the word in a different way, as if it has something to do with metaphysical impossibility. Here's an example (one of many!) of how he employs the term:
"Hilbert’s Hotel is absurd. But if an actual inﬁnite were metaphysically possible, then such a hotel would be metaphysically possible. It follows that the real existence of an actual inﬁnite is not metaphysically possible."
That's from his refereed article in The Blackwell Companion to Natural Theology (2009), although he repeats it verbatim in various other places. As far as I can tell, it's just an invalid argument. In particular, Craig is unequivocally mistaken that his conclusion follows as he claims it does---unless of course the word "absurd" means something specialized, and entails in some way metaphysical impossibility. But I can't find that term ever defined or characterized in such a way, not even in Craig's own writings.
What do you guys think? Is Craig wrong that his conclusion follows from the premises? Or does the word "absurd" have some specialized meaning in philosophical discourse? Or something else that I'm missing?
EDIT: After receiving some curious responses, I think perhaps I've been unclear about my question. So here's my attempt at clarification:
Obviously, Craig is taking "absurd" to mean something that entails metaphysical impossibility. So, his argument as quoted isn't invalid when interpreted as such. Instead, my question could be rephrased as follows:
Is Craig's exposition of the argument precise and unambiguous?
Unless the term "absurd" has some specialized meaning in philosophy, then it seems the answer is no. In that case, it would be (IMO) unclear exactly what Craig means. But if "absurd" does have a specialized meaning, then I'd like to know.