Saturday, October 23, 2021

James A. Lindsay (Mathematician) vs. William Lane Craig on Actual Infinities and the Classical Theistic Concept of God

  

. . . if apologists like [William Lane] Craig want to take the tack that actual infinites exist only in the abstract, as I would, then since a divine being must exemplify an actual infinity of positive properties, such a divine being is itself necessarily abstract. On the other hand, if apologists like Craig wish to revise the claim that there are actual infinites present in the deity—making a case by special pleading for their increasingly abstruse God—then they face the fact that the existence of each infinity implies a larger infinity. This hand is no good for the apologist, though, because it undermines the meaningfulness of a “most high” being entirely, as we have seen. Curiously, then, given the situation, both “being infinite” and “not being infinite” seem to be positive properties for God, undermining Gödel’s second axiom.

 

There is no winning here. God simply cannot be “Most High,” neither finite nor infinite, neither quantitative nor qualitative. There is no such thing. Anselm’s argument ins only half-baked, due to a lack of solid understanding of imprecisely used concepts thrown about in a religious, and therefore, inappropriate, context. Of course, if the ontological argument actually did succeed in getting off the ground, the believer would be besought by the fact that it applies equally well for Muslims to believe in Allah, for the cantankerous to believe in Irony the Equivocator, and for any sort of divine being conceived as “most high.” It would still require a substantial amount of ink (and hopefully, though doubtfully, no more blood) to attempt to justify one choice over another. (James A. Lindsay, Dot Dot Dot: Infinity Plus God Equals Folly [Onus Books, 2013], 182-83)