Failing to Debunk the Kalam Cosmological Argument of William Lane Craig

This video claims Craig is self-contradictory in his use of the mathematical idea of infinity.

Craig draws on Vilenkin's (et. al.) understanding of the "singularity." But Vilenkin speaks of temperatures in the singularity being "infinitely high" and the density of space becomes "infinitely high." The criticism is: Craig believes infinities do not exist, but he endorses the view of a cosmic singularity "which is riddled with infinities." (Says the video) Plus, says the unnamed woman doing the commentary, Craig and theists claim their God is "infinite and eternal." Re. the unnamed woman, I'll call her "Gretchen."



1. Craig affirms (following mathematician Lawrence Hilbert) the impossibility of an actual infinite.



2. Craig affirms Vilenkin's understanding of the cosmic singularity as being infinitely dense and having an infinitely high temperature.

3. Therefore, Craig contradicts himself.

But I think Gretchen commits a fallacy of equivocation on the term "infinite," as modifying "density." This means the singularity is a single point, with no denumerable points. I don't think Gretchen understands the Craig-Hilbert point which is that, conceptually, actual infinities are incoherent and lead to logical absurdities. Like, e.g., Hilbert's famous "hotel." But to couple "infinite" with "density" is to use the term, not to apply to any set of discrete entities, but metaphorically to describe the fully singular nature of one partless entity.

When conjoined with "temperature" to describe the heat of the singularity, it must be taken to mean somethign like "immeasurably high temperature." The temperature of the singularity could, in principle, be measured had we access to it and the instruments capable of measuring it. The temperature in the singularity would have a number, like all other physical events. Therefore the temperature would not be, literally, "infinite" (whatever that might mean, if anything).

One more point: many theologians do not claims God is "infinite and eternal." Gretchen here lacks theological and philosophical understanding. In the literature "infinite" and "eternal" do not mean the same thing. If, e.g., God is non-temporal outside his relation to creation, then "infinity" does not apply to God's existence. Bill Craig has written a lot about this subject. Gretchen, obviously, is ignorant of it.

After five minutes of watching Gretchen set this up, thinking she has shown a logical contradiction in Craig's reasoning, misunderstanding some basic terminology, and equivocating on "infinity," I see that she doesn't understnad what's going on, so I've decided not to watch any more.