Here's my contribution:
RationalWiki -- William Lane Craig
Quote:William Craig denied the Number Zero
In his debate with Professor Sir Peter Millican, a great philosopher at Oxford University, Craig said (beginning at the 1:18:00 mark) that the "number zero probably does not exist".[76] Just prior to that and in other debates, Craig treats the concept of infinite sets as being equinumerous, a view that was popular among mathematicians prior to the proofs of Georg Cantor, but which have been universally abandoned among all mathematicians. While he incorrectly cites the BGV theorem as supporting an "absolute beginning" to the Universe, Craig rejects Cantor's theorem, a mathematical proof that relies upon no physical presuppositions about the Cosmos, which is the case with the BGV theorem, which assumes a 4-dimension Lorentzian metric on a pseudo-Riemannian manifold where superluminal information exchange ("faster than light" communication) is a physical impossibility, hence, the past incompleteness of certain geodesics in inflationary models of the Universe [77]. It should also be noted that Craig rejects Professor Vilenkin's naturalistic model of the Universe which he says that he "interacts with" [78], but, in fact, outright rejects.[79] Of course, Dr. Craig does not reveal to any of his audiences that he thinks that some of Professor Vilenkin's ideas are fundamentally flawed. For instance, Vilenkin subscribes to multiverse theory, which Craig is himself critical of.[80] In his debate with Professor Alex Rosenberg, Craig states, "Even if our universe is just a tiny part of a so-called multiverse composed of many universes their (the BGV) theorem requires that the multiverse itself must have had an absolute beginning."[81] However, the BGV theorem [82] nowhere contains the word "multiverse" nor does it make any reference to it whatsoever. This is a prima facie example of Craig making things up to suit his "argument of the moment".
Misunderstanding of transfinite arithmetic
In his debate with Professor Millican and elsewhere, Craig claims that "infinity minus infinity is undefined in transfinite arithmetic..." This claim is abjectly false -- in transfinite arithmetic, infinity minus infinity is indeterminate. A mathematical operation that is indeterminate has more than one solution,[83] in many instances, an infinite number of solutions, but such is typical. Consider the following equation: 2x + 3y = 16. Under the set of real numbers, there are an infinite number of solutions, that is, values of 'x' and 'y' that will make the equation true. But, there is absolutely nothing wrong with this; in physics, one can have a general solution to a differential equation, and from there, the initial conditions will specify the particular solution of the equations. This is fundamentally different than saying that something is undefined, which means that there is no solution to the problem. Craig's understanding of set theory, and mathematics, in general, is woefully inadequate.
It should be noted that the idea of a countably infinite set (such as Professor Sir Roger Penrose's Conformal cyclic cosmology model)[84] is simply an example of a veridical paradox,[85] such as the Monty Hall problem[86] or Hilbert's Hotel.[87] A veridical paradox is one which produces a result that appears absurd, but is demonstrated to be true nevertheless.
Appeal to the now-discredited Opera experiment
During the debate with Millican, Craig appeals to the now-discredited Opera experiment[88] to support the idea of "absolute simultaneity" of events. Craig is a proponent of the long-abandoned neo-Lorentzian conception of "relativity",[89] which enjoys no support (including from Vilenkin) among physicists alive today.
RationalWiki -- William Lane Craig
