Here he claims that "abstract thought (as classical philosophers pointed out) is inherently an immaterial ability and thus it cannot arise from the brain or from any material organ". Actually, there's no evidence at all for this claim. As far as we know, abstract thought is no different from any kind of brain activity, carried out by our neurons and synapses. And if it does not "arise from the brain", what could it possibly arise from?
Abstract reasoning is actually not significantly different from any other kind of reasoning, a point of view espoused for the specific case of mathematical reasoning by George Lakoff and Rafael Nunez in their book Where Mathematics Come From: How The Embodied Mind Brings Mathematics Into Being.
Egnor claims that "Mental activity always has meaning—every thought is about something. Computation always lacks meaning in itself." This is a classic blunder, made by people who have little understanding of the nature of computation. Of course computations have meaning. When we sum the infinite series 1+1/4+1/9+... using a program such as Maple, by typing sum(1/n^2,n=1..infinity); who can reasonably deny that the answer Π2/6 it produces has meaning? This classic error was debunked as long ago as 1843, when Ada Lovelace wrote, "Many persons who are not conversant with mathematical studies, imagine that because the business of the engine is to give its results in numerical notation, the nature of its processes must consequently be arithmetical and numerical, rather than algebraical and analytical. This is an error. The engine can arrange and combine its numerical quantities exactly as if they were letters or any other general symbols; and in fact it might bring out its results in algebraical notation, were provisions made accordingly." This is an abstract example, but if you want examples related to the real world, just consider the data collected and processed to produce weather predictions. If these computations had no meaning, how is it that short-term weather forecasts are so accurate?
Egnor goes on to justify his bogus claim by saying, "A word processing program doesn't care about the opinion that you’re expressing when you use it." But what does this have to do with anything? A secretary that types up letters also probably doesn't care about the content of the letters the boss dictates; does this mean he/she has no mind? How did we get from "meaning" to "caring"? It's a huge non sequitur that Egnor doesn't bother to explain.
In another screed, Egnor repeats for the n'th time his bogus claims about the minds of animals. He writes, "No animal (except man) can do statistics, because statistical reasoning is abstract and only human beings are capable of abstract thought." But, as usual, he ignores the evidence against his claim, and provides not a shred of evidence in favor of it. All he does is assert. (Three links: one, two, three. I can produce many more.)
He closes with this, which is one of the least self-aware claims I've ever seen: "Only human beings can reason abstractly because only human beings have rational souls. Rational souls have an immaterial aspect—a spiritual aspect, because we are created in the Image of our Creator, who is a Spirit. That's a scientific inference."
No, that's just religious babble.