First, at the beginning of his post, Shallit engages in an ad hominem argument--essentially, "my opponent is ignorant and/or evil, so you should disregard what he or she says." Shallit claims that Egnor "knows little about linguistics, philosophy, or ethology." Such an argument is not really that compelling, especially since Shallit fails, in my opinion, to prove Egnor's supposed ignorance.
Second, Shallit is himself guilty of doing something he accuses Egnor of doing. In response to Egnor's claim that "reason is an immaterial power of the mind...[which] cannot logically be produced by a material thing," Shallit asserts: "This is vintage Egnor--a flat assertion, made with no evidence..." Later, he quotes Egnor: "This immaterial power of the soul is precisely what makes man qualitatively different from every other living thing. And I am not 'forced to lean on supernaturalism' by pointing this out. I'm merely making an observation that's obvious to all." Shallit responds:
Souls don't exist; there's no evidence for them. There's no evidence for "immaterial powers." Egnor's claim is disputed by many, and it's a plain lie to say "it's obvious to all."
It's ironic that Shallit accuses Egnor of making "a flat assertion, made with no evidence," and then proceeds to make a number of flat assertions himself, with no evidence. As a matter of fact, the idea that "there's no evidence for [the existence of souls]" is itself "disputed by many," including a number of philosophers. For example, Shallit might try reading J.P. Moreland's The Soul: How We Know It's Real and Why It Matters (Chicago: Moody Publishers), which presents quite a number of arguments for the existence of the soul.
Finally, I find it additionally ironic that Shallit is both a mathematician and an atheist. This is because atheism arguably fails to provide a rationale for accepting the truth of mathematics. As Nancy R. Pearcey and Charles B. Thaxton note in The Soul of Science: Christian Faith and Natural Philosophy:
...the puzzle remains that mathematics makes claims that go beyond the empirical world, while remaining uncannily accurate in its application to that world. Through mathematical formulations we grasp enough of what the world is like to fly a man to the moon, create a microchip, or remove a tumor from the brain. But there is no explanation why this remarkable consonance exists between the ideas in the human mind and the order of the physical world....
This is the dilemma of contemporary mathematical philosophy. The amazing "fit" of mathematical concepts to the physical world cries out for explanation--but without the assumption of divine creation by a reasonable God, there is no explanation. Mathematicians must act on sheer faith--a faith that lacks any basis. (p. 159)
Image of Jeffrey Shallit from Wikipedia.org