Critique of J. Kim's "P is not equal to NP by Modus Tollens"

This paper is a critique of version three of Joonmo Kim's paper entitled "P is not equal to NP by Modus Tollens. [arXiv:1403.4143v3]" After summarizing Kim's proof, we note that the logic that Kim uses is inconsistent, which provides evidence that the proof is invalid. To show this, we will consider two reasonable interpretations of Kim's definitions, and show that "P is not equal to NP" does not seem to follow in an obvious way using any of them.