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JoshuaZ comments on Open Thread: May 2010, Part 2 - Less Wrong
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I'm not aware of any strong emphasis on this argument. It seems at first glance to be problematic at multiple levels.
One problem with your approach is that humans have evolved in a single, very well-behaved universe. So we have intuition both from instinct and from internalized experience that makes it very hard for us to tell what is actually a logical contradiction and what is not. Indeed, one of the reasons I suspect that so many people have issues with things like special and general relativity as well as quantum mechanics is that they can't get over that these aspects of the universe don't fit well with their intuitions.
Consider for a moment what a universe would look like where 1 + 1 did not equal 2. What would that look like? It isn't clear to me that this is even a meaningful question. But that may be because these concepts are so ingrained in us that we can't think without them. Thus, it may be that math works well for understanding the universe because humans have no other option. One could imagine us meeting an alien species that has some completely different but very effective way of understanding the universe that isn't isomorphic to math at all.
Logical operation is quite well defined, with or without regards to human perception of that logic. The idea that logic may not be understood does not contradict the idea that an internal logic (may) underlie physical systems. (Note, maybe see my clarification below, here. )
Granted logic is somewhat mysterious and it is hard to imagine what a different kind of logic would look like. However, that is immaterial to my idea. The idea is just that you have signatures of illogic (e.g., both statements (a.) if A, then B, and (b.) if A, then not B, both true at the same time) which seem to be non-present in physical systems.