I have been reading about the problems of deductive and formal reasoning and lately finished the book on Goedel's proof by Nagel and Newman.
It got clear to me, that for every formal system, there exists a meta-system that can be derived (or used) to help to understand the nature of the original formal system. Some point out, that for intelligence, you would need to have meta-intelligence to derive understanding of what intelligence is. Some conclude further, that the meta-intelligence is "god" and can not be understood by intelligence. Somehow this is circular reasoning, and will not give "better" memes. What can be derived from this sort of reasoning however is some reaction we humans show to inconsistent reasoning. Meta-control mechanisms (= emotions) will point out that some processes are wasting time. See also a quote Marvin made in the newsgroup comp.ai.philosophy:
"I think that I've said before, that philosophy is mostly bad psychology. The most common reaction that "normal" people have to such propositions is -- after a few moments of thought -- to LAUGH! This is because, I'm sure, that the detection of absurdities (which include both asserting inconsistent propositions and exhibiting tabooed views of certain body-parts) activates certain brain centers that are used to prevent the rest of the brain from continuing normal reasoning. In other words, the machinery that prevents you from "taking it seriously". There's some more about this in chapter 27 of The Society of Mind.
Classical monotonic consistent logic was one of the first good ideas that came with the era of modern technical thinking about thinking. It came in the infancy of what we now call cognitive science. Philosophers played an important role in developing it.
Today that young organism, cognitive science, is approach puberty or, perhaps, middle age. Philosophers, it seems to me, with the exception of Dennet, Sloman, and a very few others, are fixated in that infantile stage. "
