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I studied philosophy in university and I recall that one of my tutors for symbolic logic was trying to walk me through a problem by saying that if you have a large enough set of premises, two of them will inevitably contradict one another. I've always had trouble understanding (and consequently, accepting) this proposition because: if one conceives of reality as a set of claims (e.g., I am right-handed, electron X is in position Y, 2 + 2 = 4, etc.) there are an infinite number of "premises" to the "argument" that is reality and consequently reality is self-contradictory. Am I missing something here? Can you explain which of us is right about this and in which sense? I should mention that I don't necessarily have a problem with reality being self-contradictory, but that really throws symbolic logic out the window (and doesn't throw it out the window at the same time)! Thanks to all respondents for their time.
-JAK

Better: There's a fairly simple proof that this is false. Just consider the theory consisting of the sentence letters p1, p2, .... This theory is clearly consistent. It'd be an amusing question just how easy the proof is, i.e., exactly what sorts of theories are needed for the proof.

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