This one surprised me.
I often point out in my discussions the bounds of logic (including different kinds of logic), and where logic is not applicable or is a discipline that is merely ancillary to some other, more pertinent discipline. I’ve often made the point that logic is merely one branch of philosophy, and that it does not apply as some sort of absolute law or penumbra underlying all of existence. Logic applies only in chains of implication.
Rules of logic, for example, do not govern the scientific method. In first order logic, A and Not A are contradictions. But in science, just because one theory is false does not mean that some other theory is true. I’ve recently used the examples of Newton, Einstein, and Heisenberg to make this point. Newton’s work was not rendered false by Einstein, and Einstein’s work was not rendered false by Heisenberg. The reason for that is that those men dealt with matters that were not chains of implication.
Now, that is not to say that they did not employ logic in the course of their work — they did indeed employ logic each time they solved an equation or simplified a mathematical expression, for example. But science, like logic, is a branch of philosphy. It can prove nothing to be true, but only proves things to be false. It is based upon a different principle than logic. Logic is based on the principle of non-contradiction, but science is based on the principle of falsifiability.
Another example I’ve brought up is the futility of applying logic to subjective emotion and experience. A man can be both overweight AND knowledgable about the perils of obesity. Calling such a man “illogical” is misguided. It is so often the case that what a man knows and what he wills are two different things. Smoking is along those same lines.
With respect to my mentioning often the inability to prove one’s own existence, that is again an indictment of logic in a situation where logic does not apply. Such a proof is obviously a futile exercise in begging the question; therefore, logic fails to validate our existence, and well it should.
With respect to the issue of being unable to prove a negative, I only rebut it, so far as I know, when I encounter it. I don’t bring it up out of the blue, but I do quickly point out its absurdity — particularly when it has been invoked in an attempt to prove a point. That seems only right, especially here at Straight Dope.
Nevertheless, I have left the impression with you that I over-logicate, even when at least half my discussion of logic is to point out how irrelevant it is. I will have to examine how I can improve my expository skills. Thanks for the advice.