Will the real mathematical logic please stand up.

[BaalChatzaf]

Here is a pretty good summary of the field of mathematical (or formal) logic as it exists, as opposed to the cartoon animated version presented, from time to time, by some Objectivists.

http://en.wikipedia.org/wiki/Mathematical_Logic

You will not find anything effete or bitten with hatred mentioned in the above article.

One may fairly raise the question as to how useful mathematical logic is.

Its main application has been in the field of computer science, to wit, determining the class of mathematical functions which could in principle be computed (in finite time). An offshoot of that study is the theory of feasible computations, which determines which problems can be solved in polynomial time and which can only be solved in exponential time. The theory of NP Complete and NP Hard problems is one of the important developments of this theory.

Boolean algebra has been used for nearly fifty years to determine the optimal circuitry for standard computations in von Neuman type computers. The idea is to minimize either the number of switching components necessary to do the computation or minimize the amount of "wiring" connecting the components. It turns out that the problem of computing optimal circuits is NP Complete so engineers are still required to use their wits to solve this problem, rather than plugging it into an algorithm.

In quantum physics there has been investigation into the problem of applying classical logic in quantum theoretic matters. It turns out the classical logic with the law of the excluded middle collides with the famous double slit experiment. Some resolution has been found by using logic whose underlying algebra is weaker than that for distributive lattices. Since the result of the double slit is a matter of empirical fact, it is of some importance to find out where and why classical logical cannot handle the matter. Ideally we would like our formal logic to be at home in the world of facts. If classical logic has difficulty, then what system that is "nearly classical" will fit in with the facts?

Ba'al Chatzaf