Rethinking logic: logic in relation to mathematics,evolution, and method

摘要

Godel's theorem showing the impossibility of proving the consistency of arithmetic raises serious questions about the role of logic in mathematics and indeed in science in general. One consequence of this is that the axiomatic approach to discovery is of necessity somewhat limited. The goal of encoding knowledge within a system that would permit the logical deduction of all truths is no longer viable, if indeed it ever was. What then can serve as a "logic of discovery"?