Abstract of the lecture
A childhood interest in maps fostered my taste for structure and precision as well as curiosity about the world. Aptitude for mathematics emerged, and a leaning toward language and philosophy. In college I majored in mathematics with honors reading in mathematical logic. This subject was offbeat in America, but later gained glory through G?del's theorem and computer theory. I revealed in the rigor and economy of Whitehead and Russell's reduction of mathematics to a few symbols of logic and set theory. I even enhanced it, as had Tarski and G?del.
Besides reducing concepts by definitions, Whitehead and Russell reduced theory to axioms. Contradiction then threatened, in Russell's paradox of the class of all non-self-members. His solution involved complicating the grammar and infinitely reduplicating the objects of mathematics. I freed his solution from these drawbacks. This strengthened the system, again threatening contradiction. None has been found.
The paradoxes and G?del's theorem reveal the power of classes, in contrast to elementary logic. It is misleading to say mathematics reduces to logic. Say to logic and set theory.
Some balk at assuming classes and other abstract objects. But what does assuming an object consist in? Not in direct specification, but in repeated reference to an unspecified object of a specified sort. This lends structure to science. Science needs classes but no properties or meanings. These are in trouble over identity and difference.
As my logico-mathematical concerns rounded off in middle life, my attention turned more to the philosophy of natural science. But tidy parsimony is a beacon for natural science as well, and for its philosophy.