BRACERS Record Detail
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BR has read his paper on mathematical logic which has given him "much new information." "It is fifty years since I worked seriously at mathematical logic and almost the only work that I have read since that date is Gödel's. I realized, of course, that Gödel's work is of fundamental importance, but I was puzzled by it. It made me glad that I was no longer working at mathematical logic. If a given set of axioms leads to a contradiction, it is clear that at least one of the axioms must be false. Does this apply to school-boys' arithmetic, and, if so, can we believe anything that we were taught in youth?"
"I should like to make a few general remarks about my state of mind while Whitehead and I were doing the Principia. What I was attempting to prove was, not the truth of the propositions demonstrated, but their deducibility from the axioms. And, apart from proofs, what struck me as important was the definitions."
"More generally, Aristotelian logic is almost exclusively concerned with propositional functions having only one variable. The philosophies of Spinoza, Leibniz and Hegel are entirely dependent on this limitation."
"If you can spare the time, I should like to know, roughly, how, in your opinion, ordinary mathematics—or, indeed, any deductive system—is affected by Gödel's work."
Record last modified 2015/05/19
Created/last modified by wolfeaa