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A very good introductory talk on the philosophy of mathematics by Ray Monk. He considers the issue of the nature of mathematical truth, what mathematics is actually about, and discusses the views of Plato, Aristotle, Immanuel Kant, Frege and Bertrand Russell…
From the time of Plato onwards, people have regarded mathematical truth as an ideal. Unlike ordinary, empirical truth, it is held that mathematical truth is eternal, incorrigible, and certain. This talk looks at the ways in which philosophers have tried to account for the special nature of mathematical truth.
Ray Monk is a British philosopher well known for his writings on Wittgenstein, Bertrand Russell, and the physicist J. Robert Oppenheimer.
This talk is part of the Philosophy Cafe series given at the University of Southampton. Subtitles/transcript have been added.
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well in defense of pythagoras, all sides that can't be expressed as whole numbers aren't in the world. ;)
Delightful talk by Monk, thank you for posting this!
Mathematics is model, and model is a simplified representation of reality. Things like knowledge and human mind are also models (simplified representation of reality). This, in my view, was what Kant was talking about.
I trust the next posted lecture will be about Godel's Incompleteness Theorem which, to my limited understanding, if it doesn't eviscerate Frege and Russell's notions about objective truth in mathematics (even more so than Russell's paradox), it at least sheds important light on how to think about their ideas.
And when Monk uses the word "class" is that the same as the more frequently used "set"?
So Kant was partly right, Mathematics is analytical after all. IT's about the consequences of axioms, which consequences are implied in the given axioms (tautology). And Russel and his friend shows it's all an extension of Logic.
He didn't even mention Godel :(
I added subtitles/transcript.
I'd like to hear the Q&A period. Do you have a link to the original recording?
Math is actually a priori analytic though, isn't it? All the relationships of numbers are true by internal symmetry of the terms being used. The definition of each number implies and contains it's definition and relationship to other numbers.
Observation of numerical relationships in the world might be synthetic, but pure mathematics is always analytic, isn't it?
Thank you very much.
thank you – really enjoyed that