0

Quote from Sir Edmund Taylor Whittaker from his essay in the symposium “What is Science?” written in 1955. He was discussing non-Euclidean geometry and the role of the parallel postulate in Euclidean geometry that led to the discussion of axioms in mathematics for centuries after Euclid’s Elements.

It now came to be accepted that the business of the mathematician is to deduce the logical consequences of the axioms he assumes at the basis of his work, without regard to whether these axioms are true or not; their truth or falsehood is the concern of another type of man of science - a physicist or a philosopher.

What are your thoughts on axioms in mathematics in general? Do you agree with Whittaker?

Paul Ash
  • 1,828
  • 2
    Big discussion here: https://math.stackexchange.com/questions/366834/does-mathematics-require-axioms – ShyPerson Aug 29 '21 at 19:32
  • Thanks guys!! Down the rabbit hole I go. – Paul Ash Aug 29 '21 at 19:45
  • 2
    Most physicists and engineers believe that infinite things and infinite processes don't exist in the real world. The fact that since Cantor many pure mathematicians have chosen to found their subject (pure mathematics) on infinite sets and infinite processes does put underlying tensions between applied mathematicians and pure mathematicians over the foundations of mathematics (assuming that all mathematics is indeed one extended body of knowledge, involving a single consistent language, with a single set of axiomatic foundations to be agreed). [Which it might not be] – James Arathoon Aug 29 '21 at 22:42
  • Connected : https://math.stackexchange.com/q/3791934 – Jean Marie Aug 30 '21 at 07:56
  • Yes, mathematicians are happy to adjust axioms as necessary, and employ logic more intensively than physicists and philosophers—but mathematicians are not pure logicians: they're ultimately still after useful systems, which either consistently models reality or which helps to develop or further unpack ideas. – ryang Aug 30 '21 at 08:51
  • Useful: Stewart Shapiro, We hold these truths to be self-evident (RSL, 2009) – Mauro ALLEGRANZA Sep 06 '21 at 14:10

0 Answers0