On Tuesday, September 25, 2018 at 7:36:48 PM UTC-5, Bruce wrote: > > Elementary arithmetic, such as 2+2=4, is tautologically true. In other > words, if is true by virtue of the meaning of the terms involved. It has no > ontological content outside itself. So arithmetic is used in physics, but > that does not mean that anyone necessarily assumes arithmetic realism, or > platonism. Mathematics is used because it is useful, not because it is true > in any sense other than tautologically. > > Arithmetic (and, indeed, all of mathematics) can be regarded as a formal > system, with a number of defined symbols and rules of inference. Any > sequence of the allowed symbols can be written down. Any such sequence is a > theorem if it can be derived from the basic axioms using the allowed rules > of inference. If it cannot be so derived, it is not a theorem. The status > of some sequences of symbols may be undecidable; and some sequences may be > true for other reasons, even though they are not theorems. There is little > else to mathematics than this. > > Bruce >
When the subject of 'what is mathematics' comes up, I say now "It's a genre of fiction, maybe the most useful one." In the context of what's true, like the recent Michael Atiyah proof (or many say not-proof) of the Riemann Hypothesis, and in another case of the abc conjecture [ https://www.quantamagazine.org/titans-of-mathematics-clash-over-epic-proof-of-abc-conjecture-20180920/ ], I say "If it isn't formalized in and proven in Coq yet, it's not true." Take 2+2=4. A proof in Coq: [ https://brilliant.org/discussions/thread/2-2-4-in-coq/ ]. This is "What's true in mathematics is just what some computer outputs." And that's that. :) - pt -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
