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 [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
