Our late friend Reuben Hersh was interested in these questions. --- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505
505 670-9918 Santa Fe, NM On Mon, Sep 6, 2021, 7:58 PM Eric Charles <eric.phillip.char...@gmail.com> wrote: > As I said a few days ago: I think traditionally, "mathematical" would > have been synonymous with "rigorous deduction from a minimal number of > axioms", but I doubt that approach is clear cut anymore. > > I am pretty confident that modern mathematics is WAY more open-field than > that. The Stanford Encyclopedia of Philosophy seems to agree with that > intuition, though I think it is an even broader topic than implied by just > this entry: Non-Deductive Methods in Mathematics (Stanford Encyclopedia > of Philosophy) > <https://plato.stanford.edu/entries/mathematics-nondeductive/> > > > <echar...@american.edu> > > > On Mon, Sep 6, 2021 at 11:19 AM Barry MacKichan < > barry.mackic...@mackichan.com> wrote: > >> Briefly, and in my opinion, mathematics can only make claims like ‘if A >> is true then B is true’. To say B is true, you must also say A is true. >> Eventually you have to go back to the beginning of the deductive chain, and >> the truth of the initial statement is inductive, not deductive or >> mathematics. You can predict the time and place of an eclipse, and this >> prediction is based on mathematics and a mathematical model of reality — >> Newton’s laws in this case. But the truth of this prediction is inductive >> since the initial positions and velocities for the calculation are >> inductive, as is the applicability of Newton’s laws to reality, and even >> the ‘fact’ that mathematics can describe the universe is inductive. >> >> And Einstein showed that the applicability of Newton’s laws was in fact >> wrong and offered a new model — which we inductively accept as true, if >> only provisionally. >> >> Mathematics cannot prove any statement about the real world. Any such >> statement will depend at some point on an inductive truth or a definition. >> >> —Barry >> >> On 3 Sep 2021, at 18:10, thompnicks...@gmail.com wrote: >> >> Ok, is mathematics (logic, etc.) a way of arriving at true propositions >> distinct from observation or are mathematical truths different from >> empirical truths? >> >> - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . >> FRIAM Applied Complexity Group listserv >> Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam >> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com >> FRIAM-COMIC http://friam-comic.blogspot.com/ >> archives: http://friam.471366.n2.nabble.com/ >> > - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . > FRIAM Applied Complexity Group listserv > Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam > un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > FRIAM-COMIC http://friam-comic.blogspot.com/ > archives: http://friam.471366.n2.nabble.com/ >
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