> On 15 Sep 2020, at 20:16, 'Brent Meeker' via Everything List > <everything-list@googlegroups.com> wrote: > > > > On 9/15/2020 5:04 AM, Bruno Marchal wrote: >>> On 14 Sep 2020, at 19:32, 'Brent Meeker' via Everything List >>> <everything-list@googlegroups.com> wrote: >>> >>> >>> >>> On 9/14/2020 2:27 AM, Bruno Marchal wrote: >>>>> So if the axioms are conventions and the rules of inference are >>>>> conventions, then conventionalism is true. >>>> >>>> Not at all. You can say that the choice of axioms/definition is >>>> conventional (the rules of inference here are informal), but the non >>>> conventional part is in what follows from them, >>> ?? That's like saying that painting stop signs red is a convention, but >>> the fact that stop signs are red is not. >> ? >> >> It is more like saying that the axioms of arithmetic, and the definition of >> prime numbers, are conventional but that the truth of Euclid’s statement >> “there is no biggest prime” is not; or that the definition of group is >> conventional, but that the classification of finite simple groups is not. > > What is entailed by a convention is conventional.
My point is that the definition, the choice of axioms, etc. can arguably considered conventional, or even contingent, relying on our goal, which can be local and related to some human interest. Why study symmetries? Why study smooth varieties, or why study Saturn, Mars, … Where the convention stops is when we derive the consequences of the axioms, or the truth about the objects that we defined. It is the same in math and in physics. A witnessing of this is the use of computer in sorts of mathematical experimental exploration, like just observing where the Riemann critical zeros are. We have looked at billions of them, and they are all well situated on the critical line, confirming the Rieman Hypothesis “experimentally”. Now mathematician want proof, but, even if we find it, the result can hardly be described as conventional. If I was, let us convene that all zeroes behave well, and let us convene to send me the one million of dollars prize :) Bruno > > Brent > > -- > 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 view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/652aebc2-4550-73b7-e803-f8083743264c%40verizon.net. -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/3E6D3573-F8C7-4227-9A69-B7A485E29181%40ulb.ac.be.
