In article <email@example.com>, Han de Bruijn <firstname.lastname@example.org> wrote:
> On Jan 24, 11:02 am, LudovicoVan <ju...@diegidio.name> wrote: > > On Jan 23, 8:31 pm, LudovicoVan <ju...@diegidio.name> wrote: > > > > > On Jan 23, 7:47 pm, Craig Feinstein <cafei...@msn.com> wrote: > > > > > > [...] > > > > In our real world, it is a known fact that 3+4=7. But how can we be > > > > sure that there are no invisible pixies running around taking balls > > > > away from us causing us to think that 3+4=7 when really 3+4=8? > > > > > > My point is that mathematics is considered a deductive science, in > > > > which everything is absolutely certain. But how can mathematics prove > > > > that the above scenario cannot be true? > > > > > I don't think mathematics is a deductive science: mathematics is > > > hardly a science at all. OTOH, in a world were 3+4=7, I'd also expect > > > 1=/=0: i.e. no mathematical fact exists in isolation... > > > > Thinking: It is logic that grounds mathematics, i.e. it is logic that > > gives mathematics its initial premise and final validation. > > > > -LV > > How can that be, if Mathematical Logic is a branch of mathematics ? > It is NOT logic that grounds mathematics. It is rather mathematics > that grounds logic. (And physics grounds mathematics, but that is .. > quite another story)
Except that, at least historically, mathematics preceded physics.
Agriculture and Commerce, but not physics, preceded mathematics (agriculture gave rise to geometry and commerce to arithmetic).