2010/8/2 Brent Meeker <meeke...@dslextreme.com> > On 8/1/2010 3:42 PM, Quentin Anciaux wrote: > > > > 2010/8/2 Brent Meeker <meeke...@dslextreme.com> > >> On 8/1/2010 3:24 PM, Brian Tenneson wrote: >> >> I quite agree that counting and the existence of numbers are different. >> >> The Peano axioms for numbers makes it seem like numbers are not dependent >> on us humans to exist which entails that there are infinite sets by assuming >> an induction property held by (sets of) numbers. >> >> So while counting may not have been around forever, numbers have, >> independent of us humans. The Peano axioms are totally free of human >> baggage >> >> >> I don't think so. Where's the natural instance of "successor". "This is >> a successor of that" seems to me a human conceptualization based on the >> mental equivalent of moving pebbles into a group. That it can be done >> indefinitely is merely a convenient assumption. >> >> Brent >> >> > The only problem is if numbers were a human invention... other humans could > come with a prime number that is even and not 2... There would exists a > biggest number, 1+1=2 could be false somewhere sometime (even by following > the rules that makes 1+1=2 true always)... > > > They can and do. In modulo two arithmetic 1+1=0. You can invent all kinds > of number systems or other logics and axiomatic systems. > > You did not read entirely... quoting: 'even by following the rules that makes 1+1=2 true always'
rules == axiomatic systems. So if you use the standard definition of addition in base 10.. 1+1=2 always, if it's a human invention, it can be otherwise somewhere sometimes even if you use the standard definition of addition in base 10. > > > Mathematical truth are independent of humans, life and the universe and the > rest, it's nonsense if it's otherwise. > > > What's "it's" in the above sentence? > It's, is the fact that mathematical truths are independent of humans. Quentin > > Brent > > > > Quentin > > > >> >> and did not need Peano to utter them in order for numbers to exist. >> Consequently, I believe most if not all of math is discovered. >> >> The formalism for counting as describing a one-to-one correspondence to a >> (formally defined) finite set of numbers also exists independent of humans >> in the same way that the unit circle exists. The formalism for counting is >> of course not how biological machines such as we count; the formalism is >> just meant to intuitively express what we actually do when we count. >> >> Brent Meeker wrote: >> >> On 7/29/2010 3:28 PM, Mark Buda wrote: >> >> Quantum mechanics suggests maybe not. If there were no conscious observers >> to collapse the wave function of the universe after the big bang, then what, >> pray tell, would constitute an atom that might be counted? >> >> This assumes that conscious observers are necessary to collapse the wave >> function, of course. >> -- >> Mark Buda <her...@acm.org> >> I get my monkeys for nothing and my chimps for free. >> >> >> ------------------------------ >> On Jul 29, 2010 2:01 PM, Brian Tenneson >> <tenn...@gmail.com><tenn...@gmail.com>wrote: >> >> Numbers existed before people on this rock began to understand them. If >> not number of atoms in the universe, then the number of cells in organisms >> one day prior to 10,000 years ago. or anything really, that had the >> potential to be counted, one day prior to 10,000 years ago. >> >> >> I don't think the existence of some number of distinct things is the same >> as the "existence" of numbers. Numbers are defined by order and successor - >> neither of which are present or implicit in a mere collection of atoms or >> anything else. >> >> Brent >> -- >> You received this message because you are subscribed to the Google Groups >> "Everything List" group. >> To post to this group, send email to everything-l...@googlegroups.com. >> To unsubscribe from this group, send email to >> everything-list+unsubscr...@googlegroups.com. >> For more options, visit this group at >> http://groups.google.com/group/everything-list?hl=en. >> >> >> -- >> You received this message because you are subscribed to the Google Groups >> "Everything List" group. >> To post to this group, send email to everything-l...@googlegroups.com. >> To unsubscribe from this group, send email to >> everything-list+unsubscr...@googlegroups.com. >> For more options, visit this group at >> http://groups.google.com/group/everything-list?hl=en. >> >> >> -- >> You received this message because you are subscribed to the Google Groups >> "Everything List" group. >> To post to this group, send email to everything-l...@googlegroups.com. >> To unsubscribe from this group, send email to >> everything-list+unsubscr...@googlegroups.com<everything-list%2bunsubscr...@googlegroups.com> >> . >> For more options, visit this group at >> http://groups.google.com/group/everything-list?hl=en. >> > > > > -- > All those moments will be lost in time, like tears in rain. > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To post to this group, send email to everything-l...@googlegroups.com. > To unsubscribe from this group, send email to > everything-list+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en. > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To post to this group, send email to everything-l...@googlegroups.com. > To unsubscribe from this group, send email to > everything-list+unsubscr...@googlegroups.com<everything-list%2bunsubscr...@googlegroups.com> > . > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en. > -- All those moments will be lost in time, like tears in rain. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
