2010/8/2 Brent Meeker <meeke...@dslextreme.com> > On 8/2/2010 12:13 AM, Quentin Anciaux wrote: > > > > 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. > > > But that's like saying if you speak according to the rules of English you > will utter English sentences. It doesn't make English a fact of nature. > > Meaning of words can change and do change. Meaning of english words are dependant of humans. Meaning of mathematical thruths aren't.

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> > > >> >> >> 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. > > > Ah. The point in question is asserted. > > Brent > No, it's about the meaning. If mathematical truth are dependant on humans they mean utlimately nothing at all. So it's nonsensical. Quentin -- > 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.