Quentin Anciaux wrote: > 2009/6/6 Torgny Tholerus <tor...@dsv.su.se>: > >> Jesse Mazer skrev: >> >>> >>>> Date: Sat, 6 Jun 2009 16:48:21 +0200 >>>> From: tor...@dsv.su.se >>>> To: everything-list@googlegroups.com >>>> Subject: Re: The seven step-Mathematical preliminaries >>>> >>>> Jesse Mazer skrev: >>>> >>>>> Here you're just contradicting yourself. If you say BIGGEST+1 "is then >>>>> a natural number", that just proves that the set N was not in fact the >>>>> set "of all natural numbers". The alternative would be to say >>>>> BIGGEST+1 is *not* a natural number, but then you need to provide a >>>>> definition of "natural number" that would explain why this is the case. >>>>> >>>> It depends upon how you define "natural number". If you define it by: n >>>> is a natural number if and only if n belongs to N, the set of all >>>> natural numbers, then of course BIGGEST+1 is *not* a natural number. In >>>> that case you have to call BIGGEST+1 something else, maybe "unnatural >>>> number". >>>> >>> OK, but then you need to define what you mean by "N, the set of all >>> natural numbers". Specifically you need to say what number is >>> "BIGGEST". Is it arbitrary? Can I set BIGGEST = 3, for example? Or do >>> you have some philosophical ideas related to what BIGGEST is, like the >>> number of particles in the universe or the largest number any human >>> can conceptualize? >>> >> It is rather the last, the largest number any human can conceptualize. >> More natural numbers are not needed. >> > > What is the last number human can invent ? Your theory can't explain > why addition works... If N is limited, then addition can and will (in > human lifetime) create "number" which are still finite and not in N. >

It is very unlikely that anyone will get to the number 10^10^100 by addition. :-) Would agree that a any given time there is a largest number which has been conceived by a human being? > N can be defined solelly as the successor function, you don't need > anything else. You just have to assert that the function is true > always. > > >>> Also, any comment on my point about there being an infinite number of >>> possible propositions about even a finite set, >>> >> There is not an infinite number of possible proposition. >> > > Prove it please. > That would seem to turn on the meaning of "possible". Many (dare I say "infinitely many") things are logically possible which are not nomologically possible (although the posters on this list seem to doubt that). 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-list@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 -~----------~----~----~----~------~----~------~--~---