Quentin Anciaux wrote: > 2009/6/9 Torgny Tholerus <tor...@dsv.su.se>: > >> Jesse Mazer skrev: >> >>> >>>> Date: Sat, 6 Jun 2009 21:17:03 +0200 >>>> From: tor...@dsv.su.se >>>> To: everything-list@googlegroups.com >>>> Subject: Re: The seven step-Mathematical preliminaries >>>> >>>> My philosophical argument is about the mening of the word "all". To be >>>> able to use that word, you must associate it with a value set. >>>> >>> What's a "value set"? And why do you say we "must" associate it in >>> this way? Do you have a philosophical argument for this "must", or is >>> it just an edict that reflects your personal aesthetic preferences? >>> >>> >>>> Mostly that set is "all objects in the universe", and if you stay >>>> >>> inside the >>> >>>> universe, there is no problems. >>>> >>> *I* certainly don't define numbers in terms of any specific mapping >>> between numbers and objects in the universe, it seems like a rather >>> strange notion--shall we have arguments over whether the number 113485 >>> should be associated with this specific shoelace or this specific >>> kangaroo? >>> >> When I talk about "universe" here, I do not mean our physical universe. >> What I mean is something that can be called "everything". It includes >> all objects in our physical universe, as well as all symbols and all >> words and all numbers and all sets and all other universes. It includes >> everything you can use the word "all" about. >> > > It includes all set, but no all set as it N includes all natural > number but not all natural number... excuse-me but this is non-sense. > Either N exists and has an infinite number of member and is > incompatible with an ultrafinitist view or N does not exists because > obviously N cannot be defined in an ultra-finitist way,

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That's not obvious to me. You're assuming that N exists apart from whatever definition of it is given and that it is the infinite set described by the Peano axioms or equivalent. But that's begging the question of whether a finite set of numbers that we would call "natural numbers" can be defined. To avoid begging the question we need some definition of "natural" that doesn't a priori assume the set is finite or infinite; something like, "A set of numbers adequate to do all arithmetic we'll ever need" (unfortunately not very definite). The problem is the successor axiom, if we modify it to S{n}=n+1 for n e N except for the case n=N where S{N}=0 and choose sufficiently large N it might satisfy the "natural" criteria. Brent > any set that > contains a finite number of natural number (and still you haven't > defined what it is in an ultrafinitist way) are not the set N. > > Also any operation involving two number (addition/multiplication) can > yield as result a number which has the same property as the departing > number (being a natural number) but is not natural number... Also > induction and inference cannot work in such a context. > > >> For you to be able to use the word "all", you must define the "domain" >> of that word. If you do not define the domain, then it will be >> impossible for me and all other humans to understand what you are >> talking about. >> > > Well you are the first and only human I know who don't understand > "all" as everybody else does. > > Quentin Anciaux > > >> -- >> Torgny Tholerus >> >> > > > > --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---