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: email@example.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. 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. > You can only > create a finite number of proposition with finite length during your > lifetime. What is a lifetime . What is truth ? Either you ****CAN*** define a limit or you ***CAN'T***. > Just like the number of natural numbers are unlimited but > finite, so are the possible propositions unlimited but finte. ****EVERY*** ***MEMBER*** of the set ***N*** is ****************************FINITE********************************* >> or about my question about whether you have any philosophical/logical >> argument for saying all sets must be finite, > > 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. Mostly > that set is "all objects in the universe", and if you stay inside the > universe, there is no problems. But as soon you go outside universe, > you must be carefull with what substitutions you do. If you have "all" > quantified with all object inside the universe, you can not substitute > it with an object outside the universe, because that object was not > included in the original statement. > >> as opposed to it just being a sort of aesthetic preference on your >> part? Do you think there is anything illogical or incoherent about >> defining a set in terms of a rule that takes any input and decides >> whether it's a member of the set or not, such that there may be no >> upper limit on the number of possible inputs that the rule would >> define as being members? (such as would be the case for the rule 'n is >> a natural number if n=1 or if n is equal to some other natural number+1') > > In the last sentence you have an implicite "all": The full sentence > would be: For all n in the universe hold that n is a natural number if > n=1 or if n is equal to some other natural number+1. And you may now be > able to understand, that if the number of objects in the universe is > finite, then this sentence will just define a finite set. > > -- > Torgny Tholerus > > > > I will read the rest (and others) email later unfortunatelly. -- 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 firstname.lastname@example.org 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 -~----------~----~----~----~------~----~------~--~---