Jesse Mazer skrev:
> > Date: Wed, 10 Jun 2009 09:18:10 +0200
> > From: tor...@dsv.su.se
> > To: email@example.com
> > Subject: Re: The seven step-Mathematical preliminaries
> > Jesse Mazer skrev:
> >>> Date: Tue, 9 Jun 2009 18:38:23 +0200
> >>> From: tor...@dsv.su.se
> >>> To: firstname.lastname@example.org
> >>> Subject: Re: The seven step-Mathematical preliminaries
> >>> 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.
> >> OK, so how do you say I should define this type of "universe"? Unless
> >> you are demanding that I actually give you a list which spells out
> >> every symbol-string that qualifies as a member, can't I simply provide
> >> an abstract *rule* that would allow someone to determine in principle
> >> if a particular symbol-string they are given qualifies? Or do you have
> >> a third alternative besides spelling out every member or giving an
> >> abstract rule?
> > You have to spell out every member.
> Where does this "have to" come from? Again, is it something you have a
> philosophical or logical definition for, or is it just your aesthetic
It is, as I said above, for me and all other humans to understand what
you are talking about. It is also for to be able to decide what
deductions or conclusions or proofs that are legal or illegal. It has
nothing to do with my aesthetic preference.
> > Because in a *rule* you are
> > (implicitely) using this type of "universe", and you will then get a
> > circular definition.
> A good rule (as opposed to a 'bad' rule like 'the set of all sets that
> do not contain themselves') gives a perfectly well-defined criteria
> for what is contained in the universe, such that no one will ever have
> cause to be unsure about whether some particular symbol-string they're
> given at belongs in this universe. It's only "circular" if you say in
> advance that there is something problematic about rules which define
> infinite universes, but again this just seems like your aesthetic
> preference and not something you have given any philosophical/logical
> justification for.
What do you mean by "some particular symbol-string"?
I suppose that you mean by this is: If you take any particular
symbol-string from this universe, then no one will ever have cause to be
unsure about whether this symbol-string belongs in this universe. So
you are defining "this universe" by supposing that you have "this
universe" to start with. Is that not a typical circular definition?
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