Date: Feb 28, 2013 5:16 PM
Subject: Re: Matheology § 222 Back to the roots
On 28 Feb., 22:29, Virgil <vir...@ligriv.com> wrote:
> > > You think that describing this situation as
> > > "there is a line which contains all FISs
> > > of d"
> > > is sensible.
> > Every FIS of d.
> In standard languages, including both English and German,
> "not all x" and "not every x" both require existence of an x which is
> not whatever is under discussion.
These languages are not suitable to talk about mathematical infinity.
IN infinite sets "not all x" is a triviality, because "all x" is a
faslity. Even the set "all natural numbers have divisor 1" is wrong,
because there is no thing named "all natural numbers". Every natural
number can be divided by 1 without remainder.
"Every natural number is positive." Correct.
"All natural numbers are positive." False. At least completely
meaningless like "tutum trara is blue".