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Topic: Matheology § 224
Replies: 84   Last Post: Apr 20, 2013 4:43 PM

 Messages: [ Previous | Next ]
 Peter Percival Posts: 20 Registered: 4/11/13
Re: Matheology § 224
Posted: Apr 13, 2013 1:04 PM

Nam Nguyen wrote:

> On 12/04/2013 6:59 PM, fom wrote:
> > On 4/12/2013 8:45 AM, Nam Nguyen wrote:
> >> On 12/04/2013 3:29 AM, Alan Smaill wrote:
> >>> Nam Nguyen <namducnguyen@shaw.ca> writes:
> >>>

> >>>> But what is "meta-logic of the meta-language", in the context of FOL
> >>>> structure? Or is that at best just intuition and at worst just a
> >>>> buzzword?

> >>>
> >>> You tell us that it is possible to reason about language structures.
> >>> What logic are you using to do that -- or is that at best just
> >>> intuition?

> >>
> >> I've used FOL ( _First Order Logic_ ) definitions that one should be
> >> familiar with.
> >>

> >
> > Nam,
> >
> > I told you before. The textbooks are very bad about
> > all of these things.

>
> > ==========================================
>
> > ==========================================
> >
> > With the first two definitions technically being
> > axioms because the symbols may not be eliminated
> > through substitution. That is why the signature
> > is formally introduced initially as
> >
> > <<M, |M|>, <c, 2>, <e, 2>>
> >
> > Obviously, I cannot specify an infinite domain.

>
> Exactly, fom. You, I, et al. don't seem to have a disagreement here.
>
> What we seem to have is a difference in understanding in where we
> _can_ go from here, i.e., from one "cannot specify an infinite
> domain"!
>
> My presentation over the years is that it does _not_ matter
> what, say, Nam, fom, Frederick, Peter, ... would do to
> "specify an infinite domain", including IP (Induction Principle),
> a cost will be exacted on the ability to claim we know, verify,
> or otherwise prove, in FOL level or in metalogic level.

If you wish to formalize your model theory you may do so in, say, ZFC.
You then get omega axiomatically.

> The opponents of the presentation seem to believe that with IP
> we could go as far as proving/disproving anything assertion,
> except it would be just a matter of time. Which sounds like
> Hilbert's false paradigm of a different kind.
>
> That's the difference on the two sides.

A side is a line segment, i.e., a continuum of a certain kind. You, on
the other hand, seem to be an isolated point.

Date Subject Author
4/12/13 Alan Smaill
4/12/13 namducnguyen
4/12/13 Frederick Williams
4/12/13 fom
4/13/13 namducnguyen
4/13/13 fom
4/13/13 namducnguyen
4/13/13 fom
4/13/13 namducnguyen
4/13/13 Peter Percival
4/13/13 namducnguyen
4/13/13 Peter Percival
4/13/13 namducnguyen
4/13/13 Peter Percival
4/13/13 namducnguyen
4/13/13 Jesse F. Hughes
4/14/13 namducnguyen
4/14/13 namducnguyen
4/14/13 namducnguyen
4/14/13 Peter Percival
4/14/13 fom
4/14/13 namducnguyen
4/14/13 fom
4/14/13 namducnguyen
4/14/13 namducnguyen
4/14/13 fom
4/14/13 namducnguyen
4/14/13 namducnguyen
4/14/13 namducnguyen
4/14/13 Jesse F. Hughes
4/14/13 namducnguyen
4/14/13 Jesse F. Hughes
4/14/13 namducnguyen
4/16/13 namducnguyen
4/16/13 namducnguyen
4/16/13 Jesse F. Hughes
4/16/13 namducnguyen
4/16/13 fom
4/17/13 namducnguyen
4/17/13 fom
4/17/13 namducnguyen
4/17/13 Jesse F. Hughes
4/17/13 Jesse F. Hughes
4/17/13 namducnguyen
4/20/13 namducnguyen
4/17/13 Frederick Williams
4/17/13 Frederick Williams
4/17/13 fom
4/17/13 Frederick Williams
4/17/13 fom
4/17/13 fom
4/18/13 namducnguyen
4/18/13 Frederick Williams
4/18/13 namducnguyen
4/19/13 Frederick Williams
4/19/13 namducnguyen
4/20/13 Frederick Williams
4/19/13 Frederick Williams
4/19/13 namducnguyen
4/20/13 Frederick Williams
4/14/13 Jesse F. Hughes
4/14/13 namducnguyen
4/14/13 namducnguyen
4/14/13 Jesse F. Hughes
4/14/13 namducnguyen
4/14/13 Peter Percival
4/15/13 Peter Percival
4/14/13 namducnguyen
4/14/13 namducnguyen
4/13/13 Frederick Williams
4/13/13 Peter Percival
4/13/13 Peter Percival
4/13/13 namducnguyen
4/15/13 Peter Percival
4/13/13 fom
4/13/13 namducnguyen
4/13/13 Peter Percival
4/13/13 namducnguyen
4/13/13 Frederick Williams
4/14/13 Frederick Williams
4/14/13 namducnguyen
4/13/13 Peter Percival
4/13/13 namducnguyen
4/13/13 namducnguyen