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

 Messages: [ Previous | Next ]
 Frederick Williams Posts: 2,164 Registered: 10/4/10
Re: Matheology S 224
Posted: Apr 19, 2013 7:55 AM

Nam Nguyen wrote:
>
> On 18/04/2013 7:19 AM, Frederick Williams wrote:

> > Nam Nguyen wrote:
> >>
> >> On 17/04/2013 8:48 AM, fom wrote:

> >>> On 4/17/2013 9:36 AM, Frederick Williams wrote:
> >>>> Nam Nguyen wrote:
> >>>>

> >>>>> "x is in a non-empty subset of S" could be _expressed_ as a FOL language
> >>>>> expression: x e S' /\ Ay[ y e S' -> y e S].
> >>>>>
> >>>>> On the other hand, in "x is proven to be in a non-empty subset of S",
> >>>>> the _meta phrase_ "is proven" can not be expressed by a FOL language:
> >>>>> "is proven" pertains to a meta truth, which in turns can't be equated
> >>>>> to a language expression: truth and semantics aren't the same.

> >>>>
> >>>> "x is in a non-empty subset of S" can be expressed in the language of a
> >>>> first order theory with a binary predicate e. The intended meaning of e
> >>>> is given by the non-logical axioms of that theory.

> >>
> >> Frederick seemed to be confused: what I'm doing here has nothing to
> >> do with formal systems, theories, axioms of formal systems.

> >
> > You wrote:
> >
> > '"x is in a non-empty subset of S" could be _expressed_ as a FOL
> > language expression: x e S' /\ Ay[ y e S' -> y e S].'
> >
> > How does the FOL expression express "x is in a non-empty subset of S"?
> > It can only do so if "e" has a particular meaning. How is that meaning
> > established?

>
> By establishing the interpretation that "e" would mean "is a member of".

How is that done? Note that "is a member of" does not have one
meaning.

> > Also, as I remarked elsewhere, "x e S' /\ Ay[ y e S' -> y e S]" doesn't
> > express "x is in a non-empty subset of S".

>
> Why?

It says that x is in S' and S' is a subset of S.

--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting

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