|
|
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
|
|
