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

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 Frederick Williams Posts: 2,164 Registered: 10/4/10
Re: Matheology S 224
Posted: Apr 20, 2013 5:53 AM

Nam Nguyen wrote:
>
> On 19/04/2013 8:42 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 a first order
> > language which has a binary relation symbol 'e' interpreted as the 'is
> > an element of' relation between sets (though not in the way you have
> > written).

>
> Which specific way that I've used the symbol 'e' contrary to its usual
> interpretation?
>

> > What makes you think that there is no first order language
> > with a unary predicate (say) 'p' with 'px' interpreted as 'x is proven'
> > among formulae? I refer you to provability logic.

>
> If "provability logic" isn't First Order Logic, then it's not relevant
> to the context I'm talking _here about Def-1, Def-2_ .

If. My remark was about your claim that "x is in a non-empty subset of
S" could be expressed as a FOL formula, but "x is proven to be in a
non-empty subset of S" could not. It depends on what predicate and
relation symbols are in the language and how they are interpreted. My
'px' may be a formula in a FO language, just as your 'x e y' may be.

--
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