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

 Messages: [ Previous | Next ]
 namducnguyen Posts: 2,777 Registered: 12/13/04
Re: Matheology S 224
Posted: Apr 19, 2013 9:08 PM

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_ .

>
> When you wrote 'truth and semantics aren't the same' did you mean 'truth
> and syntax aren't the same'? Or, perhaps, syntax and semantics aren't
> the same; though G\"odel and Carnap taught us that a lot of semantics
> can be reduced to syntax (but not all, pace Tarski).

I'm talking about what I already said above: "truth and semantics
aren't the same".

The formula "m=n" has the semantics that the individual m equals to
the individual n. Yet, what's the truth value of this formula?

Do you understand now that "truth and semantics aren't the same"?

--
----------------------------------------------------
There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI
----------------------------------------------------

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