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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 18, 2013 10:12 PM

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".
>
> 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?

--
----------------------------------------------------
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