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

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 namducnguyen Posts: 2,777 Registered: 12/13/04
Re: Matheology S 224
Posted: Apr 19, 2013 11:18 PM

On 19/04/2013 5:55 AM, Frederick Williams wrote:
> 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.

So how many meanings it would have? 10? 14? Can you list out all the
meanings it would have?

>
>>> 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.

How does that contradict that it would express "x is in a non-empty
subset of S", in this context where we'd borrow the expressibility
of L(ZF) as much as we could, as I had alluded before?

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