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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 14, 2013 4:40 PM

On 14/04/2013 9:19 AM, Nam Nguyen wrote:
> On 14/04/2013 12:44 AM, Nam Nguyen wrote:
>> On 13/04/2013 7:10 PM, Jesse F. Hughes wrote:
>
>>
>> Now that that has been spelled out, however unnecessarily, what's next?
>>
>> Can you or they give me a straightforward statement of understanding
>> or not understanding of Def-1, Def-2, F, F' I've requested?
>>

>
> I don't remember if I asked Chris Menzel directly or he might have just
> been in the post, but once (iirc) I wondered if there is a way to
> express something like "There are infinitely many individuals" _without_
> any non-logical symbols.
>
> I did define the "Mx (Many quantifier) and 0x (Null quantifier)" in:
>
>
> <quote>
>
> (1) Mx[P(x)] df= There exist more than one x such that P(x).
> (2) 0x[P(x)] df= There exists no x such that P(x).
>
> </quote>
>
> And in the post:
>
>
>
> I did define:
>
> - The "I-form (Inductive) of infinity expression":
>
> (I)P(*) <-> Ex[P(x)] /\ AxEy[P(x) -> (P(y) /\ Ez(y = x + Sz))]
>
> - The "aI-form (anti-Inductive) of infinity expression":
>
> (aI)P(*) <-> Ex[P(x)] /\ AxEy[P(x) -> (P(y) /\ (x < y))]
>
> The long and short of it I've been frustrated that the Many Quantifier
> Mx doesn't make a lot of logical sense: how many should be logically
> considered as "many"? But now I see in Mx and 0x (The Null quantifier)
> a quite relevancy to the relativity of the truth values of cGC and its
> negation ~cGC.
>
> The difficulty in the Mx quantifier is actually a reflection on the
> need of introducing to FOL new logical quantifiers:
>
> - Ix (There are infinitely many x's)
> - Fx (There are finitely many x's)
>
> Where some of the _traditional_ rules of inference on these two new
> quantifiers are:
>
> - Ix <-> ~Fx /\ Fx <-> ~Ix
> - Ix -> Ex.
>
> And of one of the new "Anti-Inference" rules is:
>
> - From Fx one shall _not_ infer Ex.
>
> More properties and rules might be forwarded, but these definitions
> will bring more crisp the reasons why the there exists the relativity
> of the truth values of cGC and its negation ~cGC
>
> [To be continued ...]

Apropos out of nothing, the caveat here is that the issue of the
relativity of the truth value of cGC in the naturals is an _independent_
issue from the suggested new FOL with the 2 new quantifiers Ix and Fx.

And one doesn't have to discuss about these 2 new quantifier in
discussing the issue of cGC.

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