Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 fom Posts: 1,968 Registered: 12/4/12
Re: Matheology S 224
Posted: Apr 14, 2013 5:41 PM

On 4/14/2013 3:40 PM, Nam Nguyen wrote:
> 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.
>

Then you are proving a point.

You do not present that which is requested of you.

You present what is irrelevant.

So, I just wasted my time in another post
correcting statements you made without relevance.

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