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: >> >> https://groups.google.com/group/sci.logic/msg/8fd316ddcfc09e5c?hl=en >> >> <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: >> >> http://groups.google.com/group/comp.ai.philosophy/msg/58615203416c4d7e?hl=en >> >> >> >> 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.