
Re: Matheology S 224
Posted:
Apr 14, 2013 6:58 PM


On 14/04/2013 4:28 PM, Nam Nguyen wrote: > On 14/04/2013 3:41 PM, fom wrote: >> 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 Def1, Def2, 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 nonlogical 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 "Iform (Inductive) of infinity expression": >>>> >>>> (I)P(*) <> Ex[P(x)] /\ AxEy[P(x) > (P(y) /\ Ez(y = x + Sz))] >>>> >>>>  The "aIform (antiInductive) 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 "AntiInference" 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. > > Jeezus! Can you just calm down chill out a little bit? > > That post of mine about the new quantifiers was written > for 2 reasons: > >  While waiting for Peter et al. to confirm a closure > on my Def1 and Def2 which is important to my entire > thesis about cGC, I was just _voluntarily thinking aloud_ > what _a possible postcGC new logic_ might look like; > and I indicated I've not completed all necessary thoughts > there yet. > > _Nobody_ had requested of me to do so and your rambling > "requested of [Nam]" here is baseless. > >  There might be those who might appreciate how the underlying > rationale behind the new quantifiers would explain the presented > existing relativity of cGC in the current FOL framework. > > If you're not one of those, feel free to ignore that post. > > Why are you not careful reflecting on what was written there, > before pouring acidity into the conversation?
Also, if you'd like to help the debate about my cGC thesis, why don't you offer a closure on my Def1 and Def2.
I'm serious in saying that it's crucial to my thesis about cGC. If such a simple definition of setmembership truthrelativity is technically wrong, inconsistent, or what have you, of course my entire thesis would falter to pieces. And you will never hear me attempt on the relativity of cGC truth anymore.
But I do need a closure on these 2 definitions.
  There is no remainder in the mathematics of infinity.
NYOGEN SENZAKI 

