
Re: Matheology S 224
Posted:
Apr 16, 2013 8:08 AM


Nam Nguyen <namducnguyen@shaw.ca> writes:
> On 14/04/2013 9:29 PM, Jesse F. Hughes wrote: >> Nam Nguyen <namducnguyen@shaw.ca> writes: >> >>> On 14/04/2013 7:40 PM, Jesse F. Hughes wrote: >>>> Nam Nguyen <namducnguyen@shaw.ca> writes: >>>> >>>>> On 14/04/2013 4:58 PM, Nam Nguyen wrote: >>>>>> 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: >>>>>>>>>>> >>>>>>>>>>> Can you or they give me a straightforward statement of understanding >>>>>>>>>>> or not understanding of Def1, Def2, F, F' I've requested? >>>>> >>>>>> 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. >>>>> >>>>> Naturally _everyone_ who could constructively contribute to the closure >>>>> would be welcomed. And if I miss anyone in the below list I'd like >>>>> to apologize in advance. >>>>> >>>>> In particular, with some reasons no so important of my own, I'd >>>>> like appreciate in advance if Chris Menzel, Herman Rubin, Franz >>>>> Fritsche, Aatu Koskensilta, George Greene, Dave Seaman, Rupert, >>>>> Jim Burns, could offer some analysis and closure on my Def1 and Def2 >>>>> as presented in: >>>>> >>>>> http://groups.google.com/group/sci.math/msg/e6f47fad548fbb97?hl=en >>>> >>>> You sure seem eager for some comments. I know I'm not on the list, >>>> but I'll bite. >>> >>> First is my nontechnical caveat about the list of names. It obviously >>> can only be a finite list so any in which way I would have listed, >>> an apparent "offending" would occur however unintentionally. And I >>> did apologize in advance for that. To prove the point, after I sent >>> out the list I realized I forgot to mention Mike Oliver. The reason >>> for the finite list, as I've said is of _my own reason but isn't an_ >>> _important one_ . >>> >>> Based on some dialogs in the past, I believe correctly or incorrectly >>> those I mentioned _might_ be aware of some of the technical motivation >>> behind my presenting for years. That's all: just the motivation; I >>> certainly did _not_ chose the list based on who I'd think be "on my >>> side", so to speak. >>> >>> In any rate, I did invite "_everyone_ who could constructively >>> contribute ...". >>> >>>> >>>> , >>>>  Given a set S: >>>>  >>>>  Def1  If an individual (element) x is defined to be in S in a finite >>>>  manner or inductively, then x being in S is defined an absolute >>>>  truth. >>>>  >>>>  Def2  If an individual (element) x isn't defined to be in S in a >>>>  finite manner or inductively, then then x being in S, or not, >>>>  is defined as a relative truth, or falsehood, respectively >>>>  >>>>  Would you et al. understand Def1 and Def2 definitions now? >>>> ` >>>> >>>> I don't understand the definitions at all, because I don't know what >>>> it means that "x is defined to be in S in a finite manner or >>>> inductively." >>> >>> Let's do the finite case first, and I will address the "inductively" >>> case after. >>> >>> The finite case is the quite similar to the definition of FOL >>> syntactical theorems, where a proof of a formula is a _finite_ >>> _sequence of proofsteps_ conforming to a certain patterns (of >>> application of rules of inference). We have no choice but take >>> for granted what certain priori, "finite", "sequence", "steps", >>> etc... would mean. >>> >>> What Def1 says in the finite case is that given a set S, if an >>> element x is proven, verified to be in a nonempty _finite subset_ >>> of S then x being a member of S is defined to be an absolute truth. >>> Naturally here we also take for granted what it'd mean by "finite >>> subset", an element being in a set or not, to know or to verify an >>> element to be or not to be in a finite set, etc... >> >> It seems to me that we are mixing syntactic and semantic notions here. > > It only appears so; and there's no mixing or mixed up. >> >> Do you mean: let t and s be any terms of the language of ZF (or >> whatever) and suppose that >> >> ZF  (E x)(x c s & x != {} & x is finite & t in x) >> >> then "t in s" is an absolute truth. > > As the presenter, and for clarity purposes, I'm going to reiterate what > I emphasized with Rupert in a related thread: my presentation _is about_ > _language structures_ and _not about formal systems_ . > > Hence, any counter argument using formal system, formal system > provability, such as "" or the like, will _not be within_ the > parameters, the assumptions, the _context of my presentation_ > and I'd have an option not to address it. > > If I use part of the language L(ZF), I'll only use it as a _shorthand_ > _notation_ for _what I present in meta level_ .
Fine.
So, let M be a language structure for ZF, and let x and S be elements of M. Then,
if x is proven/verified to be in a nonempty subset of S, then x in S is an /absolute truth/.
So, some questions:
Is there any difference between "x is proven to be in a nonempty subset of S" and "x is in a nonempty subset of S"?
Why the nonempty subset of S stuff?
x in S <> x in {x} & {x} c S, so *every* element of S is in some nonempty subset of S.
Gotta run. I may try to look at the rest later.
 Jesse F. Hughes
"I talk with bigger fish who are playing different games."  James S Harris has a way with the metaphor.

