
Re: Matheology S 224
Posted:
Apr 14, 2013 11:54 PM


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. > > 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. > >>> In fact, I understand almost none of that phrase. I don't know what >>> it means for x to be "defined to be in S", much less so defined "in a >>> finite manner or inductively". >> >> I'm not sure I understand your objection here: isn't defining a set S >> is defining certain elements x's _to be in S_ ? > > That's certainly not how I would put it. Is there any difference > between the following two statements? > > x is defined to be in S. > > x is in S. > >>> So, there you have it  a response >> >> Sure. Likewise I think I've explained your concern, in the finite case. >> >> Are you with me so far? > > Not particularly, but we'll see how it goes. > I'm going to be offline for tonight. I'll continue tomorrow or so.
Cheers,
  There is no remainder in the mathematics of infinity.
NYOGEN SENZAKI 

