On 14/04/2013 7:40 PM, Jesse F. Hughes wrote: > Nam Nguyen <firstname.lastname@example.org> 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 Def-1, Def-2, 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 Def-1 and Def-2. >>> >>> I'm serious in saying that it's crucial to my thesis about >>> cGC. If such a simple definition of set-membership truth-relativity >>> 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 Def-1 and Def-2 >> 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 non-technical 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: > | > | Def-1 - 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. > | > | Def-2 - 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 Def-1 and Def-2 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 proof-steps_ 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 Def-1 says in the finite case is that given a set S, if an element x is proven, verified to be in a non-empty _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...
> > 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_ ? > > 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?
-- ---------------------------------------------------- There is no remainder in the mathematics of infinity.