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Topic: Matheology § 224
Replies: 84   Last Post: Apr 20, 2013 4:43 PM

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namducnguyen

Posts: 2,699
Registered: 12/13/04
Re: Matheology S 224
Posted: Apr 14, 2013 11:54 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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 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...

>
> 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
----------------------------------------------------


Date Subject Author
4/12/13
Read Re: Matheology § 224
Alan Smaill
4/12/13
Read Re: Matheology § 224
namducnguyen
4/12/13
Read Re: Matheology § 224
Frederick Williams
4/12/13
Read Re: Matheology § 224
fom
4/13/13
Read Re: Matheology § 224
namducnguyen
4/13/13
Read Re: Matheology § 224
fom
4/13/13
Read Re: Matheology § 224
namducnguyen
4/13/13
Read Re: Matheology § 224
fom
4/13/13
Read Re: Matheology § 224
namducnguyen
4/13/13
Read Re: Matheology § 224
Peter Percival
4/13/13
Read Re: Matheology § 224
namducnguyen
4/13/13
Read Re: Matheology § 224
Peter Percival
4/13/13
Read Re: Matheology § 224
namducnguyen
4/13/13
Read Re: Matheology § 224
Peter Percival
4/13/13
Read Re: Matheology § 224
namducnguyen
4/13/13
Read Re: Matheology S 224
Jesse F. Hughes
4/14/13
Read Re: Matheology S 224
namducnguyen
4/14/13
Read Re: Matheology S 224
namducnguyen
4/14/13
Read Re: Matheology S 224
namducnguyen
4/14/13
Read Re: Matheology S 224
Peter Percival
4/14/13
Read Re: Matheology S 224
fom
4/14/13
Read Re: Matheology S 224
namducnguyen
4/14/13
Read Re: Matheology S 224
fom
4/14/13
Read Re: Matheology S 224
namducnguyen
4/14/13
Read Re: Matheology S 224
namducnguyen
4/14/13
Read Re: Matheology S 224
fom
4/14/13
Read Re: Matheology S 224
namducnguyen
4/14/13
Read Re: Matheology S 224
namducnguyen
4/14/13
Read Re: Matheology S 224
namducnguyen
4/14/13
Read Re: Matheology S 224
Jesse F. Hughes
4/14/13
Read Re: Matheology S 224
namducnguyen
4/14/13
Read Re: Matheology S 224
Jesse F. Hughes
4/14/13
Read Re: Matheology S 224
namducnguyen
4/16/13
Read Re: Matheology S 224
namducnguyen
4/16/13
Read Re: Matheology S 224
namducnguyen
4/16/13
Read Re: Matheology S 224
Jesse F. Hughes
4/16/13
Read Re: Matheology S 224
namducnguyen
4/16/13
Read Re: Matheology S 224
fom
4/17/13
Read Re: Matheology S 224
namducnguyen
4/17/13
Read Re: Matheology S 224
fom
4/17/13
Read Re: Matheology S 224
namducnguyen
4/17/13
Read Re: Matheology S 224
Jesse F. Hughes
4/17/13
Read Re: Matheology S 224
Jesse F. Hughes
4/17/13
Read Re: Matheology S 224
namducnguyen
4/20/13
Read Re: Matheology S 224
namducnguyen
4/17/13
Read Re: Matheology S 224
Frederick Williams
4/17/13
Read Re: Matheology S 224
Frederick Williams
4/17/13
Read Re: Matheology S 224
fom
4/17/13
Read Re: Matheology S 224
Frederick Williams
4/17/13
Read Re: Matheology S 224
fom
4/17/13
Read Re: Matheology S 224
fom
4/18/13
Read Re: Matheology S 224
namducnguyen
4/18/13
Read Re: Matheology S 224
Frederick Williams
4/18/13
Read Re: Matheology S 224
namducnguyen
4/19/13
Read Re: Matheology S 224
Frederick Williams
4/19/13
Read Re: Matheology S 224
namducnguyen
4/20/13
Read Re: Matheology S 224
Frederick Williams
4/19/13
Read Re: Matheology S 224
Frederick Williams
4/19/13
Read Re: Matheology S 224
namducnguyen
4/20/13
Read Re: Matheology S 224
Frederick Williams
4/14/13
Read Re: Matheology S 224
Jesse F. Hughes
4/14/13
Read Re: Matheology S 224
namducnguyen
4/14/13
Read Re: Matheology S 224
namducnguyen
4/14/13
Read Re: Matheology S 224
Jesse F. Hughes
4/14/13
Read Re: Matheology S 224
namducnguyen
4/14/13
Read Re: Matheology S 224
Peter Percival
4/15/13
Read Re: Matheology § 224
Peter Percival
4/14/13
Read Re: Matheology § 224
namducnguyen
4/14/13
Read Re: Matheology § 224
namducnguyen
4/13/13
Read Re: Matheology § 224
Frederick Williams
4/13/13
Read Re: Matheology § 224
Peter Percival
4/13/13
Read Re: Matheology § 224
Peter Percival
4/13/13
Read Re: Matheology § 224
namducnguyen
4/15/13
Read Re: Matheology § 224
Peter Percival
4/13/13
Read Re: Matheology § 224
fom
4/13/13
Read Re: Matheology § 224
namducnguyen
4/13/13
Read Re: Matheology § 224
Peter Percival
4/13/13
Read Re: Matheology § 224
namducnguyen
4/13/13
Read Re: Matheology § 224
Frederick Williams
4/14/13
Read Re: Matheology § 224
Frederick Williams
4/14/13
Read Re: Matheology § 224
namducnguyen
4/13/13
Read Re: Matheology § 224
Peter Percival
4/13/13
Read Re: Matheology § 224
namducnguyen
4/13/13
Read Re: Matheology § 224
namducnguyen

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