Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Jesse F. Hughes

Posts: 9,776
Registered: 12/6/04
Re: Matheology S 224
Posted: Apr 16, 2013 8:08 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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 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.

>
> 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 non-empty 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 non-empty
subset of S" and "x is in a non-empty subset of S"?

Why the non-empty subset of S stuff?

x in S <-> x in {x} & {x} c S,

so *every* element of S is in some non-empty 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.


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

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.