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

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 namducnguyen Posts: 2,777 Registered: 12/13/04
Re: Matheology S 224
Posted: Apr 20, 2013 4:43 PM

On 17/04/2013 9:53 PM, Nam Nguyen wrote:
> On 17/04/2013 5:56 AM, Jesse F. Hughes wrote:
>

>> Footnotes:
>> [1] I won't use "[", since it has no different meaning than "{" as
>> near as I can figger, and serves only to confuse me.

>
> See. You're confused there: '[' encodes/represents an individual and
> has nothing to do with set. In fact, in the following set-string:
>
> (1') { {, [[]] }
>
> the second occurrence of '{' encodes/represents an individual, and
> has nothing to do with set, the way the 1st occurrence would.
>
>

> > Iow, would you acknowledge that if a set is finite, we can _encode_
> > any of its set-membership truth or falsehood?

>
> Let me ask you a simpler question:
>
> Would you now acknowledge that if a set is finite, we can _encode_
> the set?

Assuming you understand that for a finite set we can _encode_
structure theoretical truths of FOL expressions, formulas, I'll
go ahead the case of Def-1 inductive (infinite) case.

(The caveat is if we don't see eye-to-eye on the this finite case
of Def-1, we wouldn't go further and would be back to the finite case).

<quote>

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

</quote>

Before addressing the "inductively" case of Def-1, let me preempt
slightly and give a peek into a simple example of a relativistic
truth, regarding to set-membship.

Let U0, U1, U3 be sets defined as:

- U0 = { [] }
- U1 = {} c this.set
- U2 = U0 u U1

Now our SN (Set Notation) language) has been augmented with:

- 'c' which stands for 'is a subset'.
- 'u' stands for set union operation,
- 'this.set' stands for the underlying set in the context,
(U1 in the example above).

Now then the formula Axy[x=y] is relativistically true about
the set-membership of U2.

Note that there's nothing relativistic the set existence U2 itself:
it's either a singleton, or not: nothing in between. But it's the
truth, the knowledge, the description, the interpretation, of or
about the set existence that is relativistic.

"Truth" therefore is a relativistic notion in general (in this context).

--
----------------------------------------------------
There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI
----------------------------------------------------

Date Subject Author
4/12/13 Alan Smaill
4/12/13 namducnguyen
4/12/13 Frederick Williams
4/12/13 fom
4/13/13 namducnguyen
4/13/13 fom
4/13/13 namducnguyen
4/13/13 fom
4/13/13 namducnguyen
4/13/13 Peter Percival
4/13/13 namducnguyen
4/13/13 Peter Percival
4/13/13 namducnguyen
4/13/13 Peter Percival
4/13/13 namducnguyen
4/13/13 Jesse F. Hughes
4/14/13 namducnguyen
4/14/13 namducnguyen
4/14/13 namducnguyen
4/14/13 Peter Percival
4/14/13 fom
4/14/13 namducnguyen
4/14/13 fom
4/14/13 namducnguyen
4/14/13 namducnguyen
4/14/13 fom
4/14/13 namducnguyen
4/14/13 namducnguyen
4/14/13 namducnguyen
4/14/13 Jesse F. Hughes
4/14/13 namducnguyen
4/14/13 Jesse F. Hughes
4/14/13 namducnguyen
4/16/13 namducnguyen
4/16/13 namducnguyen
4/16/13 Jesse F. Hughes
4/16/13 namducnguyen
4/16/13 fom
4/17/13 namducnguyen
4/17/13 fom
4/17/13 namducnguyen
4/17/13 Jesse F. Hughes
4/17/13 Jesse F. Hughes
4/17/13 namducnguyen
4/20/13 namducnguyen
4/17/13 Frederick Williams
4/17/13 Frederick Williams
4/17/13 fom
4/17/13 Frederick Williams
4/17/13 fom
4/17/13 fom
4/18/13 namducnguyen
4/18/13 Frederick Williams
4/18/13 namducnguyen
4/19/13 Frederick Williams
4/19/13 namducnguyen
4/20/13 Frederick Williams
4/19/13 Frederick Williams
4/19/13 namducnguyen
4/20/13 Frederick Williams
4/14/13 Jesse F. Hughes
4/14/13 namducnguyen
4/14/13 namducnguyen
4/14/13 Jesse F. Hughes
4/14/13 namducnguyen
4/14/13 Peter Percival
4/15/13 Peter Percival
4/14/13 namducnguyen
4/14/13 namducnguyen
4/13/13 Frederick Williams
4/13/13 Peter Percival
4/13/13 Peter Percival
4/13/13 namducnguyen
4/15/13 Peter Percival
4/13/13 fom
4/13/13 namducnguyen
4/13/13 Peter Percival
4/13/13 namducnguyen
4/13/13 Frederick Williams
4/14/13 Frederick Williams
4/14/13 namducnguyen
4/13/13 Peter Percival
4/13/13 namducnguyen
4/13/13 namducnguyen