
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 setstring: > > (1') { {, [[]] } > > the second occurrence of '{' encodes/represents an individual, and > has nothing to do with set, the way the 1st occurrence would. > > I asked you previously: > > > Iow, would you acknowledge that if a set is finite, we can _encode_ > > any of its setmembership 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 Def1 inductive (infinite) case.
(The caveat is if we don't see eyetoeye on the this finite case of Def1, we wouldn't go further and would be back to the finite case).
For convenience, I had before:
<quote>
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
</quote>
Before addressing the "inductively" case of Def1, let me preempt slightly and give a peek into a simple example of a relativistic truth, regarding to setmembship.
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 setmembership 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 

