
Re: Matheology S 224
Posted:
Apr 18, 2013 10:12 PM


On 18/04/2013 7:19 AM, Frederick Williams wrote: > Nam Nguyen wrote: >> >> On 17/04/2013 8:48 AM, fom wrote: >>> On 4/17/2013 9:36 AM, Frederick Williams wrote: >>>> Nam Nguyen wrote: >>>> >>>>> "x is in a nonempty subset of S" could be _expressed_ as a FOL language >>>>> expression: x e S' /\ Ay[ y e S' > y e S]. >>>>> >>>>> On the other hand, in "x is proven to be in a nonempty subset of S", >>>>> the _meta phrase_ "is proven" can not be expressed by a FOL language: >>>>> "is proven" pertains to a meta truth, which in turns can't be equated >>>>> to a language expression: truth and semantics aren't the same. >>>> >>>> "x is in a nonempty subset of S" can be expressed in the language of a >>>> first order theory with a binary predicate e. The intended meaning of e >>>> is given by the nonlogical axioms of that theory. >> >> Frederick seemed to be confused: what I'm doing here has nothing to >> do with formal systems, theories, axioms of formal systems. > > You wrote: > > '"x is in a nonempty subset of S" could be _expressed_ as a FOL > language expression: x e S' /\ Ay[ y e S' > y e S].' > > How does the FOL expression express "x is in a nonempty subset of S"? > It can only do so if "e" has a particular meaning. How is that meaning > established?
By establishing the interpretation that "e" would mean "is a member of". > > Also, as I remarked elsewhere, "x e S' /\ Ay[ y e S' > y e S]" doesn't > express "x is in a nonempty subset of S".
Why?
  There is no remainder in the mathematics of infinity.
NYOGEN SENZAKI 

