
Re: Matheology § 224
Posted:
Apr 13, 2013 2:10 PM


On 13/04/2013 11:47 AM, Peter Percival wrote: > Nam Nguyen wrote: > >> Peter asked me specifically what the relativity of >> truth value of a formula be in the context of language >> structure. >> >> And I gave a clear cut example of an F being absolutely true >> in a M, and the truth of a F' being relativistic in the same M. >> >> Would you or would you not understand, in that example, that >> the truth of a F' is relativistic as defined there? > > An example is not the same as a definition. An example may help to > explain a definition but it cannot stand in place of a definition.
You might not be aware but I already defined that when discussing with Rupert in the other related thread.
But here in this thread I already mentioned with you that structure theoretical truth is defined in term of setmembership truth.
Therefore, it's sufficient to define what it means by absolute/relative setmembership truth.
Given a set S:
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
Would you et al. understand Def1 and Def2 definitions now?
If you do, the truthvalue an formula F in a structure M being relative would be just a consequential definition from Def2.
  There is no remainder in the mathematics of infinity.
NYOGEN SENZAKI 

