On 3/22/2013 6:40 PM, Virgil wrote: > In article <1-KdnWUae4shRdHMnZ2dnUVZ_s-dnZ2d@giganews.com>, > fom <fomJUNK@nyms.net> wrote: > >> On 3/22/2013 4:49 PM, WM wrote: >>> >>> Fools stay together. >>> >> >> As observed before: >> >> Ex(phi(x)) -> Ax(phi(x)) >> >> is true in Wolkenmuekenheim > > And, far too often, so is > > Ax(phi(x)) -> Ex(phi(x)). >
Is that one not always true?
AxP(x) -> P(t)
P(t) -> ExP(x)
are both axiomatic.
That is not your background, however.
One of my objections involving the failure to distinguish foundational investigation from other types is that the body of mathematical statements used for practical application are not obtained with free variables in the premises and do not make assertions having free variables in the conclusions.
The "actuality" of any mathematical object in set theory as an instantiated object only occurs within the proper interior of a proof since the language has no individual constants.
Hence, my unhealthy fascination concerning the role of description theory.