Date: Mar 22, 2013 10:09 PM
Author: Virgil
Subject: Re: Matheology � 224

In article <FImdnfw3_ePXa9HMnZ2dnUVZ_q-dnZ2d@giganews.com>,
fom <fomJUNK@nyms.net> wrote:

> 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)


Couldn't Ax(phi(x)) be true when Ex(phi(x)) isn't?
E.G.,
All four sided triangles have less than three sides.
and
There is a four sided triangle having less than three sides.

> 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.

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