ONT Re: Model Theory

[Jon Awbrey <jawbrey@oakland.edu>]

¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤

John Collier wrote (JC):
Jon Awbrey wrote (JA):

JA, quoting Chang & Keisler:

    | We shall say that @S@ is 'inconsistent'
    | iff we have @S@ |- q for all sentences q.
    | Otherwise, we say that @S@ is 'consistent'.

JC: I am not going to answer this one, Jon.
    I have other work to do.

JA: I am guessing that you did not intend your remark to serve
    as an example of a self-referent performative contradiction,
    so I will just thank you for participating in this experiment
    as long as you did.  To sum it up from where I stand and look
    at it, we have established that usage differs in regard to the
    concept of consistency, even among those thinkers who have been
    blessed to flourish in the light of Twentieth Century Mannerism,
    that some people care about usage and its differentiations, that
    is, so long as they have nothing better to do, and that is enough
    for my purposes, since it releases our pro-academic inhibitions
    against thinking for ourselves, and, well, allows us to begin
    thinking for ourselves, which means, most likely, that we may
    find no point of convergence within our finite lifetimes,
    however much hope we may have that there might be one,
    somewhere, somewhen, somehow.  So goes my Canon in D.

JC: Jon,  The definitions make no difference whatsoever to logic,
    as long as they are introduced predicatively.  I see no reason
    to spend time with this.  They can however be misleading.  Consider,
    if you will, the reference of the term "inconstant".

The escape viscosity of logic from definition makes me swoon,
So hie me away to look up "impredicate" in my well-worn rune,
But why do I get a suggesture that I have just been e-mooned?
And here I imagined that you would appreciate the definition
Of formless forms of constituent inconsistency that elide to
Draw any distinction at all in a space of syntactic instants,
Posing a form of constancy that is constant all too constant.

Jon Awbrey

¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤