[FOM] Seeking sage advice on terminology

[paul at personalit.net]

Given that one implies merely the existence of some unspecified proof in 
PA, while the other implies the existence of a specific proof which is 
given, one may always say "there is a proof of FLT such that _____" vs. 
"the proof of FLT such that _____," and in each case the blank _____ 
will be filled in with a different condition, either by referring to a 
system in which there is a proof, PA, or by referring to a unique proof 
in PA.  Sage advice this may not be, but it's one way to talk about this 
that avoids multiplication of terminology by leveraging the difference 
between existential quantification and definite description in our 
language of use.

-paul hollander

>
> When I write about proofs of FLT I always have trouble finding a 
> graceful terminology to distinguish proving FLT in PA versus proving 
> in proof theory that PA |- FLT.
>
> I don't mean the conceptual distinction is difficult.  I mean I'd like 
> a cleaner terminology for it so i don't keep using "proof" to mean two 
> different things.  Maybe the literature I have been reading does have 
> a solution but if so I have not absorbed it.
>
> Do people here have conventions they use?
>
> best, Colin