SUO: Re: Monoclonal Antebodies
On Fri, Jun 13, 2003 at 02:46:33PM -0400, Jon Awbrey wrote:
> o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
>
> i apollogize for being so plodding, chris, but i have deliberately
> put myself in a "keep it concrete and simple" frame of mind for the
> sake of my (auto-)tutorial exercises,
All the more reason to put them back on the Ontology list where they can
be nicely organized and easy to review. I really don't know why, other
than that you like to hear yourself talk and think others find it
equally thrilling, you do not make use of that perfectly good forum.
Your voice there is the dominant one by design and those who are truly
interested can study your thoughts undisturbed.
> so let me just try to think of some of the simpler questions that have
> always worried me here.
>
> 1. how does one, working solely within your favorite version of fol,
> express the fact that functions are special cases of relations?
>
> 2. how does one, within the bounds of fol reason alone,
> manage simple types of isomorphisms, like the fact
> that a function of type f : X -> (Y -> Z) is ~=~
> to a function of type f' : Y -> (X -> Z)?
I am rather confounded as to the relevance of these questions. FOL is a
framework for defining classes of languages and a certain type of
mathematical semantics for those languages. In and of itself it has
nothing to do with the concepts involved in your questions. Both of the
questions can only arise in contexts in which one has a notion of
function, relation, and isomorphism. Typically, that's set theory. In
the case of (1), one provides familiar definitions of the notions of
function and relation, from which it follows (or not, as the case may
be) that the former is a species of the latter. Analogously for (2).
I don't even see what your questions have to do with FOL, unless you are
simply alluding to tired old arguments about unintended interpretations.
Chris Menzel