SUO: Policy On Substitutions
Pat Hayes wrote:
>
> > [Pat Hayes wrote:]
> > >
> > > Yes, I entirely agree. In fact there is a way
> > > to transcribe all of Hobbs' axioms and schemas
> > > (he has all this stuff worked out in enormous detail)
> > > into a slightly odd version of FOL (one that ought to
> > > appeal to Jon Awbry) in which every open sentence can
> > > be seen as a relation name (so you can write things
> > > like (R & Q)(a,b) to mean R(a,b) & Q(a,b) ), and all
> > > the 'things' in Hobbs' ontology become ways of talking
> > > about the things you or I would think were really there.
> > > (The cute part of this mapping is that one gets *exactly*
> > > the same conclusions, somewhat undercutting the ontological
> > > claims being made. Sorry, couldn't help a bit of public
> > > gloating there.)
>
> [Robert Kent wrote:]
> >
> > I don't know why this would appeal to Jon Awbry,
> > but I question why it is seen as a slightly odd
> > version of FOL. The idea that "every open sentence
> > can be seen as a relation name" seems quite natural,
>
> Yes, I agree it is natural (and an old idea), and to category theory folk
> it is like breathing, but it isn't part of the usual syntactic or inferential
> rules of FOL, is all I meant: it is much more like higher-order logic (HOL)
> than first-order.
>
> The revised KIF coming shortly will
> move a small step in this direction
> but by no means all the way.
>
> > and appears in my category-theory approach --
> > starting with any (type) language L one can
> > generate an associated, and more inclusive,
> > type language expr(L) whose relation names
> > consist of all open L-sentences. You don't
> > even need to write explicitly '(R & Q)(a,b)';
> > just use 'R(a,b) & Q(a,b)' itself.
>
> Yes: in a type-theoretic version of HOL they could both be more properly
> written as (lambda (x y) (R(x, y) & Q(x, y))) (a,b). This is why I thought
> Jon Awbrey would like it, since everything is a function, just as he thinks
> it should be. Even the propositional connectives like AND, and even quantifiers,
> can be seen as functions.
>
> > What is precisely meant by your statement that
> > "one gets exactly the same conclusions"?.
>
> Sorry, I meant that this transcription of Hobbs' ontology preserves all the
> conclusions he is able to draw (under transliteration). Never mind, it would
> take too long to explain it and its not really important, other than being another
> little nugget in the overwhelmingly large pile of evidence suggesting that extensional
> FOL is the ontology language of choice.
>
> Pat Hayes
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Pat, Robert, & All,
If you failed to notice the sign above the
cache-value-of-ideas register as you came
in the door, then let me just call your
attention to the copy on your table:
| All combinations are already on the menu,
| Therefore no substitutions are necessary.
If this is not sufficiently self-explanatory,
then perhaps I can attempt to rephrase it
in the style to which you have formerly
been a customer, if not, indeed,
a longtime hostage to fartune:
| [
| [ Lambda
| [ Quote [ Alice ]
| ]
| [ Quote [ You can get anything you want at Alice's Restaurant ]
| ]
| ]
| [ Awbrey ]
| ]
In this particular establishment, we consider the entire culinary artifice
of substitution, aside from inducing a rather unsociable and sloppy way of
speaking, to be a decadent, irreducibly casual, and unsophisticated manner
of whipping up the requisite varieties of formal delectations, one that is
literally bound to incite, by way of its risible intermediary associations,
an unwholesome range of extremely unsatisfactory connotative sensations on
the palate of the formal appetite. It is the art of the unappetizing dish,
those whose complexes of poly-unsaturates have never in the history of our
formal cookery proven to be completely digestible, and thus to be eschewed.
Perhaps you have been led to believe that there are no alternatives,
If that is the case, then you have my sincerest of sympathies,
and I will do what I can to re-dress your grease-essences,
but first -- I am due for breakfast, a bit of coffee,
and since it is Sunday and my birthday,
a mimosa,
or maybe,
just two.
Until Then,
Jon 'Andre' Awbrey
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