> I base those definitions on semantics of the CL core,
> which is "typeless" -- i.e., there is only one type
> of entity and no formal distinction between individuals
> or relations. (01)
I don't get the relevance of this, in fact I'm not even sure I
understand this claim. This is like saying that for CL there is no dog
(particulars) versus cats (ontological types), because there is no
saying whether 'fido' is going to be interpreted as an individual or a
class. CL is a language, it does not decide the ontological nature of
individuals, it allows to represent it. (02)
> PG> Although I gather that if the original motivation is
> > ontological the idea is that instance_of is a primitive
> > (that would not ask for a definition).
>
> True, and I believe that is the motivation Barry Smith
> would prefer. However, my point is that we need to adopt
> a methodology that will enable us to deliver a solution
> to the ONTAC WG without resolving the debates between
> nominalists and realists.
>
> Therefore, my proposal is agnostic with respect to that
> debate: adopt a version of logic, such as CL, and define
> instance_of in terms of the syntactic features of CL.
> Nominalists can accept that solution as stated, and
> realists can think of it as a "quick-and-dirty" method
> of avoiding a commitment. (03)
No, your proposal is not agnostic, that was my point. Your
'definition' does not work because (y x) has to be false (in CL yes, I
know, in other cases it's mere non sense) in the relevant cases. (04)
> PG> But the main point might just be that the types are
> > individuals. That point only should make the definition
> > you're suggesting fail, because (y x) would either
> > yield non-sense or in the best case falsehood.
>
> CL is truly agnostic. (y x) is *never* nonsense (i.e.,
> something that would cause a syntax error). (05)
Did I say otherwise? Let me precise: what comes up with CL falls under
the best case scenario, it allows to have a falsehood rather than non
sense. (06)
> If y is
> not a monadic relation, the result is simply false. (07)
And that's not an issue for your definition? (08)
> And there is no reason why you can't write
>
> (and (y x) (x y))
>
> You can even write (x x). CL provides ways of interpreting
> all such statements. If they're contradictory, that's
> your problem, not CL's. (09)
No, John. The only way the statement you wrote would come true would
be if x was not an instance_of y. Or am I delusional that bad? If the
ontological types are individuals, they can't come up as predicates. (010)
In fact, the realist -- if you want to use this language -- has the
advantage that she can define monadic predicates corresponding to an
ontological type (that would come up as a z, neither the x nor the y
you had). Free for anybody to play with predicates, on this
ontologically sound basis. Now the nominalist can reject that and have
just as many predicates as she wants since she doesn't have to claim
that instance_of is non empty. That the use of those predicates is
then not ontologcially grounded is just the very nominalistic claim.
There's no sitting in between two seats. (011)
Pierre (012)
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