[SCL] Re: Observation

[Christopher Menzel]

> Right.  Slightly odd suggestion: make Rel be true of all sequences of 
> things in the intersection of I and R, and make it be false (even of 
> the empty sequence) if there aren't any.  That way, one could write 
> Rel(P Q R ...) to 'declare' a lot of them at once, and more pointedly, 
> (not Rel( ) ) is true inside GOFOL, not otherwise. so it can be used 
> to say that one is inside the GOFOL sublanguage.

Can do that.

>> I think we were a little unclear on the following point yesterday.  So
>> long as "P" has been designated a constant in our particular SCL
>> language, we get all theorems of the form:
>>
>> ...P... -> (EF)...F...
>>
>> e.g.,
>>
>> Px -> (EF)Fx
>>
>> regardless of whether or not "P" occurs as an argument to another
>> predicate in our axioms somewhere.
>
> Seems to me that this brings back the Horrocks sentences.

No, not for "traditional" first-order SCL languages, i.e., SCL 
languages in which no predicate constants are simultaneously individual 
constants (and in which one does not allow variables in pred position). 
  The point Ian seemed to be making against SCL was that there are 
sentences in HIS familiar first-order language that suddenly change 
their logical properties when you interpret THAT VERY LANGUAGE via SCL 
model theory. Not so on our latest SCL model theory in which the 
relation between R and I is unspecified.  The logical properties of a 
traditional first-order SCL language are identical whether interpreted 
a la Tarski or a la SCL.  What you *can't* do is start with a gonzo 
type-free SCL language and expect that a superficially traditional 
first-order sentence ripped from that context will have the same 
logical properties when interpreted a la Tarski.  But I can't see that 
THAT is any more problematic than the fact that you can't rip an 
arbitrary sentence out of a context in which it is interpreted 
according to the model theory for, say, free logic and complain that 
its logical properties are different interpreted a la Tarski.  If you 
want to pull a sentence from an arbitrary SCL language into a 
traditional first-order framework, you'll have to use an App/Pred 
translator or restricted quantifiers.

>> Being a possible argument is not a
>> property conferred upon an expression in real time, so to say, but 
>> ahead
>> of time in virtue, before we write anything down, in virtue of
>> stipulating that the given expression is a constant.
>
> Well, Im not sure what this stipulating amounts to.

Same as with any language.  This is the standard way in which a 
language is defined.  Granted, we're thinking about the web where these 
matters aren't always so neat...

> Like, here I am, a softbot somewhere, and I come across a piece of 
> SCL: how do I know which of the relation symbols have been designated 
> a constant? Designated where, and by who? I think we have to have some 
> way of recognizing from the syntax how to interpret the language. If 
> that requires knowing what has been stipulated, then the syntax has to 
> have a way to indicate stipulation.

I think that is exactly what we will have to say, else there will be no 
way to avoid Horrocks sentences.

-chris