>Kathy and Pat,
>
>I agree with Pat's explanation, but I think it could be made
>somewhat clearer by distinguishing the base domain D from
>the domain D' of *all* relations over D for second-order logic
>(and then a domain D'' of *all* relations over D', etc.).
>
>PH> The key semantic difference between the other logics is
> > that they all impose conditions on the domain, requiring
> > it to contain some entities as a result of containing others.
> > So for example, classical second-order logic semantics
> > requires that the domain is contain all relations
> > over the base domain.
>
>I would rephrase the last sentence in the following way:
>
> So for example, classical second-order logic semantics
> starts with the given base domain D and introduces
> another domain D' of *all* relations over D. (01)
That is closer to the usual formulation, and
probably clearer, yes. And it is that extended
domain D' which the second-order quantifiers
range over. (02)
>
>I just wanted to give different names D, D', D'', etc.
>to distinguish the base domain D from any domains that
>may be introduced by implicit assumptions.
>
>CL allows the domain D to contain relations, but it doesn't
>require D to contain *all possible* relations. (03)
or indeed any relations, if you want to exclude
them: CL has the notion of a 'segregated dialect'
to allow for this textbook first-order case. (04)
Pat (05)
>John
>
>
>
>
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