>John writes:
>In previous discussions, I stated one definition of type, and
>Barry stated another. The the pros and cons of either one are
>moot points, since the semantics of "type" will be determined
>by whatever version of logic is adopted. If CL is the logic,
>then types would be represented by monadic relations in CL,
>which would be represented as restrictions on the quantifiers
>in typed dialects of CL. An instance of a type would be anything
>in a given model for which the corresponding relation is true. (01)
I note that there is a second way in which types can be represented
in CL, which I am confident John will agree is possible: (02)
we introduce two sorts of individual variables, (03)
x, y, z ... for instances (particulars) (04)
u, v, w ... for types (05)
together with a two-place predicate instance_of to assert things like (06)
Fido instance_of dog. (07)
In this way we can quantify, harmlessly, over types, and yield
(albeit trivially) some of the benefits of second-order logic.
BS (08)
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