[Inquiry] Re: Logic Of Relatives

[Jon Awbrey]

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LOR.  Note 53

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The preceding exercises were intended to beef-up our
functional literacy skills to the point where we can
read our functional alphabets backwards and forwards
and to ferret out the local functionalites that may
be immanent in relative terms no matter where they
locate themselves within the domains of relations.
I am hopeful that these skills will serve us in
good stead as we work to build a catwalk from
Peirce's platform to contemporary scenes on
the logic of relatives, and back again.

By way of extending a few very tentative plancks,
let us experiment with the following definitions:

1.  A relative term 'p' and the corresponding relation P c X x Y are both
    called "functional on relates" if and only if P is a function at X,
    in symbols, P : X -> Y.

2.  A relative term 'p' and the corresponding relation P c X x Y are both
    called "functional on correlates" if and only if P is function at Y,
    in symbols, P : X <- Y.

When a relation happens to be a function, it may be excusable
to use the same name for it in both applications, writing out
explicit type markers like P : X x Y, P : X -> Y, P : X <- Y,
as the case may be, when and if it serves to clarify matters.