[Inquiry] Re: Logic Of Relatives

[Jon Awbrey]

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LOR.  Note 18

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Speaking very strictly, we need to be careful to
distinguish a "relation" from a "relative term".

1.  The relation is an 'object' of thought
    that may be regarded "in extension" as
    a set of ordered tuples that are known
    as its "elementary relations".

2.  The relative term is a 'sign' that denotes certain objects,
    called its "relates", as these are determined in relation
    to certain other objects, called its "correlates".  Under
    most circumstances, one may also regard the relative term
    as denoting the corresponding relation.

Returning to the Othello example, let us take up the
2-adic relatives "lover of ---" and "servant of ---".

Ignoring the many splendored nuances appurtenant to the idea of love,
we may regard the relative term 'l' for "lover of ---" to be given by
the following equation:

'l'  =  B:C +, C:B +, D:O +, E:I +, I:E +, O:D.

If for no better reason than to make the example more interesting,
let us put aside all distinctions of rank and fealty, collapsing
the motley crews of attendant, servant, subordinate, and so on,
under the heading of a single service, denoted by the relative
term 's' for "servant of ---".  The terms of this service are:

's'  =  C:O +, E:D +, I:O +, J:D +, J:O.

The term I:C may also be implied, but, since it is
so hotly arguable, I will leave it out of the toll.

One more thing that we need to be duly wary about:
There are many different conventions in the field
as to the ordering of terms in their applications,
and it happens that different conventions will be
more convenient under different circumstances, so
there does not appear to be much of a chance that
any one of them can be canonized once and for all.

In the current reading, we are applying relative terms
from right to left, and so our conception of relative
multiplication, or relational composition, will need
to be adjusted accordingly.

Jon Awbrey

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