Changes

===Commentary Note 8.3===

===Commentary Note 8.3===

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

Speaking very strictly, we need to be careful to

distinguish a "relation" from a "relative term".

# 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.

1.  The relation is an 'object' of thought

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

    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,

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:

    called its "relates", as these are determined in relation

    to certain other objects, called its "correlates".  Under

    as denoting the corresponding relation.

Returning to the Othello example, let us take up the

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

2-adic relatives "lover of ---" and "servant of ---".

Ignoring the many splendored nuances appurtenant to the idea of love,

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:

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.

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

If for no better reason than to make the example more interesting,

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

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.

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.

 

 

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.

===Commentary Note 8.4===

===Commentary Note 8.4===