relations, bonds and links LO29734

From: Don Dwiggins (d.l.dwiggins@computer.org)
Date: 12/27/02


Replying to LO29692 --

Continuing the dynamic relationship, replying specifically to Leo's LO29692:
> Re-plying At's sheets of wholeness- relations, bonds and links

>> There exists in Symbolic Logic a branch called the logic of relationships.
>> In it any transitive relationship is symbolised by xRy while a reflexsive
>> relationship is symbolised by xR.

> I suspect that symmetry is an important aspect of this branche of logic. I
> will try to find some references to do some further studies.

As I remember it, the basic categorization of binary relations that's
taught in logic classes is:

Reflexive: xRx is true for all x (also Antireflexive: xRx is false for all
x)

Symmetric: xRy implies yRx (also Antisymmetric: xRy implies not yRx)

Transitive: xRy and yRz implies xRz

A relation R that is reflexive, symmetric, and transitive is called an
equivalence relation; a simple example is "is the same height as" among
people. A relation that is antireflexive, antisymmetric, and transitive
is a kind of ordering relation, e.g. "is taller than" among people.

>> I think its (1) the awareness to, (2) the learning of and (3) taking care
>> of relationships within the LO. In my work on the 7Es (seven
>> essentialities of creativity) i think of relationships xRy in the most
>> general manner as the associativity pattern x#R#y of wholeness. I
>> write it usually as X*Y*Z. Just explore such three-membered patterns
>> irrespective how simple or complex the three members are. As you
>> also have suggested.

> I wonder what # might be.

In my previous message on this thread, I mentioned my interest in roles.
I think here that the # (or *) stand for roles in the relationship. For
example, in "John * marriage * Jane", the first * is "husband" and the
second "wife". This can get hairy if you get caught up in it -- consider
what the *s might mean in "John * husband * marriage * wife * Jane" (where
I've made each role an entity in its own right)? After that, it's turtles
all the way down.

Also, of course, not all relations are binary (involving exactly two
entities). In an earlier posting on this list, I proposed the idea that
in an N-person organization, there are 2^N-1 (2 to the Nth power, less
one) "things" to care for. Other than the N people, these are all
relations (and thus involve the people in many roles).

Consider the ternary relation family(John, Jane, Jenny) involving husband,
wife, and daughter. This implies the binary relationships marriage(John,
Jane), father-daughter(John, Jenny), and mother-daughter(Jane, Jenny) (the
latter two don't have single word names, so I've cobbled up names from the
roles). John then has three roles in this context: father, husband, and
what's traditionally called "man of the family".

-- 

Don Dwiggins d.l.dwiggins@computer.org

The very first lesson that we have a right to demand that logic shall teach us is how to make our ideas clear; and a most important one it is, depreciated only by minds who stand in need of it. -- C.S. Peirce

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