Vernacular identity: property of a thing.
Mathematical identity: relation between a
thing and itself or between two equal things.
Examples of the properties of a thing (which
fall into the category of vernacular identity)
are its color, size, speed, shape, and weight,
all of which are derived from holistic relation,
which can be defined as "relative difference."
But Anton alleges that there is another kind
of identity that is derived from self-relation.
Requests for examples or evidence of such iden-
tity have been answered only with examples of
relations between different things. NO example
of a "mathematical identity" (a thing that is
itself free from anything else) has been shown.
The reason that no example of a "mathematic
identity" can be shown may be explained by the
fact that any tangible variety of identity is
a product of the relations of differing subsets,
and thus measurable identity is difference, not
"same as." Therefore, the only identity that
exists pertaining to self-relation is zero
identity, is no, or null, identity.
We can see this expressed perfectly in the
identity matrix, which defines the attributes
of the identities of the entities across the top
relative to the entities along the left side:
1 2 3 4 5
_______________
1 | 0 1 2 3 4 |
| |
2 |-1 0 1 2 3 |
| |
3 |-2 -1 0 1 2 |
| |
4 |-3 -2 -1 0 1 |
| |
5 |-4 -3 -2 -1 0 |
-----------------
3 has the attribute of 2 relative to 1, and by
symmetry, 1 has the attribute of -2 relative to 3.
Wherever a "0" appears, there is "self-relation."
The measure of identity that an entity attains by
relation to itself is zero, zip, nada, null, no-
thing, or void. Therefore, what Anton has defined
as "mathematic identity" is nowhere to be found.
But this "0" is still important. It means that the
self-relation of anything to itself is equal to the
self-relation of any other thing to itself and of
all things to all things (since the sum of all the
attributes in the matrix equals 0 -- the difference
between "all difference" and "all difference" is 0;
and therefore, difference is, as a rule, conserved).
This is the central structure of the conservation
of identity. So Anton's "mathematic identity" IS
valid in a profoundly holistic sense, and it is
the center piece of radical holism: zero mechanics.
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