# KEHOME/knowledge/identify/identity.txt
# 1999/4/28

#==========#
# Identity #
#==========#

Rand and Peikoff discuss three aspects of identity.

1. identity & existence
Rand, IOE, page 56
	"The units of the concepts 'existence' and
	'identity' are every entity, attribute, action,
	event, or phenomenon (including consciousness)
	that exists, has ever existed or will ever
	exist."
Peikoff, OPAR, page 6,7
	"Ayn Rand offers a new formulation of this axiom:
	existence is identity. She does not say 'existence
	has identity' -- which might suggest that identity
	is a feature separable from existence ...
	Existence and identity are indivisible; either
	implies the other. ... Why, one might ask, use
	two concepts to identify one fact? ...
	several perspectives on a single fact ...
	consider it from different aspects or in
	different contexts ..."
I interpret this to mean that "existence" and "identity"
are the tops of two different hierarchies (views), with
the same primitive units (at the bottom of the hierarchy)
but with different intermediate concepts.  Although I
would say that
	"existence is all existent"
in one hierarchy and
	"identity is all existent"
in the other hierarchy, I don't think it is correct to
say that
	"identity is existence"
because "identity" and "existence" are in different
hierarchies.

2. identity of an existent
Peikoff, OPAR, page 6
	"The 'identity' of an existent means that which it
	is, the sum of its attributes or characteristics."
In my KR language, the relations of an existent are
expressed as
	"existent isin relationship"
so I would translate Peikoff's statement as
	"identity is all [existent isin relationship]"
or simply
	"identity is all relation"

3. law of identity
Rand, AS, page 942
	"Whatever you choose to consider, be it an object,
	an attribute or an action, the law of identity
	remains the same.  A leaf cannot be a stone at the
	same time, it cannot be all red and all green at the
	same time, it cannot freeze and burn at the same time.
	A is A. Or, if you wish it stated in simpler language:
	You cannot have your cake and eat it, too."
I would translate Rand's statement as
	"identity is [existent is either A or not A]"
or
	"identity is [A is A]"

A similar characterization is given in
H.W.B. Joseph, "An Introduction to Logic", page 13 -- laws of thought
	law of identity:	A is A
	law of contradiction:	A cannot be B and not be B
	law of excluded middle:	A either is or is not B
In my KR language, I would translate these laws as
	A is B
	not ((A isa B) and (A isa not B))
	either (A isa B) or (A isa not B)
or
	existent is existent
	not existent is all B and not B
	existent is either B or not B
("is all ... and ..." applies to two or more "requisite" conditions.)



My current interpretation of Rand's meaning
===========================================

	identity is all relation

From the appropriate point of view, this is
the same as

	identity is all existent

Here's the reasoning.  The whole "trick" depends on the fact
that the concept hierarchy itself is defined by relations. 

1. The hierarchy 
    existent 
        entity 
        characteristic 
        relation 
is defined by 
    entity isa existent 
    characteristic isa existent 
    relation isa existent 
2. "delete" entity and characteristic, and "file" them
under relation: 
    existent 
        relation 
            [entity isa existent] 
            [characteristic isa existent] 
            other relations 
3. This makes existent an invalid concept, because it does not
consist of two or more units, so "merge" existent and relation,
i.e., 
    existent is relation 
yielding the hierarchy 
    existent 
        [relation is existent] 
        [entity isa existent] 
        [characteristic isa existent] 
        other relations 
4. Define identity as 
    identity is all relation 
which is the same as 
    identity is all existent 
Q.E.D. 

NOTE:
Since
    existence is all existent
Rand's statement that
    identity is existence
is true in this view.
