# KEHOME/doc/RandMcCullough.html # Nov/7/2005 Apr/29/2009
I started at the lowest level
entity_1 is an existent. entity_2 is an existent.and abstracted to the highest level concepts. I discovered some new concepts [proposition names] which differ in detail from Rand's concepts, but are the same in spirit, and express the same facts of reality.
This note compares Ayn Rand's axiomatic concepts (EXISTENCE, IDENTITY, CONSCIOUSNESS) with the McCullough axiomatic concepts (existence, identity, consciousness).
All propositions in this note are in English. A double colon (::) separates the proposition name from the proposition.
The MKR propositions for the McCullough axiomatic concepts are given in KEHOME/kb/axiom.ho.
h0 :: existent / entity_1 / entity_2According to Rand there are two different, but equivalent, ways to describe the facts of reality for entity_1 and entity_2. The first view of facts regarding the entities is
EXISTENCE :: existent / entity_1 / entity_2 / entity_1 exists. / entity_2 exists.The second view of facts regarding the entities is
IDENTITY :: existent / entity_1 / entity_2 / entity_1 is entity_1. / entity_2 is entity_2.Rand says, "EXISTENCE IS IDENTITY.", which is an equivalence between two hierarchies.
existence :: { entity_1 exists. entity_2 exists. } identity :: { entity_1 is entity_1. entity_2 is entity_2. }To get the most general form of facts of reality, we abstract as follows. First integrate entity_1 and entity_2 into entity.
existent / entity // entity_1 // entity_2 / fact // existence :: entity exists. // identity :: entity is entity.Then abstract from entity to existent.
existence :: existent exists. identity :: existent is existent.McCullough says, "existence IS identity.", which is an equivalence between two facts.
To get Rand's statement of these two facts, we change from singular form to plural form
existence :: all existents exist. identity :: existent is existent. universe is all existents. existence :: universe exists. identity :: existent is existent.In Rand's words
existence :: EXISTENCE exists. identity :: A is A.
existent / entity // entity_1 // entity_2 // man / fact // consciousness :: man is CONSCIOUSNESS. // perceiving :: man can perceive entity. // consciousness IS perceiving. # equivalent facts
identity :: entity is entity.to a more specific fact as follows.
existent / entity / characteristic / fact // identity :: entity is its characteristics.
existent / entity // man / characteristic // attribute /// conscious // action /// identify / fact // identity :: entity is its characteristics. // consciousness :: man is conscious. // identification :: man can identify entity. // consciousness IS identification. # equivalent factsTo get Rand's statement about CONSCIOUSNESS, we need a little deduction.
man is CONSCIOUSNESS. man is conscious. CONSCIOUSNESS is conscious.