Ayn Rand axiomatic concepts and proposition names

# 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.

Metaphysics

Rand concepts: EXISTENCE, IDENTITY

We start our hierarchy with two entities.

h0 ::
existent
/  entity_1
/  entity_2

According 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.

McCullough concepts: existence, identity

The McCullough axiomatic concepts refer to the facts of reality, instead of the hierarchies. Specifically

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.

more facts: Rand CONSCIOUSNESS, McCullough consciousness

Now we add man (conscious entity -- animal level).

existent
/  entity
//    entity_1
//    entity_2
//    man
/  fact
//    consciousness :: man is CONSCIOUSNESS.
//    perceiving    :: man can perceive entity.
//    consciousness IS perceiving.  # equivalent facts

Epistemology

Here we reduce the general axiomatic concepts to more specific concepts.

characteristics

What is the nature of an entity? We reduce the previous fact

identity :: entity is entity.

to a more specific fact as follows.

existent
/  entity
/  characteristic
/  fact
//    identity :: entity is its characteristics.

conscious, identify

Man is more than an animal (conscious entity -- human level).

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 facts

To get Rand's statement about CONSCIOUSNESS, we need a little deduction.

man is CONSCIOUSNESS.
man is conscious.
CONSCIOUSNESS is conscious.