Identity

"To exist is to be something, to possess identity. A thing is itself; or, in the traditional formula, A is A."

The Axiom

Identity is the fact that everything that exists has a specific nature. To exist is not to exist as an indeterminate nothing, but to exist as SOMETHING - with specific characteristics, attributes, and properties that make it what it is and not something else.

The classical formulation is: A is A

This means:

• A thing is what it is
• A thing acts according to its nature
• A thing cannot be itself and not itself simultaneously
• A thing cannot possess contradictory attributes in the same respect at the same time

The Law of Identity in Detail

Every existent has:

• Specific characteristics that constitute its identity
• Specific actions it can and cannot perform
• Specific relationships it can enter into with other existents

Examples:

• Water at sea level boils at 100°C, not at any random temperature
• A stone falls when dropped, it doesn't float upward
• A human requires oxygen to survive, not methane
• 2 + 2 = 4, not 5 or 3 or any other number

Foundation of Logic

The Law of Identity is the foundation of all logic and reasoning:

Law of Non-Contradiction

From Identity follows: ¬(P ∧ ¬P) - a proposition cannot be both true and false simultaneously. This is explored in detail in Law of Non-Contradiction.

Law of Excluded Middle

Either P or ¬P must be true - there is no middle ground between a thing being itself and not being itself.

All Valid Reasoning

Every logical argument depends on terms maintaining consistent identity throughout the argument. If A could be both A and not-A, no reasoning would be possible.

Implications for Knowledge

Identity makes knowledge possible:

• Concepts: We can form concepts because things have specific identities we can categorize
• Causality: Things act according to their identity - same cause, same effect
• Measurement: We can measure because things have specific, stable characteristics
• Science: Natural laws are possible because things act according to their nature

Relationship to Other Axioms

Identity is a corollary of Existence:

• To exist = to exist as something
• Existence without identity is impossible
• "Pure existence" without any characteristics is a contradiction

Identity is grasped by Consciousness:

• Consciousness identifies what exists
• The act of consciousness is the identification of identity
• To be conscious is to be conscious of something AS something

Common Errors

"Identity is just a human construct"
No - humans IDENTIFY identity, we don't create it. A rock has specific characteristics whether humans exist to recognize them or not.

"Things are constantly changing, so A is not A"
Change is the alteration of identity OVER TIME. At any given moment, a thing is what it is. Ice becoming water doesn't violate identity - it means H₂O molecules at different temperatures have different properties.

"Quantum mechanics proves identity doesn't apply"
Quantum entities still have specific properties (mass, charge, spin). Uncertainty in measurement doesn't mean uncertainty in identity. Probabilistic behavior is still lawful behavior.

"Eastern philosophy shows A can be not-A"
Contradictions cannot exist in reality. Any claim that something both is and isn't simultaneously is either:

• Using terms in different senses
• Referring to different times
• Referring to different respects
• Simply false

Foundation for Property Rights

Identity is crucial for Private Property and Ownership:

• Objects maintain their identity independent of possession
• Ownership is a relationship between a person (with identity) and objects (with identity)
• Self-ownership depends on humans having specific identity as rational beings

Foundation for Ethics

Because humans have a specific identity as rational beings who must act to survive, ethics becomes possible:

• Humans have specific requirements for survival (food, shelter, freedom to think)
• Human actions have specific consequences based on the identity of reality
• Values are objective because they're based on the identity of human nature

This leads directly to The Non-aggression Principle - because humans have specific identity as rational beings who require freedom to act according to their judgment to survive.

The Primacy of Identity

Nothing can violate its own identity:

• Contradictions cannot exist (Law of Non-Contradiction)
• Wishes cannot alter facts (Primacy of Existence)
• Things cannot act against their nature

This is why Socialism is impossible - it attempts to violate the identity of human nature and economic law.