A is A and the Law of Causality: Basic Metaphysics

A is A is Aristotle's Law of Identity. Rand adopted this as a basic axiom. It is one of the cornerstones of Objectivism. The law states that everything that exists has a specific, particular nature. Every thing one perceives has characteristics that are inherent in its nature. These characteristics are apprehended and can be described. An entity may be described as smooth, blue, round, etc. A person may be tall, slim, and intelligent. These traits give an entity its identity. The particular traits or characteristics are not important. The number of traits is not important. The fact that every entity has traits is what matters.

An entity without form, without traits, is a non-entity. It does not exist. It would be nothing. To exist is to have identity. Identity is the concept of the aspects of existence. Existence requires something to exist as a particular something, with a particular identity. It can not have multiple identities. It is what it is and can be nothing else. A horse is not a camel and a house is not an automobile. Every characteristic of a specific entity is part of its identity.

There can be no contradictions. Entities can not be one thing and another simultaneously. Explicit in the concept of identity is the corollary that reality has a specific nature. Having a definite nature and an identity means it is knowable. Existing according to its nature and identity is without contradictions.

Man has fallible perceptions and can perceive an entity rightly or wrongly, but the entity itself is not subject to one's perceptions or whims. It is what it is. The characteristics of its existence are not subject to the will of man. If a color blind man cannot perceive properly, the color of an entity, it does not change the true nature or color of the entity. A magician and an observer see the same event, but only the magician has the better perspective and understanding. Either way, knowledge of the characteristics of an entity is independent of its nature; its nature is what it is, whether someone or no one knows it.

The Law of Causality is also a fundamental law essential to Objectivism. It is related to the Law of Identity. It is the result of the interactions of entities, or the action of a single entity, having identity, applied over time. Actions, identified are the result of the Law of Causality. No action can occur without an entity. Action, presupposes existence of an entity for an action to occur or exist.

Actions themselves have a particular nature and depend upon the entity or entities' individual identity and characteristics. Action is the change of a particular characteristic of an entity. If a moon changes location while it orbits its planet, it has changed, but it is bound to the nature of its characteristics and those of the other objects involved. The gravity, mass, speed, etc., are factors and characteristics of the entities involved which the actions are dependent upon. Actions change the nature of an entity, but only within the confines of the nature of the entity or entities involved in the action. They cannot produce an action contrary to their nature. Change is dependent upon and determined by the properties of the entities involved whether the action is momentary or continual. For example: A body such as a moon may impact another body and stop or it may bounce off and continue on a new path, continuously changing characteristic of location or speed. For something to change it must be acted upon by some prior action. This is a cause- thus the term Causality.

A change is an effect of a cause or action. A cause is the result of a prior cause or causes, and each cause is the result of and dependent upon the specific nature of the agents and their identities that affect the change. Newton's laws of motion are a good example.

The Law of Identity and the Law of Causality are interrelated. According to objectivist metaphysics all existents in existence are subject to these laws. The law of Identity declares that all existents are real, with identifiable attributes, but not subject to one's apprehension. Existence exists and the Law of Causality explains the means by which that which exists operates. These laws are the essential foundation for a philosophy congruent with logic.

Objectivism: More of the Basics
Introducing Objectivism - Rand's own words in less than ten minutes. https://www.youtube.com/watch?v=8VSBG...
"Reality exists as an objective absolute. Facts are facts." Ayn Rand (Time frame 2:24)

Respectfully,
O.A.

Addendum: A is A (though commonly referred to as Aristotle's law of identity) has been claimed by some to be more properly attributed to Gottfried Lebnitz, while the law of non-contradiction is that of Aristotle.
Regardless, together they are essential elements of the law of identity.