Objectivist metaphysics
All of Objectivism rests on Objectivist metaphysics and Objectivist epistemology: the study of what is and how we know it. The key tenets of the Objectivist metaphysics are (1) the Primacy of Existence, (2) the Law of Identity (Aristotle's "A is A"), and (3) the Axiom of Self-Consciousness. In addition, (4) the Law of Causality is a corollary of the Law of Identity. The Primacy of Existence states that reality (the universe, that which is) exists independently of human consciousness. The Law of Identity states that anything that exists is qualitatively determinate, that is, has a fixed, finite nature. The Axiom of Self-Consciousness is the proposition that one is conscious. The Law of Causality states that things act in accordance with their natures. These propositions are all held in Objectivism to be axiomatic. According to Objectivism, the proof of a proposition's being axiomatic is that it is both (a) self-evident and (b) cannot coherently be denied, because any argument against the proposition would have to suppose its truth.
The Primacy of Existence
The Primacy of Existence premise says that reality is objective: the universe exists independently of the particular psychological states (beliefs, desires, etc.) of individual cognizers. This view was also held by Aristotle. Objectivism distinguishes The Primacy of Existence from the Primacy of Consciousness (a view held by Plato, George Berkeley and G. W. F. Hegel). The Primacy of Consciousness holds that consciousness is prior to existence. It is the view that one could, in principle, be conscious exclusively and entirely of one's self. Objectivism rejects this view: it holds that objects present themselves to consciousness in such a way that they must be genuinely "other," that is, non-identical to one's own consciousness. This axiom is the basis of the Objectivist refutation of both theism and idealism. Though Objectivism grants that some particular existents are mental (e.g., minds, thoughts, desires, intentions), it holds that, if what fundamentally exists is independent of any consciousness, then the universe as a whole is neither the creation of a divine consciousness nor itself mental. (This argument is laid out in Chapter 1 of Leonard Peikoff's Objectivism: The Philosophy of Ayn Rand).
The Law of Identity
The Law of Identity states that everything that exists has an identity. In saying this, Objectivism is asserting more than the tautology of self-identity (i.e., "everything is identical to itself"). It is asserting that everything that exists has a specific nature, consisting of various properties or characteristics (as Rand wrote, "to be is to be something in particular"). Moreover, Objectivism holds that the properties and characteristics in question must exist each in a specific measure or degree; in this respect "identity" also means finitude. According to Objectivism, then, everything that exists has a specific finite nature. To have a specific, finite nature, is incompatible with having a self-contradictory nature. Therefore, the whole of reality is noncontradictory; though contradictions might exist in thought, there are no contradictions in the real world.
The Axiom of Consciousness
This axiom amounts to the first-person judgment, "I am conscious" (each person can truthfully assert this for himself). For Rand, this fact is a corollary of the axiom of existence. She writes that "consciousness is conscious," affirming both that the thinker is conscious and that he is conscious of something external to himself. She writes, "If nothing exists, there can be no consciousness: a consciousness with nothing to be conscious of is a contradiction in terms" (Atlas Shrugged, p. 1015). Though the axiom of consciousness has antecedents (most famously in the thought of Descartes), Objectivism distinguishes itself by holding that the Primacy of Existence (see above) is co-fundamental with the axiom of self-consciousness, so that consciousness and its contents are no more certain or fundamental than mind-independent reality.
The Law of Causality
Each thing's specific nature determines how it acts. This principle is Objectivism's formulation of the Law of Causality; it is held to be a corollary of the Law of Identity (see above). Contemporary philosophers define the Law of Causality differently, e.g., as "Every event has a cause." Objectivism rejects this contemporary definition because it leads to paradoxes concerning free will and cosmology. A further implication of the Objectivist account of causality concerns explanation: since genuine explanation is causal, nature can only be explained in terms of nature (i.e., without reference to the supernatural).
Mind and body
Another Objectivist doctrine deserves mention here: Objectivism rejects the mind-body dichotomy, holding that the mind and body are an integrated whole. Though this doctrine may sound like a stance in the philosophy of mind — a doctrine concerning the relationship between consciousness (mind) and brain (body) — it is not. Rather, it amounts chiefly to the assertions that (a) there are both mental existents and physical existents, and (b) existents of both sorts have genuine causal powers, though whether entities of either sort, or their causal powers, can be reductively explained is another matter. This doctrine represents a rejection of any forced choice between Marxian materialism and Christian spiritualism. Marxists hold that the material factors of production have metaphysical priority over consciousness. Christians hold that reality is fundamentally spiritual. Objectivism rejects both views: physical entities and mental entities both exist, and neither is more real than the other. Though this doctrine may entail the rejection of eliminativism, Objectivism does not offer any particular metaphysical or scientific explanation of the relationship between mind and body in the philosophy of mind. However, Harry Binswanger, a prominent Objectivist philosopher, argues in his lecture course, "The Metaphysics of Consciousness," in favor of substance dualism. He rejects not only eliminativism and materialism, but even the property dualism of David Chalmers and the emergentism of John Searle.