Fundamental

A characteristic is fundamental when the greatest number of a thing's other characteristics depend on it. Objectivism uses the notion in two places: to identify which characteristic a definition should name, and to identify which propositions cannot be reduced any further and so function as axioms.

“The essential distinguishing characteristic(s) is the one that explains the greatest number of the others.”
   ~ Ayn Rand, "Definitions", Introduction to Objectivist Epistemology

Fundamental in definitions

Every existent has an unlimited number of characteristics. A definition cannot list them, so it must select — and the question is whether the selection is a matter of convenience or of fact.

Objectivism holds that it is a matter of fact. Among the characteristics that distinguish a thing from others in its category, one will explain the largest number of the rest. That is the fundamental one, and naming it is what a definition is for.

Man is the standard illustration. A human being is a featherless biped, a tool user, a language user, a rational animal. All are true; only one of them accounts for the others. Tools and language and the rest follow from the capacity to reason; nothing follows from featherlessness. So "rational animal" is the definition and the others are consequences. See Rule of Fundamentality and Concept formation.

Two things follow:

• Definitions are contextual, not arbitrary. What is known determines which dependencies are visible. A child defines "man" by what he can observe; a philosopher by what he can integrate. If both proceeded correctly the later definition expands the earlier rather than contradicting it. See Context.
• Getting it wrong has consequences. A definition that names a derived characteristic leaves the concept without an explanatory centre, and reasoning from it will keep needing exceptions.

Fundamental in the hierarchy

The second use concerns the order of knowledge. A proposition is fundamental in this sense when nothing more basic can be offered in support of it — when any attempt to prove it must already assume it.

The axioms are the limiting case:

• Existence exists. Any statement whatever asserts that something is. Denying it asserts that the denial exists.
• A is A. Any statement identifies something as something. Denying identity requires the denial to be what it is rather than something else.
• Consciousness is conscious. Any statement is made by someone aware of something. See Axiom of Consciousness.

These are not fundamental because nobody has managed to prove them. They are fundamental because proof is a process of reducing a claim to what is more basic, and there is nothing more basic than these — every proof already uses them. Demanding a proof of an axiom is a stolen concept. See Hierarchy and Proof.

The two senses are one

Both uses turn on the same relation: dependence. In a definition, the fundamental characteristic is the one the others depend on. In the structure of knowledge, the fundamental proposition is the one other propositions depend on. What Objectivism claims in both cases is that the dependence is a fact about the subject matter and not a decision about how to organise a subject.

This is also what Rand's Razor enforces: concepts are not to be multiplied beyond necessity, and are to be resolved into their irreducible primaries.

Common misunderstandings

• That "fundamental" means important. Importance depends on purpose. Fundamentality is a matter of how many other characteristics rest on this one, and it can be established or disputed by evidence.
• That a contextual definition is a provisional one. Contextual means established within a known body of knowledge, with a known scope. It does not mean held pending confirmation. See Certainty.
• That axioms are assumptions the system starts from. An assumption could be replaced with another. An axiom is presupposed by any attempt to argue at all, including an attempt to argue against it.
• That naming a fundamental characteristic denies the others matter. The concept subsumes every characteristic of its units. The definition identifies which one explains the rest.

See also

• Rule of Fundamentality · Concept formation · Concept · Conceptual Common Denominator
• Axioms · Axiom of Consciousness · Proof · Hierarchy · Context
• Rand's Razor · Identity · Existence · Logic
• Fallacy of the stolen concept · Floating Abstraction

Discussion

• Axioms used in metaphysics or epistemology
• Attribute vs quality
• A criticism of Objectivist epistemology

References

• Rand, Ayn. "Definitions" and "Axiomatic Concepts", Introduction to Objectivist Epistemology. The Objectivist, 1967.
• Peikoff, Leonard. Objectivism: The Philosophy of Ayn Rand, chapters 1 and 4.