Proof

Proof is the process of establishing a conclusion by reducing it, through a chain of logical steps, to the evidence of the senses. Objectivism holds that proof is therefore hierarchical rather than merely formal: a valid deduction from premises that were never themselves reduced proves nothing.

“Proof is the process of deriving a conclusion step by step from the evidence of the senses, each step being taken in accordance with the laws of logic.”
   ~ Leonard Peikoff, Objectivism: The Philosophy of Ayn Rand, chapter 4

The two requirements

A proof has to satisfy both of the following, and most bad arguments satisfy one:

• Logical validity. Each step must follow. This is the concern of logic, and it is necessary.
• Reduction. The chain must terminate in something perceived. Premises have to be traceable down the hierarchy to first-level concepts and the observations they were formed from.

Dropping the second gives rationalism: elaborate deductive structures resting on premises nobody has connected to anything. Dropping the first gives a heap of observations that support no conclusion. See Empiricism and Reason.

This is why Objectivism treats "proof" as a wider notion than formal derivation. Establishing that a concept is validly formed is part of proving propositions made from it, because a term with no referents cannot make a proposition true. See Concept formation and Floating Abstraction.

Where proof stops

A chain of proof cannot be infinite, and it cannot be circular. It terminates in two places, and neither is an admission of weakness.

• The axioms. Existence exists; A is A; consciousness is conscious. These cannot be proved because every proof uses them. Demanding a proof of an axiom is a stolen concept: the demand presupposes what it questions.
• The perceptual level. The senses do not report conclusions and so are not subject to proof; they are the standard against which conclusions are checked. Perception is valid not because it has been validated by something else, but because it is the base of all validation. See Perception.

Objectivism marks these off as self-evident rather than proved. The distinction matters: a self-evident item is not an exception granted to keep the system running, it is what makes proving anything possible.

The onus of proof

The obligation to prove falls on the person asserting something, not on the person declining to accept it. Objectivism draws this from the nature of proof rather than from debating convention: a claim with no reduction offered has not entered the true-false classification at all.

A claim advanced with no evidence is arbitrary. It is not improbable, not unrefuted, and not a candidate awaiting disproof — it is to be dismissed, because there is nothing there to evaluate. This is what disposes of "you can't prove it isn't so." See Arbitrary and Certainty.

Common misunderstandings

• That proof requires certainty about everything connected to the conclusion. It requires meeting the standard within the full context of available evidence. Setting the bar at omniscience is the skeptic's move, not a high standard. See Skepticism.
• That deduction is the only form. Induction is the process by which the general premises deduction uses are established in the first place. A philosophy that accepted only deduction would have nothing to deduce from.
• That an unprovable claim might still be true. If nothing whatever bears on a claim, it has no cognitive status. This is different from a claim that has evidence but has not yet been established.
• That proof and persuasion are the same. Whether a chain reduces to perceptual evidence is a fact about the chain. Whether anyone is convinced by it is a fact about them.

See also

• Logic · Reason · Hierarchy · Context · Certainty
• Axioms · Perception · Senses · Fundamental
• Arbitrary · Truth · Knowledge · Fact
• Induction · Rationalism · Empiricism · Skepticism
• Fallacy of the stolen concept · Floating Abstraction · Fallacies

Discussion

• Axioms used in metaphysics or epistemology
• How does Objectivism disprove skepticism?
• Introduction to Logic by H.W.B. Joseph

References

• Rand, Ayn. "Axiomatic Concepts", Introduction to Objectivist Epistemology. The Objectivist, 1967.
• Rand, Ayn. "Galt's Speech", For The New Intellectual. Random House, 1961.
• Peikoff, Leonard. Objectivism: The Philosophy of Ayn Rand, chapters 4 and 5.