North Texas Objectivist Society (NTOS) Message Board › Metaphysics: What's the angle of a corollary?

Metaphysics: What's the angle of a corollary?

Old T.
OldToad
Group Organizer
Dallas, TX
Post #: 1,047
Causality is best classified as a corollary of identity. A "corollary" is a self-evident implication of already established knowledge. A corollary of an axiom is not itself an axiom; it is not self-evident apart from the principle(s) at its root (an axiom, by contrast, does not depend on an antecedent context). Nor is a corollary a theorem; it does not permit or require a process of proof; like an axiom, it is self-evident (once its context has been grasped). It is, in effect, a new angle on an established principle, which follows immediately once one grasps its meaning and the principle on which it depends.

Many of the most important truths in philosophy occupy this intermediate status. They are neither axioms nor theorems, but corollaries—most often, corollaries of axioms. In fact, the essence of metaphysics, according to Objectivism, is the step-by-step development of the corollaries of the existence axiom. The main purpose of this chapter is to unravel systematically the implications of "Existence exists."

—Leonard Peikoff, Objectivism:The Philosophy of Ayn Rand, “Reality.”
Old T.
OldToad
Group Organizer
Dallas, TX
Post #: 1,048
A "corollary" is the something that follows immediately from a prior statement without further proof, and even the attempt to deny it requires reliance on the first statement. For example, the law of identity can be expressed as "A is A." A corollary is "A is not B." The following are more examples of usage of the word by Ayn Rand.

Example:
The primacy of existence (of reality) is the axiom that existence exists, i.e., that the universe exists independent of consciousness (of any consciousness), that things are what they are, that they possess a specific nature, an identity. The epistemological corollary is the axiom that consciousness is the faculty of perceiving that which exists—and that man gains knowledge of reality by looking outward. The rejection of these axioms represents a reversal: the primacy of consciousness—the notion that the universe has no independent existence, that it is the product of a consciousness (either human or divine or both). The epistemological corollary is the notion that man gains knowledge of reality by looking inward (either at his own consciousness or at the revelations it receives from another, superior consciousness).
—Ayn Rand, The Ayn Rand Letter, "The Metaphysical Versus The Man-Made."

Example:
Now what I say is: before your conscious apparatus, the faculty of consciousness, is aware of something, it is not conscious, and certainly there is no "I." But when you become aware, implicit in your first sensation are certain axiomatic concepts. And they are what? That you exist, that the outside world exists, and that you are conscious. The baby could not conceptualize this, but it's implicit; without that implication he couldn't be aware of anything. Therefore it's not an "innate idea," it's a corollary of the fact of consciousness.
—Ayn Rand, Introduction to Objectivist Epistemology, “Appendix—Axiomatic Concepts.”

Example:
"The law of identity does not permit you to have your cake and eat it, too. The law of causality does not permit you to eat your cake before you have it. But if you drown both laws in the blanks of your mind, if you pretend to yourself and to others that you don't see—then you can try to proclaim your right to eat your cake today and mine tomorrow, you can preach that the way to have a cake is to eat it first, before you bake it, that the way to produce is to start by consuming, that all wishers have an equal claim to all things, since nothing is caused by anything. The corollary of the causeless in matter is the unearned in spirit.
—Ayn Rand, Atlas Shrugged, "This Is John Galt Speaking."

Example:
The political aspects of Atlas Shrugged are not its theme, but one of the consequences of its theme. The theme is: the role of the mind in man's existence and, as a corollary, the presentation of a new code of ethics—the morality of rational self-interest.
—Ayn Rand, Capitalism: the Unknown Ideal, "Is Atlas Shrugging?"

Example:
Observe the basic principle governing justice in all these cases: it is the principle that no man may obtain any values from others without the owners' consent—and, as a corollary, that a man's rights may not be left at the mercy of the decision, the arbitrary choice, the irrationality, the whim of another man.
—Ayn Rand, Capitalism: the Unknown Ideal, "Appendix: The Nature of Government".

Example:
Only one aspect of sex is a legitimate field for legislation: the protection of minors and of unconsenting adults. Apart from criminal actions (such as rape), this aspect includes the need to protect people from being confronted with sights they regard as loathsome. (A corollary of the freedom to see and hear, is the freedom not to look or listen.) Legal restraints on certain types of public displays, such as posters or window displays, are proper—but this is an issue of procedure, of etiquette, not of morality.
—Ayn Rand, The Ayn Rand Letter, "Thought Control--Part III."

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