Since concepts, in the field of cognition, perform a function similar to that of numbers in the field of mathematics, the function of a proposition is similar to that of an equation: it applies conceptual abstractions to a specific problem.

A proposition, however, can perform this function only if the concepts of which it is composed have precisely defined meanings. If, in the field of mathematics, numbers had no fixed, firm values, if they were mere approximations determined by the mood of their users—so that “5,” for instance, could mean five in some calculations, but six-and-a-half or four-and-three-quarters in others, according to the users’ “convenience”—there would be no such thing as the science of mathematics.

Copyright © 1986 by Harry Binswanger. Introduction copyright © 1986 by Leonard Peikoff. All rights reserved. For information address New American Library.


Excerpts from The Ominous Parallels, by Leonard Peikoff. Copyright © 1982 by Leonard Peikoff. Reprinted with permission of Stein and Day Publishers. Excerpts from The Romantic Manifesto, by Ayn Rand. Copyright © 1971, by The Objectivist. Reprinted with permission of Harper & Row, Publishers, Inc. Excerpts from Atlas Shrugged, copyright © 1957 by Ayn Rand, The Fountainhead, copyright © 1943 by Ayn Rand, and For the New Intellectual, copyright © 1961 by Ayn Rand. Reprinted by permission of the Estate of Ayn Rand. Excerpts from Philosophy: Who Needs It, by Ayn Rand. Copyright © 1982 by Leonard Peikoff, Executor, Estate of Ayn Rand. Reprinted by permission of the Estate of Ayn Rand. Excerpts from “The Philosophy of Objectivism” lecture series. Copyright © 1976 by Leonard Peikoff. Reprinted by permission. Excerpts from Alvin Toffler’s interview with Ayn Rand, which first appeared in Playboy magazine. Copyright © 1964. Reprinted by permission of Alvin Toffler. All rights reserved including the right of reproduction in whole or in part in any form. Used by arrangement with Plume, a member of Penguin Group (USA), Inc.