Mathematics is a science of method (the science of measurement, i.e., of establishing quantitative relationships), a cognitive method that enables man to perform an unlimited series of integrations. Mathematics indicates the pattern of the cognitive role of concepts and the psycho-epistemological need they fulfill.

With the grasp of the (implicit) concept “unit,” man reaches the conceptual level of cognition which consists of two interrelated fields: the conceptual and the mathematical. The process of concept-formation is, in large part, a mathematical process.

A vast part of higher mathematics, from geometry on up, is devoted to the task of discovering methods by which various shapes can be measured—complex methods which consist of reducing the problem to the terms of a simple, primitive method, the only one available to man in this field: linear measurement. (Integral calculus, used to measure the area of circles, is just one example.)

In this respect, concept-formation and applied mathematics have a similar task, just as philosophical epistemology and theoretical mathematics have a similar goal: the goal and task of bringing the universe within the range of man’s knowledge—by identifying relationships to perceptual data.

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.