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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.

“The Cognitive Role of Concepts”
Introduction to Objectivist Epistemology, 64

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.

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