Mathematics

  • Introduction to Objectivist Epistemology
    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.
  • Introduction to Objectivist Epistemology
    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.
  • Introduction to Objectivist Epistemology

    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.