Category Archives: Mathematics and Isomorphism

Functions Are Not Seen, But Must Be Understood

Functions are not seen, but must be understood. (Catherine Blanche King, private communication)

A systematic explanation, then, requires a normative theoretical framework.  The basic terms and relations of such a framework would specify the distinctions and correlations that articulate the causes, which are not necessarily visible, of events that are apparent to all.  (CWL 15,  Editors’ Introduction, lv) (Continue reading)

Theoretical Breakthroughs of Euclid, Newton, Hilbert, Einstein, and Lonergan

To help the reader gain an appreciation of Lonergan’s achievement of Modern Macroeconomic Field Theory we will, in each section, print leading excerpts, then highlight the key concepts of those excerpts. We will comment on the historically-significant advances in geometry of Euclid and Hilbert, in physics of Newton and Einstein, and in macroeconomics of Lonergan.

  • Euclid’s great achievement was his rigorous deduction of geometry.
  • Hilbert’s great achievement was his employment of implicit definition to reorder Euclid’s geometry.
  • Newton’s two great achievements were unifying the isolated insights of Galileo and Kepler into a unified system of mechanics and his invention of the calculus.
  • One of the great achievements of Einstein was the invention of the field theories of Special Relativity, General Relativity, and Gravitation.
  • One of Lonergan’s several great achievements was his systematization of macroeconomic phenomena in his Modern Macroeconomic Field Theory. He combined the technique of implicit definition introduced by Hilbert and the concept of a field theory developed by Faraday and Einstein; and he developed an explanatory macroeconomics, which is general, invariant, and relevant in any instance. (Continue reading)

Why Economists Don’t Flock to Functional Macroeconomic Dynamics

Economists don’t have the methodological and conceptual toolkit needed for appreciation of FMD’s scientific and historical significance.

  • They don’t know what they don’t know.
    • They’re not methodologists and don’t know what constitutes good theory.
    • They never read CWL 3, pages 3-172 and 490-97 and, thus, they never studied the canons of empirical method, especially the Canon of Parsimony and the Canon of Complete Explanation; they have no idea of the deficiencies of their method.
  • Thus, they lack a purely scientific and explanatory heuristic.
    • They do not adequately distinguish description vs. explanation.
    • They do not know the type of answer they’re seeking, i.e. their known unknown.
    • They do not put questions in the right order to discover basic terms of scientific significance.
    • They are mired in muddy premises and disorienting assumptions.
    • They are unable to employ a scientific, dynamic heuristic adequate for analysis of a current, purely dynamic process.
    • They don’t understand what constitutes the normative system’s requirement for  concomitance, continuity, and equilibrium of flows.
  • They lack a background in theoretical physics. They don’t understand the principles and abstract laws of hydrodynamics, electric circuits, or field theory.  Nor do they understand adequately the idea of continuity and the conditions of equilibrium in macroeconomic dynamics.  They are unaware of analogies from physics applicable on the basis of isomorphism to the phenomena of Functional Macroeconomic Dynamics. (Continue reading.)