Category Archives: David Hilbert

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)

A Lonergan Sampler

This Sampler will be supplemented as time allows, but I want to publish now to a) demonstrate the breadth and depth of the knowledge that Lonergan brought to Macroeconomic Dynamics, and b) inspire readers to compare their perspective to his.  His thinking ranged over mathematics, natural science, method, history, philosophy, theology, and art.

CWL 3, Insight: A Study of Human Understanding

Now the principles and laws of a geometry are abstract and generally valid propositions. 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)