Lonergan’s achievement – like the achievements of Euclid, Newton, and Einstein – was “to bring together many scattered theorems by setting up a unitary basis that would handle all of them and a great number of others as well.” Note in the excerpts below these phrases
a field of greater generality
an enlarged and radically different field
(analytical) level of system
one single organized subject
a determinate systematic structure
a determinate field
a single explanatory unity
the stability of the sets and patterns of dynamic relationships
Generalization comes with Newton, who attacked the general theory of motion, laid down its pure theory, identified Kepler’s and Galileo’s laws by inventing the calculus, and so found himself in a position to account for any corporeal motion known.Aristotle, Ptolemy, Copernicus, Galilei, and Kepler had all been busy with particular classes of moving bodies.Newton dealt in the same way with all.He did so by turning to a field of greater generality, the laws of motion, and by finding a deeper unity in the apparent disparateness of Kepler’s ellipse and Galilei’s time squared. … Similarly the non-Euclidean geometers and Einstein went beyond Euclid and Newton. … The non-Euclideans moved geometry back to premises more remote than Euclid’s axioms, they developed methods of their own quite unlike Euclid’s, and though they did not impugn Euclid’s theorems, neither were they very interested in them; casually and incidentally they turn them up as particular cases in an enlarged and radically different field. … Einstein went beyond Newton by employing the new geometries to make time an independent variable; and as Newton transformed the formulation and interpretation of Kepler’s laws, so Einstein transforms the Newtonian laws of motion. … It is, we believe, a scientific generalization of the old political economy and of modern economics that will yield the new political economy which we need. … Plainly theway out is through a more general field. [CWL 21, 6-7]Continue reading →
The Weekend Wall Street Journal, 2/5-6/2022, featured Frank Wilczek’s (MIT) column entitled “We’re All Still Living in Euclid’s World.” The article prompts further thinking about how space, space-time, and generalized coordinatesunderly Bernard Lonergan’s pretio-quantitalFunctional Macroeconomic Dynamics, AKA Macroeconomic Field Theory. (continue reading)
The non-Euclideans moved geometry back to premises more remote than Euclid’s axioms, they developed methods of their own quite unlike Euclid’s, and though they did not impugn Euclid’s theorems, neither were they very interested in them; casually and incidentally they turn them up as particular cases in an enlarged and radically different field. Continue reading →
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 andEinstein, 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)