Plato's Math Errors Mislead Us Still
4. Many “suspect that there is a very beautiful theory of economics out there” awaiting discovery. Plato’s enchanting faith that the “fabric of reality” is mathematical, remains strong among physicists and their imitators.
5. Faith within mathematics itself has been shaken. Gödel, perhaps the greatest logician since Aristotle (Plato’s star pupil), proved it has internal gaps. Gödel’s Incompleteness Theorem says very roughly that systems of deductions from axioms may have truths that can’t be proven. (see comments below for further reading).
6. Math is also externally incomplete. Many recognizable or named patterns (and their logic) remain beyond its grasp. Can math help in understanding the average sentence or story? Or the patterns called tartan or tragedy? Semantic and visual and mathematical patterns are cognitively distinct.
7. Semantic and visual patterns may be partially mathematically describable. But much linguistic or visual meaning can’t be captured mathematically (and math is mostly beyond words).
8. Mathematically descriptive ≠ usefully predictive. See “Newton pattern vs Darwin pattern.”
10. Even statistics and probability can’t always help. They’re basically historical and limited by needing independent variables and stable relationships (which social sciences often lack).
Can math sum up all patterns? Is that a “rational” faith?
Illustration by Julia Suits, The New Yorker Cartoonist & author of The Extraordinary Catalog of Peculiar Inventions.
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