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Suggestions for popular accounts of the Lobachevsky/Kant situation?
As any mathematician or even good philosopher, and many physicists or even readers of Dostoevsky know, Lobachevsky's non-Euclidean geometry detroyed Kant's main thesis in his Critique of Pure Reason, to wit, that there exists a priori synthetic truths. Fine, I know that, but if I want to recommend a popular book related this history, without too many technical details but also not down to idiot level, to someone who is not a mathematician, philosopher, physicist, or reader of Dostoevsky, what books exist, if any? A search on Google turned up some books but none which would appeal to the lay reader. Please, actual recommendations; wisecracks tend to be less amusing that their authors thinks.
Yahoo does not register when I try to select Bob's answer as best answer. I tried this on different days and from different browsers.
I would have rated it "thorough and informative" even though he could not come up with any books (reasonable, if there are none).
My comments, down to the restricted number of characters allowed, would have been:
"Thanks, I downloaded those sources, and will enjoy reading them. You're probably right about the layman's version.The Antinomies contained a kernel of Model Theory, formalists are still healthy despite Gödel, but even physicists were not applying anything like Riemannian manifolds,let alone Kant?"
1 Answer
- 8 years agoFavorite Answer
Whether or not Lobachevsky's geometry is incompatible with Kant's philosophy is disputed (CF. Ernst Cassirer). There are scholars who believe Kant, who was adept in physics, knew of the possibility of non-euclidean geometry and anticipated it in his system.
See http://www.academia.edu/531648/Between_Euclid_Kant...
In particular, I remember a passage from the critique of pure reason in which Kant remarks that it is possible for one to construct a system of concepts that defies our intuitions about objects, but that it would be merely formal and incapable of being represented in a manifold of pure intuition. Indeed, this rebuke of "empty formalism" was how many reacted to Lobachevsky's geometry as well as to the arithmetic of Dedekind.
Perhaps have a look at "The Fact of Modern Mathematics: Geometry, Logic, and Concept Formation in Kant and Cassirer" By Heis.
As for an explanation for the layman, I doubt you will find it because there is usually no market for such things.
Source(s): I'm smart
