Reblog: Kant & Leibniz on Space and Implications in Geometry


Mathematicians and philosophers are fairly content to share credit for Rene Descartes, possibly because he was able to provide catchy, easy-to-popularize cornerstones for both fields.

Immanuel Kant, these days at least, is almost exclusively known as a philosopher, and that he was also a mathematician and astronomer is buried in the footnotes. If you stick to math and science popularizations you’ll probably pick up (as I did) that Kant was one of the co-founders of the nebular hypothesis, the basic idea behind our present understanding of how solar systems form, and maybe, if the book has room, that Kant had the insight that knowing gravitation falls off by an inverse-square rule implies that we live in a three-dimensional space.

Frank DeVita here writes some about Kant (and Wilhelm Leibniz)’s model of how we understand space and geometry. It’s not technical in the mathematics sense, although I do appreciate the background in Kant’s philosophy which my Dearly Beloved has given me. In the event I’d like to offer it as a way for mathematically-minded people to understand more of an important thinker they may not have realized was in their field.

Frank DeVita

        

Kant’s account of space in the Prolegomena serves as a cornerstone for his thought and comes about in a discussion of the transcendental principles of mathematics that precedes remarks on the possibility of natural science and metaphysics. Kant begins his inquiry concerning the possibility of ‘pure’ mathematics with an appeal to the nature of mathematical knowledge, asserting that it rests upon no empirical basis, and thus is a purely synthetic product of pure reason (§6). He also argues that mathematical knowledge (pure mathematics) has the unique feature of first exhibiting its concepts in a priori intuition which in turn makes judgments in mathematics ‘intuitive’ (§7.281). For Kant, intuition is prior to our sensibility and the activity of reason since the former does not grasp ‘things in themselves,’ but rather only the things that can be perceived by the senses. Thus, what we can perceive is based…

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Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there.

1 thought on “Reblog: Kant & Leibniz on Space and Implications in Geometry”

  1. As Joseph knows, I have a framed portrait of Kant in my dining room (I have to stop calling things that; now it’s our dining room) that was taken from a set of prints from the Moscow Observatory — I believe from the 1940s — celebrating people who had made contributions to astronomy. I like that I have a souvenir recognizing Kant as an astronomer.

    It used to bother me that people call the nebular hypothesis “the Laplace theory” when Kant’s work on it was earlier. (I have also heard it called “the Kant-Laplace theory,” but, I think, usually by philosophers.) However, then Wikipedia told me that Kant himself may have gotten the rudiments of it from Swedenborg, and no one ever calls it “the Swedenborg-Kant-Laplace” theory, as far as I’ve heard.

    I hope that DeVita’s article called back ideas for you (regarding both Leibniz and Kant) that I tried to explain to you in our cabin on the Amsterdam-Newcastle ferry while fighting off seasickness.

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