Mathematics for Humans: Kant’s Philosophy of Arithmetic Revisited–A Podcast.

2 min readSep 29, 2025

By Robert Hanna and Scott Heftler

In “Mathematics for Humans: Kant’s Philosophy of Arithmetic Revisited,” Robert Hanna revisits Immanuel Kant’s much-criticized views on mathematics in general and arithmetic in particular. In so doing, he makes a case for the claim that Kant’s theory of arithmetic is not subject to the most familiar and forceful objection against it, namely, that his doctrine of the dependence of arithmetic on time is plainly false, or even worse, simply unintelligible. On the contrary, Kant’s doctrine about time and arithmetic is highly original, fully intelligible, and with qualifications due to the inherent limitations of his conceptions of arithmetic and
logic, to an important extent defensible. Hanna’s argument has three stages. In the first stage, he reconstructs Kant’s argument for the synthetic apriority of arithmetic (section II). In the second stage, he develops a new account of Kant’s notorious doctrine of the dependence of arithmetic on time (section III). And finally, in the third stage, he develops a correspondingly new account of the Kantian notion of arithmetical construction (section IV).

REFERENCE

(Zwarenstein, 2024). Zwarenstein, C. “Numbers Game: Is Math the Language of Nature or Just a Human Construct?” Salon. 27 July. Available online at URL = <https://www.salon.com/2024/07/27/numbers-game-is-math-the-language-of-nature-or-just-a-human-construct/>.

***

You can find an accessible but also fully detailed podcast on Hanna’s “Mathematics for Humans: Kant’s Philosophy of Arithmetic Revisited,” created by Scott Heftler and other friends of Philosophy Without Borders, HERE.

And you can also download and read or share a .pdf of the full text of “Mathematics for Humans: Kant’s Philosophy of Arithmetic Revisited” by clicking on the Download tab directly below.

Download