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We are finite knowers. This is a platitude. But it easy to lose sight of what the platitude means. Part of what it means is that we do not know everything; that the amount of things we know is finite — perhaps in the mathematical sense of the term, but certainly, and more importantly, in…

I recently wrote about the unity of Kant’s cognitive powers. Just now I was reading an article by Arata Hamawaki, “Cartesian Skepticism, Kantian Skepticism, and Two Conceptions of Self-consciousness”, published in The Logical Alien: Conant and his Critics, edited by Sofia Miguens. Hamawaki writes something that may seem to contradict the claims that I made…

Recently somebody on Twitter (using the handle @robotsneedpoems) complained to me about the Critique of Pure Reason: It’s crazy to me how confident K[ant] is in his ability to discern discrete cognitive faculties just by reasoning them out. He keeps plowing ahead, constructing a mind-numbingly complex account out of more or less thin air. I…

David Lewis, in his 1986 book On the Plurality of Worlds, argues that properties are sets. Any property should be taken as “the set of all its instances — all of them, this- and other-worldly alike. Thus the property of being a donkey comes out as the set of all donkeys, the donkeys of other…

In his blog post ‘The End of Analytic Philosophy’, Liam Bright paints a starkly pessimistic — almost Spenglerian — view of the current state of what we still call analytic philosophy. I choose that last phrase with care. Once there may have been a coherent conception of philosophy as the discipline whose task it is…

High school mathematics education focuses on calculation. It’s all about getting the right answer to some problem, like finding the x such that x² + 3x = 18. This almost entirely excludes the notion of a mathematical proof, to the point that there are highly educated people who have never even heard of the concept.…

Do Peano’s axioms define the natural numbers? Would it be possible for any system of axioms to do so? Some musings after Mathieu Marion’s article ‘Wittgenstein on Surveyability of Proofs’. (I don’t think there’s anything original in here; it’s just me thinking through the topic.) What are the natural numbers? Of course, they’re 0, 1,…