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Kantian and Cartesian scepticism
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…
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On the Unity of Kant’s Many Cognitive Powers
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…
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On the Claim that Properties are Sets
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…
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On the end of analytic philosophy
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…
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Mathematical proof: a primer
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.…
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Peano and the natural numbers
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,…
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Ted Sider on Vagueness, Logic and Reality
For my Philosophy of Time course, my students and I read the second chapter of Ted Sider’s Four-Dimensionalism (2001). It’s called “Against Presentism” and serves very well as an introduction to attacks on that particular position. Perhaps I’ll blog about this chapter later on: as a defender of presentism, I certainly have some critical thoughts.…