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On knowledge and belief
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…
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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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The 50 book challenge
In 2019, I read 27 books. But I wanted to read more. I wanted to find a way to motivate myself to pick up a book in the evening, rather than spend time on my phone, or the internet, or playing a computer game, or doing who knows what. I love reading books. But it’s…
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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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I stepped into – God’s World – today –
(After Dickinson) I stepped into – God’s World – today – It fully to – Explore His Landscaping was – Total His Seasons were – the Four I saw – an Isle – of Fantasy – Was floating down – the Street A place where burning – Bodies – came When Minds – had failed…
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Trump’s Failure
For months, Donald Trump has laid the groundwork for his post-election strategy: refuse to concede, start legal challenges, undermine the legitimacy of the democratic process and of Biden’s victory. And yet, this strategy continues to surprise me. And it should surprise you too, for it makes little sense. How is it possible that at this…