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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…
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Two sonnets on rocks
I wrote two sonnets today. First, one about rocks. Then, another one about rocks, but now starting from (a variant on) the line “He cracked her open to her very core.” Sonnet. On the Topic of Rocks O rocks, o little rocks, you small parts of the EarthO rough detachèd flakes from off our Mother’s…
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Evangelist of Nature
This is my letter to the WorldThat never wrote to Me —The simple News that Nature told —With tender Majesty Her Message is committedTo Hands I cannot see —For love of Her — Sweet — countrymen —Judge tenderly — of Me On a first reading of this Emily Dickinson poem (#519 in the Franklin edition),…
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W. F. Hermans (2011)
Die liefde heet ik geen manie die ieder voelt voor zijn genie ik lees zijn boeken vol emotie en kniel dan neder in devotie voor W. F. Hermans, kloeke held die ons de Waarheid heeft verteld die in de kern der wereld zag en niets vond dan wat hoongelach. Mijn hart versnelt als ik hem…
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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.…