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Probability for Philosophers - by Oak - Offhand Quibbles

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I try to lay out the basic bits1 of probability theory which I find especially useful for epistemology. It’s a bit more technical than what I’ve seen online, but I hope it’s still fairly accessible; my target audience is high-school me. For an interesting alternative exposition, see Jaynes’ Probability Theory: The Logic of Science (Ch. 1-2).2 I also try to show that our primitive talk about beliefs and knowledge shouldn’t become deprecated. I should note that this later section is heavily influenced by Williamson’s Knowledge and Its Limits and by general exposure to Williamsonian Thought (e.g., via the formal epistemology graduate seminar at Oxford). Let W be a set. For familiarity, call its elements worlds, and its subsets propositions. A proposition φ is true at some world w just in case w is in φ. Thus, we’ve identified each proposition with the set of worlds at which it’s true. Our logical operators (⊤, ⊥, ¬, ∧, ∨) correspond to the set operators (W, ∅, C, ⋂, ⋃). They work as expec

Probability for Philosophers ...and people who call themselves 'Bayesians' on the internet Oak Aug 13, 2024 12 3 2 Share I try to lay out the basic bits 1 of probability theory which I find especially useful for epistemology. It’s a bit more technical than what I’ve seen online, but I hope it’s still fairly accessible; my target audience is high-school me. For an interesting alternative exposition, see Jaynes’ Probability Theory: The Logic of Science (Ch. 1-2). 2 I also try to show that our primitive talk about beliefs and knowledge shouldn’t become deprecated. I should note that this later se

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