8083
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Boole applied normal algebra to logic, aiming at an algebra of thought [Boole, by Devlin]
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Full Idea:
Boole proposed to use the entire apparatus of a school algebra class, with operations such as addition and multiplication, methods to solve equations, and the like, to produce an algebra of thought.
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From:
report of George Boole (The Laws of Thought [1854]) by Keith Devlin - Goodbye Descartes Ch.3
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A reaction:
The Stoics didn’t use any algebraic notation for their study of propositions, so Boole's idea launched full blown propositional logic, and the rest of modern logic followed. Nice one.
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8686
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Boole made logic more mathematical, with algebra, quantifiers and probability [Boole, by Friend]
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Full Idea:
Boole (followed by Frege) began to turn logic from a branch of philosophy into a branch of mathematics. He brought an algebraic approach to propositions, and introduced the notion of a quantifier and a type of probabilistic reasoning.
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From:
report of George Boole (The Laws of Thought [1854], 3.2) by Michèle Friend - Introducing the Philosophy of Mathematics
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A reaction:
The result was that logic not only became more mathematical, but also more specialised. We now have two types of philosopher, those steeped in mathematical logic and the rest. They don't always sing from the same songsheet.
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22277
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Boole's method was axiomatic, achieving economy, plus multiple interpretations [Boole, by Potter]
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Full Idea:
Boole's work was an early example of the axiomatic method, whereby intellectual economy is achieved by studying a set of axioms in which the primitive terms have multiple interpretations.
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From:
report of George Boole (The Laws of Thought [1854]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 02 'Boole'
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A reaction:
Unclear about this. I suppose the axioms are just syntactic, and a range of semantic interpretations can be applied. Are De Morgan's Laws interpretations, or implications of the syntactic axioms? The latter, I think.
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7322
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Constitutive scepticism is about facts, and epistemological scepticism about our ability to know them [Miller,A]
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Full Idea:
We should distinguish 'constitutive scepticism' (about the existence of certain sorts of facts) from the traditional 'epistemological scepticism' (which concedes that the sort of fact in question exists, but questions our right to claim knowledge of it).
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From:
Alexander Miller (Philosophy of Language [1998], 4.7)
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A reaction:
I would be inclined to call the first type 'ontological scepticism'. Miller is discussing Quine's scepticism about meaning. Atheists fall into the first group, and agnostics into the second. An important, and nicely simple, distinction.
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7325
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Dispositions say what we will do, not what we ought to do, so can't explain normativity [Miller,A]
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Full Idea:
Dispositional facts are facts about what we will do, not about what we ought to do, and as such cannot capture the normativity of meaning.
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From:
Alexander Miller (Philosophy of Language [1998], 6.2)
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A reaction:
Miller is discussing language, but this raises a nice question for all behaviourist accounts of mental events. Perhaps there is a disposition to behave in a guilty way if you do something you think you shouldn't do. (Er, isn't 'guilt' a mental event?)
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7324
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Explain meaning by propositional attitudes, or vice versa, or together? [Miller,A]
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Full Idea:
Grice wants to explain linguistic meaning in terms of the content of propositional attitudes, Dummett has championed the view that propositional attitudes must be explained by linguistic meaning, while Davidson says they must be explained together.
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From:
Alexander Miller (Philosophy of Language [1998], 6.1)
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A reaction:
A useful map. My intuition says propositional attitudes come first, for evolutionary reasons. We are animals first, and speakers second. Thought precedes language. A highly social animal flourishes if it can communicate.
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7328
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The principle of charity is holistic, saying we must hold most of someone's system of beliefs to be true [Miller,A]
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Full Idea:
Properly construed, the principle of charity is a holistic constraint applying, not to individual beliefs, but rather to systems of belief: we must interpret a speaker so that most of the beliefs in his system are, by our lights, true.
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From:
Alexander Miller (Philosophy of Language [1998], 8.7)
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A reaction:
This is a lot more plausible than applying the principle to individual sentences, particularly if you are in the company of habitual ironists or constitutional liars.
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