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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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7903
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The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
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Full Idea:
The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
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From:
Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
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A reaction:
What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').
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22808
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Liberalism is minimal government, or individual rights, or equality [Avineri/De-Shalit]
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Full Idea:
Liberalism has been defended as a theory of minimal government, or as a theory of basic individual rights, or as an egalitarian philosophy.
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From:
Avineri,S/De-Shalit,A (Intro to 'Communitarianism and Individualism' [1992], §5)
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A reaction:
Minimal government tends towards anarchist liberalism, but then what grounds the right to be free of government? Presumably any sensible theory of rights has to be egalitarian. What could ground unequal rights?
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22806
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Communitarians avoid oppression for the common good, by means of small mediating communities [Avineri/De-Shalit]
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Full Idea:
Because of the mediating structures of small communities, communitarians are less fearful [than liberals] of the emergence of an oppressive government as a result of the politics of the common good.
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From:
Avineri,S/De-Shalit,A (Intro to 'Communitarianism and Individualism' [1992], §5)
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A reaction:
A politics of the common good has an obvious implicit conservatism because the central consensus is always likely to disapprove of errant individuals, of all sorts. Only individual rights can block an oppressive government.
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22807
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If our values are given to us by society then we have no grounds to criticise them [Avineri/De-Shalit]
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Full Idea:
If communitarians are right that we are not free to choose, but rather that our values are determined by our community, the individualists say, then there is no reason to criticise the values of one's society.
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From:
Avineri,S/De-Shalit,A (Intro to 'Communitarianism and Individualism' [1992], §5)
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A reaction:
This is an obvious challenge, but if one's concept of community is a forum for free debate then it can be overcome. There is no avoiding the fact, though, that a good community always needs a high degree of consensus.
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