12 ideas
| 8083 | Boole applied normal algebra to logic, aiming at an algebra of thought [Boole, by Devlin] |
| 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. | |
| From: report of George Boole (The Laws of Thought [1854]) by Keith Devlin - Goodbye Descartes Ch.3 | |
| 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. |
| 7727 | Boole's notation can represent syllogisms and propositional arguments, but not both at once [Boole, by Weiner] |
| Full Idea: Boole introduced a new symbolic notation in which it was possible to represent both syllogisms and propositional arguments, ...but not both at once. | |
| From: report of George Boole (The Laws of Thought [1854], Ch.3) by Joan Weiner - Frege | |
| A reaction: How important is the development of symbolic notations for the advancement of civilisations? Is there a perfect notation, as used in logical heaven? |
| 8686 | Boole made logic more mathematical, with algebra, quantifiers and probability [Boole, by Friend] |
| 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. | |
| From: report of George Boole (The Laws of Thought [1854], 3.2) by Michèle Friend - Introducing the Philosophy of Mathematics | |
| 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. |
| 22277 | Boole's method was axiomatic, achieving economy, plus multiple interpretations [Boole, by Potter] |
| 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. | |
| From: report of George Boole (The Laws of Thought [1854]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 02 'Boole' | |
| 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. |
| 4261 | The Lottery Paradox says each ticket is likely to lose, so there probably won't be a winner [Bonjour, by PG] |
| Full Idea: The Lottery Paradox says that for 100 tickets and one winner, each ticket has a .99 likelihood of defeat, so they are all likely to lose, so there is unlikely to be a winner. | |
| From: report of Laurence Bonjour (Externalist Theories of Empirical Knowledge [1980], §5) by PG - Db (ideas) | |
| A reaction: The problem seems to be viewing each ticket in isolation. If I buy two tickets, I increase my chances of winning. |
| 4255 | Externalist theories of knowledge are one species of foundationalism [Bonjour] |
| Full Idea: Externalist theories of knowledge are one species of foundationalism. | |
| From: Laurence Bonjour (Externalist Theories of Empirical Knowledge [1980], Intro) | |
| A reaction: I don't see why there shouldn't be a phenomenalist, anti-realist version of externalism, which just has 'starting points' instead of a serious commitment to foundations. |
| 4257 | The big problem for foundationalism is to explain how basic beliefs are possible [Bonjour] |
| Full Idea: The fundamental question that must be answered by any acceptable version of foundationalism is: how are basic beliefs possible? | |
| From: Laurence Bonjour (Externalist Theories of Empirical Knowledge [1980], §I) | |
| A reaction: This question seems to be asking for a justification for basic beliefs, which smacks of 'Who made God?' Look, basic beliefs are just basic, right? |
| 4256 | The main argument for foundationalism is that all other theories involve a regress leading to scepticism [Bonjour] |
| Full Idea: The central argument for foundationalism is simply that all other possible outcomes of the regress of justifications lead inexorably to scepticism. | |
| From: Laurence Bonjour (Externalist Theories of Empirical Knowledge [1980], §I) | |
| A reaction: If you prefer coherence to foundations, you need the security of reason to assess the coherence (which seems to be an internal foundation!). |
| 4258 | Extreme externalism says no more justification is required than the truth of the belief [Bonjour] |
| Full Idea: The most extreme version of externalism would be one that held that the external condition required for justification is simply the truth of the belief in question. | |
| From: Laurence Bonjour (Externalist Theories of Empirical Knowledge [1980], §II) | |
| A reaction: The question is, why should we demand any more than this? The problem case is, traditionally, the lucky guess, but naturalist may say that these just don't occur with any regularity. We only get beliefs right because they are true. |
| 4259 | External reliability is not enough, if the internal state of the believer is known to be irrational [Bonjour] |
| Full Idea: External or objective reliability is not enough to offset subjective irrationality (such as unexplained clairvoyance). | |
| From: Laurence Bonjour (Externalist Theories of Empirical Knowledge [1980], §IV) | |
| A reaction: A good argument. Where do animals fit into this? If your clairvoyance kept working, in the end you might concede that you 'knew', even though you were baffled about how you managed it. |
| 4260 | Even if there is no obvious irrationality, it may be irrational to base knowledge entirely on external criteria [Bonjour] |
| Full Idea: It may be that where there are no positive grounds for a charge of irrationality, the acceptance of a belief with only external justification is still subjectively irrational in a sense that rules out its being epistemologically justified. | |
| From: Laurence Bonjour (Externalist Theories of Empirical Knowledge [1980], §IV) | |
| A reaction: A key objection. Surely rational behaviour requires a judgement to be made before a belief is accepted? If you are consistently clairvoyant, you must ask why. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |