11 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. |
| 10369 | How fine-grained Kim's events are depends on how finely properties are individuated [Kim, by Schaffer,J] |
| Full Idea: How fine-grained Kim's events are depends on how finely properties are individuated. | |
| From: report of Jaegwon Kim (Events as property exemplifications [1976]) by Jonathan Schaffer - The Metaphysics of Causation 1.2 | |
| A reaction: I don't actually buy the idea that an event could just be an 'exemplification'. Change seems to be required, and processes, or something like them, must be mentioned. Degrees of fine-graining sound good, though, for processes too. |
| 8976 | If events are ordered triples of items, such things seem to be sets, and hence abstract [Simons on Kim] |
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Full Idea:
If Kim's events are just the ordered triple of |
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| From: comment on Jaegwon Kim (Events as property exemplifications [1976]) by Peter Simons - Events 2.1 | |
| A reaction: You might reply that the object, and maybe the attribute, are concrete, and the time is natural, but the combination really is an abstraction, even though it is located (like the equator). Where is the set of my books located? |
| 8975 | Events cannot be merely ordered triples, but must specify the link between the elements [Kim, by Simons] |
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Full Idea:
Kim's events cannot just be the ordered triple of |
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| From: report of Jaegwon Kim (Events as property exemplifications [1976]) by Peter Simons - Events 2.1 | |
| A reaction: Why should they even be in that particular order? This requirement rather messes up Kim's plan for a very streamlined, Ockhamised ontology. Circles have symmetry at all times. Is 'near Trafalgar Square' a property? |
| 8974 | Events are composed of an object with an attribute at a time [Kim, by Simons] |
| Full Idea: Kim's events are exemplifications by an object of an attribute at a time...It does not make events basic entities, as the three constituents are more basic, but it gives identity conditions (two events are the same if object, attribute and time the same). | |
| From: report of Jaegwon Kim (Events as property exemplifications [1976]) by Peter Simons - Events 2.1 | |
| A reaction: [Aristotle is said to be behind this] I am more sympathetic to this view than the claim that events are primitive. If a pebble is ellipsoid for a million years, is that an event? I think the concept of a 'process' is the most fruitful one to investigate. |
| 8977 | Since properties like self-identity and being 2+2=4 are timeless, Kim must restrict his properties [Simons on Kim] |
| Full Idea: Since some tautologously universal properties such as self-identity or being such that 2+2=4 apply to all things at all times, that is stretching Kim's events too far. Candidate properties need to be realistically restricted, and it is unclear how. | |
| From: comment on Jaegwon Kim (Events as property exemplifications [1976]) by Peter Simons - Events 2.1 | |
| A reaction: You could deploy Schoemaker's concept of natural properties in terms of the source of causal powers, but the problem would be that you were probably hoping to then use Kim's events to define causation. Answer: treat causation as the primitive. |
| 8980 | Kim's theory results in too many events [Simons on Kim] |
| Full Idea: The criticism most frequently levelled against Kim's theory is that it results in an unacceptable plurality of finely differentiated events, because of the requirement for identity of the constituent property. | |
| From: comment on Jaegwon Kim (Events as property exemplifications [1976]) by Peter Simons - Events 4.4 | |
| A reaction: This may mean that the Battle of Waterloo was several trillion events, which seems daft to the historian, but it doesn't to the physicist. A cannon firing is indeed an accumulation of lots of little events. |
| 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? |