11 ideas
| 15527 | Defining terms either enables elimination, or shows that they don't require elimination [Lewis] |
| Full Idea: To define theoretical terms might be to show how to do without them, but it is better to say that it shows there is no good reason to want to do without them. | |
| From: David Lewis (How to Define Theoretical Terms [1970], Intro) |
| 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. |
| 15530 | A logically determinate name names the same thing in every possible world [Lewis] |
| Full Idea: A logically determinate name is one which names the same thing in every possible world. | |
| From: David Lewis (How to Define Theoretical Terms [1970], III) | |
| A reaction: This appears to be rigid designation, before Kripke introduced the new word. |
| 1556 | By nature people are close to one another, but culture drives them apart [Hippias] |
| Full Idea: I regard you all as relatives - by nature, not by convention. By nature like is akin to like, but convention is a tyrant over humankind and often constrains people to act contrary to nature. | |
| From: Hippias (fragments/reports [c.430 BCE]), quoted by Plato - Protagoras 337c8 |
| 15528 | A Ramsey sentence just asserts that a theory can be realised, without saying by what [Lewis] |
| Full Idea: If we specify a theory with all of its terms, and then replace all of those terms with variables, we can then say that some n-tuples of entities can satisfy this formula. This Ramsey sentence then says the theory is realised, without specifying by what. | |
| From: David Lewis (How to Define Theoretical Terms [1970], II) | |
| A reaction: [I have compressed Lewis, and cut out the symbolism] |
| 15526 | There is a method for defining new scientific terms just using the terms we already understand [Lewis] |
| Full Idea: I contend that there is a general method for defining newly introduced terms in a scientific theory, one which uses only the old terms we understood beforehand. | |
| From: David Lewis (How to Define Theoretical Terms [1970], Intro) | |
| A reaction: Lewis is game is to provide bridge laws for a reductive account of nature, without having to introduce something entirely new to achieve it. The idea of bridge laws in scientific theory is less in favour these days. |
| 15529 | It is better to have one realisation of a theory than many - but it may not always be possible [Lewis] |
| Full Idea: A uniquely realised theory is, other things being equal, certainly more satisfactory than a multiply realised theory. We should insist on unique realisation as a standard of correctness unless it is a standard too high to be met. | |
| From: David Lewis (How to Define Theoretical Terms [1970], III) | |
| A reaction: The point is that rewriting a theory as Ramsey sentences just says there is at least one realisation, and so it doesn't meet the highest standards for scientific theories. The influence of set-theoretic model theory is obvious in this approach. |
| 15531 | The Ramsey sentence of a theory says that it has at least one realisation [Lewis] |
| Full Idea: The Ramsey sentence of a theory says that it has at least one realisation. | |
| From: David Lewis (How to Define Theoretical Terms [1970], V) |