|
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.
|
|
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.
|
|
12298
|
Genuine motion, rather than variation of position, requires the 'entire presence' of the object [Fine,K]
|
|
Full Idea:
In order to have genuine motion, rather than mere variation in position, it is necessary that the object should be 'entirely present' at each moment of the change. Thus without entire presence, or existence, genuine motion will not be possible.
|
|
From:
Kit Fine (In Defence of Three-Dimensionalism [2006], p.6)
|
|
A reaction:
See Idea 4786 for a rival view of motion. Of course, who says we have to have Kit Fine's 'genuine' motion, if some sort of ersatz motion still gets you to work in the morning?
|
|
12296
|
4-D says things are stretched in space and in time, and not entire at a time or at a location [Fine,K]
|
|
Full Idea:
Four-dimensionalists have thought that a material thing is as equally 'stretched out' in time as it is in space, and that there is no special way in which it is entirely present at a moment rather than at a position.
|
|
From:
Kit Fine (In Defence of Three-Dimensionalism [2006], p.1)
|
|
A reaction:
Compare his definition of 3-D in Idea 12295. The 4-D is contrary to our normal way of thinking. Since I don't think the future exists, I presume that if I am a 4-D object then I have to say that I don't yet exist, and I disapprove of such talk.
|
|
18882
|
You can ask when the wedding was, but not (usually) when the bride was [Fine,K, by Simons]
|
|
Full Idea:
Fine says it is acceptable to ask when a wedding was and where it was, and it is acceptable to ask or state where the bride was (at a certain time), but not when she was.
|
|
From:
report of Kit Fine (In Defence of Three-Dimensionalism [2006], p.18) by Peter Simons - Modes of Extension: comment on Fine p.18
|
|
A reaction:
This is aimed at three-dimensionalists who seem to think that a bride is a prolonged event, just as a wedding is. Fine is, interestingly, invoking ordinary language. When did the wedding start and end? When was the bride's birth and death?
|
|
12297
|
Three-dimensionalist can accept temporal parts, as things enduring only for an instant [Fine,K]
|
|
Full Idea:
Even if one is a three-dimensionalist, one might affirm the existence of temporal parts, on the grounds that everything merely endures for an instant.
|
|
From:
Kit Fine (In Defence of Three-Dimensionalism [2006], p.2)
|
|
A reaction:
This seems an important point, as belief in temporal parts is normally equated with four-dimensionalism (see Idea 12296). The idea is that a thing might be 'entirely present' at each instant, only to be replaced by a simulacrum.
|