|
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.
|
|
14528
|
Maybe modal thought is unavoidable, as a priori recognition of necessary truth-preservation in reasoning [Hale/Hoffmann,A]
|
|
Full Idea:
There are 'transcendental' arguments saying that modal thought is unavoidable - recognition, a priori, of the necessarily truth-preserving character of some forms of inference is a precondition for rational thought in general, and scientific theorizing.
|
|
From:
Bob Hale/ Aviv Hoffmann (Introduction to 'Modality' [2010], 1)
|
|
A reaction:
So the debate about the status of logical truths and valid inference, are partly debates about whether out thought has to involve modality, or whether it could just be about the actual world. I take possibilities and necssities to be features of nature.
|
|
20653
|
Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson]
|
|
Full Idea:
There are six 'reductive levels' in science: social groups, (multicellular) living things, cells, molecules, atoms, and elementary particles.
|
|
From:
report of H.Putnam/P.Oppenheim (Unity of Science as a Working Hypothesis [1958]) by Peter Watson - Convergence 10 'Intro'
|
|
A reaction:
I have the impression that fields are seen as more fundamental that elementary particles. What is the status of the 'laws' that are supposed to govern these things? What is the status of space and time within this picture?
|