|
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.
|
|
12887
|
A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim]
|
|
Full Idea:
A whole must possess an attribute peculiar to and characteristic of it as a whole; there must be a characteristic relation of dependence between the parts; and the whole must have some structure which gives it characteristics.
|
|
From:
Rescher,N/Oppenheim,P (Logical Analysis of Gestalt Concepts [1955], p.90), quoted by Peter Simons - Parts 9.2
|
|
A reaction:
Simons says these are basically sensible conditions, and tries to fill them out. They seem a pretty good start, and I must resist the temptation to rush to borderline cases.
|
|
11248
|
Necessary truths can be two-way relational, where essential truths are one-way or intrinsic [Politis]
|
|
Full Idea:
An essence is true in virtue of what the thing is in itself, but a necessary truth may be relational, as the consequence of the relation between two things and their essence. The necessary relation may be two-way, but the essential relation one-way.
|
|
From:
Vassilis Politis (Aristotle and the Metaphysics [2004], 2.3)
|
|
A reaction:
He is writing about Aristotle, but has in mind Kit Fine 1994 (qv). Politis cites Plato's answer to the Euthyphro Question as a good example. The necessity comes from the intrinsic nature of goodness/piety, not from the desire of the gods.
|