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8083
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Boole applied normal algebra to logic, aiming at an algebra of thought [Boole, by Devlin]
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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.
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From:
report of George Boole (The Laws of Thought [1854]) by Keith Devlin - Goodbye Descartes Ch.3
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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.
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8686
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Boole made logic more mathematical, with algebra, quantifiers and probability [Boole, by Friend]
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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.
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From:
report of George Boole (The Laws of Thought [1854], 3.2) by Michčle Friend - Introducing the Philosophy of Mathematics
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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.
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22277
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Boole's method was axiomatic, achieving economy, plus multiple interpretations [Boole, by Potter]
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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.
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From:
report of George Boole (The Laws of Thought [1854]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 02 'Boole'
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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.
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16730
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If matter is entirely atoms, anything else we notice in it can only be modes [Gassendi]
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Full Idea:
Since these atoms are the whole of the corporeal matter or substance that exists in bodies, if we conceive or notice anything else to exist in these bodies, that is not a substance but only some kind of mode of the substance.
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From:
Pierre Gassendi (Syntagma [1658], II.1.6.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 22.4
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A reaction:
If the atoms have a few qualities of their own, are they just modes? If they are genuine powers, then there can be emergent powers, which are rather more than mere 'modes'.
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16619
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We observe qualities, and use 'induction' to refer to the substances lying under them [Gassendi]
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Full Idea:
Nothing beyond qualities is perceived by the senses. …When we refer to the substance in which the qualities inhere, we do this through induction, by which we reason that some subject lies under the quality.
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From:
Pierre Gassendi (Syntagma [1658], II.1.6.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 07.1
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A reaction:
He talks of 'induction' (in an older usage), but he seems to mean abduction, since he never makes any observations of the substances being proposed.
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16593
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Atoms are not points, but hard indivisible things, which no force in nature can divide [Gassendi]
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Full Idea:
The vulgar think atoms lack parts and are free of all magnitude, and hence nothing other than a mathematical point, but it is something solid and hard and compact, as to leave no room for division, separation and cutting. No force in nature can divide it.
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From:
Pierre Gassendi (Syntagma [1658], II.1.3.5), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 03.2
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A reaction:
If you gloatingly think the atom has now been split, ask whether electrons and quarks now fit his description. Pasnau notes that though atoms are indivisible, they are not incorruptible, and could go out of existence, or be squashed.
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16729
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How do mere atoms produce qualities like colour, flavour and odour? [Gassendi]
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Full Idea:
If the only material principles of things are atoms, having only size, shape, and weight, or motion, then why are so many additional qualities created and existing within the things: color, heat, flavor, odor, and innumerable others?
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From:
Pierre Gassendi (Syntagma [1658], II.1.5.7), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 22.4
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A reaction:
This is pretty much the 'hard question' about the mind-body relation. Bacon said that heat was just motion of matter. I would say that this problem is gradually being solved in my lifetime.
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