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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 Michèle 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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14067
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Clay and statue are two objects, which can be named and reasoned about [Gibbard]
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Full Idea:
The piece of clay and the statue are 'objects' - that is to say, they can be designated with proper names, and the logic we ordinarily use will still apply.
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From:
Allan Gibbard (Contingent Identity [1975], I)
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A reaction:
An interesting indication of the way that 'object' is used in modern analytic philosophy, which may not be the way that it is used in ordinary English. The number 'seven', for example, seems to be an object by this criterion.
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12887
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A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim]
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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.
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From:
Rescher,N/Oppenheim,P (Logical Analysis of Gestalt Concepts [1955], p.90), quoted by Peter Simons - Parts 9.2
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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.
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14076
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Essentialism is the existence of a definite answer as to whether an entity fulfils a condition [Gibbard]
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Full Idea:
Essentialism for a class of entities is that for one entity and a condition which it fulfills, the question of whether it necessarily fulfills the condition has a definite answer apart from the way the entity is specified.
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From:
Allan Gibbard (Contingent Identity [1975], VII)
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A reaction:
Yet another definition of essentialism, but resting, as usual in modern discussions, entirely on the notion of necessity. Kit Fine's challenge is that if you investigate the source of the necessity, it turns out to be an essence.
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14070
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A particular statue has sortal persistence conditions, so its origin defines it [Gibbard]
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Full Idea:
A proper name like 'Goliath' denotes a thing in the actual world, and invokes a sortal with certain persistence criteria. Hence its origin makes a statue the statue that it is, and if statues in different worlds have the same beginning, they are the same.
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From:
Allan Gibbard (Contingent Identity [1975], III)
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A reaction:
Too neat. There are vague, ambiguous and duplicated origins. Persistence criteria can shift during the existence of a thing (like a club which changes its own constitution). In replicated statues, what is the status of the mould?
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14074
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Leibniz's Law isn't just about substitutivity, because it must involve properties and relations [Gibbard]
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Full Idea:
As a general law of substitutivity of identicals, Leibniz's Law is false. It is a law about properties and relations, that if two things are identical, they have the same properties and relations. It only works in contexts which attribute those.
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From:
Allan Gibbard (Contingent Identity [1975], V)
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A reaction:
I'm not convinced about relations, which are not intrinsic properties. Under different descriptions, the relations to human minds might differ.
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14078
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Only concepts, not individuals, can be the same across possible worlds [Gibbard]
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Full Idea:
It is meaningless to talk of the same concrete thing in different possible worlds, ...but it makes sense to speak of the same individual concept, which is just a function which assigns to each possible world in a set an individual in that world.
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From:
Allan Gibbard (Contingent Identity [1975], VII)
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A reaction:
A lovely bold response to the problem of transworld identity, but one which needs investigation. It sounds very promising to me. 'Aristotle' is a cocept, not a name. There is no separate category of 'names'. Wow. (Attach dispositions to concepts?).
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