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Ideas for 'Mahaprajnaparamitashastra', 'The Laws of Thought' and 'On the Frame of Reference'

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3 ideas

5. Theory of Logic / A. Overview of Logic / 2. History of Logic

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.

5. Theory of Logic / G. Quantification / 4. Substitutional Quantification

10009	Substitutional quantification is just a variant of Tarski's account [Wallace, by Baldwin]
	Full Idea: In a famous paper, Wallace argued that all interpretations of quantifiers (including the substitutional interpretation) are, in the end, variants of that proposed by Tarski (in 1936).
	From: report of Wallace, J (On the Frame of Reference [1970]) by Thomas Baldwin - Interpretations of Quantifiers
	A reaction: A significant-looking pointer. We must look elsewhere for Tarski's account, which will presumably subsume the objectual interpretation as well. The ontology of Tarski's account of truth is an enduring controversy.

5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof

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.