Combining Texts

All the ideas for 'Letters to Edward Stillingfleet', 'The Laws of Thought' and 'Tractatus'

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7 ideas

4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic

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.

7727	Boole's notation can represent syllogisms and propositional arguments, but not both at once [Boole, by Weiner]
	Full Idea: Boole introduced a new symbolic notation in which it was possible to represent both syllogisms and propositional arguments, ...but not both at once.
	From: report of George Boole (The Laws of Thought [1854], Ch.3) by Joan Weiner - Frege
	A reaction: How important is the development of symbolic notations for the advancement of civilisations? Is there a perfect notation, as used in logical heaven?

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 / 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.

9. Objects / D. Essence of Objects / 3. Individual Essences

15990	Every individual thing which exists has an essence, which is its internal constitution [Locke]
	Full Idea: I take essences to be in everything that internal constitution or frame for the modification of substance, which God in his wisdom gives to every particular creature, when he gives it a being; and such essences I grant there are in all things that exist.
	From: John Locke (Letters to Edward Stillingfleet [1695], Letter 1), quoted by Simon Blackburn - Quasi-Realism no Fictionalism
	A reaction: This is the clearest statement I have found of Locke's commitment to essences, for all his doubts about whether we can know such things. Alexander says (ch.13) Locke was reacting against scholastic essence, as pertaining to species.

9. Objects / E. Objects over Time / 10. Beginning of an Object

16706	Generation is when local motions aggregate to become a single subject [Nicholas of Autrecourt]
	Full Idea: In the case of natural things there is only local motion. When from such motion there follows an aggregation of natural bodies that are gathered to one another and acquire the nature of a single subject, this is called generation.
	From: Nicholas of Autrecourt (Tractatus [1335], Ch. 1)
	A reaction: This is explosive atomistic corpuscularianism, three centuries before its appointed date. He was duly suppressed. Can he give an account of the 'nature of a single subject' in this way?

11. Knowledge Aims / B. Certain Knowledge / 1. Certainty

15994	If it is knowledge, it is certain; if it isn't certain, it isn't knowledge [Locke]
	Full Idea: What reaches to knowledge, I think may be called certainty; and what comes short of certainty, I think cannot be knowledge.
	From: John Locke (Letters to Edward Stillingfleet [1695], Letter 2), quoted by Simon Blackburn - Quasi-Realism no Fictionalism
	A reaction: I much prefer that fallibilist approach offered by the pragmatists. Knowledge is well-supported belief which seems (and is agreed) to be true, but there is a small shadow of doubt hanging over all of it.