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All the ideas for 'Letters to Edward Stillingfleet', 'The Poverty of Philosophy' and 'works'

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5 ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle

15941	For intuitionists excluded middle is an outdated historical convention [Brouwer]
	Full Idea: From the intuitionist standpoint the dogma of the universal validity of the principle of excluded third in mathematics can only be considered as a phenomenon of history of civilization, like the rationality of pi or rotation of the sky about the earth.
	From: Luitzen E.J. Brouwer (works [1930]), quoted by Shaughan Lavine - Understanding the Infinite VI.2
	A reaction: [Brouwer 1952:510-11]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy

18247	Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro]
	Full Idea: In his early writing, Brouwer took a real number to be a Cauchy sequence determined by a rule. Later he augmented rule-governed sequences with free-choice sequences, but even then the attitude is that Cauchy sequences are potential, not actual infinities.
	From: report of Luitzen E.J. Brouwer (works [1930]) by Stewart Shapiro - Philosophy of Mathematics 6.6
	A reaction: This is the 'constructivist' view of numbers, as espoused by intuitionists like Brouwer.

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.

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.

24. Political Theory / D. Ideologies / 11. Capitalism

21994	The handmill gives feudalism, the steam mill capitalism [Marx]
	Full Idea: The handmill gives you society with the feudal lord; the steam mill society with the industrial capitalist.
	From: Karl Marx (The Poverty of Philosophy [1847], p.202), quoted by Peter Singer - Marx 7
	A reaction: If technology dictates social structure, then feudalism is still with us, in low-tech industries. What if the steam mill had been invented in 1300?