Combining Texts

All the ideas for 'fragments/reports', 'Between Facts and Norms' and 'works'

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4 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15941	For intuitionists excluded middle is an outdated historical convention [Brouwer]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 / C. Structure of Objects / 6. Constitution of an Object

6019	If someone squashed a horse to make a dog, something new would now exist [Mnesarchus]
	Full Idea: If, for the sake of argument, someone were to mould a horse, squash it, then make a dog, it would be reasonable for us on seeing this to say that this previously did not exist but now does exist.
	From: Mnesarchus (fragments/reports [c.120 BCE]), quoted by John Stobaeus - Anthology 179.11
	A reaction: Locke would say it is new, because the substance is the same, but a new life now exists. A sword could cease to exist and become a new ploughshare, I would think. Apply this to the Ship of Theseus. Is form more important than substance?

22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention

15672	Actions norms are only valid if everyone possibly affected is involved in the discourse [Habermas]
	Full Idea: Only those action norms are valid to which all possibly affected persons could agree as participants in rational discourse.
	From: Jürgen Habermas (Between Facts and Norms [1996], p.107), quoted by James Gordon Finlayson - Habermas Ch.6:79
	A reaction: This remark stands somewhere between Kant and Rawls. The Holocaust stands behind Habermas's philosophy. The thought, I suppose, is that it would never have happened if everybody had been fully involved in the original discourse about it.