Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Inventing Logical Necessity' and 'Intuitionism and Formalism'

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8 ideas

4. Formal Logic / E. Nonclassical Logics / 7. Paraconsistency

12452	Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer]
	Full Idea: Not to the mathematician, but to the psychologist, belongs the task of explaining why ...we are averse to so-called contradictory systems in which the negative as well as the positive of certain propositions are valid.
	From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.79)
	A reaction: Was the turning point of Graham Priest's life the day he read this sentence? I don't agree. I take the principle of non-contradiction to be a highly generalised observation of how the world works (and Russell agrees with me).

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics

12451	Scientific laws largely rest on the results of counting and measuring [Brouwer]
	Full Idea: A large part of the natural laws introduced by science treat only of the mutual relations between the results of counting and measuring.
	From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.77)
	A reaction: His point, I take it, is that the higher reaches of numbers have lost touch with the original point of the system. I now see the whole issue as just depending on conventions about the agreed extension of the word 'number'.

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism

12454	Intuitionists only accept denumerable sets [Brouwer]
	Full Idea: The intuitionist recognises only the existence of denumerable sets.
	From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.80)
	A reaction: That takes you up to omega, but not beyond, presumably because it then loses sight of the original intuition of 'bare two-oneness' (Idea 12453). I sympathise, but the word 'number' has shifted its meaning a lot these days.

12453	Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer]
	Full Idea: Neo-intuitionism sees the falling apart of moments, reunited while remaining separated in time, as the fundamental phenomenon of human intellect, passing by abstracting to mathematical thinking, the intuition of bare two-oneness.
	From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.80)
	A reaction: [compressed] A famous and somewhat obscure idea. He goes on to say that this creates one and two, and all the finite ordinals.

10. Modality / A. Necessity / 6. Logical Necessity

12189	Logical necessity involves a decision about usage, and is non-realist and non-cognitive [Wright,C, by McFetridge]
	Full Idea: Wright espouses a non-realist, indeed non-cognitive account of logical necessity. Crucial to this is the idea that acceptance of a statement as necessary always involves an element of decision (to use it in a necessary way).
	From: report of Crispin Wright (Inventing Logical Necessity [1986]) by Ian McFetridge - Logical Necessity: Some Issues §3
	A reaction: This has little appeal to me, as I take (unfashionably) the view that that logical necessity is rooted in the behaviour of the actual physical world, with which you can't argue. We test simple logic by making up examples.

19. Language / A. Nature of Meaning / 5. Meaning as Verification

10117	Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman]
	Full Idea: The concern of mathematical intuitionists was that the use of certain forms of inference generates, not contradiction, but unjustified assertions.
	From: report of Luitzen E.J. Brouwer (Intuitionism and Formalism [1912]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6
	A reaction: This seems to be the real origin of the verificationist idea in the theory of meaning. It is a hugely revolutionary idea - that ideas are not only ruled out of court by contradiction, but that there are other criteria which should also be met.

19. Language / A. Nature of Meaning / 7. Meaning Holism / b. Language holism

7320	Holism cannot give a coherent account of scientific methodology [Wright,C, by Miller,A]
	Full Idea: Crispin Wright has argued that Quine's holism is implausible because it is actually incoherent: he claims that Quine's holism cannot provide us with a coherent account of scientific methodology.
	From: report of Crispin Wright (Inventing Logical Necessity [1986]) by Alexander Miller - Philosophy of Language 4.5
	A reaction: This sounds promising, given my intuitive aversion to linguistic holism, and almost everything to do with Quine. Scientific methodology is not isolated, but spreads into our ordinary (experimental) interactions with the world (e.g. Idea 2461).

23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues

7903	The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
	Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
	From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
	A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').