3 ideas
18844 | You would cripple mathematics if you denied Excluded Middle [Hilbert] |
Full Idea: Taking the principle of Excluded Middle away from the mathematician would be the same, say, as prohibiting the astronomer from using the telescope or the boxer from using his fists. | |
From: David Hilbert (The Foundations of Mathematics [1927], p.476), quoted by Ian Rumfitt - The Boundary Stones of Thought 9.4 | |
A reaction: [p.476 in Van Heijenoort] |
19000 | Read 'all ravens are black' as about ravens, not as about an implication [Belnap] |
Full Idea: 'All ravens are black' might profitably be read as saying not that being a raven 'implies' being black, but rather something more like 'Consider the ravens: each one is black'. | |
From: Nuel D. Belnap (Conditional Assertion and Restricted Quantification [1970], p.7), quoted by Stephen Yablo - Aboutness 04.5 | |
A reaction: Belnap is more interested in the logic than in the paradox of confirmation, since he evidently thinks that universal generalisations should not be read as implications. I like Belnap's suggestion. |
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'). |