5 ideas
16901 | The equivalent algebra model of geometry loses some essential spatial meaning [Burge] |
Full Idea: Geometrical concepts appear to depend in some way on a spatial ability. Although one can translate geometrical propositions into algebraic ones and produce equivalent models, the meaning of the propositions seems to me to be thereby lost. | |
From: Tyler Burge (Frege on Apriority (with ps) [2000], 4) | |
A reaction: I think this is a widely held view nowadays. Giaquinto has a book on it. A successful model of something can't replace it. Set theory can't replace arithmetic. |
17914 | He made a molten sea, which was ten cubits across, and thirty cubits round the edge [Anon (Kings)] |
Full Idea: And he made a molten sea, ten cubits from the one brim to the other; it was round all about, and his height was five cubits: and a line of cubits did compass it round about. | |
From: Anon (Kings) (11: Book of Kings 1 [c.550 BCE], 7:23) | |
A reaction: In the sixth century BCE, this appears to give 3 as the value of Pi, though perhaps it shouldn't be taken too literally! |
16902 | Peano arithmetic requires grasping 0 as a primitive number [Burge] |
Full Idea: In the Peano axiomatisation, arithmetic seems primitively to involve the thought that 0 is a number. | |
From: Tyler Burge (Frege on Apriority (with ps) [2000], 5) | |
A reaction: Burge is pointing this out as a problem for Frege, for whom only the logic is primitive. |
16892 | Is apriority predicated mainly of truths and proofs, or of human cognition? [Burge] |
Full Idea: Whereas Leibniz and Frege predicate apriority primarily of truths (or more fundamentally, proofs of truths), Kant predicates apriority primarily of cognition and the employment of representations. | |
From: Tyler Burge (Frege on Apriority (with ps) [2000], 1) |
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'). |