5 ideas
9935 | Mathematical truth is always compromising between ordinary language and sensible epistemology [Benacerraf] |
Full Idea: Most accounts of the concept of mathematical truth can be identified with serving one or another of either semantic theory (matching it to ordinary language), or with epistemology (meshing with a reasonable view) - always at the expense of the other. | |
From: Paul Benacerraf (Mathematical Truth [1973], Intro) | |
A reaction: The gist is that language pulls you towards platonism, and epistemology pulls you towards empiricism. He argues that the semantics must give ground. He's right. |
17927 | Realists have semantics without epistemology, anti-realists epistemology but bad semantics [Benacerraf, by Colyvan] |
Full Idea: Benacerraf argues that realists about mathematical objects have a nice normal semantic but no epistemology, and anti-realists have a good epistemology but an unorthodox semantics. | |
From: report of Paul Benacerraf (Mathematical Truth [1973]) by Mark Colyvan - Introduction to the Philosophy of Mathematics 1.2 |
9936 | The platonist view of mathematics doesn't fit our epistemology very well [Benacerraf] |
Full Idea: The principle defect of the standard (platonist) account of mathematical truth is that it appears to violate the requirement that our account be susceptible to integration into our over-all account of knowledge. | |
From: Paul Benacerraf (Mathematical Truth [1973], III) | |
A reaction: Unfortunately he goes on to defend a causal theory of justification (fashionable at that time, but implausible now). Nevertheless, his general point is well made. Your theory of what mathematics is had better make it knowable. |
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'). |
5957 | Absurd superstitions make people atheist, not disharmony in nature [Plutarch] |
Full Idea: Men have never thought the universe godless on the ground of detecting some fault in stars or seasons; ..it is the ridiculous things that superstition does that makes people say it would be better if there were no gods at all. | |
From: Plutarch (14: Superstition [c.85], §12) | |
A reaction: Not true, I would say. Absurd superstitions do discredit belief in the supernatural, but earthquakes are a disharmony in nature, and a nasty one at that. Nowadays we have other explanations to rival those of religion. |