6 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'). |
| 22817 | Citizenship involves a group of mutually supporting rights, which create community and equality [Miller,D] |
| Full Idea: The idea of citizenship is that rights support each other. Protective and welfare rights provide a basis for a political role. This underpins a sense of membership, and an obligation to provide welfare. Rights confer equal status and self-respect. | |
| From: David Miller (Community and Citizenship [1989], 3) | |
| A reaction: A helpful eludation of what a richer concept of citizenship than mere membership might look like. Communitarians have a different concept of rights from that of liberals. |
| 22816 | Socialists reject nationality as a false source of identity [Miller,D] |
| Full Idea: The socialist tradition has been overwhelmingly hostile to nationality as a source of identity, usually regarding it merely as an artificially created impediment to the brotherhood of man. | |
| From: David Miller (Community and Citizenship [1989], 2) | |
| A reaction: I have some sympathy with this, especially when nationalism is expressed in terms of enemies, but the question of what community a person can plausibly identify with is difficult. We start in hunter gather tribes of several hundred. |