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. |
7272 | Maybe lots of qualia lead to intentionality, rather than intentionality being basic [Gildersleve] |
Full Idea: A common modern reductive view of the mind is that a hierarchy of intentional systems eventually produce qualia, but it might be the other way around. The mind is 'qualia-upon-qualia', with units of minimal qualia building up into intentional thought. | |
From: Harry Gildersleve (talk [2005]), quoted by PG - Db (ideas) | |
A reaction: If qualia are seen as existing at the most basic level of the brain, this may well imply panpsychism. It certainly says that basic brain cells are capable of minimal experiences. The idea that thought is essentially qualitative is very intriguing. |
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'). |