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. |
10245 | One geometry cannot be more true than another [Poincaré] |
Full Idea: One geometry cannot be more true than another; it can only be more convenient. | |
From: Henri Poincaré (Science and Method [1908], p.65), quoted by Stewart Shapiro - Philosophy of Mathematics | |
A reaction: This is the culminating view after new geometries were developed by tinkering with Euclid's parallels postulate. |
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. |
4375 | Evaluations are not disguised emotions; instead, emotion is a type of evaluation [Achtenberg] |
Full Idea: The emotivist gets things backwards: evaluations are not disguised emotions; instead, emotions are types of evaluation. | |
From: Deborah Achtenberg (Cognition of Value in Aristotle's Ethics [2002], 6.1) | |
A reaction: A nice comment, though a bit optimistic. It is certainly a valuable corrective to emotivist to pin down the cognitive and evaluative aspects of emotion, rather than regarding them as 'raw' feelings. |