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. |
| 6171 | Beliefs are states of the head that explain behaviour, and also items with referential truth-conditions [McGinn] |
| Full Idea: We view beliefs both as states of the head explanatory of behaviour, and as items possessed of referential truth-conditions. | |
| From: Colin McGinn (The Structure of Content [1982]), quoted by Mark Rowlands - Externalism Ch.6 | |
| A reaction: McGinn wants to build a two-part account of meaning on this point, which Rowlands resists. Hume just wanted to define belief by a feeling, but it seems obvious that truth must also be involved. |