6 ideas
| 5435 | An interpreter of a text, because of wider knowledge, can understand it better than its author [Schleiermacher, by Mautner] |
| Full Idea: Schleiermacher proposed that an interpreter of a text may be in a better position to see the author's life and work and historical setting as a whole, and so understand the text better than its author. | |
| From: report of Friedrich Schleiermacher (works [1825]) by Thomas Mautner - Penguin Dictionary of Philosophy p.248 | |
| A reaction: This sounds like a very quaintly old-fashioned enlightenment view which has been swept away by post-modernism, which is why I agree with it. We have a perspective on Descartes now which he could never have dreamt of. |
| 22028 | Unity emerges from understanding particulars, so understanding is prior to seeing unity [Schleiermacher] |
| Full Idea: We only gradually arrive at the knowledge of the inner unity via the understanding of individual utterances, and therefore the art of explication is also presupposed if the inner unity is to be found....The task is infinite, and can never be accomplished. | |
| From: Friedrich Schleiermacher (works [1825], p.235), quoted by Terry Pinkard - German Philosophy 1760-1860 06 | |
| A reaction: [p.235 in ed Bowie 1998] This is the first statement of the hermeneutic circle, which needs whole to grasp parts, and parts to grasp whole. Personally I think the dangers of circles in philosophy are greatly exaggerated. |
| 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. |