7 ideas
| 21916 | Philosophers can't be religious, and don't need to be; philosophy is perilous but free [Schopenhauer] |
| Full Idea: No one who is religious attains to philosophy; he does not need it. No one who really philosophizes is religious; he walks without leading-strings, perilously but free. | |
| From: Arthur Schopenhauer (Manuscript remains [1855], II p.241-3), quoted by Peter B. Lewis - Schopenhauer 3 | |
| A reaction: This is a direct reply to the opposite view expressed by Schleiermacher (and quoted by Lewis). I would say that to be a philosopher one must give priority to the philosophy, ahead of any religious beliefs. Thinking must be free. |
| 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. |
| 21924 | As the subject of willing I am wretched, but absorption in knowledge is bliss [Schopenhauer] |
| Full Idea: As the subject of willing I am an exceedingly wretched being, and all our suffering consistd in willing, ...but as soon as I am absorbed in knowledge, I am blissfully happy and nothing can assail me. | |
| From: Arthur Schopenhauer (Manuscript remains [1855], I p.137), quoted by Peter B. Lewis - Schopenhauer 4 | |
| A reaction: So the source of his pessimism is subjection to his own will. However, since becoming absorbed in knowledge is an easy task for a scholar, he has little to grumble about. Nietzsche mocked the great pessimist for playing the flute every day. |
| 21915 | To deduce morality from reason is blasphemy, because it is holy, and far above reason [Schopenhauer] |
| Full Idea: To deduce from reason [Vernunft] the moral element in conduct is blasphemy. In this element there is expressed the better consciousness which lies far above all reason. expresses itself in conduct as holiness, and is the true salvation of the world. | |
| From: Arthur Schopenhauer (Manuscript remains [1855], I p.47), quoted by Peter B. Lewis - Schopenhauer 3 | |
| A reaction: Aimed at Kant. Only Plato could inspire a non-religious person to write about morality is such terms. Maybe also the stoic ideal of beautiful deeds (given the supreme value Schopenhauer placed on the arts). |