5 ideas
| 13166 | Essences are no use in mathematics, if all mathematical truths are necessary [Mancosu] |
| Full Idea: Essences and essential properties do not seem to be useful in mathematical contexts, since all mathematical truths are regarded as necessary (though Kit Fine distinguishes between essential and necessary properties). | |
| From: Paolo Mancosu (Explanation in Mathematics [2008], §6.1) | |
| A reaction: I take the proviso in brackets to be crucial. This represents a distortion of notion of an essence. There is a world of difference between the central facts about the nature of a square and the peripheral inferences derivable from it. |
| 3597 | Foundations need not precede other beliefs [Wittgenstein] |
| Full Idea: I do not explicitly learn the propositions that stand fast for me. I can discover them subsequently like the axis around which a body rotates. | |
| From: Ludwig Wittgenstein (On Certainty [1951], §152), quoted by Michael Williams - Problems of Knowledge Ch.14 | |
| A reaction: A nice metaphor for the way in which axioms are derived. It is also close to Quine's metaphor of the 'net' of understanding, with the centre area 'standing fast'. Not neat and tidy, though. |
| 3596 | Total doubt can't even get started [Wittgenstein, by Williams,M] |
| Full Idea: Wittgenstein remarked that if you tried to doubt everything, you would not get as far as doubting anything. | |
| From: report of Ludwig Wittgenstein (On Certainty [1951]) by Michael Williams - Problems of Knowledge Ch.14 |
| 4721 | If you are not certain of any fact, you cannot be certain of the meaning of your words either [Wittgenstein] |
| Full Idea: If you are not certain of any fact, you cannot be certain of the meaning of your words either. | |
| From: Ludwig Wittgenstein (On Certainty [1951], §114) | |
| A reaction: A wonderfully challenging aphorism. I suspect that it is true, but not really a problem. We all know the meaning of 'Loch Ness Monster', as long as we don't get too fussy. And for local objects I am happy that I know the facts. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |