10 ideas
| 18281 | In mathematics everything is algorithm and nothing is meaning [Wittgenstein] |
| Full Idea: In mathematics everything is algorithm and nothing is meaning; even when it doesn't look like that because we seem to be using words to talk about mathematical things. | |
| From: Ludwig Wittgenstein (Philosophical Grammar [1932], p.468), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 13 'Constr' | |
| A reaction: I would have thought that an algorithm needs some raw material to work with. This leads to the idea that meaning arises from rules of usage. |
| 10580 | Mathematics is both necessary and a priori because it really consists of logical truths [Yablo] |
| Full Idea: Mathematics seems necessary because the real contents of mathematical statements are logical truths, which are necessary, and it seems a priori because logical truths really are a priori. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 10) | |
| A reaction: Yablo says his logicism has a Kantian strain, because numbers and sets 'inscribed on our spectacles', but he takes a different view (in the present Idea) from Kant about where the necessity resides. Personally I am tempted by an a posteriori necessity. |
| 10579 | Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo] |
| Full Idea: Saying 'the number of Fs is 5', instead of using five quantifiers, puts the numeral in quantifiable position, which brings expressive advantages. 'There are more sheep in the field than cows' is an infinite disjunction, expressible in finite compass. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 08) | |
| A reaction: See Hofweber with similar thoughts. This idea I take to be a key one in explaining many metaphysical confusions. The human mind just has a strong tendency to objectify properties, relations, qualities, categories etc. - for expression and for reasoning. |
| 10577 | Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo] |
| Full Idea: Objects like me have a few essential properties, and numerous accidental ones. Abstract objects are a different story. The intrinsic properties of the empty set are mostly essential. The relations of numbers are also mostly essential. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 01) |
| 10578 | We are thought to know concreta a posteriori, and many abstracta a priori [Yablo] |
| Full Idea: Our knowledge of concreta is a posteriori, but our knowledge of numbers, at least, has often been considered a priori. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 02) |
| 6606 | Consider: "Imagine this butterfly exactly as it is, but ugly instead of beautiful" [Wittgenstein] |
| Full Idea: Suppose someone were to say: "Imagine this butterfly exactly as it is, but ugly instead of beautiful"?! | |
| From: Ludwig Wittgenstein (Philosophical Grammar [1932], §127), quoted by Robert Fogelin - Walking the Tightrope of Reason | |
| A reaction: This reminds us that the concept of supervenience was originally introduced in aesthetics. Beauty is supervenient on physical form. But "Imagine how someone else might look at this butterfly and think it was ugly". |
| 536 | We should follow the law in public, and nature in private [Antiphon] |
| Full Idea: A man can best conduct himself in harmony with justice, if when in company of witnesses he upholds the laws, and when alone without witnesses he upholds the edicts of nature. | |
| From: Antiphon (fragments/reports [c.439 BCE], B44), quoted by Anon (Oxy) - Oxyrhynchus Papyrus XI.1364 | |
| A reaction: I'm not sure how you identify the 'edicts of nature', without guidance from other people or the law. Natural behaviour can be pretty grim. |
| 1557 | To gain the greatest advantage only treat law as important when other people are present [Antiphon] |
| Full Idea: The way to get maximum advantage to yourself from justice is to treat the laws as important when other people are present, but when there is nobody else with you to value the demands of nature. | |
| From: Antiphon (fragments/reports [c.439 BCE], B44A), quoted by Anon (Oxy) - Oxyrhynchus Papyrus 1364A | |
| A reaction: This looks like a pretty good description of the majority of people active in politics. |
| 540 | The way you spend your time will form your character [Antiphon] |
| Full Idea: One's character must necessarily grow like that with which one spends the greater part of the day. | |
| From: Antiphon (fragments/reports [c.439 BCE], B62), quoted by John Stobaeus - Anthology 3.31.41 |
| 539 | Nothing is worse for mankind than anarchy [Antiphon] |
| Full Idea: Nothing is worse for mankind than anarchy. | |
| From: Antiphon (fragments/reports [c.439 BCE], B61), quoted by (who?) - where? |