9 ideas
| 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) |
| 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? |
| 22375 | Moral judgements need more than the relevant facts, if the same facts lead to 'x is good' and 'x is bad' [Foot] |
| Full Idea: It is suggested that anyone who has considered all the facts which could bear on his moral position has ipso facto produced a 'well founded' moral judgement, ...How 'x is good' can be well founded when 'x is bad' is equally well founded is hard to see. | |
| From: Philippa Foot (Moral Arguments [1958], p.96) | |
| A reaction: This seems to be a warning to particularists, if they hope that moral judgements just emerge from the facts. It doesn't rule out physicalist naturalism about morality, if the attitudes we bring to the facts have arisen out of further facts. |
| 22378 | We can't affirm a duty without saying why it matters if it is not performed [Foot] |
| Full Idea: I do not know what could be meant by saying it was someone's duty to do something unless there was an attempt to show why it mattered if this sort of thing was not done. | |
| From: Philippa Foot (Moral Arguments [1958], p.105) | |
| A reaction: The Kantian idea assumes that duty is an absolute, and yet each duty rests on a particular maxim which is going to be universalised. So why should that maxim be universalised, and not some other? |
| 22377 | Whether someone is rude is judged by agreed criteria, so the facts dictate the value [Foot] |
| Full Idea: Whether a man is speaking of behaviour as rude or not rude, he must use the same criteria as anyone else. ...We have here an example of a non-evaluative premise from which an evaluative conclusion can be deduced. | |
| From: Philippa Foot (Moral Arguments [1958], p.104) | |
| A reaction: We would now call 'rude' a 'thick' ethical concept (where 'good' is 'thin'). Her powerful point is, I take it, that evidence is always relevant to judgements of thick concepts, so there is no fact-value gap. 'Rude' has criteria, but 'good' may not. |
| 22376 | Facts and values are connected if we cannot choose what counts as evidence of rightness [Foot] |
| Full Idea: To show that facts and values are connected we must show that some things do and some things don't count in favour of a moral conclusion, and that no one can choose what counts as evidence for rightness or wrongness. | |
| From: Philippa Foot (Moral Arguments [1958], p.99) | |
| A reaction: But what sort of facts might do the job? I can only think of right functioning and health as facts which seem to imply value. Pleasure and misery don't quite get there. |