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) |
| 1590 | The just man does not harm his enemies, but benefits everyone [Plato] |
| Full Idea: First, Socrates, you told me justice is harming your enemies and helping your friends. But later it seemed that the just man, since everything he does is for someone's benefit, never harms anyone. | |
| From: Plato (Clitophon [c.372 BCE], 410b) | |
| A reaction: Socrates certainly didn't subscribe to the first view, which is the traditional consensus in Greek culture. In general Socrates agreed with the views later promoted by Jesus. |
| 3236 | Equality of opportunity without equality of respect would create a very inhuman society [Williams,B] |
| Full Idea: A highly rational, efficient and unmitigated application of the idea of equality of opportunity, while abandoning the idea of equality of respect as vague and nostalgic, would lead to a quite inhuman society. | |
| From: Bernard Williams (The Idea of Equality [1962], §3) |
| 3234 | Equality seems to require that each person be acknowledged as having a significant point of view [Williams,B] |
| Full Idea: Equality seems to require that each person is owed an effort at identification; they should not be seen as a surface to which a label can be applied, but one should try to see the world (including the label) from their point of view. | |
| From: Bernard Williams (The Idea of Equality [1962], §2) |
| 3233 | Equality implies that people are alike in potential as well as in needs [Williams,B] |
| Full Idea: Supporters of equality have asserted that people are alike in certain things they could do or achieve, as well as in the things that they need and could suffer. | |
| From: Bernard Williams (The Idea of Equality [1962], §2) |
| 3235 | It is a mark of extreme exploitation that the sufferers do not realise their plight [Williams,B] |
| Full Idea: It is a mark of extreme exploitation or degradation that those who suffer it do NOT see themselves differently from the way they are seen by the exploiters. | |
| From: Bernard Williams (The Idea of Equality [1962], §2) |