10 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) |
| 22410 | Maybe the unthinkable is a moral category, and considering some options is dishonourable or absurd [Williams,B] |
| Full Idea: One might have the idea that the unthinkable was itself a moral category. ...Regarding certain things even as alternatives is itself something to be regarded as dishonourable or morally absurd. | |
| From: Bernard Williams (A Critique of Utilitarianism [1973], 2) | |
| A reaction: He's very tentative about this, but I think it is a powerful moral idea. See Kekes. He is particularly aiming at utilitarians, who happily assess vile possibilities. |
| 22408 | Consequentialism assumes that situations can be compared [Williams,B] |
| Full Idea: The emphasis on the necessary comparability of situations is a peculiar feature of consequentialism in general. | |
| From: Bernard Williams (A Critique of Utilitarianism [1973], 2) | |
| A reaction: A nice point. Utilitarians might achieve comparison by totting up the happiness in each situation, but once you include the consequences of the consequences the problems are obvious. Was 1789 a good thing? Too early to say. |
| 22411 | For a consequentialist massacring 7 million must be better than massacring 7 million and one [Williams,B] |
| Full Idea: Making the best of a bad job is a consequentialist maxim, and it will have something to say even pn the difference between massacring seven million and massacring seven million and one. | |
| From: Bernard Williams (A Critique of Utilitarianism [1973], 2) | |
| A reaction: If every life counts, the consequentialists have got something right here. Not caring exactly how many were massacred is a sort of callousness (even when the number can't be established). |
| 22409 | We don't have a duty to ensure that others do their duty [Williams,B] |
| Full Idea: If the goodness of the world were to consist in people's fulfilling their obligations, it would by no means follow that one of my obligations was to bring it about that other people kept their obligations | |
| From: Bernard Williams (A Critique of Utilitarianism [1973], 2) | |
| A reaction: If the maxim of my action is 'ensure that everyone does their duty', presumably that can be universalised. Nelson thought so. It just sounds like a hideous world of self-righteous interference. |
| 22407 | Utilitarianism cannot make any serious sense of integrity [Williams,B] |
| Full Idea: Utilitarianism cannot hope to make sense, at any serious level, of integrity. | |
| From: Bernard Williams (A Critique of Utilitarianism [1973], 1) | |
| A reaction: There will be obvious problems with this. 'My whole platoon got killed, but looking on the bright side, I preserved my integrity'. Once a theory commits entirely to one value, it then has no way to make sense of rival values. |
| 19945 | Jew and Greeks, bond and free, male and female, are all one in Christ [Paul] |
| Full Idea: There is neither Jew nor Greek, there is neither bond nor free, there is neither male nor female; for ye are all one in Christ Jesus. | |
| From: St Paul (09: Galatians [c.55], 3.28) | |
| A reaction: No wonder women and slaves were enthusiastic about Christianity. This verse is powerful and influential, even if it was largely ignored by Christian rulers. Consider the relative positions of women in Islam and Christendom. |