6 ideas
| 15130 | If a property is possible, there is something which can have it [Williamson] |
| Full Idea: Barcan's axiom says if there can be something that has a certain property, then there is something that can have that property. It and its converse are not obviously correct or incorrect. They claim that it is non-contingent what individuals there are. | |
| From: Timothy Williamson (Laudatio: Prof Ruth Barcan Marcus [2011], p.1) | |
| A reaction: Williamson defends the two Barcan formulas, but the more I understand them the less plausible they sound to me. |
| 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) |
| 10994 | Conditionals are true if minimal revision of the antecedent verifies the consequent [Stalnaker, by Read] |
| Full Idea: Stalnaker proposes that a conditional is true if its consequent is true in the minimal revision in which the antecedent is true, that is, in the most similar possible world in which the antecedent is true. | |
| From: report of Robert C. Stalnaker (works [1970]) by Stephen Read - Thinking About Logic Ch.3 | |
| A reaction: A similar account of counterfactuals was taken up by Lewis to give a (rather dubious) account of causation. |