6 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) |
| 12191 | Counterfactuals are true if logical or natural laws imply the consequence [Goodman, by McFetridge] |
| Full Idea: Goodman's central idea was: 'If that match had been scratched, it would have lighted' is true if there are suitable truths from which, with the antecedent, the consequent can be inferred by means of a logical, or more typically natural, law. | |
| From: report of Nelson Goodman (The Problem of Counterfactual Conditionals [1947]) by Ian McFetridge - Logical Necessity: Some Issues §4 | |
| A reaction: Goodman then discusses the problem of identifying the natural laws, and identifying the suitable truths. I'm inclined to think counterfactuals are vaguer than that; they are plausible if coherent reasons can be offered for the inference. |
| 22393 | I don't understand the idea of a reason for acting, but it is probably the agent's interests or desires [Foot] |
| Full Idea: I am sure I do not understand the idea of a reason for acting, and I wonder whether anyone else does either. I incline to the view that all such reasons depend either on the agent's interests (meaning here what is in his interest) or else on his desires. | |
| From: Philippa Foot (Reasons for Actions and Desires [1972], p.156 Post) | |
| A reaction: It seems common to assume that a reason for an action must be something rational, but it makes sense to say that the reason for someone's action was an irrational whim. Is the reason for an action just the cause of the action? |