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| 10580 | Mathematics is both necessary and a priori because it really consists of logical truths |
| 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 |
| 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 |
| 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) | |||
| A reaction: There's a shift here, from his own 'properties' to the 'intrinsic properties' of the abstracta. Presumably his own 'intrinsic' properties are not accidental. In fact, intrinsic properties tend to be essential properties, I think. |
| 10578 | We are thought to know concreta a posteriori, and many abstracta a priori |
| 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) | |||
| A reaction: Personally I think numbers are rooted in experience, though pure arithmetic has travelled a long way since it started. I doubt whether arithmetic is possible without counting things. I don't think I believe in the 'pure' a priori. |