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) |
| 16009 | When we seek our own 'freedom' we are just trying to avoid responsibility [Kierkegaard] |
| Full Idea: In all our own 'freedom' we actually seek one thing: to be able to live without responsibility. | |
| From: Søren Kierkegaard (Attack Upon Christendom [1855], p.290) | |
| A reaction: That's the plan when I win the lottery. [SY] |
| 14409 | I am a presentist, and all language and common sense supports my view [Bigelow] |
| Full Idea: I am a presentist: nothing exists which is not present. Everyone believed this until the nineteenth century; it is writing into the grammar of natural languages; it is still assumed in everyday life, even by philosophers who deny it. | |
| From: John Bigelow (Presentism and Properties [1996], p.36), quoted by Trenton Merricks - Truth and Ontology | |
| A reaction: The most likely deniers of presentism seem to be physicists and cosmologists who have overdosed on Einstein. On the whole I vote for presentism, but what justifies truths about the past and future. Traces existing in the present? |