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. |
4242 | Pure supervenience explains nothing, and is a sign of something fundamental we don't know [Nagel] |
Full Idea: Pure, unexplained supervenience is never a solution to a problem but a sign that there is something fundamental we don't know. | |
From: Thomas Nagel (The Psychophysical Nexus [2000], §III) | |
A reaction: This seems right. It is not a theory or an explanation, merely the observation of a correlation which will require explanation. Why are they correlated? |
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) |
2975 | That honey is sweet I do not affirm, but I agree that it appears so [Timon] |
Full Idea: That honey is sweet I do not affirm, but I agree that it appears so. | |
From: Timon (On Sensations (frags) [c.285 BCE]), quoted by Diogenes Laertius - Lives of Eminent Philosophers 09.104-5 |