10 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) |
| 10269 | Mathematics eliminates possibility, as being simultaneous actuality in sets [Putnam] |
| Full Idea: Mathematics has got rid of possibility by simply assuming that, up to isomorphism anyway, all possibilities are simultaneous actual - actual, that is, in the universe of 'sets'. | |
| From: Hilary Putnam (What is Mathematical Truth? [1975], p.70), quoted by Stewart Shapiro - Philosophy of Mathematics 7.5 |
| 12899 | The timid student has knowledge without belief, lacking confidence in their correct answer [Lewis] |
| Full Idea: I allow knowledge without belief, as in the case of the timid student who knows the answer but has no confidence that he has it right, and so does not believe what he knows. | |
| From: David Lewis (Elusive Knowledge [1996], p.429) | |
| A reaction: [He cites Woozley 1953 for the timid student] I don't accept this example (since my views on knowledge are rather traditional, I find). Why would the student give that answer if they didn't believe it? Sustained timid correctness never happens. |
| 12897 | To say S knows P, but cannot eliminate not-P, sounds like a contradiction [Lewis] |
| Full Idea: If you claim that S knows that P, and yet grant that S cannot eliminate a certain possibility of not-P, it certainly seems as if you have granted that S does not after all know that P. To speak of fallible knowledge just sounds contradictory. | |
| From: David Lewis (Elusive Knowledge [1996], p.419) | |
| A reaction: Starting from this point, fallibilism seems to be a rather bold move. The only sensible response seems to be to relax the requirement that not-P must be eliminable. Best: in one epistemic context P, in another not-P. |
| 12898 | Justification is neither sufficient nor necessary for knowledge [Lewis] |
| Full Idea: I don't agree that the mark of knowledge is justification, first because justification isn't sufficient - your true opinion that you will lose the lottery isn't knowledge, whatever the odds; and also not necessary - for what supports perception or memory? | |
| From: David Lewis (Elusive Knowledge [1996]) | |
| A reaction: I don't think I agree. The point about the lottery is that an overwhelming reason will never get you to knowing that you won't win. But good reasons are coherent, not statistical. If perceptions are dubious, justification must be available. |
| 12895 | Knowing is context-sensitive because the domain of quantification varies [Lewis, by Cohen,S] |
| Full Idea: The context-sensitivity of 'knows' is a function of contextual restrictions on the domain of quantification. | |
| From: report of David Lewis (Elusive Knowledge [1996]) by Stewart Cohen - Contextualism Defended p.68 | |
| A reaction: I think the shifting 'domain of quantification' is one of the most interesting features of ordinary talk. Or, more plainly. 'what are you actually talking about?' is the key question in any fruitful dialogue. Sophisticated speakers tacitly shift domain. |
| 19562 | We have knowledge if alternatives are eliminated, but appropriate alternatives depend on context [Lewis, by Cohen,S] |
| Full Idea: S knows P if S's evidence eliminates every alternative. But the nature of the alternatives depends on context. So for Lewis, the context sensitivity of 'knows' is a function of contextual restrictions ln the domain of quantification. | |
| From: report of David Lewis (Elusive Knowledge [1996]) by Stewart Cohen - Contextualism Defended (and reply) 1 | |
| A reaction: A typical modern attempt to 'regiment' a loose term like 'context'. That said, I like the idea. I'm struck by how the domain varies during a conversation (as in 'what we are talking about'). Domains standardly contain 'objects', though. |