7 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) |
| 3400 | Things must have parts to intermingle [Gassendi] |
| Full Idea: If you are no larger than a point, how are you joined to the whole body, which is so large? …and there can be no intermingling between things unless the parts of them can be intermingled. | |
| From: Pierre Gassendi (Objections to 'Meditations' (Fifth) [1641]), quoted by Jaegwon Kim - Philosophy of Mind p.131 | |
| A reaction: As Descartes says that mind is distinct from body because it is non-spatial, it doesn't seem quite right to describe it as a 'point', but the second half is a real problem. Being non-spatial is a real impediment to intermingling with spatial objects. |
| 18052 | An assertion aims to add to the content of a context [Stalnaker, by Magidor] |
| Full Idea: Stalnaker starts with the general thesis that the role of a successful assertion of s is to update the context by adding to it the content of s. | |
| From: report of Robert C. Stalnaker (Assertion [1978]) by Ofra Magidor - Category Mistakes 5.3.2 | |
| A reaction: This is to be compared with criteria of meaningfulness, such as verificationism, and with Grice's rules of conversational implicature. Presumably if you assert what the context presupposes, you fail to assert, without being meaningless. |
| 14718 | An assertion is an attempt to rule out certain possibilities, narrowing things down for good planning [Stalnaker, by Schroeter] |
| Full Idea: Stalnaker's guiding idea is that in making an assertion the speaker is trying to get the audience to rule out certain possibilities. ....If all goes well, further planning will proceed on the basis of a smaller and more accurate range of possibilities. | |
| From: report of Robert C. Stalnaker (Assertion [1978]) by Laura Schroeter - Two-Dimensional Semantics | |
| A reaction: This sounds intuitively rather plausible, and is a nice original thought. This is what we pay clever chaps like Stalnaker to come up with. It seems to imply some notion of verisimilitude (qv. under 'truth'), depending on how much narrowing happens. |