8 ideas
| 17447 | Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck] |
| Full Idea: In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal. | |
| From: report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3 | |
| A reaction: This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'. |
| 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) |
| 8872 | It is widely supposed that externalism cannot be reconciled with first-person authority [Davidson] |
| Full Idea: It has been widely supposed that externalism, which holds that the contents of a person's propositional attitudes are partly determined by factors of which the person may be ignorant, cannot be reconciled with first-person authority. | |
| From: Donald Davidson (Epistemology Externalized [1990], p.197) | |
| A reaction: It is certainly a bit puzzling if you go around saying 'Actually, people don't know their own thoughts'. Davidson aims to defend first-person authority. The full story is developed in Tyler Burge's views on 'anti-individualism'. |
| 8874 | It is hard to interpret a speaker's actions if we take a broad view of the content [Davidson] |
| Full Idea: It will explain a speaker's actions far better if we interpret him as he intended to be interpreted, than if we suppose he means and thinks what someone else might mean and think who used the same words 'correctly'. | |
| From: Donald Davidson (Epistemology Externalized [1990], p.199) | |
| A reaction: This comes down to the fact that our actions have to be motivated by internal meanings. If I defer to experts on the essence of gold, I still buy gold according to how I myself understand it. So meaning has two components? |
| 8873 | The cause of a usage determines meaning, but why is the microstructure of water relevant? [Davidson] |
| Full Idea: While I agree that the usual cause of the use of the word determines what it means, I do not see why sameness of microstructure is necessarily the relevant similarity that determines my reference of the word 'water'. | |
| From: Donald Davidson (Epistemology Externalized [1990], p.198) | |
| A reaction: This is a problem for essentialists who build their views on semantic considerations. But the stability of what causes 'water' thoughts is the microstructure of water. However, that is an explantion of meaning, not a definition of it. |