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Full Idea
If we stipulate the meaning of 'the number of x's' so that it makes Hume's Principle true, we must accept Hume's Principle. But a precondition for this stipulation is that Hume's Principle be accepted a priori.
Clarification
Hume's Principle defines numbers by one-to-one correspondences
Gist of Idea
If we stipulate the meaning of 'number' to make Hume's Principle true, we first need Hume's Principle
Source
Paul Horwich (Stipulation, Meaning and Apriority [2000], §9)
Book Ref
'New Essays on the A Priori', ed/tr. Boghossian,P /Peacocke,C [OUP 2000], p.163
A Reaction
Yet another modern Quinean argument that all attempts at defining things are circular. I am beginning to think that the only a priori knowledge we have is of when a group of ideas is coherent. Calling it 'intuition' might be more accurate.
| 1824 | To name something, you must already have an idea of what it is [Epicurus, by Diog. Laertius] |
| 2191 | Relations of ideas are known by thought, independently from the world [Hume] |
| 18262 | For Kant analytic knowledge needs complex concepts, but the a priori can rest on the simple [Coffa on Kant] |
| 5526 | With large numbers it is obvious that we could never find the sum by analysing the concepts [Kant] |
| 16915 | A priori intuitions can only concern the objects of our senses [Kant] |
| 4430 | All a priori knowledge deals with the relations of universals [Russell] |
| 5411 | We can know some general propositions by universals, when no instance can be given [Russell] |
| 9353 | We explain away a priori knowledge, not as directly empirical, but as indirectly holistically empirical [Devitt] |
| 13406 | A priori knowledge is analytic - the structure of our concepts - and hence unimportant [Papineau] |
| 12389 | Knowledge is a priori if the experience giving you the concepts thus gives you the knowledge [Kitcher] |
| 9341 | Meanings and concepts cannot give a priori knowledge, because they may be unacceptable [Horwich] |
| 9334 | If we stipulate the meaning of 'number' to make Hume's Principle true, we first need Hume's Principle [Horwich] |
| 2727 | Red and green being exclusive colours seems to be rationally graspable but not analytic [Audi,R] |
| 2728 | The concepts needed for a priori thought may come from experience [Audi,R] |
| 17726 | Examining accurate, justified or grounded concepts brings understanding of the world [Jenkins] |