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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.
9339 | A priori knowledge (e.g. classical logic) may derive from the innate structure of our minds [Horwich] |
9342 | Understanding needs a priori commitment [Horwich] |
9341 | Meanings and concepts cannot give a priori knowledge, because they may be unacceptable [Horwich] |
9331 | How do we determine which of the sentences containing a term comprise its definition? [Horwich] |
9333 | A priori belief is not necessarily a priori justification, or a priori knowledge [Horwich] |
9332 | Meaning is generated by a priori commitment to truth, not the other way around [Horwich] |
9334 | If we stipulate the meaning of 'number' to make Hume's Principle true, we first need Hume's Principle [Horwich] |