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Single Idea 9334

[filed under theme 12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts ]

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.


The 7 ideas from 'Stipulation, Meaning and Apriority'

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