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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 23 ideas from Paul Horwich

2798 Probability of H, given evidence E, is prob(H) x prob(E given H) / prob(E) [Horwich]
2799 Bayes' theorem explains why very surprising predictions have a higher value as evidence [Horwich]
8432 Analyse counterfactuals using causation, not the other way around [Horwich]
8431 Problems with Goodman's view of counterfactuals led to a radical approach from Stalnaker and Lewis [Horwich]
9339 A priori knowledge (e.g. classical logic) may derive from the innate structure of our minds [Horwich]
9341 Meanings and concepts cannot give a priori knowledge, because they may be unacceptable [Horwich]
9342 Understanding needs a priori commitment [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]
23299 Horwich's deflationary view is novel, because it relies on propositions rather than sentences [Horwich, by Davidson]
6332 The common-sense theory of correspondence has never been worked out satisfactorily [Horwich]
6336 No deflationary conception of truth does justice to the fact that we aim for truth [Horwich]
6337 The deflationary picture says believing a theory true is a trivial step after believing the theory [Horwich]
6334 The function of the truth predicate? Understanding 'true'? Meaning of 'true'? The concept of truth? A theory of truth? [Horwich]
6335 The redundancy theory cannot explain inferences from 'what x said is true' and 'x said p', to p [Horwich]
6338 We could know the truth-conditions of a foreign sentence without knowing its meaning [Horwich]
6339 Logical form is the aspects of meaning that determine logical entailments [Horwich]
6340 There are Fregean de dicto propositions, and Russellian de re propositions, or a mixture [Horwich]
6341 Right translation is a mapping of languages which preserves basic patterns of usage [Horwich]
6342 Some correspondence theories concern facts; others are built up through reference and satisfaction [Horwich]
6344 Truth is a useful concept for unarticulated propositions and generalisations about them [Horwich]