Ideas from 'Philosophical Insignificance of A Priori Knowledge' by David Papineau [2010], by Theme Structure

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1. Philosophy / G. Scientific Philosophy / 3. Scientism
All worthwhile philosophy is synthetic theorizing, evaluated by experience
7. Existence / D. Theories of Reality / 10. Ontological Commitment / e. Ontological commitment problems
Our best theories may commit us to mathematical abstracta, but that doesn't justify the commitment
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
A priori knowledge is analytic - the structure of our concepts - and hence unimportant
12. Knowledge Sources / E. Direct Knowledge / 1. Intuition
Intuition and thought-experiments embody substantial information about the world
19. Language / B. Meaning / 3. Meaning as Verification
Verificationism about concepts means you can't deny a theory, because you can't have the concept