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Full Idea
Our empirically best-supported theories may commit us to certain abstract mathematical entities, but this does not necessarily mean that this is what justifies our commitment. That we are committed doesn't explain why we should be.
Gist of Idea
Our best theories may commit us to mathematical abstracta, but that doesn't justify the commitment
Source
David Papineau (Philosophical Insignificance of A Priori Knowledge [2010], §4)
A Reaction
A nice point. It is only a slightly gormless scientism which would say that we have to accept whatever scientists demand. Who's in charge here - scientists, mathematicians or philosophers? Don't answer that...
13407 | All worthwhile philosophy is synthetic theorizing, evaluated by experience [Papineau] |
13406 | A priori knowledge is analytic - the structure of our concepts - and hence unimportant [Papineau] |
13408 | Intuition and thought-experiments embody substantial information about the world [Papineau] |
13409 | Our best theories may commit us to mathematical abstracta, but that doesn't justify the commitment [Papineau] |
13410 | Verificationism about concepts means you can't deny a theory, because you can't have the concept [Papineau] |