an established body of knowledge. By that I mean fields in which we have (empirical) grounds for believing our knowledge is at least an approximation or heading in the right direction.
There are set theory experts, but no empirical data on the subject.
Most of the usefulness of these experts comes from their knowledge of discovered facts like “axiom system X implies theorem Y about sets”, not statements like “axiom system X is the truth about sets”
But lots of philosophy is also conditional in character: if you accept commitments x, y, and z, then you should also accept commitment w—or your position will be inconsistent or pragmatically incoherent or some such. And anyway, being conditional does not mean that mathematics has empirical content. It is not an empirical claim that the Pythagorean theorem follows from Euclid’s axioms (or some suitable formalization of them). So, Larks’ complaint still seems right to me: a field of inquiry need not have empirical content in order to have experts.
There are set theory experts, but no empirical data on the subject.
Most of the usefulness of these experts comes from their knowledge of discovered facts like “axiom system X implies theorem Y about sets”, not statements like “axiom system X is the truth about sets”
But lots of philosophy is also conditional in character: if you accept commitments x, y, and z, then you should also accept commitment w—or your position will be inconsistent or pragmatically incoherent or some such. And anyway, being conditional does not mean that mathematics has empirical content. It is not an empirical claim that the Pythagorean theorem follows from Euclid’s axioms (or some suitable formalization of them). So, Larks’ complaint still seems right to me: a field of inquiry need not have empirical content in order to have experts.