The indispensability argument says (roughly) that if you have ample reason to accept an empirical scientific theory that makes indispensable use of mathematics, and that theory entails that numbers exist, then you have ample reason to accept that numbers exist. The argument affirms the antecedent of this conditional, and concludes that you have ample reason to believe that numbers exist. What is striking about this argument is that it seems to show that the empirical reasons that suffice for accepting a scientific theory also suffice for accepting a metaphysical claim.
Elliott SoberIt is an interesting fact about model selection that the evidence at hand can indicate that a model known to be false will be more predictively accurate than a model known to be true. This opens the door to a kind of instrumentalism.
Elliott SoberTrait X is fitter than trait Y in a population of organisms if those organisms have other biological traits T and live in an environment that has properties E. The theory of natural selection is filled with statements of this form.
Elliott SoberUnfortunately, philosophers of science usually regard scientific realism and scientific anti-realism as monistic doctrines. The assumption is that there is one goal of all scientific inference - finding propositions that are true, or finding propositions that are predictively accurate. In fact, there are multiple goals. Sometimes realism is the right interpretation of a scientific problem, while at other times instrumentalism is.
Elliott SoberIt can be a necessary conceptual truth that pains are painful without this ruling out the physicalist thesis that immaterial minds are impossible or the thesis that conscious states supervene on physical states. The necessity involved in these claims is nomological necessity, not metaphysical necessity (assuming that these are different).
Elliott SoberOne influential philosophical position about the use of probability in science holds that probabilities are objective only if they are based on micro-physics; all other probabilities should be interpreted subjectively, as merely revealing our ignorance about physical details. I have argued against this position, contending that the objectivity of micro-physical probabilities entails the objectivity of macro-probabilities.
Elliott Sober