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Elliott Sober

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“"Methodological naturalism" and "metaphysical naturalism" are terms that often surface in the continuing battle between evolutionary biology and creationism/intelligent design. The methodological thesis says that scientific theories shouldn't postulate supernatural entities; the metaphysical thesis says that no such entities exist. In this debate, God is the supernatural entity at issue; the question isn't whether science gets to talk about mathematical entities if Platonism is correct.”

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“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.”

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“The indispensability argument seeks to assimilate the epistemology of metaphysical statements to the epistemology of statements that are obviously empirical. I think it fails to achieve this goal. The argument does not refute the Carnapian thesis that scientific theories and metaphysical claims differ epistemologically - observations can provide evidence for the former, but not for the latter.”

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