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I introduce and discuss three theses concerning fact/value entanglement in science: Value Neutrality, Propitious Entanglement, and Pernicious Entanglement. Value Neutrality is made implausible by much recent work in philosophy of science. Propitious Entanglement is made implausible by value pluralism. Pernicious Entanglement threatens the authority of science in society. A paradox between three normative principles Entanglement, Value Pluralism, and Authority results. Most philosophers in the past have resolved the paradox by rejecting either Entanglement or Value Pluralism. I describe, but do not here endorse, a Feyerabendian resolution according to which science should not be given any special authority in society.