Realism, Objectivity, and Evaluation

This chapter discusses “realist pluralism” in mathematics and morality. It argues that, under the assumption of pluralism, factual questions get deflated while practical -- i.e., what-to-do -- questions do not. It then uses this contrast to formulate a radicalization of Moore’s Open Question Argument. Practical questions remain open even when the facts, including the evaluative facts, come cheaply. The chapter concludes that practical realism must be false, but practical questions are objective in a paradigmatic respect. Conversely, mathematical realism is true, but mathematical questions fail to be objective. An important upshot of the discussion is that the concepts of realism and objectivity, which are widely identified, are actually in tension.