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The argument clearly depends on the assumption that if "good" were definable, it would be an analytic truth about "good," an assumption many contemporary moral realists like Richard Boyd and Peter Railton reject.
After 1929, his primary mathematical preoccupation entailed resolving the account of logical necessity he had articulated in the Tractatus Logico-Philosophicus—an issue which had been fiercely pressed by Frank P. Ramsey.