Conventionalism was adopted by logical positivists, chiefly A. J. Ayer and Carl Hempel, and extended to both mathematics and logic. To deny rationalism, Ayer sees two options for empiricism regarding the necessity of the truth of formal logic (and mathematics): 1) deny that they actually are necessary, and then account for why they only appear so, or 2) claim that the truths of logic and mathematics lack factual content – they are not "truths about the world" – and then explain how they are nevertheless true and informative. John Stuart Mill adopted the former, which Ayer criticized, opting himself for the latter. Ayer's argument relies primarily on the analytic/synthetic distinction.