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. The French
philosopher Pierre Duhem espoused a broader conventionalist view encompassing all of science. Duhem was skeptical that human perceptions are sufficient to understand the "true," metaphysical nature of reality and argued that scientific laws should be valued mainly for their predictive power and correspondence with observations.
Karl Popper broadened the meaning of conventionalism still more. In
The Logic of Scientific Discovery, he defined a "conventionalist stratagem" as any technique that is used by a theorist to evade the consequences of a falsifying observation or experiment. Popper identified four such stratagems: • introducing an ad hoc hypothesis that makes the refuting evidence seem irrelevant; • modifying the
ostensive definitions so as to alter the content of a theory; • doubting the reliability of the experimenter; declaring that the observations that threaten the tested theory are irrelevant; • casting doubt on the acumen of the theorist when he does not produce ideas that can save the theory. Popper argued that it was crucial to avoid conventionalist stratagems if
falsifiability of a theory was to be preserved. It has been argued that the
standard model of cosmology is built upon a set of conventionalist stratagems. In the 1930s, a Polish philosopher
Kazimierz Ajdukiewicz proposed a view that he called radical conventionalism – as opposed to moderate conventionalism developed by
Henri Poincaré and
Pierre Duhem. Radical conventionalism was originally outlined in
The World-Picture and the Conceptual Apparatus, an article published in “Erkenntnis” in 1934. The theory can be characterized by the following theses: (1) there are languages or – as Ajdukiewicz used to say – conceptual apparatuses (schemes) which are not intertranslatable, (2) any knowledge must be articulate in one of those languages, (3) the choice of a language is arbitrary, and it is possible to change from one language to another. Therefore, there is a conventional or decisional element in all knowledge (including perceptual). In his later writings – under the influence of
Alfred Tarski – Ajdukiewicz rejected radical conventionalism in favour of a semantic epistemology. ==Legal philosophy==