Conventionalism

Conventionalism is the philosophical attitude that fundamental principles of a certain kind are grounded on (explicit or implicit) agreements in society, rather than on external reality. Although this attitude is commonly held with respect to the rules of grammar, its application to the propositions of ethics, law, science, mathematics, and logic is more controversial.

The debate on linguistic conventionalism goes back to Plato's Cratylus and the Mīmāṃsā philosophy of Kumārila Bhaṭṭa. It has been the standard position of modern linguistics since Ferdinand de Saussure's l'arbitraire du signe, but there have always been dissenting positions of phonosemantics, recently defended by Margaret Magnus and Vilayanur S. Ramachandran.

The French mathematician Henri Poincaré was among the first to articulate a conventionalist view. Poincaré's use of non-Euclidean geometries in his work on differential equations convinced him that Euclidean geometry should not be regarded as a priori truth. He held that axioms in geometry should be chosen for the results they produce, not for their apparent coherence with human intuitions about the physical world.

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.

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