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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.

Linguistics

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.

Geometry

The French mathematician Henri Poincare 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 shouldn't 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.

Philosophy

Conventionalism was adopted by logical positivists, chiefly AJ 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're not "truths about the world" - and then explain how they're 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.

Legal Philosophy

Conventionalism, as applied to legal philosophy, provides a justification for state coercion. It is one of the three rival conceptions of law constructed by Ronald Dworkin, the well respected American legal philosopher, in his ingenious work called Law's Empire. The other two conceptions of law are legal pragmatism and law as integrity.
   According to conventionalism as defined by Dworkin, a community's legal institutions should contain clear social conventions relied upon which rules are promulgated. Such rules will serve as the sole source of information for all the community members because they demarcate clearly all the circumstances in which state coercion will and won't be exercised.
   Dworkin nonetheless has argued that this justification fails to fit with facts as there are many occasions wherein clear applicable legal rules are absent. It follows that, as he maintained, conventionalism can provide no valid ground for state coercion. Dworkin himself favored law as integrity as the best justification of state coercion.
   One famous criticism of Dworkin's idea comes from Stanley Fish who opines that Dwokin, like the Critical Legal Studies movement, Marxists and adherents of feminist jurisprudence, was guilty of a false 'Theory Hope'. Fish claims that such mistake stems from their mistaken belief that there exists a general or higher 'theory' that explains or constrains all fields of activity like state coercion.
   Another criticism is based on Dworkin's assertion that positivists' claims amount to conventionalism. H. L. A. Hart, as a soft positivist, denies such claim as he'd pointed out that citizens can't always discover the law as plain matter of fact. It is however unclear as to whether Joseph Raz, an avowed hard positivist, can be classified as conventionalist as Raz has claimed that law is composed "exclusively" of social facts which could be complex, and thus difficult to be discovered.
   In particular, Dworkin has characterized law as having the main function of restraining state's coercion. Nigel Simmonds has rejected Dworkin's disapproval of conventionalism, claiming that his characterization of law is too narrow.

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