Conventionalism is a philosophical concept whereby some principles or propositions, both cognitive and ethical-political are based on conventions , agreements or choice (even implicitly) that can not be assessed in terms of truth or falsity. This conception has been the subject of deep analyses since ancient times, extending from periods of greater or lesser originality to contemporary scientific and philosophical studies.

Here we are faced with a form of methodological conventionalism: the scientist is guided by the idea of simplicity. Simplicity is synonymous with truth. This way of proceeding is based both on habit (historically it has always been proceeded in this way), and because, on a strictly pragmatic level, this approach is the only one that enables science to proceed.

Modern conventionalism can be described as a school of thought that emphasizes the conventional nature of some fundamental concepts of mathematics and physics. It starts from the discovery of non-Euclidean geometries and relativization of space and time, determined by the physics studies in the early XX century. With the non-Euclidean geometry it was called into question the spatial intuition, which stems from common sense and the psychological and physiological investigations, understood as the foundation of geometry.

The reflections of the scientist and philosopher Mach (in the works "The Analysis of Sensations" and "Knowledge and Error"), the philosopher and historian of science Duhem and especially the great mathematician J.-H. Poincaré contributed deeply to the conventionalist analysis of the development of sciences. Mach, for example, with his radical empiricism, reduced concepts and scientific theories to pragmatic means able to organize sense data in the most economic and predictively effective way. Duhem developed Mach epistemology characterizing physical theory as a system of propositions derived from certain principles that represent experimental truth in a simple and rigorous manner.

Poincaré gave an important contribution for reflection on conventionalism either denying the validity of the Kantian theory, which considers the Euclidean geometry an ‘a priori’ science, or rejecting the idea that non-Euclidean geometry (and geometric systems in general) be empirically verifiable.

These are simply conventional truths, to which experience can not impose any falsification.  Take, for example, the acceleration of a body that does not depend on the position of this body, of the neighboring bodies and their speeds. This proposition, to be verified  completely, would require that, after a certain period of time, all bodies in the universe would return in the initial positions with their initial velocities. Only in this case it could be verified if they rejoined the initial trajectories. In fact, the generalized principle of inertia implies that, at equal positions and speed, the accelerations are the same. Such a principle can never be falsified empirically.

The discoveries of the late nineteenth century seem to condemn the principle of Carnot, of Galilean relativity, that of action and reaction, the principle of conservation of mass. Poincaré argues that although these principles, on a strictly logical level, can be put back into play, after such an ad hoc rescue they would be completely useless. A principle has to be fruitful for the development of physics; when it no longer is, it has to be abandoned.

Conventionalist thesis type are also present in the work of R. Carnap in a certain period and more generally in logical positivism.

Carnap - in response to the influential objections of Quine on the opportunity to provide a clear distinction between analytic and synthetic statements on which positivism based its epistemology - would extend the conventionalist principle to some semantic aspects of language, with the proposal to consider analytic truths as the "meaning postulates", that is, conventional truths no further justified except by virtue of a pragmatic choice.

Forms of conventionalism are also present in the post-Popperian and post-positivist philosophy of science.

The most radical exponent of the "new criticism of science" was the French mathematician Edouard Le Roy, who advanced a form of nominalistic conventionalism, following which science has only an instrumental value of rule of action; the same scientific facts are a pure creation of the scientists, only the "brute facts" would manifest the character of objectivity. Poincaré takes the field against this extreme form of conventionalism, criticizing and leaving the distinction between brute and scientific fact: every fact, he argues, is a "creation of our spirit." To tell if a thing is true or not, it must be aware of the conventions on the basis of which the application acquires a precise meaning. A scientific fact is simply the translation of a brute in a statement expressed in a language more contented. The scientist is a creator in respect of the rules of the language he uses, but to experience remains the task of responding once the question has been formulated.

Duhem will argue with Poincaré on this point, advancing a conventionalistic position more marked: the task of the scientist and his creativity are not limited to language processing, but enter also into the theoretical field.

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