Comte, Isidore-Auguste-Marie-François-Xavier (1798–1857)

4. The logic of systems and the semiotic principle

Comte highlighted a history of human logics by emphasizing the necessary and reciprocal connection between the systems and institutions of signs, which are languages, and social systems. He saw social history as being affected by the systems of logic which he recognized as existing at three levels: the ‘logic of sentiments’, the ‘logic of images’ and the ‘logic of signs’. This tripartition into sentiments, images and signs contains the semiotic elements that we can recognize in Charles Peirce’s semiotic as Firstness, Secondness and Thirdness (Peirce 1966: 241) (see Peirce, C. §7).

Language appeared as a dynamic system relating political life to domestic life. It allowed for the creation of a positive science whose basis was observation but whose ideal reference was mathematical language, which arose from the logic of signs. Comte’s semiotic position explains his mathematical views. He called attention to the fact that physical science depended as much on observation guided by theory as on the proper use of a model of language, which, to him, was the language of mathematics.

As early as 1819, Comte maintained a general theory of language and signs in his Essais sur la philosophie des mathématiques (Essays on the Philosophy of Mathematics). This logic of the systems of signs in both science and aesthetics was clearly confirmed in 1852 in the second volume of Système de philosophie positive. Written long after the first and long before the second of these works, the Cours de philosophie positive contains an epistemology concerned with revealing the scientific means of demonstrating the final necessity of the human and social sciences. These sciences are ruled by a logic of systems, of which the law of three stages is the determining operational element.

The ‘positive logic’ of the Système de philosophie positive is nothing other than a combination of systems of signs (affective, imaginary and intellectual), subjected to the unification of the three systems governing sentiments, images and linguistic or mathematical symbols. Comte wanted every ‘logic of signs’ to be expressly connected with the ‘logic of images’ and the ‘logic of sentiments’. He reaffirmed the semiotic principle in 1856, in Synthèse subjective, and this led to a complete formulation showing how ‘the regular conjuncture of sentiments, images and signs’ was able ‘to inspire in us conceptions that meet our moral, intellectual and physical needs’ (1856: 27).

The logic of the systems of signs arises from ‘the interior function of language’ because, according to Hobbes, people communicate by signs, with one phenomenon becoming the sign of another phenomenon. The Table of the Fifteen Universal Laws may be considered the outcome of this logic. The reason is that this table achieves an intellectual unity through its reduction to a precise and definite number of signs, which are specific laws, valid for all phenomena.

Evidently, there is a link between the three Comtean logics and the three-stage law and an even closer link between these logics and the three sub-states of the theological stage. In fact, Comte thought that fetishism, polytheism and monotheism were at the origin of these three logics, whose development was closely connected with the system of society. The logic of sentiments originated in fetishism, the logic of images was created under polytheism, and the logic of signs (linguistic and mathematic) arose from monotheism. It is clear that this semiotic principle has important implications for Comte’s epistemology as well as for his theory of language and art.