Gaston Milhaud rejects the principle of contradiction if it is conceived as an absolute and universal rule. He claims that it only holds in some narrowly defined circumstances. According to him, the greater is mental contribution to an act of cognition the more appropriate is the application of the principle of contradiction. My analysis of his views shows that he wanted to emphasize the differences between the objective reality and its mental or linguistic representations rather than undermine the logical principle of contradiction. Parallels can be noted between Milhaud’s views on contradiction and Leon Chwistek’s theory of the multiplicity of realities, as well as Kazimierz Ajdukiewicz’s concept of the cognitive role of language.

Gaston Milhaud (1858–1918) was a French modern philosopher, who, having started from mathematics, came to philosophy (especially epistemology) and history of science. His works on the history of science were devoted to Greek science and modern science. Milhaud in his papers claimed that important concepts and principles of science (in different disciplines) result from decisions that simultaneously transcend both experience and logic. He emphasized the role of free creation and activity of the mind. The author discusses central problems of Milhaud’s thought, especially the problem of the relationship between science and philosophy.

I give arguments supporting the claim that one of the most prominent methodological results of French conventionalism – rejection of the possibility of a crucial experiment in mature empirical sciences – was formulated simultaneously by Pierre Duhem and Gaston Milhaud in 1894. Thus, I attempt to question the standard approach in philosophy and methodology of science, which attributes the said result exclusively to Duhem. I am building my case of Milhaud’s true contribution to the debate on the rejection of the existence of the experimentum crucis, made in his PhD thesis Essai sur les conditions et les limites de la certitude logique.

The end of the nineteenth century was the period when revolutionary scientific discoveries challenged well-established theories, forcing both philosophers and scientists to ask questions about the nature and certainty of scientific knowledge. A group of French scientists not only performed a thorough critique of contemporary science and its history but proposed a new model that adequately described the development of scientific knowledge. Gaston Milhaud made a significant contribution to this new description of knowledge creation. He is however rarely mentioned in the context of the theory of knowledge and remains overshadowed by his famous colleagues. Despite the fact that more than a hundred years have passed since the conventionalist philosophy of science was formulated, H. Poincaré’s, P. Duhem’s and G. Milhaud’s positions have not gained much popularity beyond the circle of philosophers of science. This article briefly outlines personal relationships within French conventionalist circle, presents important results of Milhaud’s analysis, and the reasons why philosophers do not recognize the role he played in creating a new model for the development of scientific knowledge.