ABSTRACT
The influence of scientific research on Rota’s philosophical style, discussed in Section 1.2, is particularly important in his writings on the philosophy of mathematics. His particular interpretation of mathematical entities clarifies the whole of his philosophical perspective and sheds light on a number of his writings that are difficult to interpret. Later on, I shall attempt to show how, while coming from different intellectual traditions, the reflection of Imre Lakatos (1922-1974) and that of Rota meet and articulate, reaching conclusions that sustain one another reciprocally, casting an intriguing light upon the history of mathematics and upon the contribution that conventionalism furnishes us for its understanding. As with all historiographic labels, the term “conventionalism” must also be taken with due precautions. As used here, it refers principally to a constellation of concepts regarding the economy of thought and the historicity of science, and to the names Pierre Duhem, Henri Poincaré, and (partially) Ernst Mach.1
