Scientific Project

The main objective of the project is not primarily the reconstruction of the historical connections between the three groups—which is already very interesting, because it shows some curious interactions and even affinities—, but a comparative investigation of three distinct collaborative and interdisciplinary approaches. In particular, the aim here is to analyse to what extent these approaches influenced the epistemological understanding of modern mathematics, of its language, and of its role with respect to logic and the other sciences.

This comparative analysis will shed new light on the interpretation of the central philosophical results of these three scientific enterprises, especially with respect to several classical traditions (namely empiricism, positivism, Kantian neo-criticism, and Leibnizian rationalism), but also with respect to two dominating contemporary views on mathematics: (neo-)logicism (and, in particular, version of pluralistic logicism) and mathematical structuralism (in particular, variants of so-called “methodological structuralism” discussed in Reck & Price 2000). It will also show some elements of continuity between philosophical enterprises that seem to be antagonist on first glance: e.g. the standard opposition between RMM and VC (rationalism vs. antirationalism, metaphysics vs. antimetaphysics, criticism of positivism vs. neo-positivism, spiritualism vs. scientism, etc.) will give way to a common project of redefining the alliance between philosophy and science against the excessive specialization of science (see e.g. the role of Poincaré on the RMM, or Vailati’s engagement in the University reform, or the VC unifying projects), of promoting philosophy through international conferences and journals, also beyond the institutional academic system.

The comparative approach in the project will allow to correct a major misunderstanding that often occurred in the existing scholarly literature on these authors: this is the tendency to consider one or a few members of the group as representative of the whole group, as if collaboration presupposed a preliminary standardising process. Often the research groups are presented in the literature as compact and unified organizations sharing a common philosophical agenda, whereas a detailed historical and philosophical investigation of their collaborative practices, as well as of their writings reveals a constellation of different and sometimes even incompatible conceptions.

Moreover, the project will take into serious consideration the efforts to internationalize philosophy and their epistemological counterparts, in particular, in the development of some proto-historical forms of what might now be called pluralistic logicism (Hahn, Menger, Carnap, but also Vailati and Rougier). More specifically, the investigation of different ways of understanding what is now generically called logicism, both in different authors and in different phases of a single author’s research, will prove how misleading, or at least how vacuous it is to characterize all these conceptions as examples of the same philosophy of mathematics. For example, the view of logic as the investigation of various ways of saying the same things occurs in Vailati as a heritage of Pragmatism, whereas in Hahn it results from the group readings of Wittgenstein’s Tractatus. Similarly, Carnap’s logical pluralism expressed in his famous principle of tolerance shares some features with Vailati’s pragmatistic reading of Peano’s enterprise, or to Peano’s remarks on the different ways to introduce scientific definitions in mathematics, even if the two ideas emerge in different philosophical perspectives: what is common to both is the development inside a truly collaborative and interdisciplinary research framework.

The present comparative study will show various points of connection between the collaborative and interdisciplinary approaches and certain educational and political aims, such as the vulgarization of scientific knowledge, the criticism of disciplinary boundaries or oppositions in higher education systems, and the effort to revitalize in a political perspective the positivistic idea that scientific knowledge should increase human welfare and freedom. At the same time, the present approach will also allow focusing on the underestimated influence of positivism and empiricism on the Peano School, of the Leibnizian tradition on the RMM and on the Vienna Circle, and of neo-criticism on the latter.