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Intuitionism between philosophy, mathematics and logic: mutations and long history

Special issue of Philosophia Scientiæ 29/2 (June 2025)

Guest editors: Dominique Pradelle, Marwan Rashed, Mark van Atten.

Submission deadline: February 1, 2024.

Notification date: December 1, 2024.

Submission addresses: Dominique Pradelle <>, Marwan Rashed <>, Mark van Atten <>

The present call for papers is linked to the eponymous colloquium organized in October 2021 by Dominique Pradelle, Marwan Rashed and Mark van Atten, as part of a collaboration between the Archives Husserl de Paris (UMR 8547) and Sorbonne Université, and focused on the history of intuitionism in logic, mathematics and philosophy, a history that is considered over the long term and not exclusively in one of its cardinal moments.

Contributions may concern Greek and Arabic mathematics, as well as classical mathematics. In Greek mathematics, the problem arises of distinguishing between verbal meanings and meanings based on the existence of the defined entity (Aristotle, Anal. post, II, chaps. 4, 5 6 and 7); the problem then arises as to what procedure is likely to attest to such ideal existence: is it demonstration that must rule out the presence of incompatible predicates in the definition of the mathematical entity? can this demonstration take the form of a reduction to the absurd or, as Aristotle puts it, a "reduction to the impossible" (Anal. pr., II, 25, 69 a 29-34)? Or, in accordance with Zeuthen's thesis "Die geometrische Construktion als 'Existenzbeweis' in der antiken Mathematik", Mathematische Annalen 47 (1896), pp. 222-228), did the Greek geometers adopt a constructivist stance on the existence of the ideal entities of mathematics? What does the use of the ruler and compass mean for such a construction of geometric entities? And as for the admission of infinite ideal entities (straight line, plane), is it admissible and does it require an idealization of our faculties? These problems obviously concern the relationship between logic and mathematics.

Contributions may also address the theory of demonstration in the modern era, both in mathematics and philosophy (since philosophy, for many thinkers of this period, adopted the model of an exposition ordine geometrico). In Leibniz critique de Descartes (Paris, Gallimard, 1960), Yvon Belaval contrasted Cartesian intuitionism with Leibnizian formalism, the Cartesian reliance on intellectual evidence with Leibniz's purely deductive chain of truths, and analyzed Leibniz's critique of the four rules of Cartesian method; at the same time, he showed how the consideration of infinitesimal quantities was, for Leibniz, contrary to intuition. However, he put this opposition into perspective by showing how Descartes and Leibniz both rejected the principle of the excluded middle. Should these analyses and oppositions be called into question? What exactly is the meaning of Cartesian (and Pascalian) intuitionism? Is it based solely on the concept of intellectual evidence, or on the rejection of the excluded third? Is the position opposed to intuitionism formalism, and in what sense?

Contributions may also focus on Brouwer's intuitionism and its contemporary descendants. In a number of famous articles, Brouwer questioned both the unconditional applicability of the logical principle of the excluded middle in mathematics (i.e., reductio ad absurdum) and the admission of the ideal existence of actual infinities in mathematics. In the same years, Poincaré had criticized Cantor's construction of the theory of transfinite numbers and its scaling of an infinite number of actual infinities. Intuitionism's most contemporary issues therefore revolve around the question of the limits of the applicability of logical principles (notably the excluded middle) and the limitation of infinity to a potential or becoming infinity.

Manuscripts must :

- be original, and may not be in the process of being submitted for another publication;

- be written in English, French or German;

- be prepared for anonymous double-blind evaluation;

- contain an abstract in French and an abstract in English (200-300 words);

- not exceed 40,000 characters (including spaces, abstracts, bibliography and notes);

- be in Word or OpenOffice format (;

- be sent to the following three addresses: <>; Marwan Rashed <>; Mark van Atten <>.

For article format, please consult the instructions for authors:

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