This article highlights the mathematical structure of Henri Bergson’s method. While Bergson has been historically interpreted as an anti-scientific and irrationalist philosopher, he modeled his philosophical methodology on the infinitesimal calculus developed by Leibniz and Newton in the seventeenth century. His philosophy, then, rests on the science of number, at least from a methodological standpoint. By looking at how he conscripted key mathematical concepts into his philosophy, this article invites us to re-imagine Bergson’s place in the history of Western philosophy.

The study analyzes the theoretical basis of the Philosophy for Children (P4C) program elaborated by Matthew Lipman. The aim is, firstly, to identify the main philosophical and pedagogical principles of P4C based on American pragmatism, and to locate their pedagogization and possible problems in Lipman’s thinking. Here the discussion is especially targeted to the thinking of John Dewey and George H. Mead as well as Lev Vygotsky, whom Lipman himself names as the most pivotal sources for his own thinking. On (...) the other hand, the study aims at opening up new perspectives and thematizations on P4C from the viewpoint of the continental tradition of thought. The essential principles of P4C connected with reasonableness and judgment are ultimately interpreted as a neo-Aristotelian effort to contextualize philosophy by tracing it back to moderation, the man’s ability to consider and solve problems that he meets in practical life kata ton orthon logon — by doing right things in the right place at the right time in the right way. This phronetic idea of ‘humanizing modernity’ combined with the evolution of the adult-child concept is argued to be one of the conditions for the possibility of P4C, yet leaving unsolved the basic problems involving pedagogical action as such. John Dewey’s ideas arising from the critique of the modern philosophy of consciousness, focusing on the significance of philosophy in practical human life and linked to the basic nature of human knowing and intellectual growth and, further, to the ideal of a democratic community, are shown to form the main intellectual sources of P4C. Dewey’s philosophy as a general theory of education means a solid linking of the concepts of experience and inquiry to the practice of education. This is based on the naturalistic conception of man according to which man is built in dynamic transaction with his environment, experiencing the true meanings of his ideas in the consequences of his actions as he tries to solve problematic situations. So, inquiry as a method of reflective thinking forms the basis for education based on intellectual growth. A condition for it is a context meaningful for the child in which the paradigm of inquiry can be realized authentically. It is therefore important in education to provide circumstances that stimulate the child’s curiosity, initiating a process of inquiry that further enables, through the formation of reflective habits, the development of a democratic community. The purpose of the pedagogical interaction taking place in the process of inquiry is to produce educative experiences for the child, making the pedagogical relationship vanish at the same time. The idea is that in pedagogical action the child’s subjectivity, his desire and impulses are adapted to the tradition, yet generating at the same time a prospective, reflective habit, thus freeing the educatee to think intelligently for himself. The study shows the articulation of these principles in Lipman’s practical effort to convert the classroom into a community of inquiry, but it also argues that the above-mentioned Bildung theoretical core problem of pedagogical action, related to its paradoxical special characteristics to produce autonomous subjectivity, is not thematized. In connection with this issue, the educational thinking of Kant and Hegel is discussed especially from the viewpoint of philosophy teaching. To provide a new perspective for the discussion, the study outlines the community of inquiry as an ‘educative space’ from the viewpoints of the pedagogical relationship typical of hermeneutic pedagogy and of non-reflective functional structures and phenomena based on pedagogical intuition that are linked to it. (shrink)