Paul Cortois

RésuméCette étude essaie de réunir quelques éléments en vue d'une interprétation plus complète du programme épistémologique contenu de façon extrêmement elliptique dans l'ouvrage post‐hume de Jean Cavaillès, publié en 1947 par G. Canguilhem et C. Ehresmann sous le titre Sur la logique et la théorie de la science . Afin d'arriver, plus particulière‐texte, où la «nécessité génératrice» d'une dialectique conceptuelle est évoquée, il faudra rappeler quelques aspects connus ainsi que quelques aspects moins connus du cheminement philosophique de Cavaillès.Cette reconstruction est mise en œuvre de façon détaillée dans un travail de commentaire textuel qui devait permettre de dégager le sens des formules denses et souvent allusives de Cavaillés dans son dernier ouvrage1. Il n'est pas possible de résumer ici en quelques lignes le contenu d'un tel travail. Toutefois on peut indiquer quelques conclusions qui s'en dégagent pour l'interprétation globale de l'ouvrage en question. En premier lieu il faut reconnaître la nature même du problème traité ici par Cavaillès. En second lieu on caractérise le type de position prise envers ce problème ainsi défini et en tant qu'on peut le restreindre dans un premier moment à la philosophie des mathématiques. En troisième lieu on montre que se problème subit un changement d'éclairage par le fait que cette restriction doit être levée en prenant en considération le rapport entre expérience mathématique et expiérience physique. que nous serons obligés d'entrer un peu plus, et à titre d'exemple, dam le détail de l'exégèse). Finalement on peut essayer de préciser le programme d'une dialectique conceptuelle en quelques thèses ou titres schématiques qui concement les questions majeures de la théorie de la science selon Cavaillès2

In this commemorative article the significance of Paul Feyerabend's work for philosophy of science in general is reviewed. Its unifying perspective is identified as the fight against any possible constraint on imagination (i.e. on the capacity of generating alternatives). This alternative-maximizing search was already central in Feyerabend's 'pre-anarchistic' studies. In fact, I claim that the really significant theses and arguments, as far as the intrinsic debate within the philosophy of science is concerned, were present in these earlier studies (criticism of the conditions of consistency and meaning invariance, pragmatic theory of observation, incommensurability thesis ...). The context of the 'historical turn' is sketched in which these arguments were developed as aresponse to current views on science. But these arguments do possess an independent normative significance. As Feyerabend construes them however, this independence is uncertain, because it is the value of proliferating imaginative alternatives as such which partly conditionalizes the significance of these arguments (as it conditionalizes the very value of science itself). In this way the philosophy of the critical imagination could eventually turn the critical values against the philosophy of rational criticism itself. And indeed, (1)a certain combination of the tenets concerning consistency and meaning variance undermines the idea of crucial test, and (2) in Against Method xht panegyric of the imagination (couched in a new narrative of the history of science) is used as the main weapon to override any methodological account. Philosophy of science is now convicted of what is the only deadly sin — the murder of imagination. But science itself is also accused of the same crime: it has become not merely an ideology — which is nothing to worry about — but a totalitarian ideology, monopolizing epistemic and educational claims. I argue that, although the reintroduction within philosophy of science of such questions belonging to a philosophy of culture is called for as a complement for intrinsic approaches, the Feyerabendean way of treating those questions makes it impossible to state anything about the specificity of science within culture. On the other hand two 'master ideas' still seem apt to stimulate further discussion: (1) the critique of the consistency condition, backed by the attack on the thesis of the 'relative autonomy of facts', and (2) the defence of meaning variance, backed by the pragmatic theory of observation, and leading in turn to the idea of incommensurability. At the same time this idea of incommensurability could also play a role in a philosophy of the relation between science and culture (which remains to be developed)

In what sense can the sciences be said to constitute a (set of) specific cultural tradition(s) within broader culture? This is the proper way of posing the problem of the 'two cultures' today. For G. Bachelard the opposition between 'poem' and 'theorem' was fundamental, the elements of poetical imagination being radically different from the symbolical constructions of conceptual invention. In this article a sophisticated version of this point of view is proposed. The nowadays popular attempts to bridge all gaps between the cultures by an appeal to creative imagination ('science as art', 'mathematics and poetry') are criticized. The real basis of considering research traditions nevertheless as cultural realities in a nontrivial sense is not to be found in a mediation between cognitive faculties, but has to be revealed by a comparative analysis of their respective products. In fact, science, as well as other cultural practices, is subject to variations of style (Granger, Hacking ...). Research styles are not in the first place due to external, sociological determinants, but to such factors as the necessity of individuating any idea in a work, the presence of changing images of science within each discipline, and the fundamental role of the not-yet-explicit, given the specific temporal structure of conceptual innovation with its „essential tension” (Kuhn) between the old and the new

Wittgenstein wordt wel beschouwd als een tegenstander van het ‘cognitivisme’ in de godsdienstfilosofie. Ik probeer hier aan te tonen dat Wittgenstein ook een tegenwicht biedt tegen hedendaagse benaderingen in de cultuurwetenschappen. De hedendaagse culturele antropologie is gestoeld op een combinatie van evolutionaire en cognitieve psychologie. ‘Betekenis’ wordt daarin opgevat als een cognitief proces dat zijn belichaming vindt in ons brein, en daarmee privé is. Wittgenstein wijst echter op het publieke karakter van betekenis, en op een andere notie van belichaming, die te maken heeft met dat publieke karakter alsook met betekenis als relevantie

In this expository article one of the contributions of Jean Cavailles to the philosophy of mathematics is presented: the analysis of ‘mathematical experience’. The place of Cavailles on the logico-philosophical scene of the 30s and 40s is sketched. I propose a partial interpretation of Cavailles's epistemological program of so-called ‘conceptual dialectics’: mathematical holism, duality principles, the notion of formal contents, and the specific temporal structure of conceptual dynamics. The structure of mathematical abstraction is analysed in terms of its complementary dimensions: paradigmatic generalization (domain extension, descriptive definitions, creative role of the symbolism...) and thematic reflexivity of concepts (promotion of operations to objects of a higher type).

Whatever the precise analysis of the notion of an `internal point of view', to talk about `religious traditions' is to imply that traditions of a certain kind primarily deploy an internal point of view. But what can be said about the notion of an intellectual tradition that would at the same time also be, or be connected to, a religious tradition? To some, such notions appear to border on contradiction. In accordance with the Cartesian criticism of coutume et exemple, we tend to think of an intellectual stance as the correlate of a detached view, with the rational remaining the enemy of the traditional. In that case, every application whatsoever of the predicate `intellectual' to a tradition would be flawed. According to a certain Enlightenment view, inspired by science, is it not of the very essence of the intellectual stance in general that one stand back at a critical distance from any tradition, especially one's own?In fact, historically oriented philosophers of science like Crombie, Kuhn, Laudan have reminded us of the fact that there is nothing disturbingly paradoxical in speaking of `intellectual traditions': to quote one of Kuhn's book titles, there is the "essential tension" that characterizes science in its development just as much as any other cultural tradition. This tension between the old and the new is the mark of traditions, including the ones defining the rationality or rationalities of science. We could say that Kuhn's `paradigms' already outlined the borders of specific `catholicities' for the specialized fields of scientific research traditions. If Kuhn ever had a point, it must be that science too can develop only within the framework of styles of reasoning, which is to say that it demands viewpoints that cannot be characterized as `external', at least not in an absolute, metaphysical sense of the word