The present PhD dissertation aims to examine the relation between modality and change in Aristotle’s metaphysics. -/- On the one hand, Aristotle supports his modal realism (i.e., worldly objects have modal properties - potentialities and essences - that ground the ascriptions of possibility and necessity) by arguing that the rejection of modal realism makes change inexplicable, or, worse, banishes it from the realm of reality. On the other hand, the Stagirite analyses processes by means of modal notions (‘change is the (...) actuality of what is virtual insofar as it is virtual’). In other words: to grasp what change is, one has to resort to the modal idiom of potentialities, while the fact that there is change is indicative of the fact that nature is full of modal properties. -/- Aristotle’s modal and kinetic realism finds a negative in the figure of the Megaric Diodorus Kronus. The polemical situation of Greek philosophy has indeed the dialectical advantage of not opposing the Aristotelian position to a sui generis straw man. Both in its reduction of modal judgements to temporal quantifications and in its dissolution of the reality of the state-of-being-in-motion in favour of a cinematographic view of processes, the philosophical figure of reductionist antirealism embodied by Diodorus constitutes an alternative that takes the opposite view of Aristotle’s realism. -/- The present study is structured as a discussion between these two positions. In the face of Diodorus’ antirealist challenges, Aristotle articulates modal and kinetic considerations: the answers he gives to Diodorus’ puzzles thus provide valuable insight into his metaphysics. Moreover, the examination of Aristotle’s and Diodorus’ metaphysics, because of their insight and originality, will not fail to interest the philosopher concerned with the metaphysical foundations of modern physics, insofar as the entanglement between modalities and processes is nowadays at the core of mechanics (phase spaces, path integrals, etc.). (shrink)

On entend généralement par « théorie des modèles » autant la métamathématique (ou sémantique formelle) que la sémantique des modèles des sciences non formelles. Cet article a pour objet la théorie des modèles scientifiques que Mario Bunge a développée dans Method, Models and Matter (1973). J’y analyse l’intégration théorique qu’opère Bunge des sciences formelles et des sciences expérimentales ou observationnelles, laquelle prend appui sur sa philosophie des sciences. Je la compare sommairement à la théorie des modèles de Gilles-Gaston Granger dans (...) le but évident d’en dégager les ressemblances et les dissimilitudes, mais aussi leur commun point d’achoppement : l’une comme l’autre usent en effet d’un concept non analysé dont la fonction épistémologique est pourtant capitale et produit les mêmes effets. Au centre de la théorie des modèles de Bunge se trouve le concept de simulation que je comparerai à celui qui est en usage dans les sciences de l’ordinateur et qui est de nos jours largement appliqué à diverses sciences, tant sociales que naturelles. Je conclurai sur les conséquences méthodologiques et métaphysiques de la théorie bungéenne des modèles. (shrink)

This thesis seeks to understand the nature of and relation between science and philosophy articulated in the early work of the French philosopher Gilles Deleuze. It seeks to challenge the view that Deleuze’s metaphysical and metaphilosophical position is in important part an attempt to respond to twentieth century developments in the natural sciences, claiming that this is not a plausible interpretation of Deleuze’s early thought. The central problem identified with such readings is that they provide an insufficient explanation of the (...) nature of philosophy’s contribution to the encounter between philosophy and science that they discern in Deleuze’s work. The philosophical, as opposed to scientific, dimension of the position attributed to Deleuze remains obscure. In chapter 1, it is demonstrated that this question of philosophy’s contribution to intellectual life and of how to differentiate philosophy from the sciences is a live one in Deleuze’s early thought. An alternative, less anachronistic interpretation of the parameters of Deleuze’s early project is offered. The remaining chapters of the thesis examine the early Deleuze’s understanding of the divergence between philosophy and science. Chapter 2 gives an account of Deleuze’s metaphilosophy, alongside a reconstruction of his largely implicit early understanding of science. The divergent intellectual processes and motivating concerns that account for Deleuze’s understanding of the differentiation of science and philosophy are thus clarified. In chapter 3, Deleuze’s use of mathematical and physical concepts is examined. It is argued that these concepts are used metaphorically. In chapter 4, the association between modern science and the Deleuzian concept of immanence that has been proposed by some Deleuze scholars is examined and ultimately challenged. The thesis concludes with some reflections on the significance of Deleuze’s early work for contemporary debates concerning the future of continental philosophy and the nature of philosophy more generally. (shrink)

We reconstruct essential features of Lagrange’s theory of analytical functions by exhibiting its structure and basic assumptions, as well as its main shortcomings. We explain Lagrange’s notions of function and algebraic quantity, and we concentrate on power-series expansions, on the algorithm for derivative functions, and the remainder theorem—especially on the role this theorem has in solving geometric and mechanical problems. We thus aim to provide a better understanding of Enlightenment mathematics and to show that the foundations of mathematics did not, (...) for Lagrange, concern the solidity of its ultimate bases, but rather purity of method—the generality and internal organization of the discipline. (shrink)

What is early modern philosophy? Two interpretative trends have predominated in the related literature. One, with roots in the work of Hegel and Heidegger, sees early modern thinking either as the outcome of a process of gradual rationalization (leading to the principle of sufficient reason, and to "ontology" as distinct from metaphysics), or as a reflection of an inherent subjectivity or representational semantics. The other sees it as reformulations of medieval versions of substance and cause, suggested by, or leading to, (...) early modern scientific developments. -/- This book proposes a rather different kind of explanation. It suggests that the concept of relation, specifically that of dyadic, anti-symmetrical relations, can throw light on a wide variety of developments in early modern thought, such as those concerning causality, sense perception, temporality, and the mereological approach to substance. The book argues that these relations are grounded in an interpretation of causal influence, and not in semantic theories or subjectivity. -/- Furthermore, if it is correct that the problem of unity was, for most of classical antiquity, what the problems of motion, causality and perception were for early modern thinkers, then early modern thought is much closer to the thought of Aristotle than is commonly supposed. The genesis of early modern thought might instead be taken to have occurred in opposition to one aspect of the thought of Duns Scotus (an aspect that lives on in contemporary Neo-Aristotelianism), and that can be explained once the relational perspective examined here is taken into account. (shrink)

We analyze the notions of indiscernibility and indeterminacy in the light of the Galois theory of field extensions and the generalization to \(K\) -algebras proposed by Grothendieck. Grothendieck’s reformulation of Galois theory permits to recast the Galois correspondence between symmetry groups and invariants as a Galois–Grothendieck duality between \(G\) -spaces and the minimal observable algebras that discern (or separate) their points. According to the natural epistemic interpretation of the original Galois theory, the possible \(K\) -indiscernibilities between the roots of a (...) polynomial \(p(x)\in K[x]\) result from the limitations of the field \(K\) . We discuss the relation between this epistemic interpretation of the Galois–Grothendieck duality and Leibniz’s principle of the identity of indiscernibles. We then use the conceptual framework provided by Klein’s Erlangen program to propose an alternative ontologic interpretation of this duality. The Galoisian symmetries are now interpreted in terms of the automorphisms of the symmetric geometric figures that can be placed in a background Klein geometry. According to this interpretation, the Galois–Grothendieck duality encodes the compatibility condition between geometric figures endowed with groups of automorphisms and the ‘observables’ that can be consistently evaluated at such figures. In this conceptual framework, the Galoisian symmetries do not encode the epistemic indiscernibility between individuals, but rather the intrinsic indeterminacy in the pointwise localization of the figures with respect to the background Klein geometry. (shrink)

We analyze the notion of indiscernibility in the light of the Galois theory of field extensions and the generalization to K-algebras proposed by Grothendieck. Grothendieck's reformulation of Galois theory permits to recast the Galois correspondence between symmetry groups and invariants as a duality between G-spaces and the minimal observable algebras that separate theirs points. In order to address the Galoisian notion of indiscernibility, we propose what we call an epistemic reading of the Galois-Grothendieck theory. According to this viewpoint, the Galoisian (...) notion of indiscernibility results from the limitations of the `resolving power' of the observable algebras used to discern the corresponding `coarse-grained' states. The resulting Galois-Grothendieck duality is rephrased in the form of what we call a Galois indiscernibility principle. According to this principle, there exists an inverse correlation between the coarsegrainedness of the states and the size of the minimal observable algebra that discern these states. (shrink)