La question de l’idéalisme leibnizien, qui permet d’entrer au cœur de la métaphysique de Leibniz, intéresse encore aujourd’hui de nombreux commentateurs. Ceux-ci utilisent les termes « réalisme », « idéalisme », voire « phénoménalisme », pour caractériser la métaphysique leibnizienne et un travail doit être fait pour rassembler et comparer leurs analyses, ce que nous proposons de faire d’abord dans ce mémoire. Ce sont surtout les textes mêmes de Leibniz qui seront abordés dans le présent travail et qui permettront de proposer la lecture suivante : si la métaphysique leibnizienne est réaliste en ce sens qu’elle met en place une entité elle-même « mind-independent », c'est-à-dire la monade, elle peut être considérée comme idéaliste (idéalisme substantiel), puisque cette entité, étant sans partie et sans étendue, est en ce sens idéelle. Et si tout peut se réduire à cette monade, c’est toute la fondation de la métaphysique de Leibniz qui se retrouve à être idéelle. Or, ceci ne règle pas le statut des corps qui peuvent être considérés soit comme de simples phénomènes réductibles aux perceptions des monades (idéalisme matériel), soit comme des êtres ayant une réalité indépendante d’un esprit, lesquels se réduiraient cette fois aux monades qui les composent (réalisme matériel). Face à ces deux possibilités, nous développerons une position mitoyenne qui défend l’idée que les corps sont en effet composés de monades qui leur procurent une certaine réalité, mais qu’ils dépendront toujours de l’action d’un esprit qui lui seul pourra leur procurer une certaine unité. / Many commentators try to read Leibniz either as an idealist or a realist, adding a phenomenalist reading to theses first two analyses. However, those terms are however often used with ambiguities, making Leibniz sometimes an even more complex philosopher. The first purpose of this master’s thesis is to gather and compare all these interpretations in order to clarify Leibniz’s thought. In this study, his writings will be used to defend the following interpretation : Leibniz can be considered as a realist since he develops a theory where monads act as « mind-independent » entities. Nonetheless, these monads are non-extended and without parts. Therefore, we can present an idealistic understanding of Leibniz, for they are the “basic building-blocks” of his metaphysic. Still, clarifications need to be made concerning the body. It can either be “real”, if it is seen as an aggregate of monads. Or, it can be considered a “mind-dependent” phenomenon if seen as the result of monadic perceptions. We will develop, between these two possibilities, an intermediate position stating that bodies are indeed aggregates of monads (matter realism). However they must be considered as phenomena for this same reason (phenomenalism). Corporeal aggregates require the action of the mind which alone can give them unity. On the contrary monads are said to be unum per se. Bodies are therefore phenomena but precisely well founded in the monads that compose them.

La connaissance implique une prédisposition à la connaissance, c’est-à-dire la possibilité de la relation entre un sujet (connaissant) et un objet (connaissable). D’un autre côté, il y a un état de fait, qui est la connaissance qui a lieu, de fait : la connaissance courante, ordinaire, toujours incomplète, à laquelle l’homme se trouve incessamment avoir accès ou être en train d’avoir accès. La connaissance véritable – pleine et entière – se trouve située à l’extérieur de ce domaine cognitif ordinaire ; extériorité qui implique une indisposition présente à y avoir accès. La connaissance mathématique est du premier ordre – et ce, éminemment, autrement dit, à la fois, en tant que meilleure connaissance possible et en tant que connaissance révélant, le mieux, au travers de son propre inachèvement, l’inachèvement de toute connaissance accessible (dont elle est constitutive ou auxiliaire). Du second ordre, est la connaissance eidétique (connaissance des Formes – eidê, ideai – autrement appelées Idées), qui est la connaissance du réellement réel (ontôs on) (dont l’objet, en sa saisie, ne peut que signer la réelle réalité de la connaissance elle-même). De son côté, la connaissance mathématique induit, en son inachèvement, la connaissance de son principe et élément, qu’est l’unité véritable (c’est-à-dire unique, indivisible et indifférenciée, et donc paradoxalement inconnaissable, en quoi, elle induit, elle-même, l’ordre de la connaissance véritable, qu’est l’ordre eidétique), unité censée trouver, dans l’ordre géométrique, son expression, en tant que mesure et élément communs à tout le mesurable (l’étendu) et, du même coup, à tout le dénombrable ; expression géométrique qui ne manque pas d’être problématique (aporétique), la grandeur demeurant, dans l’absolu, indéfinie, et toute grandeur étant divisible à l’infini, en grandeurs plus petites. Ainsi, se trouve attesté le fait que la disposition cognitive présente (ordinaire) est inéluctablement en deçà d’être disposition à la connaissance véritable, en ce que celle-ci devrait être notamment connaissance du principe, principe que nous pensons trouver désigné, chez Platon, sous l’expression « principe de la ligne », principe dynamique et actif, proprement non mathématique, toujours antérieur à quelque détermination (grandeur) – et, du même coup, à quelque dénombrement – que ce soit. / The knowledge implies a predisposition to the knowledge, that is the possibility of the relation between a (knowing) subject and a (knowable) object. On the other hand, there is an established fact, which is the knowledge which has de facto place : the common, ordinary, always incomplete knowledge, to which the man is continuously to have access or to be having access. The real knowledge – full and whole – is situated outside of this ordinary cognitive domain ; exteriority which implies a present indisposition to have access there. The mathematical knowledge is of the first order – and it is true eminently, in other words, at the same time, as better possible knowledge and as knowledge revealing, best, through its own incompletion, the incompletion of any accessible knowledge (whose it is constitutive or auxiliary). Of the second order, is the eidetic knowledge (knowledge of the Forms – eidê, ideai – otherwise called Ideas), which is the knowledge of the really real (ontôs on) (whose the object, in its grasp, can only sign the real reality of the knowledge itself). From her part, the mathematical knowledge leads, in its incompletion, the knowledge of its principle and element, that is the real unit (that is unique, inseparable and undifferentiated, and thus paradoxically unknowable, in what, it leads, itself, the order of the real knowledge, that is the eidetic order), unit supposed to find, in the geometrical order, its expression, as measure and element common to all the measurable (the extent) and, at the same time, to all the countable ; expression which does not miss to be problematic (aporetic), the size remaining, theoretically, indefinite, and any size being divisible in the infinity, in smaller sizes. So, is attested the fact that the present (ordinary) cognitive disposition is inevitably to be disposition to the real knowledge, in the fact that this one should be in particular knowledge of the principle, the principle which we think of finding indicated, at Plato, under the expression “principle of the line”, dynamic and active, specifically not mathematical principle, always previous to any determination (size) – and, at the same time, to any enumeration – whatsoever.

La notion de quotidien est inévitablement liée au présent. L’art découle del’expérience des individus, de leurs intentions et des circonstances propres à tout lieu.Tout artiste participe inévitablement de la vie quotidienne qu’il ou elle partage avec lepublic, de même qu’en envisageant un art « vivant », l’artiste peut réellement vivre savie afin d’enrichir, éprouver et confirmer son existence. Nous concernant, dans le cadrede notre pratique artistique, nous devons donc penser aux instants où nous rencontronsdes situations nouvelles, aux hasards de la vie quotidienne. Ceux-ci permettent des’ouvrir aux autres, à un monde indifférent, dangereux, mais aussi séduisant etfascinant. L’expérience qui en découle peut alors être considérée comme une manière deralentir le cours des choses, d’influer sur le monde en interrompant son caractèremécanique et en prolongeant les espaces, au lieu de les segmenter, ne serait-ce que pourun bref moment. Dans notre étude, l’« ici et maintenant » se manifeste au moyen d’unensemble de procédés dévolus au champ du visuel, notamment en exacerbant les traitsd’un milieu, d’un environnement, d’un lieu. Cette thèse questionne ainsi les processus d’élaboration et d’expressionintervenant dans la production de certaines oeuvres, afin de déterminer le rôle etl’importance d’une dynamique, d’un contexte, que l’on pourrait qualifier de quotidien.Il s’agira alors d’examiner les oeuvres sous la perspective de certaines caractéristiquesqui répondent de ce quotidien – l’ordinaire, ou un certain rapport au temps et à l’espace–, dans le projet de redécouvrir des formes, des cultures, avec, plus particulièrement,une attention centrée sur l’homme : sa représentation, son environnement et son modede vie constituant les trois volets de cette thèse.Cette thèse, interroge, au final, les usages quotidiens de la rencontre dans le cadrede pratiques associées à l’art contemporain, tel qu’il se fait le reflet d’une quotidiennetéamplifiée. Discours qui, s’il n’est pas nouveau, mérite cependant, selon nous, qu’il soitcontinuellement reconstruit et reconsidéré. Dans cette optique, si chacun devient sonpropre médiateur, contribuant au renouvellement et à la spectacularisation du monde, ilsemble que nous nous destinons à nous heurter de nouveau à un mur, alors que nous savons,simultanément, qu'il est de notre devoir de nous greffer à la réalité. Dans le mêmetemps, nous avons de nouveau la possibilité d’en appeler à l’universalité, afin de révélerla structure interne de la vie quotidienne contemporaine, quand bien même il s’agiraitde contempler la duplicité et l’ambiguïté de sa propre existence quotidienne1. / The notion of everyday life is inevitably linked to the present. Art arises from theexperience of individuals, their intentions and the circumstances of any place. And,every artist inevitably participates in the daily life that he / she shares with his / her audience.We must therefore think of the moments when we encounter new situations, atrandom in everyday life. It opens up to others, to a world that is indifferent, dangerous,but also seductive and fascinating. This experience would be considered as a way tostop the world, to stop the mechanical life and space, if only for a brief moment. Inshort, the "here and now" is manifested through visual tools, exacerbating, in particular,the features of a milieu, an environment, a place. This thesis attempts to narrate someprocesses involved in the production of works, in order to insist for each work on methodsof expression and transformation. It will then be a question of presenting the worksunder the sign of a daily reading, in the optics of a rediscovery of forms and, cultures,with a centered attention on the man: his representation, his environment and his modeof life are the three components of this thesis. More precisely, it is a matter of testingthese notions of "monad" and "nomad" in the real space of life. For this reason, thisstudy could be perceived as a momentum comparable to an art lived "here and now".Unlike painting, in this respect, this art is not only representable by a variety of people�� �� ����in itself, but it has a limit in that it can not solicit the same reactions from each of thesepeople. Therefore, the purpose of this thesis is that there is no imposition of a certainbehavior, at a certain time in the face of a certain work, but rather an instantaneity assumedin the face of always renewed situations. Thus, through this thesis that drawsutopias of proximity, we question an urban bodily experience that differs from the usualreferences (city-neighborhood, territorial construction and identity). Our questioningtherefore remains guided by the consideration of variations of the urban by the body andvice versa.This thesis finally becomes possible to provoke the daily use of the meeting, toplay the practices of contemporary art, become the reflection of an amplified daily life.All this is a discourse heard but whose modalities, in our opinion, are constantly to bereconsidered and rebuilt. In this hypothesis, everyone becomes his own mediatorcontributing to the renewal and spectacularization of the world. Finally, we are back onthe wall yet we know that it is our job to graft the reality. At the same time, we haveagain the possibility of appealing to universality in an attempt to reveal the internalstructure of contemporary daily life, even though it would be a question ofcontemplating the duplicity and ambiguity of one's own daily existence.

While Berkeley's position on the materialism of the world is undoubtedly idealistic, Leibniz's position is somewhat problematic: in metaphysical texts, he seems to be an idealist, while in texts concerned with natural philosophy and physics, he seems more like a dualist similar to Aristotle. We will even see that Leibniz wants to be both an idealist/phenomenalist and a realist. Moreover, in his remarks to Berkeley, he criticizes Berkeley's idealism and his rejection of matter. The aim of this paper is to map Leibniz's idealistic position, compare it with Berkeley's, and decide whether Leibniz's objections to Berkeley are justified and whether their positions are any similar

The thesis follows on Petr Vopìnka's alternative theory of sets and semisets by extending notions of in nite closeness and monad for real spaces of several variables. It speci es and explains on examples the basic terminology of this theory, namely notions of sets, semisets and domains. It brings up two worlds | an ancient and a classical one | by which it shows a dual way of looking at real functions of several variables. That is used for examining local properties like continuity, limit or derivative of a function at a point. The peak of the thesis is an alternative formulation of the implicit function theorem and the inverse function theorem. The thesis also contains translation rules, which allow us to reformulate all these results from an alternative into a traditional formulation used in mathematical analysis.

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In this thesis we see two new approaches to compose tree transducers and more general to fuse functional programs. The first abroach is based on initial algebras. We prove a new variant of the acid rain theorem for mutually recursive functions where the build function is substituted by a concrete functor. Moreover, we give a symmetric form (i.e. consumer and producer have the same syntactic form) of our new acid rain theorem where fusion is composition in a category and thus in particular associative. Applying this to compose top-down tree transducers yields the same result (on a syntactic level) as the classical top-down tree transducer composition. The second approach is based on free monads and monad transformers. In the same way as monoids are used in the theory of character string automata, we use monads in the theory of tree transducers. We generalize the notion of a tree transducer defining the monadic transducer, and we prove an according fusion theorem. Moreover, we prove that homomorphic monadic transducers are semantically equivalent. The latter makes it possible to compose syntactic classes of tree transducers (or particular functional programs) by simply composing endofunctors.

In this thesis we see two new approaches to compose tree transducers and more general to fuse functional programs. The first abroach is based on initial algebras. We prove a new variant of the acid rain theorem for mutually recursive functions where the build function is substituted by a concrete functor. Moreover, we give a symmetric form (i.e. consumer and producer have the same syntactic form) of our new acid rain theorem where fusion is composition in a category and thus in particular associative. Applying this to compose top-down tree transducers yields the same result (on a syntactic level) as the classical top-down tree transducer composition. The second approach is based on free monads and monad transformers. In the same way as monoids are used in the theory of character string automata, we use monads in the theory of tree transducers. We generalize the notion of a tree transducer defining the monadic transducer, and we prove an according fusion theorem. Moreover, we prove that homomorphic monadic transducers are semantically equivalent. The latter makes it possible to compose syntactic classes of tree transducers (or particular functional programs) by simply composing endofunctors.

Le thème central de la présente thèse est le contenu sémantique des quantificateurs logiques. Dans leur forme la plus simple, les quantificateurs permettent d’établir l’existence, ou la non-existence, d’individus répondant à une propriété. En tant que tels, ils incarnent la richesse et la complexité de la logique du premier ordre, par delà la logique propositionnelle. Nous contribuons à l’analyse sémantique des quantificateurs, du point de vue de la théorie de la dualité, dans trois domaines différents des mathématiques et de l’informatique théorique. D’une part, dans la théorie des langages formels à travers la logique sur les mots. D’autre part, dans la logique intuitionniste propositionnelle et dans l’étude de l’interpolation uniforme. Enfin, dans la topologie catégorique et dans la sémantique catégorique de la logique du premier ordre. / The unifying theme of the thesis is the semantic meaning of logical quantifiers. In their basic form quantifiers allow to state theexistence, or non-existence, of individuals satisfying a property. As such, they encode the richness and the complexity of predicate logic, as opposed to propositional logic. We contribute to the semantic understanding of quantifiers, from the viewpoint of duality theory, in three different areas of mathematics and theoretical computer science. First, in formal language theory through the syntactic approach provided by logic on words. Second, in intuitionistic propositional logic and in the study of uniform interpolation. Third, in categorical topology and categorical semantics for predicate logic.

Nesta tese, desenvolve-se um argumento explicativo da relação mente-corpo fundamentada na noção de mônada, ou substância simples, como elemento ontológico estruturante de um enfoque contemporâneo da mencionada relação. Na primeira parte da tese, de natureza crítica, analisam-se as teorias fisicistas contemporâneas da mencionada relação, a saber, a teoria de superveniência da mente, da emergência e da causação mental, com vistas a justificar a proposta de assunção de uma premissa dualista que visa, principalmente, propor, em contraste com o cenário epifenomenalista do fisicismo contemporâneo, uma ontologia da mente que seja compatível com as intuições realistas do senso comum e da psicológica popular sobre a força causal da mente no universo físico. Na segunda parte, de natureza positiva, propõe-se um argumento explicativo da relação mente-corpo partindo-se, para tanto, de uma assunção e duas premissas. A assunção afirma que a mente tem o mesmo importe ontológico da matéria física, sendo estes considerados como elementos composicionais, afirmação a qual se denomina dualismo elementar. No que se refere às premissas, propõe-se duas, a saber, a tese composicional holística, que afirma que a mente e a matéria são partes constitutivas de um todo chamado substância simples, e a tese composicional mereológica, que afirma que as substâncias simples ou mônadas compõem mereologicamente, por superveniência, a relação mente-corpo. Examinam-se também algumas objeções ao argumento monadista proposto. / This thesis offers an explanatory argument concerning the mind-body relation, an argument that is grounded on the notion of monad, or the simple substance, as an ontological element for proposing a contemporary approach to the mind-body relation. In the first part, a critique of the current physicalist theories of mind is given, namely, supervenience, emergence and mental causation, in order to justify the proposal of a dualist premiss which aims at an ontology of mind which satisfies the realistic intuitions of common sense and of folk psychology on the causal efficacy and relevance of the mind amid the physical, in opposition to the epiphenomenalist view of contemporary physicalist theories. In the second part, the positive one, we propose an explanatory argument for monadism about mind-body relations, based on an assumption and two premises. The assumption says that the mind has the same ontological import of the physical matter, and they, mind and matter, are considered to be elements entering the composition of psychophysical relations, an assumption called elementary dualism. Regarding the premises, we propose two, namely, the holistic compositional thesis, which asserts that mind and matter are parts entering the composition of true wholes called substances, and the mereological compositional thesis, which says that such simple substances compose, via supervenience, the mind-body relations. Some objections to the proposed monadist argument are examined and rejoindered as well.