Ranging from Alan Turing’s seminal 1936 paper to the latest work on Kolmogorov complexity and linear logic, this comprehensive new work clarifies the relationship between computability on the one hand and constructivity on the other. The authors argue that even though constructivists have largely shed Brouwer’s solipsistic attitude to logic, there remain points of disagreement to this day. Focusing on the growing pains computability experienced as it was forced to address the demands of rapidly expanding applications, the content maps the (...) developments following Turing’s ground-breaking linkage of computation and the machine, the resulting birth of complexity theory, the innovations of Kolmogorov complexity and resolving the dissonances between proof theoretical semantics and canonical proof feasibility. Finally, it explores one of the most fundamental questions concerning the interface between constructivity and computability: whether the theory of recursive functions is needed for a rigorous development of constructive mathematics. This volume contributes to the unity of science by overcoming disunities rather than offering an overarching framework. It posits that computability’s adoption of a classical, ontological point of view kept these imperatives separated. In studying the relationship between the two, it is a vital step forward in overcoming the disagreements and misunderstandings which stand in the way of a unifying view of logic. (shrink)

Biologists explain organisms’ behavior not only as having been programmed by genes and shaped by natural selection, but also as the result of an organism’s agency: the capacity to react to environmental changes in goal-driven ways. The use of such ‘agential explanations’ reopens old questions about how justified it is to ascribe agency to entities like bacteria or plants that obviously lack rationality and even a nervous system. Is organismic agency genuinely ‘real’ or is it just a useful fiction? In (...) this paper we focus on two questions: whether agential explanations are to be interpreted ontically, and whether they can be reduced to non-agential explanations (thereby dispensing with agency). The Kantian approach we identify interprets agential explanations non-ontically, yet holds agency to be indispensable. Attributing agency to organisms is not to be taken literally in the way we attribute physical properties such as mass or acceleration, but nor is it a mere heuristic or predictive tool. Rather, it is an inevitable consequence of our own rational capacity: as long as we are rational agents ourselves, we cannot avoid seeing agency in organisms. (shrink)

Esta enciclopédia abrange, de uma forma introdutória mas desejavelmente rigorosa, uma diversidade de conceitos, temas, problemas, argumentos e teorias localizados numa área relativamente recente de estudos, os quais tem sido habitual qualificar como «estudos lógico-filosóficos». De uma forma apropriadamente genérica, e apesar de o território teórico abrangido ser extenso e de contornos por vezes difusos, podemos dizer que na área se investiga um conjunto de questões fundamentais acerca da natureza da linguagem, da mente, da cognição e do raciocínio humanos, bem (...) como questões acerca das conexões destes com a realidade não mental e extralinguística. A razão daquela qualificação é a seguinte: por um lado, a investigação em questão é qualificada como filosófica em virtude do elevado grau de generalidade e abstracção das questões examinadas (entre outras coisas); por outro, a investigação é qualificada como lógica em virtude de ser uma investigação logicamente disciplinada, no sentido de nela se fazer um uso intenso de conceitos, técnicas e métodos provenientes da disciplina de lógica. O agregado de tópicos que constitui a área de estudos lógico-filosóficos é já visível, pelo menos em parte, no Tractatus Logico-Philosophicus de Ludwig Wittgenstein, uma obra publicada em 1921. E uma boa maneira de ter uma ideia sinóptica do território disciplinar abrangido por esta enciclopédia, ou pelo menos de uma porção substancial dele, é extrair do Tractatus uma lista dos tópicos mais salientes aí discutidos; a lista incluirá certamente tópicos do seguinte género, muitos dos quais se podem encontrar ao longo desta enciclopédia: factos e estados de coisas; objectos; representação; crenças e estados mentais; pensamentos; a proposição; nomes próprios; valores de verdade e bivalência; quantificação; funções de verdade; verdade lógica; identidade; tautologia; o raciocínio matemático; a natureza da inferência; o cepticismo e o solipsismo; a indução; as constantes lógicas; a negação; a forma lógica; as leis da ciência; o número. (shrink)

Despite the distance between the philosophies of Merleau-Ponty and of Deleuze, it is possible to discover not only analogue complicity with regard to thecriticism addressed to Husserl. In the aesthetic, for example, we note that the last thoughtsof Merleau-Ponty, present mainly in The visible and the invisible, are a constant referencefor the works that Deleuze dedicates to the painter Francis Bacon. In the present researchwe expect to define the passages on account of the reading of Husserl, and to show thepoint (...) of contact between Merleau-Ponty and Deleuze. So, we hope to change the image of apparent indifference with regard to understanding their philosophies. (shrink)

ABSTRACTThe paper focuses on the gradual separation between materialism and mechanism in early modern German philosophy. In Germany the distinction between the two concepts, originally introduced by Leibniz, was definitively stated by Wolff who was the first to provide a definition of the new philosophical term Materialismus, and of the related philosophical sect. In the first part I describe the initial identification of mechanism and materialism in German philosophy between the last decades of the seventeenth century and 1720. Mechanism is (...) here mostly conceived within a monistic metaphysics of body, which refers mainly to Hobbes and to some interpretations of Spinoza’s pantheism. This tight connection between a mechanical explanation of nature and the Deus sive natura issue leads to a negative judgement on mechanism and its materialistic implications, both charged with a form of more or less explicit atheism. In the second part I describe the gradual emancipation in Germany of mechanism fro... (shrink)

At the beginning of the seventeenth century, the sine law of refraction had been discovered. Thus, natural philosophers tried even more to find a cause of refraction and to demonstrate the law. One of them was Thomas Hobbes, who was the author of the Leviathan and also worked on optics. At first, in the Hobbes analogy , he was influenced by Ibn al-Haytham, just as Descartes was in his famous proof in the Dioptrique . In his later optical scripts Tractatus (...) Opticus I , Tractatus Opticus II , and A Minute or First Draught of the Optiques , he developed a new explanation. Rejecting a corpuscular theory of light, Hobbes conceived a ray not as a body but as a motion originating from the light source: a ray can only be the motion of a body. The normal to the sides of a ray is called 'linea lucis'. If a ray is incident into another medium with a different density, one part of the linea lucis will be in the rarer and the other in the denser medium during an imperceptibly short period. Because the resistances in the two media are different, the parts of the linea lucis will move with different velocities; as a result the linea lucis will rotate and the direction of the ray will be changed. The next explanation given in De Corpore comes closer to the first one that Hobbes set down in the analogy. It must be asked why he replaced the theory of rotation by one which seems to carry less conviction. The reason could be that the dropped theory is founded in part on basic requirements of a corpuscular theory of light. Abandoning the whole theory might have been the lesser evil for Hobbes. In two later works, the Problemata Physica and the Decameron Physiologicum , Hobbes varied his explanation without giving any proof for the sine law. It should be noted, however, that in the Decameron he refers to the proof contained in the Tractatus Opticus I, but not that given in De Corpore. (shrink)

The article examines Kant's various criticisms of the broadly Cartesian ontological argument as they are developed in the Critique of Pure Reason. It is argued that each of these criticisms is effective against its intended target, and that these targets include—in addition to Descartes himself—Leibniz, Wolff, and Baumgarten. It is argued that Kant's most famous criticism—the charge that being is not a real predicate—is directed exclusively against Leibniz. Kant's argument for this thesis—the argument proceeding from his example of a hundred (...) thalers—although it may seem to beg the question, in fact succeeds against Leibniz. It does so because the charge of begging the question can be rebutted if one makes certain Leibnizian assumptions. (shrink)

The main goal of quantum logic is the bottom-up reconstruction of quantum mechanics in Hilbert space. Here we discuss the question whether quantum logic is an empirical structure or a priori valid. There are good reasons for both possibilities. First, with respect to the possibility of a rational reconstruction of quantum mechanics, quantum logic follows a priori from quantum ontology and can thus not be considered as a law of nature. Second, since quantum logic allows for a reconstruction of quantum (...) mechanics, self-referential consistency requires that the empirical content of quantum mechanics must be compatible with the presupposed quantum ontology. Hence, quantum ontology contains empirical components that are also contained in quantum logic. Consequently, in this sense quantum logic is also a law of nature. (shrink)

The self/non-self model, first proposed by F.M. Burnet, has dominated immunology for 60 years now. According to this model, any foreign element will trigger an immune reaction in an organism, whereas endogenous elements will not, in normal circumstances, induce an immune reaction. In this paper we show that the self/non-self model is no longer an appropriate explanation of experimental data in immunology, and that this inadequacy may be rooted in an excessively strong metaphysical conception of biological identity. We suggest that (...) another hypothesis, one based on the notion of continuity, gives a better account of immune phenomena. Finally, we underscore the mapping between this metaphysical deflation from self to continuity in immunology and the philosophical debate between substantialism and empiricism about identity. (shrink)

If we consider their fundamental role in the makeup of simple substances, our understanding of Leibnizian appetites or ‘appetitions’ seems far from satisfactory. To promote a better understanding of Leibniz’s mature view of appetites, I present a new reading of the appetitive nature of simple substances, focusing on key texts where Leibniz stresses how appetites fail to reach what they strive for. Against the “standard reading,” according to which appetites are the direct causes of subsequent perceptual states, I propose an (...) alternative, more complex picture of appetitive activity within simple substances. On my account, what Leibniz typically refers to as ‘appetites’ do not directly cause subsequent states, but are strivings or desires to be in states of less unease or greater happiness, states that the creature might actually fail to enjoy. This reading of appetites, I argue, is consistent with there being an additional, distinct strand of appetitive activity, one that corresponds to the primitive forces of simple substances. In contrast to the first strand of appetitive activity, this second strand is directly causal in that its final causality is operative in the exceptionless occurrence of the series of perceptual states prescribed in the “law of the series.” The resulting picture is one in which simple substances are appetitive through and through, with teleological activity permeating the substance at the levels of both primitive and derivative forces. (shrink)

Hans Jonas developed in ‘Past and Truth’ (1991) a demonstration of the existence of God based on the ‘truth of past things’. And in ‘The Concept of God after Auschwitz’ (1984) he created a new myth of divine self-alienation in order to take away God’s responsibility for human misery. Both these texts were conceived as an alternative to a more Hegelian, objective idealist perspective on theology. This article shows that Jonas’s alternative does not fully succeed in this respect because his (...) arguments bring him back to an idealist perspective. His proof of God is revisited and explained using new insights recently developed by Robert Spaemann, whose interpretation of the proof makes it clear that many important critics of Jonas are too quick to reject his claims. The arguments of Jonas now seem to show a new strength even though they still fail to give an alternative to an objective idealist theological framework. (shrink)

How did we come to have a scientific culture -- one in which cognitive values are shaped around scientific ones? Stephen Gaukroger presents a rich and fascinating investigation of the development of intellectual culture in early modern Europe, a period in which understandings of the natural realm began to fragment.

The Zapatista Indigenous Movement from Chiapas, Mexico is an example of the anthropological dynamics between the visible and the invisible in Western culture and the possible revolution of perceiving reality as such since they had to cover their faces with masks in their rebel anti-system movement in order to be considered as having the same dignity as other human beings: they performed a revolutionary act that changed the symbolic order of the visible by the public exhibition of their colonial submission. (...) The mask gave them a face, disrupting the order of the visible with uncanny faces. In this article, a nondual model is proposed to capture the inessential ground of the given composed of endless perspectives in continuous transformation by the generation of ontological novelty: an open cognitive horizon of symbolically empty points of view irreducible to one perspective. For Krishnamurti, the revolutionary act is to see without an image in order to phenomenologically attend to things as they are beyond the known and the unknown such as Stilinovi? and Malevich pursued the dissolution of symbolic representations through art for the transformation of human reality. (shrink)

Starting with the example of irreducible quantum events, it is shown that other kinds of events also have an element of randomness. The hallmark of “genuine” events is their irreducibility to some previous conditions. A connection between this concept and the traditional notion of contingency is explored. This concept is further brought in connection with Peirce’s Firstness. Such a notion raises the problem of how to understand causation. It seems that causes deal with individual happenings. In fact, laws are only (...) general, while causal explanations necessarily involve localization in space and time and therefore indexical connection with events. When we deal with causes, we necessarily deal with their effects, which are shifted in space and delayed in time and so do not reveal the singularity of the event that is at the origin of the process. Our descriptions of events are really about the effects of the events, not the events themselves. This helps us to define what events are in all generality: an event is what cannot be fully described by our means although we have reason to assume that it is real. (shrink)

Nexuses such as exemplification are the fundamental ties that structure reality as a whole. They are “formal” in the sense of constituting the form, not the matter of reality and they are “transcendental” inasmuch as they transcend the categorial distinctions between the denizens of reality, including that between existents and non-existents. I shall advocate a moderately particularist view about (external) nexuses and argue that it provides not only the best solution to Bradley’s regress, but also an elegant account of symmetrical (...) relations (both formal and material), as well as of temporal and modal change. These advantages are illustrated by the reconstruction of an Aristotelian ontology of exemplification involving substances, kinds and material attributes. (shrink)

Les notions ou catégories de causalité et de déterminisme ont accompagné la formation des sciences modernes, et en premier lieu celle de la physique. L'usage courant de nos jours tend souvent, à tort, à les confondre, dans les remises en cause qui en sont faites en physique même. Nous nous proposons, dans ce travail, de clarifier la première de ces notions, plus exactement la causalité physique, en suivant son élaboration avec les débuts de la dynamique, à travers ses premières mises (...) en œuvre et conceptualisations qui accompagnent la mathématisation de la mécanique, avant d'être étendue à la physique d'une manière générale. Nous verrons comment, tout en s'appuyant sur l'un des aspects philosophiques traditionnels de l'idée de causalité (celui de « cause efficiente »), la causalité physique s'établit en rupture avec le sens métaphysique qui lui était précédemment attaché. Bien plutôt que dans les Principia de Newton, c'est dans la ré-élaboration par d'Alembert, dans son Traité de dynamique, des lois du mouvement formulés comme des principes, et exprimées par le calcul différentiel, que l'idée de causalité physique est expressément considérée indissociablement de son effet, qui est le changement de mouvement. Les pensées respectives de Newton et de d'Alembert sur les notions de cause et de force sont à cet égard en opposition en ce qui concerne la nature proprement physique de ce changement, considéré par d'Alembert comme immanent au mouvement, selon la cause circonscrite par son effet, alors qu'il reste mathématique et métaphysique dans la conception newtonienne de la force externe, comme substitut mathématique des causes, telle qu'elle se proposait avant Lagrange. C'est la conception physique, héritée de d'Alembert, qui devait par la suite prévaloir, à travers la mécanique analytique lagrangienne, qui permettait de réintégrer physiquement et rationnellement le concept de force dans sa transcription eulérienne différentielle. Les avatars ultérieurs de la notion de causalité, qui comprennent la causalité relativiste et les développements sur le déterminisme, font l'objet d'un travail complémentaire. (shrink)

One of the perennial questions of philosophy concerns the simple statements which say that an object is so and so or that such and such objects are so and so related: simple predicative statements. Do such statements have an ontological basis, and if so, what is that basis? The answer to this question determines—or in any case, is expressive of—a specific fundamental outlook on the world. In the course of the history of Western philosophy, various philosophers have given various answers (...) to the question of predication. This essay presents the main, crucial answers: the paradigms and theories of predication of the Sophists (and of all later radical relativists), of Plato, of Aristotle, of the Aristotelian-minded non-nominalists, of Leibniz, and of Frege. In addition, the essay follows (to some extent) the most influential—the Aristotelian or mereological—paradigm of predication in its continuity and modification through the many centuries of its reign. However, the essay is not content to adopt the merely historical point of view; it also poses the question of adequacy. Prior to Frege, there was no philosophically adequate theory of predication, and the essay points out the shortcomings (besides aspects that can be viewed as advantages) of each pre-Fregean predication theory considered in it. Frege, in the nineteenth century, brought the philosophy of predication on the right track, but his own theory of predication has its own deficits. The essay ends with the presentation of a theory of predication that the author himself considers adequate. (shrink)

In multiple parts of the Critique of Pure Reason, Kant describes how time is dependent on space – which is the fundament of his distinction between inner and outer sense. However, he does not provide us with an argument for this dependency. In this article, two reasons for this dependency thesis are introduced. The first one aims at providing a conceptual link between time and space but runs into conflict with the Transcendental Aesthetic. The second one shifts our focus from (...) the conceptual level to a priori possible objects of experience: Time cannot provide such objects, which are different from our subjective states due to its one-dimensionality. Only space makes such objects possible. (shrink)

The Ontological Dilemma of Normative Ethics. This paper pursues two goals. The first is to show that normative ethics is confronted with the following dilemma: to be coherent, this discipline is ontologically committed to acknowledge the existence of objective values, but, to be scientifically respectable, it is committed to repudiate such values. The second goal is to assess the possible solutions to this dilemma. To this end, the following strategies are discussed: Kant’s constructive objectivism, Jürgen Habermas’ “epistemic ersatzism”, Franz von (...) Kutschera’s “confirmation pragmatism”, and David Brink’s “objectivist tour de force”. The paper’s conclusion is that the dilemma cannot be solved because it rests on a clash of intuitions none of which can be given up. (shrink)

According to Leibniz's late metaphysics, sensory perception represents to us as extended, colored, textured, etc., a world which fundamentally consists only of non-spatial, colorless entities, the monads. It is a short step from here to the conclusion that sensory perception radically misleads us about the true nature of reality. In this paper, I argue that this oft-repeated claim is false. Leibniz holds that in typical cases of body perception the bodies perceived really exist and have the qualities, both primary and (...) secondary, they are perceived to have. At the same time, Leibniz holds that our perceptions of these bodies are accurate representations of the monads from which the bodies result. The contrary thesis — that our body perceptions are misrepresentations of the monads — stems from a misunderstanding of Leibniz's theory of confused concepts and his phenomenalist account of the nature of body. Clarifying these issues will have important consequences for our understanding of Leibniz's idealistic metaphysics and the manner in which that metaphysical theory is meant to support mechanistic science. (shrink)

In recent years, neuroscience has been a particularly prolific discipline stimulating many innovative treatment approaches in medicine. However, when it comes to the brain, new techniques of intervention do not always meet with a positive public response, in spite of promising therapeutic benefits. The reason for this caution clearly is the brain’s special importance as “organ of the mind”. As such it is widely held to be the origin of mankind’s unique position among living beings. Likewise, on the level of (...) the individual human being, the brain is considered the material substrate of those traits that in combination render each person unique. In view of this preeminent significance of the brain, it is understandable that, in general, interventions into the brain are considered a delicate issue and that new techniques of intervention are scrutinised with particular care. However, in doing so it is important not to go to the opposite extreme and shy away from promising new therapeutic approaches for debilitating disorders of the brain. With respect to the new techniques of brain intervention a broad interdisciplinary perspective is required to discern irrational fear from justified concern. Hence, the Europäische Akademie established a project group consisting, on the one hand, of experts from different fields of medicine who have got first-hand experience of applying the techniques at issue and, on the other hand, of philosophers and a legal expert. The task of this team was to review the state of the art with respect to each single technique of intervening in the brain, to indicate future developments, and to address the ethical and legal issues common to all of them. The project’s outcome is the book at hand. (shrink)