In this article, I argue that the interpretation of Kant's a priori in Marburg neo-Kantianism involved a historiographical problem concerning the Platonic interpretation of the history of exact sci...

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)

This paper defends the view that Newtonian forces are real, symmetrical and non-causal relations. First, I argue that Newtonian forces are real; second, that they are relations; third, that they are symmetrical relations; fourth, that they are not species of causation. The overall picture is anti-Humean to the extent that it defends the existence of forces as external relations irreducible to spatio-temporal ones, but is still compatible with Humean approaches to causation (and others) since it denies that forces are a (...) species of causation. (shrink)

Ecological and sensorimotor theories of perception build on the notion of action-dependent invariants as the basic structures underlying perceptual capacities. In this paper we contrast the assumptions these theories make on the nature of perceptual information modulated by action. By focusing on the question, how movement specifies perceptual information, we show that ecological and sensorimotor theories endorse substantially different views about the role of action in perception. In particular we argue that ecological invariants are characterized with reference to transformations produced (...) in the sensory array by movement: such invariants are transformation-specific but do not imply motor-specificity. In contrast, sensorimotor theories assume that perceptual invariants are intrinsically tied to specific movements. We show that this difference leads to different empirical predictions and we submit that the distinction between motor equivalence and motor-specificity needs further clarification in order to provide a more constrained account of action/perception relations. (shrink)

I argue that some important elements of the current cosmological model are 'conventionalist’ in the sense defined by Karl Popper. These elements include dark matter and dark energy; both are auxiliary hypotheses that were invoked in response to observations that falsified the standard model as it existed at the time.

Taking precautions to prevent harm. Whether principe de précaution, Vorsorgeprinzip, føre-var prinsippet, or försiktighetsprincip, etc., the precautionary principle embodies the idea that public and private interests should act to prevent harm. Furthermore, the precautionary principle suggests that action should be taken to limit, regulate, or prevent potentially dangerous undertakings even in the absence of absolute scientific proof. Such measures also naturally entail taking economic costs into account. With the environmental disasters of the 1980s, the precautionary principle established itself as an (...) operational concept. On the eve of the 1997 Climate Summit in Kyoto, precaution, as the precautionary principle is often referred to, has now become a key legal principle in environmental law, in general, and in current international climate negotiations, in particular, attempts to understand why. It examines in turn the natural affinity between the precautionary principle and climate change, reviews a series of issues which the principle raises, and discusses avenues which it opens paper, climate change fulfills the theoretical requirements set for the application of the precautionary principle. It comes as no surprise that the actual application of the precautionary principle in the context of climate change raises high political stakes. As a result, climate change science, in particular, and science, in general, is under the fire of politically-motivated scientific skeptics. Thus, by way of the counter-measures which must be put into effect, the precautionary principle calls for a greater sense of responsibility on the part of scientists and the public at large. Specifically, from scientists, it demands perseverance in rigor, excellence in communication, and committment to education. However, even if special efforts are made to implement the precautionary principle in the context of climate change, the success of climate change mitigation will constitute no test of the validity, the usefulness, or the efficiency of the precautionary principle. Indeed, the degree to which climate change mitigation succeeds only provides a measure of our kind's ability to manage responsibly the global commons which we inherited from our ancestors and which our generation enjoys, the global commons which we will pass on to today's children and to generations to come. (shrink)

There has been little research into the weak kindsof negating hypotheses. Hypotheses may be unfalsifiable. In this case it is impossible tofind a contradiction in some area of the conceptualsystems in which they are incorporated.Notwithstanding this fact, it is sometimes necessaryto construct ways of rejecting the unfalsifiablehypothesis at hand by resorting to some external forms of negation, external because wewant to avoid any arbitrary and subjectiveelimination, which would be rationally orepistemologically unjustified. I will consider akind of ``weak'''' (unfalsifiable) hypotheses that (...) arehard to negate and the ways for making it easy. Inthese cases the subject can ``rationally'''' decide towithdraw his hypotheses even in contexts where it is``impossible'''' to find ``explicit'''' contradictions: theuse of negation as failure (an interestingtechnique for negating hypotheses and accessing newones suggested by artificial intelligence) isilluminating. I plan to explore whether this kind ofnegation can be employed to model hypothesiswithdrawal in Poincaré''s conventionalism of theprinciples of physics and in Freudian analyticreasoning. (shrink)

In this paper, I argue for a distinction between two scales of coordination in scientific inquiry, through which I reassess Georg Simon Ohm’s work on conductivity and resistance. Firstly, I propose to distinguish between measurement coordination, which refers to the specific problem of how to justify the attribution of values to a quantity by using a certain measurement procedure, and general coordination, which refers to the broader issue of justifying the representation of an empirical regularity by means of abstract mathematical (...) tools. Secondly, I argue that the development of Ohm’s measurement practice between the first and the second experimental phase of his work involved the change of the measurement coordination on which he relied to express his empirical results. By showing how Ohm relied on different calibration assumptions and practices across the two phases, I demonstrate that the concurrent change of both Ohm’s experimental apparatus and the variable that Ohm measured should be viewed based on the different form of measurement coordination. Finally, I argue that Ohm’s assumption that tension is equally distributed in the circuit is best understood as part of the general coordination between Ohm’s law and the empirical regularity that it expresses, rather than measurement coordination. (shrink)

La nostalgie, contrairement au deuil, ne s’adresse pas à un Objet à jamais disparu, mais à un Objet partiel, idéalisé, inatteignable dans l’immédiat, souvent exprimé comme une atmosphère rappelant des expériences anciennes. Elle se vit dans une relation imaginaire qui renvoie à des satisfactions beaucoup plus archaïques de l’ordre de la toute-puissance infantile. Un travail psychique de nostalgie ne conduit pas à la disparition de cet Objet idéalisé, pérenne, mais plutôt à sa transformation.

The aim of this paper is to introduce Wittgenstein’s concept of the form of a language into geometry and to show how it can be used to achieve a better understanding of the development of geometry, from Desargues, Lobachevsky and Beltrami to Cayley, Klein and Poincaré. Thus this essay can be seen as an attempt to rehabilitate the Picture Theory of Meaning, from the Tractatus. Its basic idea is to use Picture Theory to understand the pictures of geometry. I will (...) try to show, that the historical evolution of geometry can be interpreted as the development of the form of its language. This confrontation of the Picture Theory with history of geometry sheds new light also on the ideas of Wittgenstein. (shrink)

According to Kant, we gain mathematical knowledge by constructing objects in pure intuition. This is true not only of geometry but arithmetic and algebra as well. Construction has prominent place in scholarly accounts of Kant’s views of mathematics. But did Kant have a clear vision of what construction is? The paper argues that Kant employed two different, even conflicting models of construction, depending on the philosophical issue he was dealing with. In the equivalence model, Kant claims that the object constructed (...) in intuition is equivalent to the properties included in the conceptual rule. In the overstepping model of construction, Kant argues that construction goes beyond the concept which is a “mere definition”. What is more, both models of construction can be found in the Doctrine of Method in the first Critique. The paper examines reasons that have led Kant to adopt the two models of construction, and proposes a reading that alleviates the apparent contradiction between the two models. (shrink)

ArgumentThe famousCahiersof Paul Valéry cannot be reduced to a single scientific discipline, a specific philosophical tradition, or a literary genre. For today's reader these notebooks constitute a formatsui generis, one very often characterized by an “observation of a second order”: in theCahiersValéry uses writing, drawing, and calculating not only for purposes of argumentation; he also pays attention to the significance of such writing, drawing, and calculating processes for the production of knowledge. It is particularly thepracticeof note-taking and sketching in Valéry's (...) notebooks that documents, rehearses, or questions the medial and instrumental conditions of both scientific research and artistic production. This is especially true of the early stages of theCahiersin the years beginning around 1894 when Valéry was intensely searching for notation systems that would be conducive to his research interests. At the time the problem of how to write was intrinsically bound up with the way he established his notebooks as a specific scene of writing. By closely examining a number of pages from the early notebooks I hope to show that the emerging regulation of Valéry's writing in theCahiersresults from simple operations that are noted and repeated by the writer until they gradually become procedures. What Valéry'sCahiersshow us, however, is that procedures do not always work in favor of a final synthesis, but may also give rise to a format of eternal beginning. In the following I will present some of the constitutive procedures found in Valéry's early notebooks, procedures that range from a tentative gathering together and simple forms of recursion and variation to the rehearsing or invention of symbolic or graphic forms of notation. (shrink)

A detailed argument is provided for the thesis that Dedekind was a logicist about arithmetic. The rules of inference employed in Dedekind's construction of arithmetic are, by his lights, all purely logical in character, and the definitions are all explicit; even the definition of the natural numbers as the abstract type of simply infinite systems can be seen to be explicit. The primitive concepts of the construction are logical in their being intrinsically tied to the functioning of the understanding.

Translator's summary The translated paper is an extract, published in 1945, of an unpublished thesis, of both historical and technical import, dealing with notions of definability and their relation to invariance under automorphisms. The author develops a metamathematical Galois theory, and discusses and anticipates some aspects of higher-order model theory in an informal but conceptually rich manner.

The present article discusses the thoughts of Gregory of Nazianzus in relation to virtual reality especially man-made virtual reality in all its forms. We argue that the benefits of virtual reality, such as freedom, imagination, creativity can be paradoxically curtailed by virtual reality itself, since it is highly subjective and as its medium shows, can be an a priori matrix and prison for the human being. Gregory of Nazianzus, building his theology on a firm basis on substance and contemplation, offers (...) a way out, where one acknowledges everything around us as beneficial and beautiful and therefore free, but this must be based on a firm grounding of truthfulness and guidance offered by an all-encompassing form of Divine love and creativity. (shrink)

This paper is concerned with the problem of selfidentification in the domain of action. We claim that this problem can arise not just for the self as object, but also for the self as subject in the ascription of agency. We discuss and evaluate some proposals concerning the mechanisms involved in selfidentification and in agencyascription, and their possible impairments in pathological cases. We argue in favor of a simulation hypothesis that claims that actions, whether overt or covert, are centrally simulated (...) by the neural network, and that this simulation provides the basis for action recognition and attribution. (shrink)

: Frege's philosophical writings, including the "logistic project," acquire a new insight by being confronted with Kant's criticism and Wittgenstein's logical and grammatical investigations. Between these two points a non-formalist history of logic is just taking shape, a history emphasizing the Greek and Kantian inheritance and its aftermath. It allows us to understand the radical change in rationality introduced by Gottlob Frege's syntax. This syntax put an end to Greek categorization and opened the way to the multiplicity of expressions producing (...) their own intelligibility. This article is based on more technical analyses of Frege which Claude Imbert has previously offered in other writings (see references). (shrink)

Frege's philosophical writings, including the “logistic project,” acquire a new insight by being confronted with Kant's criticism and Wittgenstein's logical and grammatical investigations. Between these two points a non-formalist history of logic is just taking shape, a history emphasizing the Greek and Kantian inheritance and its aftermath. It allows us to understand the radical change in rationality introduced by Gottlob Frege's syntax. This syntax put an end to Greek categorization and opened the way to the multiplicity of expressions producing their (...) own intelligibility. This article is based on more technical analyses of Frege which Claude Imbert has previously offered in other writings. (shrink)

Frege's philosophical writings, including the “logistic project,” acquire a new insight by being confronted with Kant's criticism and Wittgenstein's logical and grammatical investigations. Between these two points a non-formalist history of logic is just taking shape, a history emphasizing the Greek and Kantian inheritance and its aftermath. It allows us to understand the radical change in rationality introduced by Gottlob Frege's syntax. This syntax put an end to Greek categorization and opened the way to the multiplicity of expressions producing their (...) own intelligibility. This article is based on more technical analyses of Frege which Claude Imbert has previously offered in other writings. (shrink)

It is widely believed that the development of the general theory of relativity coincided with a shift in Einstein’s philosophy of science from a kind of Machian positivism to a form of scientific realism. This article criticizes that view, arguing that a kind of realism was present from the start but that Einstein was skeptical all along about some of the bolder metaphysical and epistemological claims made on behalf of what we now would call scientific realism. If we read Einstein’s (...) philosophy of science in its proper late nineteenth-and early twentieth-century philosophical context, we find that a kind of Duhemian under determinationist holism and conventionalism was more important to Einstein than either positivism or realism. And, reading his philosophy of science in its proper scientific. (shrink)

Although Pierre Duhem is well known for his conventionalist outlook and, in particular, for his critique of crucial experiments outlined in his thesis on the empirical indeterminacy of theory, he also contributed to the scholarship on the psychological profiles of scientists by revising Pascal’s famous distinction between the subtle mind and the geometric mind. For Duhem, the ideal scientist is the one who combines the defining qualities of both types of intellect. As a physicist, Duhem made important theoretical contributions to (...) the field of thermodynamics as well as to the then-nascent physical chemistry. Due to his rejection of atomism and his unrelenting critique of Maxwell’s electrodynamics, however, in his later years, Duhem’s work was surpassed and abandoned by the dominant tendencies of physics of the time. In this essay, I will discuss whether Duhem himself can be understood through the lens of his own account of the scientist’s psychological profile. More specifically, I examine whether the subtle mind – to which he seems to assign greater cognitive value – in fact plays a key role in Duhem’s critique of the English School, or if his preference for the axiomatic structure of theoretical physics shows a greater affinity with the geometric mind. (shrink)

There are many examples in the literature that suggest that indistinguishability is intransitive, despite the fact that the indistinguishability relation is typically taken to be an equivalence relation (and thus transitive). It is shown that if the uncertainty perception and the question of when an agent reports that two things are indistinguishable are both carefully modeled, the problems disappear, and indistinguishability can indeed be taken to be an equivalence relation. Moreover, this model also suggests a logic of vagueness that seems (...) to solve many of the problems related to vagueness discussed in the philosophical literature. In particular, it is shown here how the logic can handle the sorites paradox. (shrink)

The article focuses on the unifying and explanatory power of the selective realism defended by Anjan Chakravartty. Our main aim is twofold. First, we critically analyse the purported synthesis between entity realism and structural realism offered by the author. We give reasons to think that this unification is an inconvenient marriage. In the second step, we deal with certain controversial aspects of the intended unification among three metaphysical concepts: causation, laws of nature and natural kinds. After pointing out that Chakravartty’s (...) conception of laws is a plausible view that a scientific realist might endorse, we contend, on the contrary, that the concept of natural kind is dispensable in the framework of Chakravartty’s realism. (shrink)

The calculus of Natural Calculation is introduced as an extension of Natural Deduction by proper term rules. Such term rules provide the capacity of dealing directly with terms in the calculus instead of the usual reasoning based on equations, and therefore the capacity of a natural representation of informal mathematical calculations. Basic proof theoretic results are communicated, in particular completeness and soundness of the calculus; normalisation is briefly investigated. The philosophical impact on a proof theoretic account of the notion of (...) meaning is considered. (shrink)

ABSTRACTIf it seems unquestionable that C. I. Lewis is a Kantian in important respects, it is more difficult to determine what, if anything, is original about his Kantianism. For it might be argued that Lewis’ Kantianism simply reflects an approach to the a priori which was very common in the first half of the twentieth century, namely, the effort to make the a priori relative. In this paper, I will argue that Lewis’ Kantianism does present original features. The latter can (...) be detected by focusing on Lewis’ account of the method of philosophy in the first chapter of Mind and the World Order. In that context, Lewis argues that the method of philosophy should be reflective and critical. It will be my contention that this understanding of philosophy involves a therapeutic perspective, which bears important resemblances to Kant’s account of transcendental reflection in the Amphiboly of the Critique of Pure Reason. I will illustrate how this therapeutic application of reflection works in Lewis’ metaphysics. In... (shrink)

Léon Brunschvicg a été un pionnier de la philosophie des mathématiques et de l’épistémologie des sciences exactes en France. Gaston Bachelard peut être considéré comme un des héritiers les plus importants de l’épistémologie constructiviste de Brunschvicg. Les deux philosophes partagent la même conception d’une dialectique immanente de la pensée scientifique et l’idée que la philosophie consiste à construire et à analyser la logique interne du discours scientifique.

The paper investigates possible readings of the later Heisenberg's remarks on the nature of quantum states. It discusses, in particular, whether Heisenberg should be seen as a proponent of the epistemic conception of states – the view that quantum states are not descriptions of quantum systems but rather reflect the state assigning observers' epistemic relations to these systems. On the one hand, it seems plausible that Heisenberg subscribes to that view, given how he defends the notorious "collapse of the wave (...) function" by relating it to a sudden change in the epistemic situation of the observer registering a measured result. On the other hand, his remarks on quantum probabilities as "potentia" or "objective tendencies" are difficult to reconcile with such a reading. The accounts that are attributed to Heisenberg by the different possible readings considered are subjected to closer scrutiny; at the same time, their respective virtues and problems are discussed. _German_ Diese Arbeit untersucht mögliche Lesarten von Heisenbergs späten Bemerkungen über die Natur von Quantenzuständen. Insbesondere wird die Frage diskutiert, ob Heisenberg als Vertreter der epistemischen Auffassung von Quantenzuständen gelten kann – der Idee, dass Quantenzustände nicht Beschreibungen der objektiven Eigenschaften von Quantensystemen sind sondern die epistemischen Beziehungen von Beobachtern zu diesen Systemen widerspiegeln. Einerseits erscheint es plausibel, dass Heisenberg dieser Sichtweise zustimmt, wenn man sich ansieht, wie er den berüchtigten,,Kollaps der Wellenfunktion" verteidigt, indem er ihn mit einer plötzlichen Änderung in der Kenntnis des ein Messergebnis registrierenden Beobachters in Zusammenhang bringt. Andererseits sind seine Bemerkungen über quantenmechanische Wahrscheinlichkeiten als,,Potentia" oder,,objektive Tendenzen" mit einer solchen Lesart nur schwer in Einklang zu bringen. Die Positionen, die Heisenberg den verschiedenen möglichen Lesarten zufolge vertritt, werden eingehenden Untersuchungen unterzogen; gleichzeitig werden ihre jeweiligen Vorzüge und Probleme diskutiert. (shrink)

Julius König is famous for his mistaken attempt to demonstrate that the continuum hypothesis was false. It is also known that the only positive result that could have survived from his proof is the paradox which bears his name. Less famous is his 1914 book Neue Grundlagen der Logik, Arithmetik und Mengenlehre. Still, it contains original contributions to logic, like the concept of metatheory and the solution of paradoxes based on the refusal of the law of bivalence. We are going (...) to discover them by analysing the content of the book. (shrink)

In the nineteenth and twentieth centuries many mathematicians referred to intuition as the indispensable research tool for obtaining new results. In this essay we will analyse a group of mathematicians who interacted with Luitzen Egbertus Jan Brouwer in order to compare their conceptions of intuition. We will see how to the same word “intuition” very different meanings corresponded: they varied from geometrical vision, to a unitary view of a demonstration, to the perception of time, to the faculty of considering concepts (...) that habitually occur in our thinking separately. Furthermore, we will discover that these different meanings had a philosophical, very relevant counterside: they passed from a racial characterization of mathematics to a pluralistic view of it. (shrink)

El surgimiento de la teoría de la relatividad de Einstein a principios del siglo XX suscitó el debate sobre la vigencia de la filosofía kantiana. El positivista Schlick sostenía que esta quedaba refutada, pues estaba indisolublemente ligada a la física de Newton y a los conceptos de espacio y tiempo absolutos. Los neokantianos Natorp y Sellien defendían la vigencia de Kant basándose en la diferencia entre filosofía y ciencia. Cassirer y Reichenbach abogaban por un neokantismo modificado basado en principios constitutivos. (...) Y Einstein y Carnap rechazaban tanto kantismo como positivismo puros abrazando el holismo epistemológico. (shrink)

Structural Realism (SSR), as embodied in the Ramsey-sentence H of a theory H, is defended against the view that H reduces to a trivial statement about the cardinally of the domain of H, a view which arises from ignoring the central role of observation within science. Putnam's theses are examined and shown to support rather than undermine SSR. Finally: in view of its synthetic character, applied mathematics must enter into the formulation of H and hence to be shown axiomatisable; this (...) is done in the Appendix, which is the most important part of the paper. (shrink)

This article revisits Karl Popper’s falsificationist methodology with respect to three tasks. The first is to illuminate and systematize Popper’s methodological views in light of his core epistemological commitments. A second and related objective is to gauge which aspects of falsificationism should be identified as “conventionalist”—a label that Popper himself uses (albeit with qualifications) but that is compromised by and, thus, stands in need of elucidation because of Popper’s idiosyncratic understanding of conventionalism. Third, by elaborating Popper’s virtue-epistemological, dialogical model of (...) rationality, I show how Popper’s conventionalism, fallibilism, and critical rationalism form a coherent system. This system allows Popper to accord science the status of a privileged source of knowledge—without naïve appeal to authority. My systematization of Popper’s views yields an intrinsically and exegetically more satisfactory reading of Popper’s falsificationism than usual presentations. Thanks to its marked flexibility and methodological liberalism, it bypasses many standard objections but still offers sound and relevant methodological advice. With its “virtue-methodological” thrust, Popper sketches an original and promising approach to methodology, the fertility of which deserves further exploration for contemporary debates. (shrink)

A re-visitation of Joule’s experiment motivates a critical analysis of thermodynamic notions: heat, total energy, first principle, organization of a scientific theory, its relationships with logic and mathematics. A rational re-construction of thermodynamics is suggested according to the model of a problem-based organization, that Sadi Carnot applied to his formulation. The new formulation accomplishes the long time theoretical process started by Joule’s experiment within physicists community's collective mind, i.e. the process of exiting out Baconian science for suggesting a first theory (...) out Newton’s paradigm, and eventually for introducing a pluralism of incompatible physical theories. (shrink)

Authoritative appraisals have qualified this book as an “axiomatic” theory. However, given that its essential content is no more than an analogy, its theoretical organization cannot be axiomatic. Indeed, in the first edition Dirac declares that he had avoided an axiomatic presentation. Moreover, I show that the text aims to solve a basic problem (How quantum mechanics is similar to classical mechanics?). A previous paper analyzed all past theories of physics, chemistry and mathematics, presented by the respective authors non-axiomatically. Four (...) characteristic features of a new model of organizing a theory were recognized. A careful examination of Dirac’s text shows that it actually applied this kind of organization of a theory, confirming formally what Kronz and Lupher suggested through intuitive categories (pragmatism and rigour), i.e. Dirac’s formulation of Quantum mechanics represents a distinct theoretical approach from von Neumann’s axiomatic approach. However, since the second edition Dirac has changed his approach: although relying again on analogy, his theory refers to the axiomatic method. Some considerations on the odd paths which led to the present formulation of QM are added. They suggest that a new foundation of this theory needs to be found. (shrink)

Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hilbert space after entanglement as the Fourier counterpart of pseudo-Riemannian space. Gravitation can be (...) also interpreted as purely mathematical or logical “force” or “interaction” as a corollary from its ontomathematical (rather than physical) realization. The ontomathematical approach to gravitation is implicit in general relativity equating it to operators in pseudo-Riemannian space obeying the Einstein field equation and also well-known by the “geometrization of physics”. Quantum mechanics shares the same by the separable complex Hilbert space and defining “physical quantity” by the Hermitian operators on it. One can interpret special Minkowski space involved by special relativity and the qubit Hilbert space of quantum information as Fourier counterparts immediately noticing that general relativity means gravitation as the Fourier counterpart of non-Hermitian operators implying non-unitarity and the violation of energy conservation and thus destroying Pauli’s particle paradigm. Since the Standard model obeys it, this explains the impossibility of “quantum gravitation” in any framework conservatively generalizing the Standard model so that it would include gravitation along with electromagnetic, weak, and strong interactions. Einstein’s geometrization of gravitation can be continued into a purely mathematical theory of it following Euclid’s realization for geometry to be exhaustively built in a deductive and axiomatic way as well as Riemann’s parametrization of all the class of Euclidean and non-Euclidean geometries by “space curvature”, then being generalized to Minkowski space as the operators on pseudo-Riemannian space as the Einstein field equation means gravitation. The transition from mathematical gravitation to logical one can rely on the historical lesson of the pair of Lobachevski’s and Riemann’s approaches now “reversely”, i.e., from the latter to the former. Logical gravitation is linkable to Hegel’s dialectical logic and ontological dialectics abandoning their interpretations as a new zero logic substituting classical propionyl logic. The approach of ontomathematics generalizing that of ontology, traceable even to Aristotle’s reformation of Plato’s doctrine, needs Hegel’s doctrine to be formalized as a first-order logic naturally containing Boolean algebra, isomorphic to both classical propositional logic and set theory being the class of all first-order logics, as a sub-logic along with Peano arithmetic as another sub-logic. The first-order logic at issue is called Hilbert arithmetic and elaborated in detail in other papers. It allows for both self-foundation of mathematics to be internally proved as complete and furthermore, quantum mechanics reinterpreted as quantum information to be included by the qubit Hilbert space interpretable in turn as a dual and physical counterpart of Hilbert arithmetic in a narrow sense, that is, both counterparts constitute Hilbert arithmetic in a wide sense, being mathematical and physical simultaneously and thus overcoming the Cartesian dualism of “body” gapped from “mind” by an abyss. Then, the proper philosophical interpretation of gravitation to be the fundamental ontomathematical force or interaction overcomes the ridiculous belief of the Big Bang wrongly alleged to be a scientific theory. Ontomathematical gravitation suggests an omnipresent and omnitemporal medium of “God’s” creation “ex nihilo” following only the natural necessity of quantum-information conservation particularly and locally manifested as energy conservation. (shrink)

Structural Realism (SSR), as embodied in the Ramsey-sentence H* of a theory H, is defended against the view that H* reduces to a trivial statement about the cardinality of the domain of H, a view which arises from ignoring the central role of observation within science. Putnam’s theses are examined and shown to support rather than undermine SSR. Finally: in view of its synthetic character, applied mathematics must enter into the formulation of H* and hence be shown to be finitely (...) axiomatisable; this is done in the Appendix, which is the most important part of the paper. (shrink)

The Linda paradox is a key topic in current debates on the rationality of human reasoning and its limitations. We present a novel analysis of this paradox, based on the notion of verisimilitude as studied in the philosophy of science. The comparison with an alternative analysis based on probabilistic confirmation suggests how to overcome some problems of our account by introducing an adequately defined notion of verisimilitudinarian confirmation.

The aim of this thesis dissertation is to propose a novel position in the debate on scientific realism, modal empiricism, and to show its fruitfulness when it comes to interpreting the cognitive content of scientific theories. Modal empiricism is an empiricist position, according to which the aim of science is to produce empirically adequate theories rather than true theories. However, it suggests adopting a broader comprehension of experience than traditional versions of empiricism, through a commitment to natural modalities. Following modal (...) empiricism, there are possibilities in nature, and constraints on what is possible, and a theory is empirically adequate if it correctly delimits the range of possible experiences. The position rests on a situated and pragmatic conception of natural modalities and of empirical confrontation. We claim that it can do justice to the empirical success of science, while not falling prey to the problem of theory change that undermines scientific realism. We explain how constraints of necessity on phenomena can be known by induction, and how this modal epistemology fits with scientific practice. Finally, we claim that a commitment to natural modalities allows for a rich interpretation of the cognitive content of theories. Modal empiricism could renew some metaphysical debates within a pragmatist framework, by tying them to experience and not being constrained by realist prejudices. -/- L'objet de cette thèse est de proposer une position originale dans le débat sur le réalisme scientifique, l'empirisme modal, et d'en démontrer la fructuosité quand il s'agit de tirer des enseignements du contenu cognitif des théories scientifiques. L'empirisme modal est une position empiriste, suivant laquelle le but de la science n'est pas de produire des théories vraies, mais des théories empiriquement adéquate. Cependant, il propose d'adopter un cadre plus large que les versions traditionnelles d'empirisme pour penser l'expérience, en incorporant un engagement envers les modalités naturelles, ou l'idée qu'il y a du possible dans la nature, et des contraintes sur les possibles. Nos théories sont empiriquement adéquates si elles délimitent correctement l'étendue des expériences possibles. Cette position s'appuie sur une conception située et pragmatique des modalités naturelles et de la confrontation empirique. Nous prétendons qu'elle est à même de rendre justice au succès empirique des sciences, sans pour autant faire face au problème du changement théorique qui mine le réalisme scientifique. Nous expliquons comment les contraintes de nécessité sur les phénomènes peuvent être connues à l'issue d'une induction, et en quoi cette façon de voir s'accorde avec la pratique scientifique. Enfin, nous affirmons qu'un engagement envers les modalités naturelles offre une richesse interprétative à même de renouveler, dans un cadre pragmatiste, plus ouvert que le réalisme, certaines questions métaphysiques tout en les ramenant à l'expérience . (shrink)

Opinionated state of the art paper on mathematical explanation. After a general introduction to the subject, the paper is divided into two parts. The first part is dedicated to intra-mathematical explanation and the second is dedicated to extra-mathematical explanation. Each of these parts begins to present a set of diverse problems regarding each type of explanation and, afterwards, it analyses relevant models of the literature. Regarding the intra-mathematical explanation, the models of deformable proofs, mathematical saliences and the demonstrative structure of (...) mathematical induction are addressed. Regarding the extra-mathematical explanation, modal, abstract and deductive models are addressed. (shrink)

How was Poincaré’s conventionalism connected to his relationism? How, in other words, is it the case that the basic principles of geometry and mechanics are, ultimately, freely chosen conventions and that, at the same time, science reveals to us the structure of the world? This lengthy study aims to address these questions by setting Poincaré’s philosophy within its historical context and by examining in detail Poincaré’s developing views about the status and role of conventions in science and the status and (...) role of relations in science. It is argued that Poincaré was a neither a rampant conventionalist nor a pure structuralist. But he was both a conventionalist and a relationist, aiming to delineate a position which allowed room for both freely, but not arbitrarily, chosen constitutive principles of science and the acquisition of objective, though, relational knowledge of the natural world. (shrink)

In this dissertation, I present a novel account of the components that have a peculiar epistemic role in our scientific inquiries, since they contribute to establishing a form of coordination. The issue of coordination is a classic epistemic problem concerning how we justify our use of abstract conceptual tools to represent concrete phenomena. For instance, how could we get to represent universal gravitation as a mathematical formula or temperature by means of a numerical scale? This problem is particularly pressing when (...) justification for using these abstract tools comes, in part or entirely, from knowledge which is not independent from them, thus leading to threats of circularity. Achieving coordination between some abstract conceptual tools and the concrete phenomena that they are supposed to represent is usually a complex process, which involves several epistemic components. Some of these components eventually provide stable conditions for applying those abstract representations to concrete phenomena. It is in this sense of providing certain conditions of applicability that different philosophical traditions, as well as some contemporary reappraisals, view these components as constitutive or a priori. In this work, I present a new gradualist, contextualist, and relational approach to understand these constitutive components of scientific inquiry. It is gradualist inasmuch as the degree to which some component is constitutive depends on three quantifiable features: quasi-axiomaticity, generative potential, and empirical shielding. Since the quantification of these three features impinges on the history and practice of using these components in a scientific context, my approach is a contextualist one. Finally, my approach is relational in a double sense: first, it identifies ordinal relationships among epistemic components with respect to their constitutive character; second, these relationships are relative to a scientific framework of inquiry. After introducing my account and a classic example of constitutively a priori principles, i.e., Friedman’s (2001) analysis of Newtonian mechanics, I turn to my own case studies to demonstrate the advantages of my approach. Firstly, I discuss Okasha’s (2018) view of endogenization as a pervasive theoretical strategy in evolutionary biology and suggest that the constitutive character of the core Darwinian principles progressively increases with endogenization. Secondly, I apply a conceptual distinction between two varieties or scopes of coordination – general coordination and coordination in measurement – to Ohm’s work on electrical conductivity. This distinction allows me to pinpoint to what extent components along different dimensions (e.g., instrumentation, measurement, theorising, etc.) were constitutive of the forms of coordination which Ohm relied on. Thirdly, I discuss the epistemic function of the Hardy-Weinberg principle in the history and practice of population genetics. I assess this principle in terms of my account and identify approximation and stability as two components that are highly constitutive, in that they contribute to justifying its use in population genetics. Finally, applying my account to these case studies enables me to identify at least three qualitatively different types of constitutive components: domain-specific theoretical principles, material components, and domain-independent assumptions underlying reasoning abilities. In the light of my results, I draw some general conclusions on epistemic justification and scientific knowledge. (shrink)