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« Il valore delle leggi statistiche nella fisica e nelle scienze sociali » est le seul article d'Ettore Majorana qui ne soit pas de science mais sur la science. Il critique le déterminisme classique au nom du caractère intrinsèquement probabilitaire des lois en mécanique quantique et en sciences sociales entre lesquelles il établit une analogie formelle. Nous analysons son argumentation sur les plans métaphysique, physique et sociologique, avant d’évaluer la pertinence de cette épistémologie transversale. |
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These are the introduction chapters to the forthcoming collection of essays published by Springer (Synthese Library) and entitled Probabilities, Causes and Propensities in Physics. |
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The relatively recent trend seems to be to move away from General Philosophy of Science and towards the philosophies of the individual sciences and to relocate whatever content GPoS is supposed to have to the philosophies of the sciences. I argue that scepticism or pessimism about the prospects of GPoS is unwarranted. I also argue that there can be no philosophies of the various sciences without GPoS. Defending these two claims is the main target of this chapter. I will show, (...) |
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Poincaré’s conventionalism has been interpreted in many writings as a philosophical position emerged by reflection on certain scientific problems, such as the applicability of geometry to physical space or the status of certain scientific principles. In this paper I would like to consider conventionalism as a philosophical position that emerged from Poincaré’s scientific practice. But not so much from dealing with scientific problems, as from the use of two specific methodologies proper to modern mathematics and the modern natural sciences: methodological (...) |
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In the introduction to his famous book, La Science et l’hypothèse, Poincaré remarks on the necessary role and legitimacy of hypotheses. He establishes a triple classification of hypotheses, dividing them into verifiable, useful, and apparent. However, in chapter 9, entitled ‘Les hypothèses en physique’, he gives a slightly different triadic classification: natural hypotheses, indifferent hypotheses, and real generalizations. The origin of this second classification is a lecture given at the International Congress of Physics, Paris, 1900. What are the similarities and (...) |
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The purpose of this paper is to demonstrate the usefulness of the concept of possibility , and not merely that of actuality , for an inquiry into the bodily constitution of experience. The paper will study how the possibilities of action that may (or may not) be available to the subject help to shape the meaning attributed to perceived objects and to the situation occupied by the subject within her environment. This view will be supported by reference to empirical evidence (...) |
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In French mechanical treatises of the nineteenth century, Newton’s second law of motion was frequently derived from a relativity principle. The origin of this trend is found in ingenious arguments by Huygens and Laplace, with intermediate contributions by Euler and d’Alembert. The derivations initially relied on Galilean relativity and impulsive forces. After Bélanger’s Cours de mécanique of 1847, they employed continuous forces and a stronger relativity with respect to any commonly impressed motion. The name “principle of relative motions” and the (...) |
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In a recent article Merritt has claimed that current observational data provide “severe tests” falsifying the standard cosmological model. Based on Popper’s idea of conventionalism, he concludes that the introduction of some essential components of the standard cosmological model—including dark matter and dark energy—are a consequence of conventionalist stratagems. In this article, I provide more recent discoveries and discussions showing that the standard cosmological model is not built on any conventionalist stratagem. |
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Elsewhere I have tried to provide the justification of both the irreducible distinction of science and philosophy and their inevitable complementarity. Unlike empirical science, philosophy has no limit whatever as far as its possible objects are concerned. To say that there is no limit whatever to the possible objects of philosophy is to say that, strictly speaking, it has no object at all and must find its object outside itself, that is, in common sense knowledge and the natural and human (...) |
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With reference to an already existing and relatively widespread use of the expression in question, mathematical “thought experiments” (“TEs”) involve mathematical reasoning in which visualisation plays a relatively more important role. But to ensure an unambiguous and consistent use of the term, certain conditions have to be met: (1) Contrary to what has happened so far in the literature, the distinction between logical-formal thinking and experimental-operational thinking must not be ignored; (2) The separation between the context of discovery and the (...) |
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In the static field configuration, a spatially-Variable Speed of Light (VSL) scalar gravity model with Lorentz-Poincaré interpretation was shown to reproduce the phenomenology implied by the Schwarzschild metric. In the present development, we effectively cover configurations with source kinematics due to an induced sweep velocity field w. The scalar-vector model now provides a Hamiltonian description for particles and photons in full accordance with the first Post-Newtonian (1-PN) approximation of General Relativity Theory (GRT). This result requires the validity of Poincaré’s Principle (...) |
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The formalism used to describe evolutionary change in a multilevel setting can be used equally to re-describe the situation as one where all the selection occurs at the individual level. Thus, whether multilevel or individual-level selection occurs seems to be a matter of convention rather than fact. Yet, group selection is regarded by some as an important concept with factual rather than conventional elements. I flesh out an alternative position that regards groups as a target of selection in a way (...) |
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According to Kant, the axioms of intuition, i.e. space and time, must provide an organization of the sensory experience. However, this first orderliness of empirical sensations seems to depend on a kind of faculty pertaining to subjectivity, rather than to the encounter of these same intuitions with the real properties of phenomena. Starting from an analysis of some very significant developments in mathematical and theoretical physics in the last decades, in which intuition played an important role, we argue that nevertheless (...) |
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The history and philosophy of science are destined to play a fundamental role in an epoch marked by a major scientific revolution. This ongoing revolution, principally affecting mathematics and physics, entails a profound upheaval of our conception of space, space–time, and, consequently, of natural laws themselves. Briefly, this revolution can be summarized by the following two trends: by the search for a unified theory of the four fundamental forces of nature, which are known, as of now, as gravity, electromagnetism, and (...) |
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According to a common belief concerning the Mach-Boltzmann debate on atoms, the new experiments performed in microphysics at the turn of the 19th and 20th centuries confirmed Boltzmann's atomic hypothesis and disproved Mach's anti-atomic view. This paper intends to show that this belief is partially unjustified. Mach's view on atoms consists in fact of different kinds of arguments. While the new experiments in microphysics refute indeed his scientific arguments against the atomic hypothesis, his epistemological arguments are unaffected. In this regard, (...) |
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One of the most important contributions of A. Church to logic is his invention of the lambda calculus. We present the genesis of this theory and its two major areas of application: the representation of computations and the resulting functional programming languages on the one hand and the representation of reasoning and the resulting systems of computer mathematics on the other hand. |
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Brouwer’s intuitionistic program was an intriguing attempt to reform the foundations of mathematics that eventually did not prevail. The current paper offers a new perspective on the scientific community’s lack of reception to Brouwer’s intuitionism by considering it in light of Michael Friedman’s model of parallel transitions in philosophy and science, specifically focusing on Friedman’s story of Einstein’s theory of relativity. Such a juxtaposition raises onto the surface the differences between Brouwer’s and Einstein’s stories and suggests that contrary to Einstein’s (...) |
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In this chapter I investigate the prospects of integrated history and philosophy of science, by examining how philosophical issues raised by “hidden entities”, entities that are not accessible to unmediated observation, can enrich the historical investigation of their careers. Conversely, I suggest that the history of those entities has important lessons to teach to the philosophy of science. Hidden entities have played a crucial role in the development of the natural sciences. Despite their centrality to past scientific practice, however, several (...) |
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In an earlier article on this journal I argued that the problem of empirical underdetermination can for the largest part be solved by theoretical virtues, and for the remaining part it can be tolerated. Here I confront two further challenges to scientific realism based on underdetermination. First, there are four classes of theories which may seem to be underdetermined even by theoretical virtues. Concerning them I argue that (i) theories produced by trivial permutations and (ii) “equivalent descriptions” are compatible with (...) |
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The essays in this volume concern the points of intersection between analytic philosophy and the philosophy of the exact sciences. More precisely, it concern connections between knowledge in mathematics and the exact sciences, on the one hand, and the conceptual foundations of knowledge in general. Its guiding idea is that, in contemporary philosophy of science, there are profound problems of theoretical interpretation-- problems that transcend both the methodological concerns of general philosophy of science, and the technical concerns of philosophers of (...) |
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Brouwer’s view on induction has relatively recently been characterised as one on which it is not only intuitive (as expected) but functional, by van Dalen. He claims that Brouwer’s ‘Ur-intuition’ also yields the recursor. Appealing to Husserl’s phenomenology, I offer an analysis of Brouwer’s view that supports this characterisation and claim, even if assigning the primary role to the iterator instead. Contrasts are drawn to accounts of induction by Poincaré, Heyting, and Kreisel. On the phenomenological side, the analysis provides an (...) |
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While in medicine, comparison of the data supplied by a clinical syndrome with the data supplied by the biological system is used to arrive at the most accurate diagnosis, the same cannot be said of financial economics: the accumulation of statistical results that contradict the Brownian hypothesis used in risk modelling, combined with serious empirical problems in the practical implementation of the Black-Scholes-Merton model, the benchmark theory of mathematical finance founded on the Brownian hypothesis, has failed to change the Brownian (...) |
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Debates concerning the units and levels of selection have persisted for over fifty years. One major question in this literature is whether units and levels of selection are genuine, in the sense that they are objective features of the world, or merely reflect the interests and goals of an observer. Scientists and philosophers have proposed a range of answers to this question. This Element introduces this literature and proposes a novel contribution. It defends a realist stance and offers a way (...) |
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What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...) |
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The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bell’s own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic ; analytical philosophy, philosophy of science, philosophy of mathematics and decision theory and foundations of economics. (...) |
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In this paper I argue that inconsistencies in scientific theories may arise from the type of causality relation they—tacitly or explicitly—embody. All these seemingly different causality relations can be subsumed under a general strategy developed to defeat the paradoxes which inevitably occur in our experience of the real. With respect to this, scientific theories are just a subclass of the larger class of metaphysical theories, construed as theories that attempt to explain a (part of) the world consistently. All metaphysical theories (...) |
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We present a new English translation of L.E.J. Brouwer's paper ‘De onbetrouwbaarheid der logische principes’ of 1908, together with a philosophical and historical introduction. In this paper Brouwer for the first time objected to the idea that the Principle of the Excluded Middle is valid. We discuss the circumstances under which the manuscript was submitted and accepted, Brouwer's ideas on the principle of the excluded middle, its consistency and partial validity, and his argument against the possibility of absolutely undecidable propositions. (...) |
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Debido a la historicidad de la razón, más que inventariar sus principales conceptos en un momento dado nos interesa estudiar el proceso de su formación y fijación. En este artículo se ilustra ese proceso con ejemplos tomados de la historia de la física. El primer ejemplo concierne a la subordinación en el siglo XVII de los fenómenos archiconocidos de la caída libre y el movimiento de los planetas a un concepto nuevo; los restantes, tomados de la electrodinámica del siglo XIX (...) |
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After a description of the method of mathematics and empirical sciences, brief but explicit enough to show their limits with philosophical and theological reflection, I comment the harmonic relations of mutual help among them, and also, unfortunately, the historical occasions in which these limits have been trespassed. And after a fast view of the image of the world–matter and life–presented to us by nowadays established science, I recall the main items of opposition to faith posed by science, although sometimes just (...) |
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The reflection on the preconditions and evolution of science has played a decisive role in the development of Ernst Cassirer's philosophy, contributing to its functional and thus inherently pluralistic and holistic view of knowledge. To present Cassirer's conception of physics as an open symbolic formation enables us to reveal and study the radical features of his epistemological model: (1) the fundamental process of generating sense-units and meaning in its constitutive character for each attempt of objectification, (2) its driving and structuring (...) |
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Historians of philosophy have hitherto either given scant attention to Cournot and Renouvier’s views on scientific revolution, tried to read Kuhn’s concept of scientific revolution back into their works, or did not fully appreciate the extent to which these philosophers were reflecting on the works of their predecessors as well as on developments in mathematics and the sciences. Cournot’s views on cumulative development through revolution resemble Comte’s more than Kuhn’s, and his notion of progressive theoretical simplicity through revolution recalls Whewell’s (...) |
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Founding our analysis on the Geneva-Brussels approach to the foundations of physics, we provide a clarification and classification of the key concept of observation. An entity can be observed with or without a scope. In the second case, the observation is a purely non-invasive discovery process; in the first case, it is a purely invasive process, which can involve either creation or destruction aspects. An entity can also be observed with or without a full control over the observational process. In (...) |
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In this article, we redefine classical notions of theory reduction in such a way that model-theoretic preferential semantics becomes part of a realist depiction of this aspect of science. We offer a model-theoretic reconstruction of science in which theory succession or reduction is often better - or at a finer level of analysis - interpreted as the result of model succession or reduction. This analysis leads to 'defeasible reduction', defined as follows: The conjunction of the assumptions of a reducing theory (...) |
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Hume famously warned us that the ‘[The] ultimate springs and principles are totally shut up from human curiosity and enquiry’. Or, again, Newton: ‘Hitherto I have not been able to discover the cause of these properties of gravity … and I frame no hypotheses.’ Aristotelian science was concerned with just such questions, the specification of occult qualities, the real essences that answer the question What is matter, etc?, the preoccupation with circular definitions such as dormative virtues, and so on. The (...) |
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The object of this article is to show a certain proximity of Duhem to Poincaré in his first philosophical reflections. I study the relationships between the scientific practices of the two scholars, the contemporary theoretical context and their reflections. The first part of the article concerns the changes in epistemological consensus at the turn of the century. The second part will be devoted to Poincaré's reflections on the status of physical geometries and physical theories, as they appear in his texts (...) |
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Kantian philosophy of space, time and gravity is significantly affected in three ways by particle physics. First, particle physics deflects Schlick’s General Relativity-based critique of synthetic a priori knowledge. Schlick argued that since geometry was not synthetic a priori, nothing was—a key step toward logical empiricism. Particle physics suggests a Kant-friendlier theory of space-time and gravity presumably approximating General Relativity arbitrarily well, massive spin-2 gravity, while retaining a flat space-time geometry that is indirectly observable at large distances. The theory’s roots (...) |
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My target is the epistemological dimension of the realism debate. After establishing a stance voluntarist framework with a Jamesian background, drawing mostly on Wylie, Chakravarty, and van Fraassen, I argue that current voluntarists are too permissive. I show that especially various anti-realist stances but also some realist and selective realist stances block themselves from refutation by the history of science. I argue that such stances should be rejected. Finally, I propose that any disagreement that cannot be resolved by this strategy (...) |
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Much of the focus on Poincaré’s philosophy of science has been on the notion of convention, a crucial concept that has become distinctive of his position. However, other notions have received much less attention. That is the case of verifiable hypotheses. This kind of hypotheses seems to be constituted from the generalization of several observable facts. So, in order to understand what these hypotheses are, we need to know what a fact to Poincaré is. He divides facts into brute and (...) |
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We consider the problem of therelationship between the quantum and theclassical domains from the point of view that itis possible to speak of a direct physicaldescription of quantum systems havingphysical properties. We put emphasis, inevidencing it, on the specific quantum conceptof indistinguishability of identical in aconceptual way (and not in a logical way in thevein of ``da Costa's school''). In essence, thesubsequent argumentation deals with therelationship between the classical and thequantum, with the problem of the quantum theoryof measurement. Even in (...) |
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Hyperbolic geometry can be axiomatized using the notions of order andcongruence (as in Euclidean geometry) or using the notion of incidencealone (as in projective geometry). Although the incidence-based axiomatizationmay be considered simpler because it uses the single binary point-linerelation of incidence as a primitive notion, we show that it issyntactically more complex. The incidence-based formulation requires some axioms of the quantifier-type forallexistsforall, while the axiom system based on congruence and order can beformulated using only forallexists-axioms. |
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At present, there is a renewed interest in thoseaspects of Rudolf Carnap ''s LogischerAufbau der Welt that cannot just be reduced tothe tradition of logical positivism. There is, however,one of these aspects which seems to have beenneglected by the historical analyses of theAufbau''s background: what may be called aprogram for the mathematization of sense experience,as developed by Carnap in the most difficult partof his work, Chapter IV/A. It is the program of applying settheory and topology to the reconstruction of phenomenal (...) |
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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 (...) |
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