In the last times some scholars tried to characterize Einstein’s distinction between ‘constructive’ – i.e. deductive - theories and ‘principle’ theories, the latter ones being preferred by Einstein. Here this distinction is qualified by an accurate inspection on past physical theories. Some previous theories are surely non-deductive theories. By a mutual comparison of them a set of features - mainly the arguing according to non-classical logic - are extracted. They manifest a new ideal model of organising a theory. Einstein’s paper (...) of 1905 on quanta, qualified by him as a ‘principle theory’, is interpreted according to this model of theory. Some unprecedented characteristic features are manifested. At the beginning of the same paper Einstein declared one more dichotomy about the kind of mathematics in theoretical physics. These two dichotomies are recognised as representing the foundations of theoretical physics. With respect to these dichotomies the choices by Einstein in the paper on quanta are the alternative choices to Newton’s ones. This fact gives reason to the ‘revolutionary’ nature that Einstein attributed to his paper. (shrink)

According to the conventionalist doctrine of space elaborated by the French philosopher-scientist Henri Poincaré in the 1890s, the geometry of physical space is a matter of definition, not of fact. Poincaré’s Hertz-inspired view of the role of hypothesis in science guided his interpretation of the theory of relativity (1905), which he found to be in violation of the axiom of free mobility of invariable solids. In a quixotic effort to save the Euclidean geometry that relied on this axiom, Poincaré extended (...) the purview of his doctrine of space to cover both space and time. The centerpiece of this new doctrine is what he called the ‘‘principle of physical relativity,’’ which holds the laws of mechanics to be covariant with respect to a certain group of transformations. For Poincaré, the invariance group of classical mechanics defined physical space and time (Galilei spacetime), but he admitted that one could also define physical space and time in virtue of the invariance group of relativistic mechanics (Minkowski spacetime). Either way, physical space and time are the result of a convention. (shrink)

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 (...) share a common structural backbone specificially designed to defeat paradoxes, their often wildly diverging ontological claims notwithstanding. This common structure shapes the procedures which govern the invention of ideas in the context of such theories, by codifying some onto-logical a priori assumptions regarding the consistency of reality into its bare conceptual framework. Causality plays a key rôle here, because it implies conservation of identity, itself a far from simple notion. It imposes strong demands on the universalising power of the theories concerned. These demands are often met by the introduction of a metalevel which encompasses the notions of ‘system’ and ‘lawful behaviour’. In classical mechanics, the division between universal and particular leaves its traces in the separate treatment of cinematics and dynamics. The fundamental backbone’s specific gestalt thus functions as a theory’s individual signature and paves the way to a comparative historical approach towards their study. An important part of my paper therefore explores the strong connections between paradoxes as they appear and are dealt with in ancient philosophy and their re-appearance in early modern natural philosophy and science. This analysis is applied to the mechanical theories of Newton and Leibniz, with some surprising results. (shrink)

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)

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 (...) of them (e.g., phlogiston, caloric, and the ether) turned out to be fictitious. For this reason, they have figured prominently in recent debates on scientific realism. The issues I explore in this paper are entangled with those debates. I argue that our understanding of hidden entities and their role in experimental practice can be enhanced by adopting an integrated historical-cum-philosophical approach. On the one hand, philosophical reflection on the reality of those entities has a lot to gain by examining historically how they were ntroduced and investigated. On the other hand, the historical reconstruction of the careers of those entities may profit from philosophical reflection on their existence. (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.

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 (...) the latter case, the observation can be described by a symmetry breaking mechanism, through which a specific deterministic observational process is selected among a number of potential ones, as explained in Aerts’ hidden measurement approach. This is what is called a product test, or product observation, whose consequences are that outcomes can only be predicted in probabilistic terms, as it is the case in typical quantum measurements. We also show that observations can be about intrinsic (stable) properties of the observed entity, or about relational (ephemeral) properties between the observer and observed entities; also, they can be about intermediate properties, neither purely classical, nor purely quantum. Our analysis allows us to propose a general conceptual characterization of quantum measurements, as observational processes involving three aspects: (1) product observations, (2) pure creation aspects and (3) ephemeral relational properties. We also discuss the important concept of non-spatiality and emphasize some of the differences and similarities between quantum and classical/relativistic observations. (shrink)

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 (...) dynamics that touches and transforms all elements of knowledge, the a priori included, (3) the strategies of justification that allow maintaining the claim of truthfulness in spite the fact that Cassirer's open model integrates contingency and transitoriness as an inherent part of knowledge. It thus becomes clear that Cassirer's term 'symbol' cannot be reduced to its habitual representational acceptation, for its key theoretical function is to overcome the inconsistencies of dualistic epistemological models. It is this re-orientation, a kind of 'second Copernican revolution', that allows Cassirer to go beyond traditional dichotomies and to propose a larger frame in which to appreciate the diversity of human understanding. (shrink)

This paper attempts to explain the emergence of the logical empiricist philosophy of space and time as a collision of mathematical traditions. The historical development of the ``Riemannian'' and ``Helmholtzian'' traditions in 19th century mathematics is investigated. Whereas Helmholtz's insistence on rigid bodies in geometry was developed group theoretically by Lie and philosophically by Poincaré, Riemann's Habilitationsvotrag triggered Christoffel's and Lipschitz's work on quadratic differential forms, paving the way to Ricci's absolute differential calculus. The transition from special to general relativity (...) is briefly sketched as a process of escaping from the Helmholtzian tradition and entering the Riemannian one. Early logical empiricist conventionalism, it is argued, emerges as the failed attempt to interpret Einstein's reflections on rods and clocks in general relativity through the conceptual resources of the Helmholtzian tradition. Einstein's epistemology of geometry should, in spite of his rhetorical appeal to Helmholtz and Poincaré, be understood in the wake the Riemannian tradition and of its aftermath in the work of Levi-Civita, Weyl, Eddington, and others. (shrink)

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.

« 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.

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 (...) T with the definitions translating the vocabulary of a reduced theory T' to the vocabulary of T, defeasibly entails the assumptions of reduced T'. This relation of defeasible reduction offers, in the context of additional knowledge becoming available, articulation of a more flexible kind of reduction in theory development than in the classical case. Also, defeasible reduction is shown to solve the problems of entailment that classical homogeneous reduction encounters. Reduction in the defeasible sense is a practical device for studying the processes of science, since it is about highlighting different aspects of the same theory at different times of application, rather than about naive dreams concerning a metaphysical unity of science. (shrink)

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.

A few days before his death my husband requested me to write a few words of thanks on the publication of this collection of articles. He had already prepared the greater part of the volume for the press and had also decided on the title Science a Road to Wisdom. His original selection was somewhat more comprehensive, which is still partly reflected in the Preface. Knowing how much he wished to see this collection published, I respectfully and lovingly fulfil his (...) request, thanking Else M. Barth and J. J. A. Mooij for their extensive and expert care in putting the final touches to the volume. ADDITION TO THE TRANSLATION Finally, I wish to thank Peter G. E. Wesly for his willingness to undertake the translation of the book into English. c. P. C. BETH-PASTOOR IX PREFACE In this republication of a number of philosophical studies I have refrained from including articles of a specialized nature on symbolic logic and the methodology of the exact sciences. There was no cause to include my contributions towards the didactics of mathematics and physics, nor did I consider it appropriate to reprint pieces of a predominantly polemical nature. I decided, however, that a very modest selection from my purely historical work would not be out of place. (shrink)

In recent years, the question of the reliability of Machine Learning (ML) methods has acquired significant importance, and the analysis of the associated uncertainties has motivated a growing amount of research. However, most of these studies have applied standard error analysis to ML models—and in particular Deep Neural Network (DNN) models—which represent a rather significant departure from standard scientific modelling. It is therefore necessary to integrate the standard error analysis with a deeper epistemological analysis of the possible differences between DNN (...) models and standard scientific modelling and the possible implications of these differences in the assessment of reliability. This article offers several contributions. First, it emphasises the ubiquitous role of model assumptions (both in ML and traditional science) against the illusion of theory-free science. Secondly, model assumptions are analysed from the point of view of their (epistemic) complexity, which is shown to be language-independent. It is argued that the high epistemic complexity of DNN models hinders the estimate of their reliability and also their prospect of long term progress. Some potential ways forward are suggested. Thirdly, this article identifies the close relation between a model’s epistemic complexity and its interpretability, as introduced in the context of responsible AI. This clarifies in which sense—and to what extent—the lack of understanding of a model (black-box problem) impacts its interpretability in a way that is independent of individual skills. It also clarifies how interpretability is a precondition for a plausible assessment of the reliability of any model, which cannot be based on statistical analysis alone. This article focuses on the comparison between traditional scientific models and DNN models. However, Random Forest (RF) and Logistic Regression (LR) models are also briefly considered. (shrink)

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 (...) alternative to that in Tieszen’s Mathematical Intuition, and confirms a view of Gödel on his Dialectica Interpretation. (shrink)

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 (...) context of justification is to be rejected, at least in one of the main senses in which it was defended by the logical empiricists and Popper (this excludes any position which, ascribing to mathematical TEs only a heuristic role, regards them an intermediate step to attain more traditional forms of rigour); (3) The distinction between mathematical TEs and formal proofs must be regarded as one of degree, and not as a qualitative one, although this distinction may be used in a de facto way for particular or local purposes. (shrink)

This paper defends a conceptualistic version of structuralism as the most convincing way of elaborating a philosophical understanding of structuralism in line with the classical tradition. The argument begins with a revision of the tradition of “conceptual mathematics”, incarnated in key figures of the period 1850 to 1940 like Riemann, Dedekind, Hilbert or Noether, showing how it led to a structuralist methodology. Then the tension between the ‘presuppositionless’ approach of those authors, and the platonism of some recent versions of philosophical (...) structuralism, is presented. In order to resolve this tension, we argue for the idea of ‘logical objects’ as a form of minimalist realism, again in the tradition of classical authors including Peirce and Cassirer, and we introduce the basic tenets of conceptual structuralism. The remainder of the paper is devoted to an open discussion of the assumptions behind conceptual structuralism, and—most importantly—an argument to show how the objectivity of mathematics can be explained from the adopted standpoint. This includes the idea that advanced mathematics builds on hypothetical assumptions (Riemann, Peirce, and others), which is presented and discussed in some detail. Finally, the ensuing notion of objectivity is interpreted as a form of particularly robust intersubjectivity, and it is distinguished from fictional or social ontology. (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)

Jean Nicod (1893–1924) is a French philosopher and logician who worked with Russell during the First World War. His PhD, with a preface from Russell, was published under the titleLa géométrie dans le monde sensiblein 1924, the year of his untimely death. The book did not have the impact he deserved. In this paper, I discuss the methodological aspect of Nicod’s approach. My aim is twofold. I would first like to show that Nicod’s definition of various notions of equivalence between (...) theories anticipates, in many respects, the (syntactic and semantic) model-theoretic notion of interpretation of a theory into another. I would secondly like to present the philosophical agenda that led Nicod to elaborate his logical framework: the defense of rationalism against Bergson’s attacks. (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)

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)

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 (...) argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims, as well as our logical and mathematical knowledge. (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)

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 (...) very idea of using this principle as a constructive tool were born in this context. The consequences of Poincaré’s and Einstein’s awareness of this approach are analyzed. Lastly, the legitimacy and significance of a relativity-based derivation of Newton’s second law are briefly discussed in a more philosophical vein. (shrink)

The paper addresses the question of the nature and limits of philosophical thought experiments. On the one hand, experimental philosophers are right to claim that we need much more laboratory work in order to have more reliable thought experiments, but on the other hand a naturalism that is too radical is incapable of clarifying the peculiarity of thought experiments in philosophy. Starting from a historico-critical reconstruction of Kant’s concept of the “experiments of pure reason”, this paper outlines an account of (...) thought experiments in philosophy that tries to reconcile the thesis of a principled difference between scientific and philosophical TEs with the position of a methodological naturalism that does not admit any difference in kind between the methods of science and of philosophy. (shrink)

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 (...) representation, which has endured for more than fifty years despite the extent of its invalidation by experience. Without any statistical foundations, one mathematical representation has become the established approach, acting in the minds of practitioners as a “prenotion” in the sense the word is used by Durkheim, i.e. a “schematic, summary representation” which has produced a kind of spontaneous epistemology. The question arises of the persistence of this mathematical representation, which has been the basis for every financial risk modelling approach: how can its long life be explained? How was this spontaneous epistemology formed, and why did it prove to be so persistent? To address this question and offer an answer, I will test the various dynamics of scientific knowledge used with reference to financial modelling. All these dynamics are specific ways of describing the relationship between knowledge of a phenomenon and the phenomenon itself. Observing that it is impossible for the positivist approach to solve the financial puzzle, I turn to the three principal postpositivist dynamics, developed by Kuhn, Lakatos and Quine. I shall try to make to speak these representations of science for financial research, in order to reflect on the dominance of the Brownian representation in finance. We shall see that none of the epistemologies examined can explain why the Brownian representation continues to be used in mathematical finance research. I shall then propose an alternative hypothesis, concerning a significant pervading mental model that has irrigated both academics and practitioners in the financial sector: the “principle of continuity” introduced into economics by Marshall in. I consider that this principle of continuity has become a “persistent idea” in the form of a viral approach to representations, and I give this persistent idea the metaphorical name of the “Brownian virus”. Then, to explain the spread of this Brownian virus through the financial sector, the contamination of financial practices by this mental representation founded on the principle of continuity, I introduce the concept of the “financial Logos”, a discourse that structures practices and organisations, calculations, prudential regulations and accounting standards, leading to a general financialisation of society from the 1980s onwards. (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.

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. (...) We note that principled objections to the general excluded middle similar to Brouwer's had been advanced in print by Jules Molk two years before. Finally, we discuss the influence on George Griss' negationless mathematics. (shrink)

Contrary to classical physics, which was strongly objective i.e. could be interpreted as a description of mind-independent reality, standard quantum mechanics (SQM) is only weakly objective, that is to say, its statements, though intersubjectively valid, still merely refer to operations of the mind. Essentially, in fact, they are predictive of observations. On the view that SQM is universal conventional realism is thereby refuted. It is shown however that this does not rule out a broader form of realism, called here ‘open (...) realism’, restoring the notion of mind-independent reality. (shrink)

La finalidad de este artículo es mostrar la originalidad de la categoría lógica de "historicidad" propuesta por Max Weber, sugiriendo que en sus obras sobre la metodología de las ciencias histórico-sociales se puede encontrar una estimulante y precursora contribución al análisis de algunos problemas lógicos y formales referentes a la relación entre el conocimiento humano y el caos de la realidad (lo que podríamos llamar, ante litteram, "ciencia del caos"). Particularmente, considerando que en Weber el conocimiento científico no encuentra en (...) el mundo natural "hechos" a los cuales agarrarse sino un caos de acontecimientos únicos e infinitamente divisibles, el análisis se concentra en los siguientes aspectos: (a) la separación de la imputación causal de la noción de una ley (natural) necesaria; (b) la importancia atribuida a los "juicios de probabilidad" con diferentes grados de certeza; (c) la irreductibilidad de los acontecimientos individuales a modelos, leyes y tipos-(ideales) científicos; (d) los efectos asociados a la diferenciación del punto de vista de un observador científico. This paper aims at revealing the originality of Max Weber's conception of the logical category of "historicity", suggesting that in his writings on the methodology of the social sciences we can find a stimulating and forerunner contribution to the analysis of some logical and formal problems concerning the relationship between human knowledge and the chaos of reality (what we might call, antelitteram, "science of chaos"). In particular, considering that in Weber's conception scientific knowledge finds no facts "to grasp" in the natural world, but rather a chaos ofunique and infinitely divisible events, the analysis will be focused on the following aspects: (a) Weber's separation of causal imputation from the notion of necessary (natural) law; (b) the importance attached to "probability judgments" with different degrees of certainty; (c) the proclaimed irreducibility of individual events to scientific models, laws, and (ideal)-types; (d) the effects imputed to the differentiation of the point of view of a scientific observer. (shrink)

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 (...) that is not merely definitional fiat and provide a theoretical basis for this position. (shrink)

ArgumentThis paper explores how the Belgian mathematician Paul Mansion became interested in probability theory. In comparison to many other countries at the time, probability theory had a much stronger presence in Belgium. In addition, Mansion, who was an avowed Catholic militant, had found probability theory to be a useful means of reflecting on certain problems pertaining to determinism and randomness that were arising in scientific debates at the time. Mansion’s work took place during a time of consolidation of mathematical education (...) in Belgium, as well as a new interest in probabilistic results and the foundation of the Institute for Philosophy in Louvain by his friend Désiré Mercier. The present paper addresses how these aspects intersected at the turn of the twentieth century. (shrink)

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 (...) story, the philosophical roots of Brouwer’s intuitionism cannot be traced to any previously established philosophical traditions. The paper concludes by showing how the intuitionistic inclinations of Hermann Weyl and Abraham Fraenkel serve as telling cases of how individuals are involved in setting in motion, adopting, and resisting framework transitions during periods of disagreement within a discipline. (shrink)

Context: Varela’s neurophenomenology was conceived from the outset as a criticism and dissolution of the “hard problem” of the physical origin of consciousness. Indeed, the standard (….

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 (...) intuition comes into play in a fundamentally different way to that which Kant had foreseen: in the form of a formal or “categorical” yet not sensible intuition. We show further that the statement that our space is mathematically three-dimensional and locally Euclidean by no means follows from a supposed a priori nature of the sensible or subjective space as Kant claimed. In fact, the three-dimensional space can bear many different geometrical and topological structures, as particularly the mathematical results of Milnor, Smale, Thurston and Donaldson demonstrated. On the other hand, it has been stressed that even the phenomenological or perceptual space, and especially the visual system, carries a very rich geometrical organization whose structure is essentially non-Euclidean. Finally, we argue that in order to grasp the meaning of abstract geometric objects, as n-dimensional spaces, connections on a manifold, fiber spaces, module spaces, knotted spaces and so forth, where sensible intuition is essentially lacking and where therefore another type of mathematical idealization intervenes, we need to develop a new form of intuition. (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)

Prompted by Hasok Chang’s conception of the history and philosophy of science (HPS) as the continuation of science by other means, I examine the possibility of obtaining scientific knowledge through philosophical criticism and reflection, in the light of four historical cases, concerning (i) the role of absolute space in Newtonian dynamics, (ii) the purported contraction of rods and retardation of clocks in Special Relativity, (iii) the reality of the electromagnetic ether, and (iv) the so-called problem of time’s arrow. In all (...) four cases it is clear that a better understanding of such matters can be achieved —and has been achieved— through conceptual analysis. On the other hand, however, it would seem that this kind of advance has more to do with philosophical questions in science than with narrowly scientific questions. Hence, if HPS in effect continues the work of science by other means, it could well be doing it for other ends than those that working scientists ordinarily have in mind. (shrink)

Jean Nicod (1893–1924) is a French philosopher and logician who worked with Russell during the First World War. His PhD, with a preface from Russell, was published under the title La géométrie dans le monde sensible in 1924, the year of his untimely death. The book did not have the impact he deserved. In this paper, I discuss the methodological aspect of Nicod’s approach. My aim is twofold. I would first like to show that Nicod’s definition of various notions of (...) equivalence between theories anticipates, in many respects, the (syntactic and semantic) model-theoretic notion of interpretation of a theory into another. I would secondly like to present the philosophical agenda that led Nicod to elaborate his logical framework: the defense of rationalism against Bergson’s attacks. (shrink)

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 (...) the truth of standard theories; instead (iii) “as if” versions of standard theories are much worse from the point of view of theoretical virtues; finally (iv) mathematically intertranslatable theories either may become empirically decidable in the future, or can be discriminated by theoretical virtues, or realists may simply plead ignorance about their claims. Secondly, I consider Stanford’s underdetermination with respect unconceived alternatives, arguing that it essentially relies on the pessimistic meta-induction from the falsity of all past theories. Therefore, it can be resisted by (a) considering the radical advancement of present with respect to past science, and (b) arguing with selective realism that past successful theories, even if false, always included some true components. (shrink)

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)

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 (...) of Relativity, i.e. the unobservability of ‘preferred’ frame movement. Poincaré’s principle fixes the amplitude of the sweep velocity field of the moving source, or equivalently the ‘vector potential’ ξ of GRT (e.g.; S. Weinberg, Gravitation and cosmology, [1972]), and provides the correct 1-PN limit of GRT. The implementation of this principle requires acceleration transformations derived from gravitationally modified Lorentz transformations. A comparison with the acceleration transformation in GRT is done. The present scope of the model is limited to weak-field gravitation without retardation and with gravitating test particles. In conclusion the model’s merits in terms of a simpler space, time and gravitation ontology—in terms of a Lorentz-Poincaré-type interpretation—are explained (e.g. for ‘frame dragging’, ‘harmonic coordinate condition’). (shrink)

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 (...) structures,quite independently of any other general philosophical aim.I claim that there are three forerunners of this program:Henri Poincaré''s essayPourquoi l''espace a trois dimensions, Chapter 4of Bertrand Russell ''s Our Knowledge of the ExternalWorld, and Jean Nicod''s La géométriedans le monde sensible. This article provides acomparison of these different instances of theabove-mentioned program. (shrink)