Après le rappel de différents contextes dans lesquels a émergé et s’est affirmée en Allemagne au xixe siècle l’idée de philosophie scientifique, l’article a pour objectif une description de la conception de Reichenbach, contrastée avec celle de plusieurs membres du Cercle de Vienne. Je montre en particulier le lien épistémologique et institutionnel entre le groupe de Reichenbach à Berlin et celui de Göttingen autour de Hilbert. J’esquisse aussi un rapprochement entre certains traits caractéristiques de la position de Reichenbach et la (...) conception régionale de l’épistémologie historique française. L’axiomatique et la métamathématique de Hilbert sont bien entendu une racine commune aux orientations suivies par Reichenbach et les épistémologues français des mathématiques. Mais l’impact de la théorie de la relativité, de la mécanique quantique et du calcul des probabilités ne fut pas moins grand et renouvela en profondeur les concepts de temps, d’espace, de substance, de cause et de loi dans une mise en question des thèses du transcendantalisme kantien qui tourna l’intérêt vers les pratiques scientifiques effectives. (shrink)

Après le rappel de différents contextes dans lesquels a émergé et s’est affirmée en Allemagne au xixe siècle l’idée de philosophie scientifique, l’article a pour objectif une description de la conception de Reichenbach, contrastée avec celle de plusieurs membres du Cercle de Vienne. Je montre en particulier le lien épistémologique et institutionnel entre le groupe de Reichenbach à Berlin et celui de Göttingen autour de Hilbert. J’esquisse aussi un rapprochement entre certains traits caractéristiques de la position de Reichenbach et la (...) conception régionale de l’épistémologie historique française. L’axiomatique et la métamathématique de Hilbert sont bien entendu une racine commune aux orientations suivies par Reichenbach et les épistémologues français des mathématiques. Mais l’impact de la théorie de la relativité, de la mécanique quantique et du calcul des probabilités ne fut pas moins grand et renouvela en profondeur les concepts de temps, d’espace, de substance, de cause et de loi dans une mise en question des thèses du transcendantalisme kantien qui tourna l’intérêt vers les pratiques scientifiques effectives. (shrink)

Part I of Frege’s Grundgesetze is devoted to the “exposition [Darlegung]” of his formal system.

Mathematical abstraction is the process of considering and ma­nipulating operations, rules, methods and concepts divested from their refe­rence to real world phenomena and circumstances, and also deprived from the content connected to particular applications. There is no one single way of per­forming mathematical abstraction. The term “abstraction” does not name a unique procedure but a general process, which goes many ways that are mostly simultaneous and intertwined; in particular, the process does not amount only to logical subsumption. I will consider (...) comparatively how philosophers consi­der abstraction and how mathematicians perform it, with the aim to bring to light the fundamental thinking processes at play, and to illustrate by signifi­cant examples how much intricate and multi-leveled may be the combination of typical mathematical techniques which include axiomatic method, invariance principles, equivalence relations and functional correspondences. (shrink)

Both Frege's Grundgesetze, and Lagrange's treatises on analytical functions pursue a foundational purpose. Still, the former's program is not only crucially different from the latter's. It also depends on a different idea of what foundation of mathematics should be like . Despite this contrast, the notion of function plays similar roles in their respective programs. The purpose of my paper is emphasising this similarity. In doing it, I hope to contribute to a better understanding of Frege's logicism, especially in relation (...) to its crucial differences with a set-theoretic foundational perspective. This should also spread some light on a question arisen by J. Hintikka and G. Sandu in a widely discussed paper, namely whether Frege should or should not be credited with the notion of arbitrary function underlying our standard interpretation of second-order logic. In section 1, I account for Lagrange's notion of function. In section 2, I advance some remarks on connected historical matters. This will provide an appropriate framework for discussing the role played by the notion of function in Frege's Grundgesetze. Section 3 is devoted to this. Some concluding remarks will close the paper. (shrink)

Dans le deuxième volume, inédit, de La Philosophie de l’Algèbre, Jules Vuillemin fait une lecture inattendue et suggestive de l’œuvre de Richard Dedekind. Nous avons essayé de comprendre, en mobilisant les idées et outils de Vuillemin, les résultats de cette lecture. Ceux-ci nous semblent poser en particulier le problème des rapports entre histoire des sciences et philosophie des sciences. Notre article propose un diptyque pour présenter les questions que nous avons voulu poser au texte de Vuillemin. D’une part, nous analysons (...) de quelle manière Vuillemin continue et approfondit le travail de Jean Cavaillès. D’autre part, nous souhaitons accentuer la distance qu’établit Vuillemin entre l’histoire mathématique et son interprétation par les filiations conceptuelles qu’il propose comme essentiellement distinguées des relations historiques. (shrink)

La question fondamentale d’Albert Lautman concerne la nature du réel et la capacité de l’esprit de l’appréhender. C’est pourquoi elle convoque les données de la physique, leur expression en concepts mathématiques et leur interprétation métaphysique qui doit préciser le rapport de la pensée humaine à la réalité du monde. L’examen des théories mathématiques les plus sophistiquées de son temps est destinée à montrer l’affinité de la genèse des concepts mathématiques avec une Dialectique supérieure, qui met en jeu les Idées, comprises (...) en un sens dérivé de Platon. Mon but est d’expliquer comment Lautman comprend les termes « Dialectique », « Idée », « genèse », simultanément sur le plan métaphysique et dans leur incarnation mathématique. Je montrerai que Lautman développe une conception très personnelle du platonisme, différente de celle de la version reçue par la tradition philosophique. Lautman rejette la séparation des Idées et du sensible, et adopte le style de pensée heideggerien pour montrer que les Idées sont mues par une Dialectique et qu’elles entretiennent une relation réciproque, dialectique, avec le sensible.Albert Lautman’s main questioning was about the nature of reality and the capacity of mind to grasp reality. The answer needs to go at the same time into the laws and tools of physics and the corresponding concepts of mathematics, and to search for the metaphysical interpretation that could give an account of the relation between scientific thought and reality. The examination of the most sophisticated mathematical theories was intended to show the affinity between the generation of mathematical concepts and the dialectical movement of Ideas. My aim is to explain how Lautman understood ‘Idea’, ‘Dialectic’, ‘genesis’ at once in a mathematical and in a metaphysical meaning. I will point out that Lautman had a very personal conception of Platonism, very different from Platonism of mathematicians of his time and very different from the traditional interpretation developed in philosophy. Lautman did not assume the separation between Ideas and the sensible world. By contrast, he adopted the Heideggerian style of thought to show the Dialectic between Ideas and the reciprocal relation between Ideas and the sensible. (shrink)

Mathematical abstraction is the process of considering and ma­nipulating operations, rules, methods and concepts divested from their refe­rence to real world phenomena and circumstances, and also deprived from the content connected to particular applications. There is no one single way of per­forming mathematical abstraction. The term “abstraction” does not name a unique procedure but a general process, which goes many ways that are mostly simultaneous and intertwined; in particular, the process does not amount only to logical subsumption. I will consider (...) comparatively how philosophers consi­der abstraction and how mathematicians perform it, with the aim to bring to light the fundamental thinking processes at play, and to illustrate by signifi­cant examples how much intricate and multi-leveled may be the combination of typical mathematical techniques which include axiomatic method, invariance principles, equivalence relations and functional correspondences. (shrink)

Mathematical abstraction is the process of considering and ma­nipulating operations, rules, methods and concepts divested from their refe­rence to real world phenomena and circumstances, and also deprived from the content connected to particular applications. There is no one single way of per­forming mathematical abstraction. The term “abstraction” does not name a unique procedure but a general process, which goes many ways that are mostly simultaneous and intertwined; in particular, the process does not amount only to logical subsumption. I will consider (...) comparatively how philosophers consi­der abstraction and how mathematicians perform it, with the aim to bring to light the fundamental thinking processes at play, and to illustrate by signifi­cant examples how much intricate and multi-leveled may be the combination of typical mathematical techniques which include axiomatic method, invariance principles, equivalence relations and functional correspondences. (shrink)

Neurosciences and cognitive sciences provide us with myriad empirical findings that shed light on hypothesised primitive numerical processes in the brain and in the mind. Yet, the hypotheses on which the experiments are based, and hence the results, depend strongly on sophisticated abstract models used to describe and explain neural data or cognitive representations that supposedly are the empirical roots of primary arithmetical activity. I will question the foundational role of such models. I will even cast doubt upon the search (...) for a general and unified philosophical foundation of an empirical science. First, it seems to me hard to draw a global and coherent view from the innumerable and piecemeal neuropsychological experiments and their variable, and sometimes uneasily compatible or fully divergent interpretations. Secondly, I think that the aim of empirical research is to describe dynamical processes, establishing correlations between different sets of data, without meaning to fix an origin or to point to a cause, let alone to a ground. From the very scientific and philosophical point of view it is essential to distinguish between explanations, which provide correlations or, at best, causal mechanisms, and grounding, which involves a claim to some form of determinism. (shrink)

Le nom de Jean Cavailles evoque pour les uns le heros de la Resistance, le combattant intrepide fusille a 40 ans par les Allemands, pour les autres le philosophe brillant qui a propose une conception neuve de la pensee logique. Cet homme ne fait pourtant qu'un, l'unite de la pensee abstraite et de l'action concrete s'arrimant chez lui dans une meme disposition ethique, disposition a prendre des risques, a vivre le risque - theorique ou pratique - comme la solution exigee (...) par un probleme rationnellement pose. Or ce chemin qui va de la position d'un probleme theorique a l'invention de sa solution, le philosophe Cavailles se demande s'il est necessaire ou contingent. L'apparition de la theorie des ensembles de Cantor par exemple est-elle le fruit necessaire du developpement de la mathematique ou bien un evenement contingent qui aurait non seulement pu ne pas se produire mais se produire selon une autre modalite? Mais si plusieurs mathematiques differentes peuvent coexister, n'est-ce pas le modele le plus rigoureux du savoir qui perd d'un coup son unite et sa necessite? Le probleme de Cavailles est de trouver comment d'un univers ancien peut sortir un nouvel univers, comment on peut allier la continuite de la demarche rationnelle et la rupture des concepts. Ce sont les voies utilisees par Cavailles pour resoudre cette question que le livre d'Hourya Benis Sinaceur degage avec une grande clarte. Loin de perdre le lecteur profane dans des considerations mathematiques et logiques qui le depasseraient, l'auteur s'emploie a cerner l'originalite de la pensee philosophique de Cavailles, en montrant comment il fait jouer les unes contre les autres les sources philosophiques auxquelles il puise pour construire une histoire du sens absolument singuliere, irreductible a l'une ou l'autre des philosophies qui l'alimentent pourtant. Entre Frege et Bolzano du cote d'une conception objectiviste des idees, et Hegel et Husserl du cote d'une logique subjectiviste, c'est-a-dire de la conscience, Cavailles tisse une voie moyenne une dialectique materielle (du contenu) sans sujet. L'auteur Ancienne eleve de l'Ecole Normale Superieure et docteur d'Etat es Lettres, Hourya Benis Sinaceur est directrice de recherche emerite au Centre National de la Recherche Scientifique. Membre du comite national d'histoire et philosophie des sciences de l'Academie internationale d'histoire des sciences, elle dirige aujourd'hui une collection d'histoire et de philosophie des sciences chez Vrin. Elle est l'auteur de: - Corps et Modeles, Paris, Vrin, Collection Mathesis, 1991, 2e edition 1999. - Le labyrinthe du continu (co-edition avec SALANSKIS J.-M.), Springer-Verlag France, 1992. - Les paradoxes de l'infini, edition francaise, avec notes et introduction, de BOLZANO Bernard, Die Paradoxien des Unendlichen, Paris, Le Seuil, 1993. - Jean Cavailles, Philosophie mathematique, Paris, PUF, 1994. - La creation des nombres, edition francaise de DEDEKIND Richard, avec notes et introductions, Paris, Vrin, Collection Mathesis, 2008. (shrink)

Hourya Benis-Sinaceur, Marco Panza, and Gabriel Sandu. Functions and Generality of Logic: Reflections on Dedekind’s and Frege’s Logicisms. Logic, Epistemology, and the Unity of Science; 37. Springer, 2015. ISBN: 978-3-319-17108-1 ; 978-3-319-36782-8, 978-3-319-17109-8.. Pp. xxi + 125.

This book, which brings together historians, philosophers and mathematicians, is a tribute to the works of Hourya Benis-Sinaceur, internationally recognized specialist of history and philosophy of mathematics.

Presentación del editor: "Es sabido que un tema acaparaba la atención de los pensadores a principios del siglo XX: la historia. Mientras tanto entraba en escena el personalismo filosófico, corriente interesada en rescatar a la persona de las ideologias. Ocupando un lugar propio dentro del personalismo, no siempre en acuerdo con los demás personalistas, destaca la figura de Maurice Nédoncelle. Su filosofia de la persona y del amor plasmada en su libro sobre la reciprocidad de las conciencias es cada vez (...) más conocida; pero lo que no habia sido analizado hasta ahora es su pensamiento sobre la historia. con este estudio se da a conocer por primera vez la filosofía de la historia de Maurice Nédoncelle. La interpretación propuesta por el autor es quizás novedosa y hasta un poco audaz, pero está convencido de que Nédoncelle profesó una filosofía de la historia y de que muchas de sus afrimaciones filosóficas brotan del deseo de dar respuesta a las interrogantes sobre la historia en la que convergían los intereses de otros filósofos. Lo que interesará al lector es descubrir el gran valor de una reflexión sobre el sentido del devenir temporal que pone al centro las relaciones interpersonales. (shrink)

In this book, the author develops a new form of structural realism and deals with the problem of representation. The work combines two distinguished developments of the Semantic View of Theories, namely Structural Realism, a flourishing theory from contemporary philosophy of science, and Ronald Giere and colleagues’ Cognitive Models of Science approach. Readers will see how replacing the model-theoretic structures that are at issue in SR with connectionist networks and activations patterns helps us to deal with the problem of representation. (...) The author suggests that cognitive structures are not only the precise formal tools for regimenting the structure of scientific theories but also the tools that the biological brain uses to capture the essential features of its environment. Therefore, replacing model-theoretic structures with cognitive structures allows us to account for the theories-reality relationship on the basis of the most reliable theories of neurology. This is how a new form of SR, called Cognitive Structural Realism is introduced through this book, which articulates and defends CSR, and shows how two diverging branches of SVT can be reconciled. This ground-breaking work will particularly appeal to people who work in the philosophy of science, philosophy of mind and cognitive sciences. (shrink)

Free Energy Principle underlies a unifying framework that integrates theories of origins of life, cognition, and action. Recently, FEP has been developed into a Markovian monist perspective. The paper expresses scepticism about the validity of arguments for Markovian monism. The critique is based on the assumption that Markovian models are scientific models, and while we may defend ontological theories about the nature of scientific models, we could not read off metaphysical theses about the nature of target systems from our theories (...) of nature of scientific models. The paper draws attention to different ways of understanding Markovian models, as material entities, fictional entities, and mathematical structures. I argue that none of these interpretations contributes to the defence of a metaphysical stance. This is because scientific representation is a sophisticated process, and properties of Markovian models—such as the property of being neither physical nor mental—could not be projected onto their targets to determine the ontological properties of targets easily. (shrink)

Probabilistic realism and syntactical positivism were two among outdated theories that Feigl criticised on account of their semantical poverty. In this paper, I argue that a refined version of probabilistic realism, which relies on what Feigl specified as the pragmatic description of the symbolic behaviour of scientists’ estimations and foresight, is defendable. This version of statistical realism does not need to make the plausibility of realist thesis dependent on the conventional acceptance of a constructed semantic metalanguage. I shall rely on (...) the Prediction Error Minimisation theory to support my probabilistic version of realism with a scientifically-informed and naturalistically plausible statistical account of the theories-world relationship which has a pragmatic ring to it. (shrink)

This book presents a unified account of the self, based on a network of knowledge sourced from several scientific accounts of selfhood. Beni constructs his ontological account of the self from the common structure that underpins the theoretical diversity that is manifested in rival and sometimes incompatible scientific accounts of the self and its aspects. The enterprise is inspired by recent structural realist theories in the philosophy of science, specifying the basic structure of the self, and explaining how representational, phenomenal, (...) and social aspects of the self are embodied within this structure. (shrink)

“Risk” is all about living a faith filled life. Within the pages of this work you will discover the year-by-year history of the ups and downs of the happenings regarding Foursquare Church. There are no sure things in this crazy epic journey called life. The only constant we can hang our hope upon is the name of Jesus. Christ has called us to live beyond what we can see and lean only to what He has said. In the parable of (...) the talents Jesus was very clear about how He felt regarding those who would not risk. In Matthew 25:28-30 He states, “‘Take the thousand and give it to the one who risked the most and get rid of this “play-it-safe-mentality” who won’t go out on a limb. Jesus rewards those who Risk. Foursquare Church and its history is one successive detail regarding progressive risking on God and his faithfulness to reward said risk. I invite you to read and risk on God. You will find great joy in discovering the rewards of a life that is lived by faith. (shrink)

Luciano Floridi’s informational structural realism takes a constructionist attitude towards the problems of epistemology and metaphysics, but the question of the nature of the semantical component of his view remains vexing. In this paper, I propose to dispense with the semantical component of ISR completely. I outline a Syntactical version of ISR. The unified entropy-based framework of information has been adopted as the groundwork of SISR. To establish its realist component, SISR should be able to dissolve the latching problem. We (...) have to be able to account for the informational structures–reality relationship in the absence of the standard semantical resources. The paper offers a pragmatic solution to the latching problem. I also take pains to account for the naturalistic plausibility of this solution by grounding it in the recent computational neuroscience of the predictive coding and the free energy principle. (shrink)

In this paper, inspired by the late twentieth century developments in philosophy of science, I propose an ontological scheme to accommodate the scientifically-informed anti-substantivalist views of the self. I call the position structural realist theory of the self. More specifically, I argue that SRS provides a middle ground for bringing a metaphysical reconciliation between the two recurring, and apparently competing forms of such anti-substantivalist views, i.e., eliminativism and pluralism. The notion of the structural self, as the underpinning pattern that is (...) the subject of the ontological commitments in SRS, is not as cumbersome as the orthodox substantivalist notion, and yet accounts for the relation of the different aspects and elements of the self by integrating them structurally into a central unifying pattern of selfhood. I use the experimental studies of Northoff et al. about the processing of the self-related stimuli in the cortical midline structure of the brain, to argue that the underlying pattern of the selfhood could be sought at the level of information processing. I also add a programmatic suggestion about how the different situated, experiential and extended aspects of the selfhood could be structurally incorporated into this underlying pattern. (shrink)

Richard Levins’s (Am Sci 54(4):421–431, 1966) paper sets a landmark for the significance of scientific model-making in biology. Colombo and Palacios (Biol Philos 36(5):1–26. 10.1007/s10539-021-09818-x, 2021) have recently built their critique of the explanatory power of the Free Energy Principle on Levins’s insight into the relationship between generality, realism, and precision. This paper addresses the issue of the plausibility of biological explanations that are grounded in the Free Energy Principle (FEP) and deals with the question of the realist fortitude of (...) FEP’s theoretical framework. It indicates that what is required for establishing the plausibility of the explanation of a target system given a model of that system is the dosage or the harmony between the generality and accuracy of explanatory models. This would also provide a basis for seeing how scientific realism could be a viable option with respect to FEP. (shrink)

The paper surveys Floridi’s attempt for laying down informational structural realism. After considering a number of reactions to the pars destruens of Floridi’s attack on the digital ontology, I show that Floridi’s enterprise for enriching the ISR by borrowing elements from the ontic form of structural realism is blighted by a haunting inconsistency. ISR has been originally developed by Floridi as a restricted and level dependent form of structural realism which remains mainly bonded within the borders of a Kantian perspective. (...) I argue that this perspective doesn’t mesh nicely with the ontic interpretation that Floridi attached to the ISR. I substantiate this claim through the assessment of Floridi’s strategy for reconciling the epistemic and ontic forms of the SR, as well as by close examination of his use of method of levels of abstraction and his notion of semantic information. My proposal is that the ISR could be defended best against the mentioned and similar objections by being interpreted as an extension of the epistemic SR. (shrink)

ABSTRACTLadyman and Ross’s account of the metaphysical component of ontic structural realism was associated with a unificationist view of the connection between fundamental physics and special sciences. The aim of the present article is to assess the sense of unification that is at issue in Ladyman and Ross’s definition of metaphysics. Given the ontic core of Ladyman and Ross’s version of structural realism, it should be assumed that the unifying endeavour is worthwhile only if the connective links that underpin unification (...) are metaphysically significant. Ladyman and Ross employed information-theoretic notions, e.g. ‘projectibility’, to account for the significance of real patterns, which underpin unification. I build upon McAllister’s engagements with the same topic, to argue that these notions fail to accomplish this objective. (shrink)

The paper proposes a way to naturalise Charles S. Peirce’s conception of the scientific method, which he specified in terms of abduction, deduction and induction. The focus is on the central issue of the economy of research in abduction and self-correction by error reduction in induction. We show how Peirce’s logic of science receives support from modern breakthroughs in computational neuroscience, and more specifically from Karl Friston’s statements of active inference and the Free Energy Principle, namely the account of how (...) organisms’ capacity to decrease the discrepancy between the expected value and actual outcomes entails the minimisation of errors in their hypotheses about the world. A scientific account of organisms’ capacity to choose policies and form expectations is aligned with Peirce’s theories of abduction and induction, and especially with the economy of research. The upshot is the recovery of Peirce’s theory of the logic of science in the context of active inquiry. (shrink)

Inspired by Ronald Giere’s cognitive approach to scientific models, Cognitive Structural Realism has presented a naturalist account of scientific representation. CSR characterises the structure of theories in terms of cognitive structures. These are informational structures embodied in the brains of scientists. CSR accounts for scientific representation in terms of the dynamical relationship between the organism and its environment. The proposal has been criticised on account of its negligence of social aspects of scientific practice. The present paper aims to chart out (...) a reply to the objection. It shows that cognitive structures do not need to be put inside the brains of single individuals. Cognitive structures are redefined as extended structures in distributed cognitive systems under Free Energy Principle. (shrink)