[A dialogue between Kant and Bolzano on mathematical knowledge.].

This paper surveys Bolzano's Beyträge zu einer begründeteren Darstellung der Mathematik (Contributions to a better-grounded presentation of mathematics) on the 200th anniversary of its publication. The first and only published issue presents a definition of mathematics, a classification of its subdisciplines, and an essay on mathematical method, or logic. Though underdeveloped in some areas (including,somewhat surprisingly, in logic), it is nonetheless a radically innovative work, where Bolzano presents a remarkably modern account of axiomatics and the epistemology of the formal sciences. (...) We also discuss the second, unfinished and unpublished issue, where Bolzano develops his views on universal mathematics. Here we find the beginnings of his theory of collections, for him the most fundamental of the mathematical disciplines. Though not exactly the same as the later Cantorian set theory, Bolzano's theory of collections was used in very similar ways in mathematics, notably in analysis. In retrospect, Bolzano's debut in philosophy was a remarkably successful one, though its fruits would only become generally known much later. (shrink)

Ce dialogue confronte deux conceptions qui dominent jusqu’à nos jours la philosophie des mathématiques : d’un côté la conception kantienne qui souligne l’irréductible apport de l’intuition dans la formulation des axiomes, ainsi que l’effectivité des procédés de construction ; de l’autre côté la conception bolzanienne qui s’efforce d’éliminer toute intervention de l’intuition au profit des démonstrations et des procédés purement conceptuels.In this dialogue, two opposed conceptions, which dominate the philosophy of mathematics till today, are confronted. Kant’s account of mathematics is (...) based upon the activity of constructing mathematical objects in pure intuition . In yielding objects for mathematics, our intuition contributes in an essential way to the formulation of mathematical truths. Against Kant, Bolzano argues that intuition has place neither in arithmetic nor in geometry and that mathematical existence consists in the possibility of the defined objects. i.e. in non-contradiction. For Bolzano, the central idea of mathematics is that of rigorous proof. (shrink)

Bernard Bolzano was born in Prague in 1781 and died in 1848 in the same city1. His major work Wissenschaftslehre was published in 1837 in Sulzbach, Germany.Since the publication of Jan Berg’s Bolza...

Jean-Paul Coujou a traduit – première en langue française –, commenté et annoté des ouvrages choisis dans l’œuvre monumentale de Francisco Suarez. Avant les trois présents volumes, il avait publié les trois premières Disputes et la XXXIe . Depuis trois..

Analytical philosophy begins with the first mathematical and philosophical works of Bolzano published between 1804 and 1817. There, Bolzano set out a project for the global reform of mathematics by means of the axiomatic method. Having completed the Wissenschaftslehre, Bolzano wrote a summary of his logic for the Größenlehre, which he sent to Exner in 1833. The correspondence between Bolzano and Exner covered some of the main subjects treated by analytical philosophy: the status of abstract objects (propositions and objective ideas), (...) intuitions, objectless ideas, the concept of object and many others. While Bolzano argued in favor of abstract entities independent of mind and of language, Exner considered them as abstractions obtained from the subjective judgments and representations. During the XlXth century, Bolzano's philosophy spread over Bohemia and Austria through manuscripts and through the first edition of Zimmermann's textbook of philosophy. The most important Brentanians, Kerry, Twardowski, Meinong and Husserl, discussed his doctrines which may also have influenced Wittgenstein and the Polish school. (shrink)

Analytical philosophy begins with the first mathematical and philosophical works of Bolzano published between 1804 and 1817. There, Bolzano set out a project for the global reform of mathematics by means of the axiomatic method. Having completed the Wissenschaftslehre, Bolzano wrote a summary of his logic for the Größenlehre, which he sent to Exner in 1833. The correspondence between Bolzano and Exner covered some of the main subjects treated by analytical philosophy: the status of abstract objects (propositions and objective ideas), (...) intuitions, objectless ideas, the concept of object and many others. While Bolzano argued in favor of abstract entities independent of mind and of language, Exner considered them as abstractions obtained from the subjective judgments and representations. During the XlXth century, Bolzano's philosophy spread over Bohemia and Austria through manuscripts and through the first edition of Zimmermann's textbook of philosophy. The most important Brentanians, Kerry, Twardowski, Meinong and Husserl, discussed his doctrines which may also have influenced Wittgenstein and the Polish school. (shrink)

« Pour la première fois peut-être la science n’est plus considérée comme simple intermédiaire entre l’esprit humain et l’être en soi, dépendant autant de l’un que de l’autre et n’ayant pas de réalité propre, mais comme un objet sui generis, original dans son essence, autonome dans son mouvement ». En écoutant les différentes contributions à ce colloque, je me suis retrouvé sur un terrain familier. Presque tous les noms des auteurs des xviie et xviiie siècles m’étaient bien connus : ceux (...) de La... (shrink)

Review of S. Lapointe: Bolzano’s Theoretical Philosophy, An Introduction.

Bernard Bolzano is increasingly recognized as one of the greatest nineteenth-century philosophers. A philosopher and mathematician of rare talent, he made ground-breaking contributions to logic, the foundations and philosophy of mathematics, metaphysics, and the philosophy of religion. Many of the larger features of later analytic philosophy first appear in his work: for example, the separation of logic from psychology, his sophisticated understanding of mathematical proof, his definition of logical consequence, his work on the semantics of natural kind terms, or his (...) anticipations of Cantor's set theory, to name but a few. To his contemporaries, however, he was best known as an intelligent and determined advocate for reform of Church and State. Based in large part on a carefully argued utilitarian practical philosophy, he developed a program for the non-violent reform of the authoritarian institutions of the Hapsburg Empire, a program which he himself helped to set in motion through his teaching and other activities. Rarely has a philosopher had such a great impact on the political culture of his homeland. Persecuted in his lifetime by secular and ecclesiastical authorities, long ignored or misunderstood by philosophers, Bolzano's reputation has nevertheless steadily increased over the past century and a half. Much discussed and respected in Central Europe for over a century, he is finally beginning to receive the recognition he deserves in the English-speaking world. This book provides a comprehensive and detailed critical introduction to Bolzano, covering both his life and works. (shrink)

Les origines grecques de la conception d'harmonie (H. Dufourt) - Du monde au matériau : le devenir-musical du timbre (A. Soulez) - La musique est-elle un langage? (R. Casati et J. Dokic) - Le devenir du matériau musical au XXe siècle (M. Solomos) - Hauteur, timbre, harmonie, synthèse (J.C. Risset) et d'autres articles...

It can be tempting to think of affect as a matter of the present moment – a reaction, a feeling, an experience or engagement that unfolds right now. This paper will make the case that affect is better thought of as not only temporally extended but as saturated with temporality, especially with the past. In and through affectivity, concrete, ongoing history continues to weigh on present comportment. In order to spell this out, I sketch a Heidegger-inspired perspective. It revolves around (...) two claims. The first is that we should understand what Heidegger calls 'Befindlichkeit' (findingness) as radical situatedness. Affectivity is a matter of 'finding oneself' constellated – thrown – into the world in ways that outrun what an individual or collective might grasp and process. The second claim is that the temporal dimension, as a relatedness to the past, takes precedence in affect's situatedness. Key to affect is the way in which the past continues to hold sway over present comportment, collectively and individually. In order to articulate this perspective, it is important to overcome the idea that affect must be understood mainly in terms of feeling or experiential states of other kinds. Better suited to grasp the idea of findingness is the concept of 'disclosive posture', as proposed by Katherine Withy. I suggest that this notion should be put at the fore of a phenomenological approach to situated affectivity. (shrink)

Epigenetics is currently one of the fastest-growing fields in the sciences. Epigenetic information not only controls DNA expression but links genetic factors with the environmental experiences that influence the traits and characteristics of an individual. What we eat, where we work, and how we live affects not only the activity of our genes but that of our offspring as well. This discovery has imposed a revolutionary theoretical shift on modern biology, especially on evolutionary theory. It has helped to uncover the (...) developmental processes leading to cancer, obesity, schizophrenia, alcoholism, and aging, and to facilitate associated medial applications such as stem cell therapy and cloning. Above the Gene, Beyond Biology explores how biologists in this booming field investigate and explain living systems. Jan Baedke offers the first comprehensive philosophical discussion of epigenetic concepts, explanations, and methodologies so that we can better understand this "epigenetic turn" in the life sciences from a philosophical perspective. (shrink)

The paper examines the interplays between logic and politics in the Polish School of Logic starting from 1914. The Polish School of Logic flourished between 1920 and 1939. Philosophically, it was influenced by Kazimierz Twardowski (1866–1938). For Twardowski logic is fundamental for every kind of human activity, professional and private and this means that every argument should be formulated and proceed by correct inferential rules. These rules involve semiotics, formal logic and methodology of science. The paper shows how this position (...) was shared by Twardowski’s students, including Jan Łukasiewicz, Stanisław Leśniewski, Kazimierz Ajdukiewicz and Tadeusz Kotrabiński, as well as by the next generation of logicians and philosophers and especially by Alfred Tarski. These authors considered logic, philosophy and science as completely neutral with respect to politics and ideology but they also considered logical skills as indispensable in political activities. (shrink)

Higher-order logic, with its type-theoretic apparatus known as the simple theory of types (STT), has increasingly come to be employed in theorizing about properties, relations, and states of affairs—or ‘intensional entities’ for short. This paper argues against this employment of STT and offers an alternative: ordinal type theory (OTT). Very roughly, STT and OTT can be regarded as complementary simplifications of the ‘ramified theory of types’ outlined in the Introduction to Principia Mathematica (on a realist reading). While STT, understood as (...) a theory of intensional entities, retains the Fregean division of properties and relations into a multiplicity of categories according to their adicities and ‘input types’ and discards the division of intensional entities into different ‘orders’, OTT takes the opposite approach: it retains the hierarchy of orders (though with some modifications) and discards the categorisation of properties and relations according to their adicities and input types. In contrast to STT, this latter approach avoids intensional counterparts of the Epimenides and related paradoxes. Fundamental intensional entities lie at the base of the proposed hierarchy and are also given a prominent part to play in the individuation of non-fundamental intensional entities. (shrink)

By and large, the conditional connective in three-valued logic has two different functions. First, by means of a deduction theorem, it can express a specific relation of logical consequence in the logical language itself. Second, it can represent natural language structures such as "if/then'' or "implies''. This chapter surveys both approaches, shows why none of them will typically end up with a three-valued material conditional, and elaborates on connections to probabilistic reasoning.

International institutions such as UNESCO are deliberating on a new standard setting instrument for neurotechnologies. This will likely lead to the adoption of a soft law document which will be the first global document specifically tailored to neurotechnologies, setting the tone for further international or domestic regulations. While some stakeholders have been consulted, these developments have so far evaded the broader attention of the neuroscience, neurotech, and neuroethics communities. To initiate a broader debate, this target article puts to discussion twenty-five (...) considerations and desiderata for recognition by a future instrument. They are formulated at different levels of abstraction, from the big picture to technical details, seek to widen the perspective of preparatory reports and transcend the narrow debate about “neurorights” which overshadows many richer and more relevant aspects. These desiderata are not an exhaustive enumeration but a starting point for discussions about what deserves and what requires protection by an international instrument. (shrink)

Evidence-Based Medicine has little consideration for mechanisms and philosophers of science and medicine have recently made pleas to increase the place of mechanisms in the medical evidence hierarchy. However, in this debate the notions of mechanisms seem to be limited to 'mechanistic processes' and 'complex-systems mechanisms,' understood as 'componential causal systems'. I believe that this will not do full justice to how mechanisms are used in biological, psychological and social sciences and, consequently, in a more biopsychosocial approach to medicine. Here, (...) I propose, following (Kuorikoski, 2009), to pay more attention to 'abstract forms of interaction' mechanisms. The present work scrutinized review articles on depression and medically unexplained pain, which are considered to be of multifactorial pathogenesis, for their use of mechanisms. In review articles on these disorders there seemed to be a range of uses between more 'abstract forms of interaction' and 'componential causal system' mechanisms. I therefore propose to expand the notions of mechanisms considered in medicine to include that of more 'abstract forms of interaction' to better explain and manage biopsychosocial disorders. (shrink)

This book provides for the first time a complete history of the doctrine of the transcendentals and shows its importance for the understanding of philosophy in the Middle Ages.

We introduce a cyclic proof system for the two-way alternation-free modal μ-calculus. The system manipulates one-sided Gentzen sequents and locally deals with the backwards modalities by allowing analytic applications of the cut rule. The global effect of backwards modalities on traces is handled by making the semantics relative to a specific strategy of the opponent in the evaluation game. This allows us to augment sequents by so-called trace atoms, describing traces that the proponent can construct against the opponent’s strategy. The (...) idea for trace atoms comes from Vardi’s reduction of alternating two-way automata to deterministic one-way automata. Using the multi-focus annotations introduced earlier by Marti and Venema, we turn this trace-based system into a path-based system. We prove that our system is sound for all sequents and complete for sequents not containing trace atoms. (shrink)

Niels Bohr and Philosophy of Physics: Twenty-First Century Perspectives examines the work, influences and legacy of the Nobel Prize physicist and philosopher of experiment Niels Bohr. While covering Bohr's groundbreaking contribution to quantum mechanics, this collection reveals the philosophers who influenced his work. Linking him to the pragmatist C.I. Lewis and the Danish philosopher Harald Høffding, it draws strong similarities between Bohr's philosophy and the Kantian way of thinking. Addressing the importance of Bohr's views of classical concepts, it discusses how (...) his interpretation of quantum mechanics now compares with a variety of issues that have arisen only since his lifetime, including decoherence and other non-collapse arguments. Balancing historical themes with contemporary ideas, Niels Bohrs and Philosophy of Physics reveals Bohr's on-going contribution to the philosophy of science and confirms his place in the history of philosophy. (shrink)

A number of well-developed theories shed light on the question, under what circumstances our beliefs enjoy epistemic justification. Yet, comparatively little is known about epistemic defeat--when new information causes the loss of epistemic justification. This book proposes and defends a detailed account of epistemic defeaters. The main kinds of defeaters are analyzed in detail and integrated into a general framework that aims to explain how beliefs lose justification. It is argued that defeaters introduce incompatibilities into a noetic system and thereby (...) prompt a structured re-evaluation process that makes a justified reinstatement of the defeated belief impossible. The account is then applied to the topic of disagreement, where it is used in an argument for conciliationism, as well as a new explanation for higher-order defeat. Throughout the book, the notion of defeat is the center of attention, while a number of new issues are discussed at the intersections of defeat and justification. Specifically, new problems are raised for broadly internalist accounts of defeat, a fully descriptive reliabilist account of defeat is provided, and the case for normative defeat is revisited. (shrink)

Forms of understanding -- Understanding as organized beliefs -- On interpretation -- Representations -- Scientific explanation -- Causal explanations -- Other types of explanations -- The pragmatics of explanation -- Not just why-questions -- A rhetorical approach to explanation -- Pluralism and the unity of science.

Forms of understanding -- Understanding as organized beliefs -- On interpretation -- Representations -- Scientific explanation -- Causal explanations -- Other types of explanations -- The pragmatics of explanation -- Not just why-questions -- A rhetorical approach to explanation -- Pluralism and the unity of science.

Kearns (2021) reconstructs Berkeley’s (1713) Master Argument as a formally valid argument against the Materialist Thesis, with the key premise the Distinct Conceivability Thesis, namely the thesis that truths about sensible objects having or lacking thinkable qualities are (distinctly) conceivable and as its conclusion that all sensible objects are conceived. It will be shown that Distinct Conceivability Thesis entails the Reduction Thesis, which states that de dicto propositional (ordinary or distinct) conceivability reduces to de re propositional (ordinary or distinct) conceivability. (...) While Kearns (2021) set out to avoid the confusion of a de re claim with a de dicto claim, which Prior (1955) accused Berkeley of, Kearns can be accused of making a similar conceptual confusion. (shrink)