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  1. Bolzano’s Mathematical Infinite.Anna Bellomo & Guillaume Massas - forthcoming - Review of Symbolic Logic:1-80.
    Bernard Bolzano (1781-1848) is commonly thought to have attempted to develop a theory of size for infinite collections that follows the so-called part-whole principle, according to which the whole is always greater than any of its proper parts. In this paper, we develop a novel interpretation of Bolzano's mature theory of the infinite and show that, contrary to mainstream interpretations, it is best understood as a theory of infinite sums. Our formal results show that Bolzano's infinite sums can be equipped (...)
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  • Mass Nouns and Plural Logic (Extended Abstract).David Nicolas - 2007 - In Proceedings of the 16th Amsterdam Colloquium. Palteam. pp. 211-244.
  • The Beyträge at 200: Bolzano's Quiet Revolution in the Philosophy of Mathematics.Jan Sebestik & Paul Rusnock - 2013 - Journal for the History of Analytical Philosophy 1 (8).
    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. (...)
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  • Bolzano and the Analytical Tradition.Sandra Lapointe - 2014 - Philosophy Compass 9 (2):96-111.
    In the course of the last few decades, Bolzano has emerged as an important player in accounts of the history of philosophy. This should be no surprise. Few authors stand at a more central junction in the development of modern thought. Bolzano's contributions to logic and the theory of knowledge alone straddle three of the most important philosophical traditions of the 19th and 20th centuries: the Kantian school, the early phenomenological movement and what has come to be known as analytical (...)
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  • A Note on the Quantum Mechanical Measurement Process.Michael Drieschner - 2013 - Philosophia Naturalis 50 (2):201-213.
    Traditionally one main emphasis of the quantum mechanical measurement theory is on the question how the pure state of the compound system 'measured system + measuring apparatus' is transformed into the 'mixture' of all possible results of that measurement, weighted with their probability: the so-called “disappearance of the interference terms”. It is argued in this note that in reality there is no such transformation, so that there is no need to account for such a transformation theoretically. _German_ Gewöhnlich liegt ein (...)
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  • Mass Nouns and Plural Logic.David Nicolas - 2008 - Linguistics and Philosophy 31 (2):211-244.
    A dilemma put forward by Schein (1993) and Rayo (2002) suggests that, in order to characterize the semantics of plurals, we should not use predicate logic, but non-singular logic, a formal language whose terms may refer to several things at once. We show that a similar dilemma applies to mass nouns. If we use predicate logic and sets, we arrive at a Russellian paradox when characterizing the semantics of mass nouns. Likewise, a semantics of mass nouns based upon predicate logic (...)
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  • Paul Rusnock. Bolzano's Philosophy and the Emergence of Modern Mathematics. Studien Zur Österreichischen Philosophie [Studies in Austrian Philosophy], Vol. 30. Amsterdam & Atlanta: Editions Rodopi, 2000. Isbn 90-420-1501-2. Pp. 218. [REVIEW]John L. Bell - 2006 - Philosophia Mathematica 14 (3):362-364.
    Bernard Bolzano , one of the leading figures of the Bohemian Enlightenment, made important contributions both to mathematics and philosophy which were virtually unknown in his lifetime and are still largely unacknowledged today. As a mathematician, he was a pioneer in the clarification and rigorization of mathematical analysis; as a philosopher, he may be considered a forerunner of the analytic movement later to emerge with Frege and Russell.Rusnock's account of Bolzano's work is laid out in five chapters and two appendices. (...)
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  • Logic and Philosophy of Mathematics in the Early Husserl.Stefania Centrone - 2009 - Dordrecht, Netherland: Springer.
    This volume will be of particular interest to researchers working in the history, and in the philosophy, of logic and mathematics, and more generally, to ...
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  • Bolzano’s Infinite Quantities.Kateřina Trlifajová - 2018 - Foundations of Science 23 (4):681-704.
    In his Foundations of a General Theory of Manifolds, Georg Cantor praised Bernard Bolzano as a clear defender of actual infinity who had the courage to work with infinite numbers. At the same time, he sharply criticized the way Bolzano dealt with them. Cantor’s concept was based on the existence of a one-to-one correspondence, while Bolzano insisted on Euclid’s Axiom of the whole being greater than a part. Cantor’s set theory has eventually prevailed, and became a formal basis of contemporary (...)
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  • Bolzano's Theory of Ground and Consequence.Armin Tatzel - 2002 - Notre Dame Journal of Formal Logic 43 (1):1-25.
    The aim of the paper is to present and evaluate Bolzano's theory of grounding, that is, his theory of the concept expressed and the relation brought into play by 'because'. In the first part of the paper (Sections 1-4) the concept of grounding is distinguished from and related to three other concepts: the concept of an epistemic reason}, the concept of causality, and the concept of deducibility (i.e., logical consequence). In its second part (Sections 5-7) Bolzano's positive account of grounding (...)
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  • EPR and the 'Passage' of Time.Friedel Weinert - 2013 - Philosophia Naturalis 50 (2):173-199.
    The essay revisits the puzzle of the ‘passage’ of time in relation to EPR-type measurements and asks what philosophical consequences can be drawn from them. Some argue that the lack of invariance of temporal order in the measurement of a space-like related EPR pair, under relativistic motion, casts serious doubts on the ‘reality’ of the lapse of time. Others argue thatcertain features of quantum mechanics establisha tensed theory of time – understood here as Possibilism or the growing block universe. The (...)
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  • Mereology.Achille C. Varzi - 2016 - Stanford Encyclopedia of Philosophy.
    An overview of contemporary part-whole theories, with reference to both their axiomatic developments and their philosophical underpinnings.
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  • La théorie bolzanienne du fondement et de la conséquence.Armin Tatzel - 2003 - Philosophiques 30 (1):191-217.
    Le but de cet article est de présenter et d’évaluer la théorie de la fondation de Bernard Bolzano, c’est-à-dire sa théorie du concept exprimé et de la relation mise en jeu par « parce que ». Dans la première partie , le concept de fondation est distingué et mis en relation avec trois autres concepts : le concept de raison épistémique, le concept de causalité et le concept de déductibilité . Dans la seconde partie , je reconstruis la théorie bolzanienne (...)
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  • On Bolzano's Concept of a Sum.Paul Rusnock - 2013 - History and Philosophy of Logic 34 (2):155 - 169.
    Alongside his groundbreaking work in logic, Bernard Bolzano (1781?1848) made important contributions to ontology, notably with his theory of collections. Recent work has done much to elucidate Bolzano's conceptions, but his notion of a sum has proved stubbornly resistant to complete understanding. This paper offers a new interpretation of Bolzano's concept of a sum. I argue that, although Bolzano's presentation is defective, his conception is unexceptionable, and has important applications, notably in his work on the foundations of arithmetic.
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  • Bolzano sur les nombres.Peter Simons - 2003 - Philosophiques 30 (1):127-135.
    Dans cet article, l’auteur présente la théorie bolzanienne du nombre. Il établit, sur la base d’une comparaison avec Frege, que la conception bolzanienne rencontre toutes les exigences d’une telle théorie tout en présentant plusieurs traits originaux, comme par exemple le fait qu’elle s’articule sur la base d’une théorie des « collections » , qui lui confèrent un intérêt philosophique certain. Tout en indiquant au passage un problème inhérent à la notion bolzanienne de Reihe, l’auteur présente la conception bolzanienne des nombres (...)
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