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Bolzano's Logic

Stockholm, Sweden: Stockholm, Almqvist & Wiksell (1962)

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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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  • Parts and Moments. Studies in Logic and Formal Ontology.Barry Smith (ed.) - 1982 - Philosophia Verlag.
    A collection of material on Husserl's Logical Investigations, and specifically on Husserl's formal theory of parts, wholes and dependence and its influence in ontology, logic and psychology. Includes translations of classic works by Adolf Reinach and Eugenie Ginsberg, as well as original contributions by Wolfgang Künne, Kevin Mulligan, Gilbert Null, Barry Smith, Peter M. Simons, Roger A. Simons and Dallas Willard. Documents work on Husserl's ontology arising out of early meetings of the Seminar for Austro-German Philosophy.
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  • The Classical Model of Science: A Millennia-Old Model of Scientific Rationality.Willem R. de Jong & Arianna Betti - 2010 - Synthese 174 (2):185-203.
    Throughout more than two millennia philosophers adhered massively to ideal standards of scientific rationality going back ultimately to Aristotle’s Analytica posteriora . These standards got progressively shaped by and adapted to new scientific needs and tendencies. Nevertheless, a core of conditions capturing the fundamentals of what a proper science should look like remained remarkably constant all along. Call this cluster of conditions the Classical Model of Science . In this paper we will do two things. First of all, we will (...)
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  • A Century of Inference: 1837-1936.B. G. Sundholm - unknown
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  • Philosophical Method and Galileo's Paradox of Infinity.Matthew W. Parker - 2008 - In Bart Van Kerkhove (ed.), New Perspectives on Mathematical Practices: Essays in Philosophy and History of Mathematics : Brussels, Belgium, 26-28 March 2007. World Scientfic.
    We consider an approach to some philosophical problems that I call the Method of Conceptual Articulation: to recognize that a question may lack any determinate answer, and to re-engineer concepts so that the question acquires a definite answer in such a way as to serve the epistemic motivations behind the question. As a case study we examine “Galileo’s Paradox”, that the perfect square numbers seem to be at once as numerous as the whole numbers, by one-to-one correspondence, and yet less (...)
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  • Substitution: An Additional Conception of Analysis in the Early Analytic and Phenomenological Traditions?: On Beaney.Sandra Lapointe - 2002 - Southern Journal of Philosophy 40 (S1):101-113.
  • Etchemendy and Bolzano on Logical Consequence.Paul Rusnock & Mark Burke - 2010 - History and Philosophy of Logic 31 (1):3-29.
    In a series of publications beginning in the 1980s, John Etchemendy has argued that the standard semantical account of logical consequence, due in its essentials to Alfred Tarski, is fundamentally mistaken. He argues that, while Tarski's definition requires us to classify the terms of a language as logical or non-logical, no such division is guaranteed to deliver the correct extension of our pre-theoretical or intuitive consequence relation. In addition, and perhaps more importantly, Tarski's account is claimed to be incapable of (...)
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  • Judgement and the Epistemic Foundation of Logic.Maria van der Schaar (ed.) - 2012 - Dordrecht, Netherland: Springer.
    This compelling reevaluation of the relationship between logic and knowledge affirms the key role that the notion of judgement must play in such a review. The commentary repatriates the concept of judgement in the discussion, banished in recent times by the logical positivism of Wittgenstein, Hilbert and Schlick, and the Platonism of Bolzano. The volume commences with the insights of Swedish philosopher Per Martin-Löf, the father of constructive type theory, for whom logic is a demonstrative science in which judgement is (...)
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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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  • Das Problem der Apagogischen Beweise in Bolzanos Beyträgen Und Seiner Wissenschaftslehre.Stefania Centrone - 2012 - History and Philosophy of Logic 33 (2):127 - 157.
    This paper analyzes and evaluates Bolzano's remarks on the apagogic method of proof with reference to his juvenile booklet "Contributions to a better founded presentation of mathematics" of 1810 and to his ?Theory of science? (1837). I shall try to defend the following contentions: (1) Bolzanos vain attempt to transform all indirect proofs into direct proofs becomes comprehensible as soon as one recognizes the following facts: (1.1) his attitude towards indirect proofs with an affirmative conclusion differs from his stance to (...)
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  • Wogegen wandte sich Husserl 1891?: Ein Beitrag zur neueren Rezeption des Verhältnisses von Husserl und Frege.Deodáth Zuh - 2012 - Husserl Studies 28 (2):95-120.
    Eine vollständige Darstellung von Edmund Husserls Verhältnis zu Gottlob Frege steht noch aus, so dass es nicht verwundert, einige Missverständnisse, dieses Verhältnis betreffend, im Umlauf zu finden. Selbst scheinbar längst überwundene systematische Dogmen tauchen wieder auf, so z.B. die Auffassung, dass Husserl nicht nur entscheidend von Gottlob Frege beeinflusst wurde, sondern darüber hinaus auch seine schärfste Frege-Kritik 1891 zurückgenommen habe. Mein Beitrag enthält eine überwiegend historisch vorgehende Entgegnung auf solche fälschlich vertretenen Ansichten wie sie sich auch in dem neu erschienenen (...)
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  • Prelude to Dimension Theory: The Geometrical Investigations of Bernard Bolzano.Dale M. Johnson - 1977 - Archive for History of Exact Sciences 17 (3):261-295.
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  • The Principle of Reductio Ad Absurdum Against a Comparative Background.Janusz Chmielewski - 1978 - Studia Semiotyczne—English Supplement 8:138-222.
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  • The Analytic-Synthetic Distinction and the Classical Model of Science: Kant, Bolzano and Frege.Willem R. De Jong - 2010 - Synthese 174 (2):237 - 261.
    This paper concentrates on some aspects of the history of the analyticsynthetic distinction from Kant to Bolzano and Frege. This history evinces considerable continuity but also some important discontinuities. The analytic-synthetic distinction has to be seen in the first place in relation to a science, i.e. an ordered system of cognition. Looking especially to the place and role of logic it will be argued that Kant, Bolzano and Frege each developed the analytic-synthetic distinction within the same conception of scientific rationality, (...)
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  • The Analytic-Synthetic Distinction and the Classical Model of Science: Kant, Bolzano and Frege.Willem R. de Jong - 2010 - Synthese 174 (2):237-261.
    This paper concentrates on some aspects of the history of the analytic-synthetic distinction from Kant to Bolzano and Frege. This history evinces considerable continuity but also some important discontinuities. The analytic-synthetic distinction has to be seen in the first place in relation to a science, i.e. an ordered system of cognition. Looking especially to the place and role of logic it will be argued that Kant, Bolzano and Frege each developed the analytic-synthetic distinction within the same conception of scientific rationality, (...)
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  • On Defining the Notion of Complete and Immediate Formal Grounding.Francesca Poggiolesi - 2016 - Synthese 193 (10).
    The aim of this paper is to provide a definition of the the notion of complete and immediate formal grounding through the concepts of derivability and complexity. It will be shown that this definition yields a subtle and precise analysis of the concept of grounding in several paradigmatic cases.
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  • The Philosophy of Bernard Bolzano: Logic and Ontology.Raul Corazzon - unknown
    volumes of his work, in his discussions of what underlay a Wissenschaftslehre or theory of science in the sense of his conception; he did so with such purity and scientific strictness, and with such a rich store of original, scientifically confirmed and fruitful thoughts, that we must count him as one of the greatest logicians of all time. He must be placed historically in fairly close proximity to Leibniz, with whom he shares important thoughts and fundamental conceptions, and to whom (...)
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  • Pavel Pudlák. Logical Foundations of Mathematics and Computational Complexity: A Gentle Introduction. Springer Monographs in Mathematics. Springer, 2013. ISBN: 978-3-319-00118-0 ; 978-3-319-00119-7 . Pp. Xiv + 695. [REVIEW]Alasdair Urquhart - 2015 - Philosophia Mathematica 23 (3):435-438.
  • 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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  • The Variety of Consequence, According to Bolzano.Johan Benthem - 1985 - Studia Logica 44 (4):389 - 403.
    Contemporary historians of logic tend to credit Bernard Bolzano with the invention of the semantic notion, of consequence, a full century before Tarski. Nevertheless, Bolzano's work played no significant rôle in the genesis of modern logical semantics. The purpose of this paper is to point out three highly original, and still quite relevant themes in Bolzano's work, being a systematic study of possible types of inference, of consistency, as well as their meta-theory. There are certain analogies with Tarski's concerns here, (...)
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  • Bolzano's Deducibility and Tarski's Logical Consequence.Paul B. Thompson - 1981 - History and Philosophy of Logic 2 (1-2):11-20.
    In this paper I argue that Bolzano's concept of deducibility and Tarski's concept of logical consequence differ with respect to their philosophical intent. I distinguish between epistemic and ontic approaches to logic, and argue that Bolzano's deducibility presupposes an epistemic approach, while Tarski's logical consequence presupposes an ontic approach.
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