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126Collections in Early BolzanoJournal for the History of Analytical Philosophy 6 (7). 2018.There are quite a few studies on late Bolzano’s notion of a collection (Inbegriff). We try to broaden the perspective by introducing the forerunner of collections in Bolzano’s early writings, namely the entities referred to by expressions with the technical term ‘et’. Special emphasis is laid on the question whether these entities are set-theoretical or mereological plenties. Moreover, similarities and differences to Bolzano’s mature conception are pointed out.
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104Functions in Frege, Bolzano and HusserlHistory and Philosophy of Logic 31 (4): 315-336. 2010.This explorative article is organized around a set of questions concerning the concept of a function. First, a summary of certain general facts about functions that are a common coin in contemporary logic is given. Then Frege's attempt at clarifying the nature of functions in his famous paper Function and Concept and in his Grundgesetze is discussed along with some questions which Freges' approach gave rise to in the literature. Finally, some characteristic uses of functional notions to be found…Read more
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85Richard Tieszen, After Gödel. Platonism and Rationalism in Mathematics and Logic.: Oxford University Press, Oxford, 2011 (review)Husserl Studies 30 (2): 153-162. 2014.It is well known that Husserl, together with Plato and Leibniz, counted among Gödel’s favorite philosophers and was, in fact, an important source and reference point for the elaboration of Gödel’s own philosophical thought. Among the scholars who emphasized this connection we find, as Richard Tieszen reminds us, Gian-Carlo Rota, George Kreisel, Charles Parsons, Heinz Pagels and, especially, Hao Wang. Right at the beginning of After Gödel we read: “The logician who conducted and recorded the most…Read more
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76Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts (edited book)Springer Verlag. 2019.This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover systematic thought on criteria for a suitable foundation in mathematics and philosophical reflections around the mathematical perspectives. The first two sections focus on the two most prominent candida…Read more
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61Logic and philosophy of mathematics in the early HusserlSpringer. 2009.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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57Begründungen bei Bolzano und beim frühen HusserlZeitschrift für Philosophische Forschung 65 (1): 5-27. 2011.Two hundred years ago Bernard Bolzano published a booklet on the philosophy of mathematics that is the first major step forward in this area since Pascal’s De l’esprit géométrique. Following Aristotelian lines Bolzano distinguishes in his opusculum two kinds of proofs, those that simply show that something is the case, and those that explain why something is the case. In his Wissenschaftslehre this contrast reappears as that between derivability and consecutivity . Husserl takes up some of Bolza…Read more
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45Essays on Husserl’s Logic and Philosophy of Mathematics (edited book)Springer Verlag. 2017.Essays on Husserl’s Logic and Philosophy of Mathematics sets out to fill up a lacuna in the present research on Husserl by presenting a precise account of Husserl’s work in the field of logic, of the philosophy of logic and of the philosophy of mathematics. The aim is to provide an in-depth reconstruction and analysis of the discussion between Husserl and his most important interlocutors, and to clarify pivotal ideas of Husserl’s by considering their reception and elaboration by some of his disc…Read more
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40Early Bolzano on ground-consequence proofsBulletin of Symbolic Logic 22 (2): 215-237. 2016.In his earlyContributions to a Better-Grounded Presentation of Mathematics Bernard Bolzano tries to characterizerigorous proofs.Rigorousis,prima facie, any proof that indicates the grounds for its conclusion. Bolzano lists a number of methodological constraints all rigorous proofs should comply with, and tests them systematically against a specific collection of elementary inference schemata that, according to him, are evidently of ground-consequence-kind. This paper intends to give a detailed a…Read more
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39Review of M. Hartimo (ed.), Phenomenology and Mathematics (review)Philosophia Mathematica 22 (1): 126-129. 2014.
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35Husserl on the 'Totality of all conceivable arithmetical operations'History and Philosophy of Logic 27 (3): 211-228. 2006.In the present paper, we discuss Husserl's deep account of the notions of ?calculation? and of arithmetical ?operation? which is found in the final chapter of the Philosophy of Arithmetic, arguing that Husserl is as far as we know the first scholar to reflect seriously on and to investigate the problem of circumscribing the totality of computable numerical operations. We pursue two complementary goals, namely: (i) to provide a formal reconstruction of Husserl's intuitions, and (ii) to demonstrat…Read more
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35Mathesis Universalis, Computability and Proof (edited book)Springer Verlag. 2019.In a fragment entitled Elementa Nova Matheseos Universalis Leibniz writes “the mathesis [...] shall deliver the method through which things that are conceivable can be exactly determined”; in another fragment he takes the mathesis to be “the science of all things that are conceivable.” Leibniz considers all mathematical disciplines as branches of the mathesis and conceives the mathesis as a general science of forms applicable not only to magnitudes but to every object that exists in our imaginat…Read more
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33Notes on Mally’s Deontic Logic and the Collapse of ModalitiesSynthese 190 (18): 4095-4116. 2013.This paper analyzes Mally’s system of deontic logic, introduced in his The Basic Laws of Ought: Elements of the Logic of Willing (1926). We discuss Mally’s text against the background of some contributions in the literature which show that Mally’s axiomatic system for deontic logic is flawed, in so far as it derives, for an arbitrary A, the theorem “A ought to be the case if and only if A is the case”, which represents a collapse of obligation. We then try to sort out and understand which axioms…Read more
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31Relational Theories of Intentionality and the Problem of Non-ExistentsIn Marian David & Mauro Antonelli (eds.), Existence, Fiction, Assumption: Meinongian Themes and the History of Austrian Philosophy, De Gruyter. pp. 1-26. 2016.
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30The Origin of the Logic of Symbolic Mathematics. Edmund Husserl and Jacob Klein (review)History and Philosophy of Logic 34 (2): 187-193. 2013.Burt C. Hopkins, The Origin of the Logic of Symbolic Mathematics. Edmund Husserl and Jacob Klein. Bloomington and Indianapolis: Indiana University Press. 2011. 592 pp. $49.95. ISBN 978-0-253-35671-...
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29Das Problem der apagogischen Beweise in Bolzanos Beyträgen und seiner WissenschaftslehreHistory and Philosophy of Logic 33 (2). 2012.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 conclu…Read more
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29Strenge Beweise und das Verbot der metábasis eis állo génos : Eine Untersuchung zu Bernard Bolzanos Beyträgen zu einer begründeteren Darstellung der MathematikHistory and Philosophy of Logic 33 (1). 2012.In his booklet "Contributions to a better founded presentation of mathematics" of 1810 Bernard Bolzano made his first serious attempt to explain the notion of a rigorous proof. Although the system of logic he employed at that stage is in various respects far below the level of the achievements in his later Wissenschaftslehre, there is a striking continuity between his earlier and later work as regards the methodological constraints on rigorous proofs. This paper tries to give a perspicuous and c…Read more
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28Der Reziprozitätskanon in den Beyträgen_ und in der _WissenschaftslehreZeitschrift für Philosophische Forschung 64 (3): 310-330. 2010.Two centuries ago Bernard Bolzano published his Contributions to a more well-founded presentation of mathematics which Goethe praised as “an opusculum of very high value”. Bolzano still seems to accept the traditional principle that that intension and extension of a concept stand in an inverse relation . In particular he claims that the concept of a genus proximum is always a component of the concept of the species which are subordinated to it. However, this does not harmonize with his simultane…Read more
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27Bolzano und Leibniz über Klarheit und DeutlichkeitArchiv für Geschichte der Philosophie 92 (3): 256-289. 2010.At a time when they had largely fallen into disrepute Bolzano reactivated the distinctions between ‚clear‘ and ‚obscure‘, ‚distinct‘ and ‚confused‘ ideas. In the central sections of this paper I offer a critical reconstruction of the explanations of these pairs of opposita which are to be found in vol. III of Bolzano's monumental Wissenschaftslehre . I then provide a detailed account of its Leibnizian counterparts that were well-known to the ‚Bohemian Leibniz‘, and finally I evaluate Bolzano's c…Read more
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24Husserl and Leibniz: Notes on the Mathesis UniversalisIn Stefania Centrone (ed.), Essays on Husserl’s Logic and Philosophy of Mathematics, Springer Verlag. pp. 1-24. 2017.The notion of mathesis universalis appears in many of Edmund Husserl’s works, where it corresponds essentially to “a universal a priori ontology”. This paper has two purposes; one, largely exegetical, of clarifying how Husserl elaborates on Leibniz’ concept of mathesis universalis and associated notions like symbolic thinking and symbolic knowledge filtering them through the lesson of the so called “bohemian Leibniz”, Bernard Bolzano; another, more properly philosophical, of examining the role t…Read more
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22Consequentia Mirabilis, Antiskeptizismus und Antinomien Über Bolzanos Beweis, daß es wenigstens eine Wahrheit an sich, daß es der Wahrheiten mehre, ja unendlich viele gebeZeitschrift für Philosophische Forschung 66 (4): 539-565. 2012.
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21Mirja Hartimo ed. Phenomenology and Mathematics. Phaenomenologia; 195. Dordrecht: Springer, 2010. ISBN 978-90-481-3728-2 ; 978-90-481-3728-2 ; 978-94-007-3196-7 . Pp. xxv + 222†: Critical Studies/Book Reviews (review)Philosophia Mathematica 22 (1): 126-129. 2014.
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17Husserls Zeichentheorie. Bemerkungen zur Ersten Logischen UntersuchungArchiv für Geschichte der Philosophie 97 (1): 66-96. 2015.Name der Zeitschrift: Archiv für Geschichte der Philosophie Jahrgang: 97 Heft: 1 Seiten: 66-96
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11Husserl and BooleIn Stefania Centrone (ed.), Essays on Husserl’s Logic and Philosophy of Mathematics, Springer Verlag. 2017.We aim at clarifying to what extent the work of the English mathematician George Boole on the algebra of logic is taken into consideration and discussed in the work of early Husserl, focusing in particular on Husserl’s lecture “Über die neueren Forschungen zur deduktiven Logik” of 1895, in which an entire section is devoted to Boole. We confront Husserl’s representation of the problem-solving processes with the analysis of “symbolic reasoning” proposed by George Boole in the Laws of Thought and …Read more
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10Theory of Science, written by Bernard BolzanoGrazer Philosophische Studien 94 (4): 625-637. 2017.
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10Husserl and SchröderIn Stefania Centrone (ed.), Essays on Husserl’s Logic and Philosophy of Mathematics, Springer Verlag. 2017.We aim at clarifying to what extent the work of the German mathematician Ernst Schröder on the algebra of logic is taken into consideration and rehashed in the work of the early Husserl, focusing on Husserl’s 1891 Review of the first volume of Schröder’s monumental Vorlesungen über die Algebra der Logik and on Husserl’s text Der Folgerungskalkül und die Inhaltslogik written in the same year. We will try to show how and why Husserl, while praising Schröder’s calculus, strongly criticizes Schröder…Read more
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8Theory of Science_, _written by Bernard BolzanoNew Content is Available for Grazer Philosophische Studien. forthcoming._ Source: _Page Count 13
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7Edgar Morscher, Normenlogik. Grundlagen – Systeme – Anwendungen. Paderborn, Mentis, 2012. 309 pp., ISBN-13: 978-3897857841 (review)Bulletin of Symbolic Logic 20 (1): 97-98. 2014.
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6Der junge Leibniz und Gott. Der Beweis der Existenz Gottes in der Dissertatio de Arte CombinatoriaStudia Leibnitiana 50 (2): 146-162. 2018.The present paper analyses the proof of the existence of God given by Leibniz in his early work, the Dissertatio de arte combinatoria of 1666. Leibniz delivers a proof by an (infinite) distinction of cases that has not always been recognized by his translators and critics.
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5Das Problem der apagogischen Beweise in Bolzanos Beyträgen_ und seiner _WissenschaftslehreHistory and Philosophy of Logic 33 (2): 127-157. 2012.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 concl…Read more
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5Bolzanos Zeichentheorie. Eine Untersuchung zu § 285 der WissenschaftslehreGrazer Philosophische Studien 83 (1): 171-198. 2011.
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Technische Universität BerlinInstitute for Philosophy, history of literature, science and technologyHeisenberg Stelle
Berlin, Germany
Areas of Specialization
Science, Logic, and Mathematics |
History of Western Philosophy |
Philosophical Traditions |
Philosophy, Misc |