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1Loss of vision: How mathematics turned blind while it learned to see more clearlyIn Benedikt Löwe & Thomas Müller (eds.), PhiMSAMP: philosophy of mathematics: sociological aspsects and mathematical practice, College Publications. pp. 87-106. 2010.To discuss the developments of mathematics that have to do with the introduction of new objects, we distinguish between ‘Aristotelian’ and ‘non-Aristotelian’ accounts of abstraction and mathematical ‘top-down’ and ‘bottom-up’ approaches. The development of mathematics from the 19th to the 20th century is then characterized as a move from a ‘bottom-up’ to a ‘top-down’ approach. Since the latter also leads to more abstract objects for which the Aristotelian account of abstraction is not well-suite…Read more
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9BibliographyJournal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 24 (2): 361-396. 1993.
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Philosophy of Mathematics has become a well-established field of philosophical inquiry. And while it is quite common to attribute philosophers before Kant, from Plato through Locke, a philosophy of mathematics, the term itself was not coined before 1800. A longish paper underlying this talk traces the history of the new term and investigates the reasons philosophers and mathematicians had for adopting a new discipline with that name. In terms of its underlying methodology, the paper combines an …Read more
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Remarks on the emergence of the concept “Spielraum” as a foundation for probability theory.
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1The usual, a commentary to trigger discussion.
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A brief presentation on occasion of Carnap’s visit to a meeting of the Indiana Philosophical Association at the same place exactly 75 ago; based on research in the archives of the IPA, the University of Pittsburgh, and the University of Konstanz. The lecture provides some hitherto unknown biographical background, a summary of Carnap's main arguments, and assigns it a place in Carnap's oeuvre.
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29BibliographyJournal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 24 (2): 365-407. 1993.
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14Frank Quinn of Jaffe-Quinn fame worked out the basics of his own account of how mathematical practice should be described and analyzed, partly by historical comparisons with 19th century mathematics, partly by an analysis of contemporary mathematics and its pedagogy. Despite his claim that for this task, "professional philosophers seem as irrelevant as Aristotle is to modern physics," this philosophy talk will provide a critical summary of his main observations and arguments. The goal is to inje…Read more
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18What the title says.
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10Brief review article.
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25Ulrich Pardey, Frege on Absolute and Relative Truth. An Introduction to the Practice of Interpreting Philosophical Texts, History of Analytic Philosophy , Palgrave Macmillian, Basingstoke-New York, 2012, xxiv+242 pp (review)Bulletin of Symbolic Logic 20 (3): 360-362. 2014.
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43Johannes von Kries: A Bio-bibliographyJournal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 47 (1): 217-235. 2016.A short biography of Johannes von Kries, followed by a bibliography of his works, containing more than 70 previously unknown works.
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7Anmerkungen zum Beweis des zweiten Gödelschen UnvollständigkeitssatzesIn Julian Nida-Rümelin & Georg Meggle (eds.), Analyomen 2, Volume I: Logic, Epistemology, Philosophy of Science, De Gruyter. pp. 31-42. 1997.
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43Midwest Workshop PhiloSTEM (Conference Report)The Reasoner 6 (6). 2012.brief conference report.
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23Slides for the second tutorial on Gödel's incompleteness theorems, held at UniLog 5 Summer School, Istanbul, June 24, 2015.
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28While Gödel’s first theorem remains valid under substitution of various provability predicates, Gödel’s second theorem does not. This is one reason to label G1 as “extensional” but to call G2 “intensional.” Although this asymmetry between G1 and G2 is known for long, no satisfying account of G2’s intensionality has been put forward. After briefly reviewing the discussion so far, the paper presents a new analysis based on two observations. First, the underestimated role of provable closure under …Read more
Bernd Buldt
Purdue University Fort Wayne
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Purdue University Fort WayneMathematicsProfessor
Areas of Specialization
Science, Logic, and Mathematics |
History of Western Philosophy |