Bernard Bolzano: Philosophy and Mathematics

Master of Logic (ILLC) Coordinated Project, University of Amsterdam, January 2018
Arianna Betti

Remember Frege? An English translation from the Fifties made the until then rather unknown, idiosyncratic philosopher and mathematician a star among analytic philosophers. Chances are that history will soon repeat itself in the case of the still little known Prague polymath Bernard Bolzano.

Requirements
None. A philosophy background is likely to be extremely helpful.

Assessment
Final written report and seminar participation.

Themes & Readings & Schedule

Week 1: Introduction: Bolzano’s Universe (January 4th, 2018, 15:30-18:30 ILLC Science Park 107 room F2.02, Amsterdam)

Central piece(s)
  • Betti, Arianna. 2012. “Bolzano’s Universe: Truth, Logic and Metaphysics.” In Categories of Being: Essays on Metaphysics and Logic, edited by Leila Haaparanta and Heikki J. Koskinen, 167–190. Oxford: Oxford University Press.
  • Bolzano, Bernard. 1833. “Einleitung zur Grössenlehre. Zweiter Abschnitt. Von der mathematischen Lehrart” In GRÖSSENLEHRE BERNARD BOLZANO EINLEITUNG ZUR GRÖSSENLEHRE UND ERSTE BEGRIFFE DER ALLGEMEINEN GRÖSSENLEHRE, Nachlass A. Nachgelassene Schriften 7:46–97. Bernard-Bolzano-Gesamtausgabe, Reihe II. Bad Canstatt: Frommann-Holzboog. English translation (‘On the Mathematical Method’) in Bolzano, Bernard. 2004. On the Mathematical Method and Correspondence with Exner: Translated by Paul Rusnock and Rolf George. Leiden. Brill.
Other literature
  • Casari, Ettore. 2016. Bolzano’s Logical System. Oxford University Press.
  • Morscher, Edgar.  2013. “Bernard Bolzano (Stanford Encyclopedia of Philosophy).” https://plato.stanford.edu/entries/bolzano/.
  • Roski, Stefan. 2017. Bolzano’s Conception of Grounding. Frankfurt am Main: Klostermann Verlag. [first and second chapter]

Week 2: Mereology: Sum, Set, Collection, Number (January 11th, 2018, 15:30-18:30 Oude Turfmarkt 141, room 1.01 tbc, Amsterdam)

Central piece(s)
  • Rusnock, Paul. 2013. “On Bolzano’s Concept of a Sum.” History and Philosophy of Logic 34 (2):155–169.
Other literature
  • Behboud, Ali. 1997. “Remarks on Bolzano’s Collections.” Grazer Philosophische Studien 53:109–15.
  • Blok, Johan. 20176. “Bolzano’s Early Quest for A Priori Synthetic Principles – Mereological Aspects of the Analytic-Synthetic Distinction in Kant and the Early Bolzano.” University of Groningen: Groningen.
  • Krickel, F. 1995. Teil Und Inbegriff: Bernard Bolzanos Mereologie. Beiträge Zur Bolzano-Forschung. Academia Verlag.

     

  • Simons, Peter. 1997. “Bolzano on Collections.” Grazer Philosophische Studien 53:87–108.
  • Mancosu, Paolo. 2009. “Measuring the size of infinite collections of natural numbers: Was Cantor’s theory of infinite number inevitable?” The Review of Symbolic Logic 2 (4):612–46. https://doi.org/10.1017/S1755020309990128.
Week 3: Mathematics as a Science: Quantity (January 18th, 2018,15:30-18:30 ILLC Science Park 107 room F2.02, Amsterdam)

Central piece(s)
Other literature (including specifically mathematical concepts)
  • Berg, Jan. 1994. “The Ontological Foundations of Bolzano’s Philosophy of Mathematics.” In Logic and Philosophy of Science in Uppsala, edited by Dag Prawitz and Dag Westerståhl, 265–271. Kluwer Academic Publishers.

Analysis and Bolzano’s Rein Analytischer Beweis (1817)

  • Kitcher, Philip. 1975. “Bolzano’s Ideal of Algebraic Analysis.” Studies in History and Philosophy of Science Part A 6 (3):229.
  • Loeb, Iris, and Stefan Roski. 2014. “The Transition from Formula-Centered to Concept-Centered Analysis: Bolzano’s Purely Analytic Proof as a Case Study.” Philosophia Scientiae 18 (1). http://www.cairn.info/revue-philosophia-scientiae-2014-1-page-113.htm.

The Infinite

Reals and measurable numbers and the continuum
  • Kurka, Petr, and Kateřina Trlifajová. n.d. “On Dynamical Continuum of Bolzano and Cauchy.” http://www.cts.cuni.cz/~kurka/publ.html
  • Rootselaar, B. van. 1964. “Bolzano’s Theory of Real Numbers.” Archive for History of Exact Sciences 2 (2):168–80.
  • Russ, Steve, and Kateřina Trlifajová. 2016. “Bolzano’s Measurable Numbers: Are They Real?” In Research in History and Philosophy of Mathematics, 39–56. Springer.
Geometry
  • Waldegg, Guillermina. 2001. “Ontological Convictions and Epistemological Obstacles in Bolzano’s Elementary Geometry.” Science & Education 10 (4):409–18. https://doi.org/10.1023/A:1011260228649.
  • Johnson, Dale M. 1977. “Prelude to Dimension Theory: The Geometrical Investigations of Bernard Bolzano” 17 (3):261–295.
Week 4: Grounding: Ground-and-Consequence, Explanation, Simplicity, Generality (January 25th, 2018,15:30-18:30 ILLC Science Park 107 room F2.02, Amsterdam)

Central piece(s)
  • Roski, Stefan. 2017. Bolzano’s Conception of Grounding. Frankfurt am Main: Klostermann Verlag (third and fourt chapter).
  • van Wierst, Pauline. 2013. “Salva Veritate – A Master Thesis on Bolzanian Analyticity and Computational Methods within Philosophical Research.” MA Thesis, Amsterdam: Vrije Universiteit Amsterdam.
  • van Wierst, Pauline. 2016. “Explanation: Lessons from Bolzano.” Munich. [draft]

Other literature

  • Centrone, Stefania. 2016. “EARLY BOLZANO ON GROUND-CONSEQUENCE PROOFS.” Bulletin of Symbolic Logic 22 (2):215–37. https://doi.org/10.1017/bsl.2016.1.
  • Poggiolesi, Francesca. 2016a. “On Defining the Notion of Complete and Immediate Formal Grounding.” Synthese 193 (10):3147–67. https://doi.org/10.1007/s11229-015-0923-x.
  • ———. 2016b. “On Constructing a Logic for the Notion of Complete and Immediate Formal Grounding.” Synthese, November, 1–24. https://doi.org/10.1007/s11229-016-1265-z.
  • Textor, Mark. 2013. “Bolzano on Conceptual and Intuitive Truth: The Point and Purpose of the Distinction.” Canadian Journal of Philosophy 43 (1):13–36. https://doi.org/10.1080/00455091.2013.774839.
  • Jong, Willem R de. 2010. “The Analytic-Synthetic Distinction and the Classical Model of Science: Kant, Bolzano and Frege.” Synthese 174 (2):237–261.

Week 5 (29 January): One individual meeting per student on the assignment (January 29th, 2018, 10:00-18:00 ILLC Science Park 107 room F2.02, Amsterdam)

February 2, 2018, 23:59: Deadline Final Assignment
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