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Dubislav and Bolzano

  • Anita KasabovaEmail author
Chapter
Part of the Boston Studies in the Philosophy and History of Science book series (BSPS, volume 273)

Abstract

This chapter deals with Dubislav’s reconstruction of Bolzano’s Kant criticism and his discussion of analyticity and analytic declarative statements (Sätze) which is central to Kant and Bolzano. Dubislav’s views are discussed, namely that Bolzano anticipated modern mathematical logic, his examination of Bolzano’s propositional functions, as well as the implications of other Bolzanian notions, such as derivability and probability. Bolzano’s contributions are reconstructed and situated in the contemporary discussion by Bolzano’s commentators. In regard to Dubislav’s (Erkenntnis 1:408–409, 1931a) account of definition, his interpretation of Bolzano and Bolzano’s replies concerning definition are reconstructed and evaluated. Dubislav brought Bolzano to the attention of the Berlin Group. The aim of this chapter is to reconstruct and evaluate their respective contributions to logic and philosophy for the current discussion in this volume.

Keywords

Compatibility Constraint Sentential Form Propositional Function Declarative Statement Propositional Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Bar-Hillel, Yehoshua. 1950. Bolzano’s definition of analytic propositions. Theoria 16: 91–117; and in Methodos 2: 32–55.Google Scholar
  2. Bar-Hillel, Yehoshua. 1952. Bolzano’s propositional logic. Archiv für mathematische Logik und Grundlagenforschung 1: 305–338.CrossRefGoogle Scholar
  3. Berg, Jan. 1999. Kant über analytische und synthetische Urteile mit Berücksichtigung der Lehren Bolzanos. In Bernard Bolzanos geistiges Erbe für das 21. Jahrhundert, ed. Edgar Morscher, 97–128. Sankt Augustin: Academia.Google Scholar
  4. Bolzano, Berhard. 1810. Beyträge zu einer begründeteren Darstellung der Mathematik (Contributions to a better grounded presentation of mathematics). Prague: Caspar Widtmann.Google Scholar
  5. Bolzano, Berhard. 1831. In Paradoxien des Unendlichen, ed. F. Přihonský. Leipzig: Reclam. 1851.Google Scholar
  6. Bolzano, Berhard. 1837. Wissenschaftslehre. Sulzbach: Seidel.Google Scholar
  7. Corcoran, John. 1993. Meanings of implication. In A philosophical companion to first-order logic, ed. I.G.Richard Hughes, 85–100. Indianapolis: Hackett.Google Scholar
  8. Couturat, Louis. 1905. Les Principes des Mathematiques: avec un appendice sur la philosophie des mathématiques de Kant. Paris: Felix Alcan.Google Scholar
  9. Dubislav, Walter. 1926. Ueber die sogenannten analytischen und synthetischen Urteile. Berlin: Weiß.Google Scholar
  10. Dubislav, Walter. 1929. Ueber Bolzano als Kritiker Kants. Philosophisches Jahrbuch 42: 357–368.Google Scholar
  11. Dubislav, Walter. 1930a. Bolzano, Bernard: Wissenschaftslehre. Erkenntnis 1: 408–409 (book review).CrossRefGoogle Scholar
  12. Dubislav, Walter. 1930b. Diskussion über Wahrscheinlichkeit. Erkenntnis 1: 264–266.Google Scholar
  13. Dubislav, Walter. 1931a. Die definition. Hamburg: Meiner.Google Scholar
  14. Dubislav, Walter. 1931b. Bolzano als Vorläufer der mathematischen Logik. Philosophisches Jahrbuch 44: 448–456.Google Scholar
  15. Dubislav, Walter. 1931c. In Neuer Anti-Kant und Atomenlehre des seligen Bolzano, ed. W. Dubislav, H. Scholz, and Franz Přihonský. Sankt Augustin: Academia. 2003.Google Scholar
  16. Dubislav, Walter. 1931d. Bernard Bolzano in memoriam. Unterrichtsblätter für Mathematik und Naturwissenschaften 37: 340–344.Google Scholar
  17. Dubislav, Walter. 1931e. Bernard Bolzano. Zum 150. Geburtstag des Philosophen. Vossische Zeitung 469, Das Unterhaltungsblatt Nr. 233 vom 5.10.1931.Google Scholar
  18. Dubislav, Walter. 1932. Bemerkungen zur Definitionslehre. Erkenntnis 3: 201–203.CrossRefGoogle Scholar
  19. Etchemendy, John. 1999. The concept of logical consequence. Chicago: CSLI Publications.Google Scholar
  20. Frege, Gottlob. 1892. Über Sinn und Bedeutung. Zeitschrift für Philosophie und philosophische Kritik, NF, 25–50.Google Scholar
  21. Grelling, Kurt. 1932. Bemerkungen zu Dubislavs “Die Definition”. Erkenntnis 3: 189–200.CrossRefGoogle Scholar
  22. Jakobson, Roman. 1980. A glance at the development of semiotics. In Selected writings. Contributions to comparative mythology. Studies in linguistics and philology, ed. Stephen Rudy and Linda R. Waugh, 199–218. Berlin: Walter de Gruyter.Google Scholar
  23. Kant, Immanuel. 1789. In Critique of pure reason, ed. Paul Guyer. Cambridge: Cambridge University Press. 2007.Google Scholar
  24. Kasabova, Anita. 2006. Bolzano’s semiotic method of explication. History of Philosophy Quarterly 3(1): 21–39.Google Scholar
  25. Künne, Wolfgang. 2006. Analyticity and logical truth. From Bolzano to Quine. In The Austrian contribution to analytic philosophy, ed. Mark Textor, 184–249. London/New York: Routledge.Google Scholar
  26. Künne, Wolfgang. 2008. Versuche über Bolzano/Essays on Bolzano. Sankt Augustin: Academia.Google Scholar
  27. Morscher, Edgar (ed.). 1999a. Bernard Bolzanos geistiges Erbe für das 21. Jahrhundert. Sankt Augustin: Academia.Google Scholar
  28. Morscher, Edgar. 1999b. Logische Allgemeingültigkeit. In Bernard Bolzanos geistiges Erbe für das 21 Jahrhundert, ed. Edgar Morscher, 179–206. Sankt Augustin: Academia.Google Scholar
  29. Morscher, Edgar. 2003. Im Spannungsfeld zwischen Kant und Leibniz—eine geistige Standortbestimmung. In Přihonský. xxi–lxxxiv.Google Scholar
  30. Přihonský, Franz. 1850. In Neuer Anti-Kant und die Atomlehre des seligen Bolzano, ed. Edgar Morscher, Christian Thiel, Heinrich Scholz, and Walter Dubislav. Sankt Augustin: Academia. 2003.Google Scholar
  31. Quine, Willard V.O. 1951. Two dogmas of empiricism. Philosophical Review 60: 20–43.CrossRefGoogle Scholar
  32. Rescher, Nicholas. 2006. The Berlin school of logical empiricism and its legacy. Erkenntnis 64: 281–304.CrossRefGoogle Scholar
  33. Sebestik, Jan. 1992. Logique et mathématique chez Bernard Bolzano. Paris: Vrin.Google Scholar
  34. Sebestik, Jan. 2007. Bolzano’s logic. The stanford encyclopedia of philosophy (Spring 2012 Edition, ed. Edward N. Zalta). http://plato.stanford.edu/entries/bolzano-logic/. Accessed 18 April 2012.
  35. Siebel, Mark. 1996. Der Begriff der Ableitbarkeit bei Bolzano. Sankt Augustin: Academia.Google Scholar
  36. Siebel, Mark. 1999. Bolzano über Ableitbarkeit. In Bernard Bolzanos geistiges Erbe für das 21. Jahrhundert, ed. Edgar Morscher, 147–178. Sankt Augustin: Academia.Google Scholar
  37. Siebel, Mark. 2002. Bolzano’s concept of consequence. The Monist 85: 580–599.CrossRefGoogle Scholar
  38. Tarski, Alfred. 1936. On the concept of logical consequence. In Logic, semantics, metamathematics. Papers from 1923 to 1938, 409–420. Indianapolis: Hackett. 1983.Google Scholar
  39. Tatzel, Armin. 2002. Bolzano’s Theory of ground and consequence. Notre Dame Journal of Formal Logic 43(1): 1–25.CrossRefGoogle Scholar
  40. Textor, Mark. 1997. Bolzano’s Sententialism. Grazer philosophische Studien 53: 181–202.Google Scholar
  41. William, Kneale, and Martha Kneale. 1962. The development of logic. Oxford: Oxford University Press.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht. 2013

Authors and Affiliations

  1. 1.Department of AnthropologyNew Bulgarian UniversitySofiaBulgaria

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