Skip to main content

Logicism Revisited in the Propositional Fragment of Leśniewski’s Ontology

  • Chapter
  • First Online:
Philosophy of Mathematics Today

Part of the book series: Episteme ((EPIS,volume 22))

Abstract

Although not so popular in the contemporary philosophical and logical scene, logicism dating from Frege and Russell was the first attempt to declare arithmetic as invariantly valid for any model involving an infinite number of individuals.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  • Inoué, T. [1989] A note on Stahl’s opposite system, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 35, 387–390.

    Article  MathSciNet  Google Scholar 

  • Inoué, T. [1991] On rejected formulas — Hintikka formula and Ishimoto formula, (abstract), The Journal of Symbolic Logic, 56, 1129.

    Google Scholar 

  • Inoué, T. [to appear, a] Some topological properties of some class of rejected formulas and satisflable formulas, (abstract), The Journal of Symbolic Logic.

    Google Scholar 

  • Inoué, T. [to appear, b] Partial interpretations of Lesniewski’s epsilon in modal and intentional logics, (abstract) The Journal of Symbolic Logic.

    Google Scholar 

  • Inoué, T., and Ishimoto, A. [1992] Cut elimination theorem and Hilbert-and Gentzen-style axiomatic rejections, Abstracts of Papers Presented to the American Mathematical Society 13, 499–500.

    Google Scholar 

  • Inoué, T., and Ishimoto, A. [in preparation] A uniform formulation of some syllogistic systems with or without Leśniewski’s epsilon, (abstract) The Journal of Symbolic Logic.

    Google Scholar 

  • Inoué, T., and Ishimoto, A. [forthcoming] A Gentzen-type formulation of the Aristotelian syllogistic and axiomatic rejection, in: Ishimoto [forthcoming].

    Google Scholar 

  • Inoué, T., Kobayashi, M., and Ishimoto, A. [forthcoming] Axiomatic rejection for the prepositional fragment of Leśniewski’s ontology.

    Google Scholar 

  • Ishimoto, A. [1970] A Schütte-type formulation of the intuitionistic functional calculus with strong negation, Bulletin of the Tokyo Institute of Technology, 100, 161–189.

    Google Scholar 

  • Ishimoto, A. [1977] A prepositional fragment of Leśniewski’s ontology, Studia Logica, 36, 285–299.

    Article  MathSciNet  Google Scholar 

  • Ishimoto, A., [1986] An idealistic approach to situation semantics, in: M. Nagao (ed.), Language and Artificial Intelligence, Amsterdam: North-Holland, 401–416.

    Google Scholar 

  • Ishimoto, A. [1989] An axiomatization of satisfiability, Memoirs of Iwafd Junior College, 15, 1–6, Iwaki: Iwaki Junior College, [in Japanese].

    Google Scholar 

  • Kanai, N. [1989] The prepositional fragment of Leśniewski’s ontology and its symplified formulation, Philosophy of Science, 21, Tokyo: Waseda University Press, 133–143, [in Japanese].

    Google Scholar 

  • Kleene, S. C, [1952] Permutability of inferences in Gentzen’s calculi LK and LJ, in: S. C. Kleene, Two Papers on the Predicate Calculus, Memoirs of the American Mathematical Society, No. 10, pp. 1–26.

    Google Scholar 

  • Kobayashi, M., and Ishimoto, A. [1982] A prepositional fragment of Leśniewski’s ontology and its formulation by the tableau method, Studia Logica, 41, 181–195.

    Article  MathSciNet  Google Scholar 

  • Łukasiewicz, J. [1951] Aristotel’s Syllogbtic from the Standpoint of Modern Formal Logic, Oxford: Clarendon Press; [French translation by F. Zaslawsky is available].

    MATH  Google Scholar 

  • Luschei, E. C. [1962] The Logical Systems of Leśniewski, Amsterdam: North-Holland, 1962.

    MATH  Google Scholar 

  • Miéville, D. [1984] Un développement des systèmes logiques de Stanislaw Leśniewski, Protothetique-Ontology-Mereology, Bern: Peter Lang.

    Google Scholar 

  • Mints, G. [1992] A Short Introduction to Modal Logic, (CSLI lecture notes, No. 30), Stanford: Center for the Study of Language and Information, Leland Stanford Junior University (distributed: Chicago: University of Chicago Press).

    MATH  Google Scholar 

  • Schütte, K. [1960] Beweistheorie, Berlin: Springer-Verlag.

    MATH  Google Scholar 

  • Schütte, K. [1960] Vollständige Systeme Modaler und Intuitionistischer Logik, Berlin: Springer-Verlag.

    MATH  Google Scholar 

  • Shimidzu, S. [1990] Constructive logic with strong negation, its soundness and completeness, in: A. Ishimoto, (ed.), The Logic of Natural Language and its Ontology, Tokyo: Taga Shuppan, pp. 241–266, [in Japanese].

    Google Scholar 

  • Słupecki, J., [1948] Z badan nad sylogistyka Arystotelesa, Travau de la Société des Sciences et des Letters de Wroclaw, Serie B, no. 6, Wroclaw.

    Google Scholar 

  • Słupecki, J. [1949–50] On Aristotelian syllogistic, Studia Philosophica, 4, 275–300, [English translation of Slupecki [1948]).

    MATH  Google Scholar 

  • Słupecki, J., Bryll, G., and Wybraniec-Skardowska, U. [1971] Theory of rejected propositions I, Studia Logica, 29, 75–123.

    Article  MathSciNet  Google Scholar 

  • Takano, M. [1991] Syntactical proof of translation and separation theorems on subsystems of elementary ontology, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 37, 129–138.

    Article  MathSciNet  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Ishimoto, A. (1997). Logicism Revisited in the Propositional Fragment of Leśniewski’s Ontology. In: Agazzi, E., Darvas, G. (eds) Philosophy of Mathematics Today. Episteme, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5690-5_12

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-5690-5_12

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6400-2

  • Online ISBN: 978-94-011-5690-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics