Advertisement

Leśniewski, Negation, and the Art of Logical Subtlety

  • Denis Miéville
Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 16)

Leśniewski essentially developed three theories: Protothetic, Ontology, and Mereology. Since his death in 1939, none of the efforts to reawaken interest in Leśniewski have had much success. In spite of his successive burials, I am among those who persevere in thinking that Leśniewski’s systems present more than a merely historical interest. The richness of Leśniewski’s alternative lies in his approach to truth and falsity, the idea of predicative levels and his conception of logic as something which, so to say, freely “expands”. Leśniewski’s systems can be called to task when it comes to the study of formal languages, the development of higher order logics, definitional procedures, the search for extreme metalinguistic rigor and the quest for an ontologically neutral language. In this paper, I focus on the following three issues. First, I consider the question of the number of operators a formal system must or can possess.

Keywords

Formal Language Classical Logic Predicate Logic High Order Logic Singular Proposition 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bain, Alexandre (1875), Logique déductive et logique inductive, vol. 1–2, Paris, Gernier Boillére.Google Scholar
  2. Boole, George (1847), The Mathematical Analysis of Logic, Oxford, Basil Blackwell, 1965.Google Scholar
  3. Castaneda, Hector-Neri (1988), ‘Negations, imperative, colors, indexical properties non-existence, and Russell’s’, in D.F. Austin (ed.), Philosophical Analysis, A Defense by Example, Dordrecht, Kluwer, 169–205.Google Scholar
  4. Corcoran, John (1973), ‘Gaps between logical theory and mathematical practice’, in M. Bunge (ed.), The Methodological Unity of Science, Dordrecht, Reidel, 23–50.Google Scholar
  5. Frey, Louis (1988), ‘De la négation á l’affirmation en logique aristotélicienne’, Travaux du Centre de Recherches Sémiologiques, n 56, 121–138.Google Scholar
  6. Gessler, Nadine (2005), Introduction á l’œuvre de S. Leśniewski III, La Méréologie, Université de Neuchâtel, Travaux de Logique.Google Scholar
  7. Leśniewski, Stanisław (1992), Collected Works 1–2, S.J. Surma, J.T. Srzednicki, D.I. Barnett (eds.), Warsaw/Dordrecht, PWN/Kluwer.Google Scholar
  8. Miéville, Denis (1984), Un développement des systémes logiques de S. Leśniewski. Protothétique. Ontologie. Méréologie, Berne, Lang.Google Scholar
  9. Miéville, Denis (1991), La négation, une étude logique, Université de Neuchâtel, Travaux de Logique 6.Google Scholar
  10. Miéville, Denis (2001), Introduction á l’œuvre de S. Leśniewski I, La protothétique, Université de Neuchâtel, Travaux de Logique.Google Scholar
  11. Miéville, Denis (2004), Introduction á l’œuvre de S. Leśniewski II, L’ontologie, Université de Neuchâtel, Travaux de Logique.Google Scholar
  12. Miéville, Denis (2006), ‘Leśniewski, une maniére originale de penser le métalangage’, in R. Pouivet & M. Rebuschi (eds.), La philosophie en Pologne 1918–1939, Paris, Vrin, 223–246.Google Scholar
  13. Peeters, Marc (2006), Introduction á l’œuvre de S. Leśniewski IV, L’œuvre de jeunesse, Université de Neuchâtel, Travaux de Logique.Google Scholar
  14. Rickey, Frederick (1972), ‘Axiomatic inscriptional syntax, part I, General syntax’, Notre Dame Journal of Formal Logic 13, 1–33.CrossRefGoogle Scholar
  15. Rickey, Frederick (1973), ‘Axiomatic inscriptional syntax, part, II, Syntax of protothetic’, Notre Dame Journal of Formal Logic 14, 1–52.CrossRefGoogle Scholar
  16. Russell, Bertrand (1903), The Principles of Mathematics, London, Allen & Unwin.Google Scholar
  17. Simons, Peter (1987), Parts. A Study in Ontology, Oxford, Clarendon Press.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Denis Miéville
    • 1
  1. 1.Université de Neuchâtel (Suisse)Switzerland

Personalised recommendations