The Growth of Logic Out of the Foundational Research in Mathematics

  • Stanislaw J. Surma
Part of the Synthese Library book series (SYLI, volume 149)


The present day logic takes its origin from too many sources to be justified univocally and exhaustively by referring merely to the particular ones. Mathematics and the foundational studies, singled out as the only major root of logic, prove to be inadequate for the purpose of the justification of our reasoning. Therefore it is quite natural that so much attention has been also paid to the motivation of logic through the philosophical analysis of our knowledge of the external world including the realm of mathematical entities. The third major root of logic lies in the sphere of our intuition. The basic problem here is how and to what extent the intuitive notions of reasoning and its linguistic forms are rendered into logic as a formal system.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Beth, E. W., ‘Semantic Entailment and Formal Derivabflity’, Mededelingen der Koninklijke Nederlandse Akademie van Wetenschappen, Afd. Letterkunde, n. s. 18 (1955), 309–342.Google Scholar
  2. [2]
    Gentzen, G., ‘Untersuchungen (über das logische Schliessen’, Mathematische Zeitschrift 39 (1934–35), 176–210 and 405–443.Google Scholar
  3. [3]
    Hilbert, D. and Bernays, P. Grundlagen der Mathematik, Vol. 1, Berlin 1934 and VoL 2, Berlin 1939.Google Scholar
  4. [4]
    Hintikka, K. J. J., ‘Form and Content in Quantification Theory’, Acta Philosophica Fennica 8 (1955), 7–55.Google Scholar
  5. [5]
    Jaśkowski, S. ‘On the Rules of Suppositions in Formal Logic’, Studia Logica, Warszawa 1934, 32 pp.Google Scholar
  6. [6]
    Pogorzelski, W. A. and Slupecki, J., ‘Basic Properties of Deductive Systems Based on Non-Classical Logics, Part I’ Studia Logica 9 (1960), 163–176. (In Polish with English summary).CrossRefGoogle Scholar
  7. [7]
    Smullyan, R., ‘Trees and Nest Structures’, J. Symbolic Logic 31 (1966), 303–321.CrossRefGoogle Scholar
  8. [8]
    Surma, S. J., ‘On the Relation of Formal Inference and Some Related Concepts’, (In Polish with English summary). Universitas Iagellonica Acta Scientiarum Litterarumque, Schedae Logicae 1 (1964), 37–55.Google Scholar
  9. [9]
    Surma, S. J., ‘Some Observations on Different Methods of Constxuing Logical Calculi’, Teoria a Metodaf Czechoslovak Academy of Sciences 6 (1974), 37–52.Google Scholar
  10. [10]
    Surma, S. J., ‘On the Axiomatic Treatment of the Theory of Models. II: Syn¬tactical Characterization of a Fragment of the Theory of Models’, Universitas Iagellonica Acta Scientiarum Litterarumque, Schedae Logicae 5 (1970), 43–55.Google Scholar
  11. [11]
    Surma, S. J., ‘A Method of the Construction of Finite Lukasiewiczian Algebras and Its Application to a Gentzen-Style Characterization of Finite Logics’, Reports on Mathematical Logic 2 (1974), 49–54.Google Scholar
  12. [12]
    Tarski, A., Über einige fundamental Begriffe der Metamathematik’, Comptes Rendus des Séances de la Societe des Sciences et des Lettres de Varsovie 23 (1930), 22–29.Google Scholar
  13. [13]
    Wajsberg, M., ‘Automatization of the Three-Valued Propositional Calculus’, Polish Logic, S. McCall (ed.), Oxford 1967, pp. 264 - 284.Google Scholar
  14. [14]
    Wybraniec-Skardowska, U., ‘On Mutual Definability of the Notions of Entailment and Inconsistency’, (In Polish with English summary). Zeszyty Naukowe Wyższef Szkoly Pedagogicznej w Opolu, seria Matematyka 15 (1975), 75–86.Google Scholar
  15. [15]
    Zandarowska, W. ‘On Certain Connections Between Consequence, Inconsistency and Completeness’, (In Polish with English summary), Studia Logica 18 (1966), 165–174.CrossRefGoogle Scholar

Copyright information

© D. Reidel Publishing Company 1981

Authors and Affiliations

  • Stanislaw J. Surma
    • 1
  1. 1.Jagiellonian University of CracowPoland

Personalised recommendations