Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
Bibliography
Beth, E. W., ‘Semantic Entailment and Formal Derivabflity’, Mededelingen der Koninklijke Nederlandse Akademie van Wetenschappen, Afd. Letterkunde, n. s. 18 (1955), 309–342.
Gentzen, G., ‘Untersuchungen (über das logische Schliessen’, Mathematische Zeitschrift 39 (1934–35), 176–210 and 405–443.
Hilbert, D. and Bernays, P. Grundlagen der Mathematik, Vol. 1, Berlin 1934 and VoL 2, Berlin 1939.
Hintikka, K. J. J., ‘Form and Content in Quantification Theory’, Acta Philosophica Fennica 8 (1955), 7–55.
Jaśkowski, S. ‘On the Rules of Suppositions in Formal Logic’, Studia Logica, Warszawa 1934, 32 pp.
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).
Smullyan, R., ‘Trees and Nest Structures’, J. Symbolic Logic 31 (1966), 303–321.
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.
Surma, S. J., ‘Some Observations on Different Methods of Constxuing Logical Calculi’, Teoria a Metodaf Czechoslovak Academy of Sciences 6 (1974), 37–52.
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.
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.
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.
Wajsberg, M., ‘Automatization of the Three-Valued Propositional Calculus’, Polish Logic, S. McCall (ed.), Oxford 1967, pp. 264 - 284.
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.
Zandarowska, W. ‘On Certain Connections Between Consequence, Inconsistency and Completeness’, (In Polish with English summary), Studia Logica 18 (1966), 165–174.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1981 D. Reidel Publishing Company
About this chapter
Cite this chapter
Surma, S.J. (1981). The Growth of Logic Out of the Foundational Research in Mathematics. In: Agazzi, E. (eds) Modern Logic — A Survey. Synthese Library, vol 149. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9056-2_2
Download citation
DOI: https://doi.org/10.1007/978-94-009-9056-2_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-9058-6
Online ISBN: 978-94-009-9056-2
eBook Packages: Springer Book Archive