Łukasiewicz, determinism, and the four-valued system of logic
-
Zuzana Rybaříková
Abstract
Jan Łukasiewicz is known primarily as the founder of the three-valued system of logic. It is also generally renowned that his reason for introducing many-valued systems of logic was an attempt to refute determinism. When he developed the three-valued and n-valued logic, he employed these systems in his arguments against determinism. On the contrary, Łukasiewicz preferred the four-valued system of logic that is not suitable for a refutation of determinism in his latest period. It seems, however, that determinism still interested Łukasiewicz, as he discussed its denial in his last work, the second edition of the book Aristotle’s syllogistic from the standpoint of modern formal logic. The aim of my paper is to introduce the issue and describe the relation of these two topics primarily in the latest period of Łukasiewicz’s work. There are several possible solutions to the issue. However, Łukasiewicz never addressed the issue clearly in his published works. Therefore, the solutions might be supported or contradicted by his unpublished works in the future.
References
Corcoran, John. 1974. Aristotelian syllogisms: Valid arguments or true universalized conditionals? Mind 83(330). 278–281. https://doi.org/10.1093/mind/lxxxiii.330.278.Search in Google Scholar
Font, Josep Maria & Petr Hájek. 2002. On Łukasiewicz’s four-valued modal logic. Studia Logica 70(2). 157–182. https://doi.org/10.1023/a:1015111314455.10.1023/A:1015111314455Search in Google Scholar
Hoefer, Carl. 2016. Causal determinism. In Edward N. Zalta (ed.), The Stanford encyclopedia of philosophy. https://plato.stanford.edu/archives/spr2016/entries/determinism-causal/ (accessed 2 September 2019).Search in Google Scholar
Kijania-Placek, Katarzyna. 2000. O pojęciu możliwości obustronnej u Łukasiewicza [On pure possibility in Łukasiewicz]. In Jan Hartman, Andrzej Biłat & Krystyna Dulińska (eds.), Filozofia i logika: W stronę Jana Woleńskiego [Philosophy and logic: Jan Woleński’s way], 139–145. Cracow: Aureus.Search in Google Scholar
Lechniak, Marek. 2000. Kilka uwag o Jana Łukasiewicza rozumieniu konieczności [Some remarks about Jan Łukasiewicz’s understanding of necessity]. Roczniki Filozoficzne/Annales De Philosophie/Annals of Philosophy 48(1). 195–221.Search in Google Scholar
Łukasiewicz, Jan. 1957. Aristotle’s syllogistic: From the standpoint of modern formal logic, 2nd edn. Oxford: Clarendon Press.Search in Google Scholar
Łukasiewicz, Jan. 1970a. Farewell lecture by professor Jan Łukasiewicz, delivered in the Warsaw University lecture hall on March 7, 1918. In Ludwik Borkowski (ed.), Selected works, 84–86. Amsterdam & Warsaw: North-Holland & Polish Scientific.Search in Google Scholar
Łukasiewicz, Jan. 1970b. On three-valued logic. In Ludwik Borkowski (ed.), Selected works, 87–88. Amsterdam & Warsaw: North-Holland & Polish Scientific.Search in Google Scholar
Łukasiewicz, Jan. 1970c. On determinism. In Ludwik Borkowski (ed.), Selected works, 110–128. Amsterdam & Warsaw: North-Holland & Polish Scientific.Search in Google Scholar
Łukasiewicz, Jan. 1970d. Philosophical remarks on many-valued systems of propositional logic. In Ludwik Borkowski (ed.), Selected works, 153–178. Amsterdam & Warsaw: North-Holland & Polish Scientific.Search in Google Scholar
Łukasiewicz, Jan. 1970e. Logistic and philosophy. In Ludwik Borkowski (ed.), Selected works, 218–235. Amsterdam & Warsaw: North-Holland & Polish Scientific.Search in Google Scholar
Łukasiewicz, Jan. 1970f. On variable functors of propositional arguments. In Ludwik Borkowski (ed.), Selected works, 311–324. Amsterdam & Warsaw: North-Holland & Polish Scientific.Search in Google Scholar
Łukasiewicz, Jan. 1970g. A system of modal logic. In Ludwik Borkowski (ed.), Selected works, 352–390. Amsterdam & Warsaw: North-Holland & Polish Scientific.Search in Google Scholar
Łukasiewicz, Jan. 1970h. Arithmetic and modal logic. In Ludwik Borkowski (ed.), Selected works, 391–400. Amsterdam & Warsaw: North-Holland & Polish Scientific.Search in Google Scholar
Łukasiewicz, Jan. 1998a. O walce duchowej [About a spiritual war]. In Jacek Juliusz Jadacki (ed.), Logika i metafizyka: Miscellanea [Logic and metaphysics: Miscellanea], 38–41. Warsaw: Wydział Filozofii i Socjologii Uniwersytetu Warszawskiego.Search in Google Scholar
Łukasiewicz, Jan. 1998b. O zasadzie wyłączonego środka [On the principle of excluded middle]. In Jacek Juliusz Jadacki (ed.), Logika i metafizyka: Miscellanea [Logic and metaphysics: Miscellanea], 53. Warsaw: Wydział Filozofii i Socjologii Uniwersytetu Warszawskiego.Search in Google Scholar
Łukasiewicz, Jan. 1998c. O pojęciu możliwości [On the concept of possiblity]. In Jacek Juliusz Jadacki (ed.), Logika i metafizyka: Miscellanea [Logic and metaphysics: Miscellanea], 237–238. Warsaw: Wydział Filozofii i Socjologii Uniwersytetu Warszawskiego.Search in Google Scholar
Łukasiewicz, Jan. 1998d. O pewnym spornym problemie arystitelesowskiej sylogistyki modalnej [On a controversial problem of Aristotle's modal syllogistic]. In Jacek Juliusz Jadacki (ed.), Logika i metafizyka: Miscellanea [Logic and metaphysics: Miscellanea], 252–265. Warsaw: Wydział Filozofii i Socjologii Uniwersytetu Warszawskiego.Search in Google Scholar
Łukasiewicz, Jan. 1998e. O zasadzie sprzeczności u Arystotelesa [On the principle of contradiction in Aristotle]. In Jacek Juliusz Jadacki (ed.), Logika i metafizyka: Miscellanea [Logic and metaphysics: Miscellanea], 345–362. Warsaw: Wydział Filozofii i Socjologii Uniwersytetu Warszawskiego.Search in Google Scholar
Łukasiewicz, Dariusz. 2011. On Jan Łukasiewicz’s many-valued logic and his criticism of determinism. Philosophia Scientae 15(2). 7–20.10.4000/philosophiascientiae.650Search in Google Scholar
Malinowski, Grzegorz. 2006. Logiki wielowartościowe [Many-valued systems of logic]. Warsaw: Państwowe wydawnictwo naukowe.Search in Google Scholar
Quine, Willard Van Orman. 1966. Three grades of modal involvement. In The ways of paradox and other essays, 156–174. New York: Random House.10.2307/j.ctv1pncnhw.28Search in Google Scholar
Smiley, Timothy. 1962. Syllogism and quantification. The Journal of Symbolic Logic 27(1). 58–72. https://doi.org/10.2307/2963679.Search in Google Scholar
Surma, Piotr. 2012. Poglądy filozoficzne Jana Łukasiewicza a logiki wielowartościowe [Jan Łukasiewicz’s philosophical views and many-valued systems of logic]. Warsaw: Semper.Search in Google Scholar
Zawirski, Zygmunt. 1932. Les logiques nouvelles et le champ de leur application. Revue de Métaphysique et de Morale 39(4). 503–519.Search in Google Scholar
© 2021 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Editorial
- An introduction: use and meaning – a special issue of Semiotica devoted to Jerzy Pelc
- Research Articles
- Functional logical semiotics of natural language
- The manner of use, the uses and sub-uses of terms in social sciences: from the functional approach to natural language to applied semiotics and the philosophy of science
- Investigations of an anti-semiote: Stanisław Lem’s semiotic ideas in light of semiotic functionalism of Jerzy Pelc
- Metaphilosophical metamorphoses of analytic philosophy of language
- Four puzzling paragraphs: Frege on ‘≡’ and ‘=’
- On how to legitimately constrain a semantic theory
- Łukasiewicz, determinism, and the four-valued system of logic
- The representation of gappy sentences in four-valued semantics
- Fictional names, their use and pragmatic interpretations
- Names of places
- Groundwork for a pragmatics for formalized languages
- Token reflexivity and logic
- Indexicals and essential demonstrations
- On the logical form and ontology of inferences in conversational implicatures
- Omnipresent meaning-interdependence and ubiquitous analyticity
- Are representations glorified receptors? On use and usage of mental representations
- Sounds and gestures of linguistic reference: the endurance of reality in the poetry of Wallace Stevens
Articles in the same Issue
- Frontmatter
- Editorial
- An introduction: use and meaning – a special issue of Semiotica devoted to Jerzy Pelc
- Research Articles
- Functional logical semiotics of natural language
- The manner of use, the uses and sub-uses of terms in social sciences: from the functional approach to natural language to applied semiotics and the philosophy of science
- Investigations of an anti-semiote: Stanisław Lem’s semiotic ideas in light of semiotic functionalism of Jerzy Pelc
- Metaphilosophical metamorphoses of analytic philosophy of language
- Four puzzling paragraphs: Frege on ‘≡’ and ‘=’
- On how to legitimately constrain a semantic theory
- Łukasiewicz, determinism, and the four-valued system of logic
- The representation of gappy sentences in four-valued semantics
- Fictional names, their use and pragmatic interpretations
- Names of places
- Groundwork for a pragmatics for formalized languages
- Token reflexivity and logic
- Indexicals and essential demonstrations
- On the logical form and ontology of inferences in conversational implicatures
- Omnipresent meaning-interdependence and ubiquitous analyticity
- Are representations glorified receptors? On use and usage of mental representations
- Sounds and gestures of linguistic reference: the endurance of reality in the poetry of Wallace Stevens
