Mathematical Logic in the History of Logic: Łukasiewicz’s Contribution and Its Reception

Abstract

Łukasiewicz introduced a new methodological approach to the history of logic. It consists of the use of modern formal logic in the research of the history of logic. Although he was not the first to use formal logic in his historical research, Łukasiewicz was the first who used it consistently and formulated it as a requirement for a historian of logic. The aim of this paper is to present Łukasiewicz's contribution and the history of its formulation. In addition, the paper will present its reception. There are two main themes in Łukasiewicz’s work on the history of logic. He discussed Stoic logic and Aristotle’s syllogistic. The second part of the paper focuses on current reception of Łukasiewicz’s contribution and on the question of whether there is a difference between knowledge about his contribution to Stoic logic and to Aristotle’s syllogistic, given that it has been hypothesised that Łukasiewicz’s contribution is currently more known among Aristotelian scholars than among those who focus on Stoic logic. Based on the papers that have appeared in the last five years at Web of Science and Scopus this hypothesis has not been confirmed.

KEYWORDS:

• Łukasiewicz
• history of logic
• Aristotle’s syllogistic
• Stoic logic
• Aristotle's logic

Acknowledgements

This paper was presented at conferences History of/in the Lvov-Warsaw School, Jan Łukasiewicz: between Lwów, Warsaw, and Dublin and Czech Gathering of Logicians 2023. The author thanks the attendees of the conferences for their valuable remarks. She is also grateful to the two anonymous reviewers of the paper for their helpful comments.

Notes

1 This might seem strange, as there were several books on the history of logic published prior to Łukasiewicz’s. The most famous was Prantl’s Geschichte der Logik im Abendlande [History of Logic in the Occident] (1855). Nonetheless, Bocheński (1961, 6–8) pointed out that Prantl lacked knowledge of logic and that a majority of his remarks were mistaken. Thus, Bocheński argued that Prantl’s work has no scientific value. Nowadays, the evaluation would be less severe, as despite its numerous weaknesses, Prantl’s book is still an impressive collection of ancient and medieval writings. However, his lack of knowledge of logic was the reason why neither Bocheński nor Sobociński saw those contributions as a part of the historiography of logic.

2 Nonetheless, Sobociński (1956, 8–9) argued that Łukasiewicz was not influenced by Mercier, who lectured on logic in Louvain, too, as Mercier was affected mainly by Port Royal Logic, which was essentially burdened by psychologism, according to Łukasiewicz.

3 Łukasiewicz claimed this before the introduction of his many-valued systems of logic.

4 In modern logic, the calculus of terms usually means the predicate calculus. However, in the Lvov-Warsaw School there were two other calculi of terms that were investigated: Leśniewski’s ontology and Aristotle’s syllogistic. Leśniewski and his students focused on the former system, Łukasiewicz and his students on the latter (see Woleński 1999, 81; Łukasiewicz 1929/1963, 103–117).

5 Mates (1953, 70) pointed out that this mistake could be found in the works of ancient authors; in other words, Prantl was not the first one to make it. He claimed that the mistake originated from the confusion between ‘is’ and ‘is true’.

6 I am grateful to the reviewer of my paper that drew my attention to the fact.

7 The list also includes articles published by 2022 as ‘online first’.