Jan Łukasiewicz and the principle of contradiction Heine, Holger

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Heine, Holger
Łukasiewicz, Jan.; Logic, Symbolic and mathematical - History.; principle of contradiction, - non-classical logic, - paraconsistency.
In 1910, the young Polish philosopher and logician Jan Łukasiewicz published a monograph titled O zasadzie sprzeczności u Arystotelesa (The Principle of Contradiction in Aristotle) in which he presents a penetrating critique of the logical and metaphysical foundations of the Aristotelian principle of contradiction and its modern descendants by applying the newly gained analytic tools of early twentieth century formal logic. Remarkably, Łukasiewicz’ aim in 1910 is to develop a non-Aristotelian logic, which he envisions as a formally constructed logic that does not include or endorse the principle of contradiction in its Aristotelian conception. The historical and philosophical importance of Łukasiewicz’ pioneering effort, and the exploration of the philosophical motivations and historical background that informed Łukasiewicz’ early work, are the central concerns of this thesis. The thesis consists of three main parts: I) A complete English translation of Łukasiewicz’ monograph (54,000 words) II) An introduction to Łukasiewicz’ monograph (20,000 words) III) A chapter-by-chapter commentary to Łukasiewicz’ work (66,000 words) (I) Except for a summary of main results of Jan Łukasiewicz’s monograph, which Łukasiewicz published as an article the same year the book appeared, no English translation of his early work has been available for more than a hundred years. The English translation of Łukasiewicz’ monograph included in this thesis presents an important part of the research undertaken for this project and provides the primary text for the discussion and analysis of Łukasiewicz’ work in both the introductory essay and the chapter-by-chapter commentary. (II) The introductory essay “Jan Łukasiewicz and the Principle of Contradiction” identifies and explores several of the most important late nineteenth and early twentieth century philosophical developments that motivated Lukasiewicz’ attempt to develop a Non-Aristotelian logic at the onset of the twentieth century. The discovery of non-Euclidean geometry, the emerging mathematically informed understanding of logic, Russell’s discovery of the paradox of naïve set theory, and Meinong’s object theory—all play a significant part in Łukasiewicz’ analysis of the logical and metaphysical foundations of the Aristotelian principle of contradiction. The main thesis defended in the introductory essay is that Łukasiewicz’ work on the principle of contradiction is best understood as an effort to find a solution to the unresolved questions posed by Hegel’s project of a dialectical logic and its opposition to the traditional Aristotelian conception of the principle of contradiction. In this view, Lukasiewicz’ work is an attempt to resolve the question about Hegel’s dialectical logic and its connection to scientific knowledge—die Logische Frage—but attempts to do so within the philosophical framework of early analytic philosophy and a mathematical understanding of formal logic. (III) Lukasiewicz' book consists of twenty comparatively brief chapters plus one chapter with a summary of his findings. The commentary focuses on issues and problems that are still subject to debate and controversy in contemporary discussions about the philosophy and history of logic.
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