On Two Squares of Opposition: the Leśniewski’s Style Formalization of Synthetic Propositions [Book Review]

Acta Analytica 28 (1):71-93 (2013)
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Abstract

In the paper we build up the ontology of Leśniewski’s type for formalizing synthetic propositions. We claim that for these propositions an unconventional square of opposition holds, where a, i are contrary, a, o (resp. e, i) are contradictory, e, o are subcontrary, a, e (resp. i, o) are said to stand in the subalternation. Further, we construct a non-Archimedean extension of Boolean algebra and show that in this algebra just two squares of opposition are formalized: conventional and the square that we invented. As a result, we can claim that there are only two basic squares of opposition. All basic constructions of the paper (the new square of opposition, the formalization of synthetic propositions within ontology of Leśniewski’s type, the non-Archimedean explanation of square of opposition) are introduced for the first time

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Andrew Schumann
University of Information Technology and Management In Rzeszow

Citations of this work

Duality in Logic and Language.Lorenz Demey, and & Hans Smessaert - 2016 - Internet Encyclopedia of Philosophy.
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Natural Density and the Quantifier “Most”.Selçuk Topal & Ahmet Çevik - 2020 - Journal of Logic, Language and Information 29 (4):511-523.

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Non-standard Analysis.Gert Heinz Müller - 2016 - Princeton University Press.
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Critique of pure reason.Immanuel Kant - 2007 - In Elizabeth Schmidt Radcliffe, Richard McCarty, Fritz Allhoff & Anand Vaidya (eds.), Late modern philosophy: essential readings with commentary. Oxford: Wiley-Blackwell. pp. 449-451.
Aristotle's Syllogistic from the Standpoint of Modern Formal Logic.JAN LUKASIEWICZ - 1951 - Revue de Métaphysique et de Morale 57 (4):456-458.

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