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

Acta Analytica 28 (1):71-93 (2013)
  Copy   BIBTEX


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



    Upload a copy of this work     Papers currently archived: 94,420

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Normatively determined propositions.Matteo Pascucci & Claudio E. A. Pizzi - 2022 - In V. Giardino, S. Linker, S. Burns, F. Bellucci, J. M. Boucheix & P. Viana (eds.), Diagrammatic Representation and Inference. Diagrams 2022. Springer. pp. 78-85.
Two Standard and Two Modal Squares of Opposition.Jiri Raclavsky - 2016 - In Jean-Yves Béziau & Gianfranco Basti (eds.), The Square of Opposition: A Cornerstone of Thought. Basel, Switzerland: Birkhäuser. pp. 119-142.
Probabilistic squares and hexagons of opposition under coherence.Niki Pfeifer & Giuseppe Sanfilippo - 2017 - International Journal of Approximate Reasoning 88:282-294.
Two Concepts of Opposition, Multiple Squares.John T. Kearns - 2012 - In Jean-Yves Béziau & Dale Jacquette (eds.), Around and Beyond the Square of Opposition. Springer Verlag. pp. 119--127.
Oppositional Geometry in the Diagrammatic Calculus CL.Jens Lemanski - 2017 - South American Journal of Logic 3 (2):517-531.


Added to PP

57 (#277,113)

6 months
12 (#311,380)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

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.
Equivalential Structures for Binary and Ternary Syllogistics.Selçuk Topal - 2018 - Journal of Logic, Language and Information 27 (1):79-93.
Natural Density and the Quantifier “Most”.Selçuk Topal & Ahmet Çevik - 2020 - Journal of Logic, Language and Information 29 (4):511-523.

View all 7 citations / Add more citations

References found in this work

Non-standard Analysis.Gert Heinz Müller - 2016 - Princeton University Press.
Critique of Pure Reason.I. Kant - 1787/1998 - Philosophy 59 (230):555-557.
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.

View all 13 references / Add more references