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The Square of Opposition Interpreted with a Decidable Modal Logic

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The Square of Opposition: A Cornerstone of Thought

Part of the book series: Studies in Universal Logic ((SUL))

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Abstract

In connection with Aquinas modal interpretation of the square of opposition the paper interprets the 24 syllogistic modes by a decidable modal logic. Those 15 modes which are not making existential presuppositions are theorems of it right away whereas the other 9 modes are theorems when adding the possibility of the antecedent.

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Notes

  1. 1.

    Weingartner [7–9]. Thomas Aquinas [4].

  2. 2.

    Schurz and Weingartner [3].

  3. 3.

    This has been shown in Weingartner [6].

  4. 4.

    Weingartner [5]. This system was called there SS1M.

  5. 5.

    For an exact formulation of these criteria see Weingartner [7] Sect. 2 and [9] Sect. 2.

  6. 6.

    See Weingartner [7] Sect. 4.3 and [8] Sect. 2.4.

  7. 7.

    See Weingartner [7] Sects. 2.1, 2.2 and 4.2, 4.4. and [8] Sect. 2.

  8. 8.

    For studies of Aristotle’s Modal Logic cf. Bochenski [1, 2].

  9. 9.

    Thomas Aquinas, De Propositionibus Modalibus 719–721 [4]. Translation by Bochenski [2], 29.09.

References

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Author information

Authors and Affiliations

  1. Department of Philosophy, University of Salzburg, Franziskanergasse 1, 5020, Salzburg, Austria

    Paul Weingartner

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  1. Paul Weingartner
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Correspondence to Paul Weingartner .

Editor information

Editors and Affiliations

  1. Research Council, University of Brazil, Rio de Janeiro, Brazil

    Jean-Yves BĂ©ziau

  2. Faculty of Philosophy, Pontifical Lateran University, Rome, Italy

    Gianfranco Basti

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Weingartner, P. (2017). The Square of Opposition Interpreted with a Decidable Modal Logic. In: Béziau, JY., Basti, G. (eds) The Square of Opposition: A Cornerstone of Thought. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-45062-9_7

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