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Modal Logic

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Arabic Logic from al-Fārābī to Averroes

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

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Abstract

Let us start by al-Fārābī’s classification of the modal propositions.

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Notes

  1. 1.

    See ([76]) for the symbols and the equivalences. I have introduced these modern symbols for convenience. These modern symbols can be found in [49] and [96], for instance.

  2. 2.

    On the modal Octagon of Buridan see [124]. On Buridan’s logic in general see [47], [101], and [103]. On Medieval logic, see [106] and on Medieval modal logic see [104].

  3. 3.

    See S. Chatti ([55], 45–71), for a full analysis of these modal propositions.

  4. 4.

    See Chatti [56] in [117] for a full analysis of these propositions and their relations.

  5. 5.

    See ([53], 339–340), for a full analysis of these tables and these relations.

  6. 6.

    See ([53], 332–353).

  7. 7.

    Here what should be written is “neg. necess” instead of “neg. assert” (see [29], 126, and [30], 100).

  8. 8.

    For an account of the conversions in some of Avicenna’s followers, see [140].

  9. 9.

    Here, there is an error in the text, for what is written is “necessarily every B is A.” Thus written, the letters B and A are not in their right places, given that Baroco is a mood of the second figure, i.e., the figure PP; so B is the middle term, and the premise should be rather “necessarily every A is B,” as we have written.

  10. 10.

    See, for instance, Riccardo Strobino in his recent article ([142], Sect. 3.1).

  11. 11.

    Here there is an error in the text, for what is written is “described as B only.” However the right letter should be C, since C is the subject of the proposition.

  12. 12.

    Note here that he does not say “ḍarūrīyya sāliba”, which would be translated by “necessary negative”, but rather “ḍarūrīyyata al-salb”, which I have translated as “necessarily negative.”

  13. 13.

    Even Ip (= I permanent) leads to Iga

  14. 14.

    Here, there is an error of editing since what is written is that “the major premise is a universal necessary negative” ([34], 157.13, my emphasis). But this could not be so, since the mood Ferison is the ninth mood and will be presented and developed by Avicenna at page 158.

  15. 15.

    See Saloua Chatti ([55]), where it is shown that the possible propositions too have an existential import.

  16. 16.

    Here there is an error in the text, not noted by the editor, for what is written is that the minor premise is absolute, but this could not be so, since the conversion leads to a possible minor premise, which with the absolute major leads to an absolute conclusion. Furthermore, the case of the mood with an absolute minor is considered just after the first one, in the sequel, where Avicenna says “If the minor is absolute, then the conclusion is a bilateral possible” ([34], 225.7)

  17. 17.

    With regard to Aristotle’s opinion about the modalities see, for instance, Marko Malink who says in his article “A reconstruction of Aristotle’s Modal Syllogistic” ([113]) the following: “In Aristotle’s modal syllogistic, however, there are no iterable modal sentential operators and, as a consequence, no de dicto modalities.” ([113], 96)

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  1. Faculty of Human and Social Sciences, University of Tunis, Tunis, Tunisia

    Prof. Saloua Chatti

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Chatti, S. (2019). Modal Logic. In: Arabic Logic from al-Fārābī to Averroes . Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-27466-5_4

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