Existential Import in Avicenna's Modal Logic

Abstract

In this paper, I raise the following problem: what propositions have an import in Avicenna's modal logic? Which ones do not? Starting from the assumption that the singular and quantified propositions have an import if they require the existence of their subject's referent(s) to be true, I first discuss the import of the absolute propositions then I analyze the import of the modal propositions by considering Avicenna's definitions and the relations between these propositions. This leads to the following results: Avicenna's general opinion is that the affirmatives, be they assertoric or modal, have an import while the negatives do not. The possible affirmative propositions are given an import both in the externalist and the internalist post-Avicennan readings, provided that the subject is not impossible. However, the theory is not always clear, for the propositions containing ‘sometimes not’ are given an import, together with the negative necessaries containing ‘as long as it is P’, despite their negative character; the necessary affirmative propositions containing ‘as long as it is P’ are given an import, although they do not require it. In addition, Avicenna's analysis of the special assertorics E and O (containing the internal conditions ‘at some times but not always’) and their contradictories is erroneous, which does not help determine their import. But when correctly analyzed, these special E and O do not have an import, while their contradictories – I and A special assertorics respectively – have an import.

The Modal Logic of Aristotelian Diagrams

“…However, from the twelfth century onwards, philosophers started to make use of these diagrams to explicate their theorizing on modalities as well [2][3][4][5]. Furthermore, historical scholarship has shown that Aristotelian diagrams for modal logic can be reconstructed from the works of many earlier authors, such as Theophrastus [6,7], Chrysippus [8,9], and Avicenna [10,11]. Today, Aristotelian diagrams not only appear in well-known textbooks on modal logic [12,13], but they are also used in applications of modal logic to a variety of philosophical and logical topics, such as paraconsistency [14,15], logic-sensitivity [16][17][18], and theories of truth [19,20].…”

Robert Kilwardby on Negative Judgement

“…This conception of existential import extended to possible things may be of Avicennian influence. On Avicenna's view, seeChatti (2016).40 NLP II:7, 381. That would put Kilwardby at odds with Thomas Aquinas.…”