History and Philosophy of Logic 34 (2):101-132 (2013)

Saloua Chatti
University of Tunis
We re-examine the problem of existential import by using classical predicate logic. Our problem is: How to distribute the existential import among the quantified propositions in order for all the relations of the logical square to be valid? After defining existential import and scrutinizing the available solutions, we distinguish between three possible cases: explicit import, implicit non-import, explicit negative import and formalize the propositions accordingly. Then, we examine the 16 combinations between the 8 propositions having the first two kinds of import, the third one being trivial and rule out the squares where at least one relation does not hold. This leads to the following results: (1) three squares are valid when the domain is non-empty; (2) one of them is valid even in the empty domain: the square can thus be saved in arbitrary domains and (3) the aforementioned eight propositions give rise to a cube, which contains two more (non-classical) valid squares and several hexagons. A classical solution to the problem of existential import is thus possible, without resorting to deviant systems and merely relying upon the symbolism of First-order Logic (FOL). Aristotle’s system appears then as a fragment of a broader system which can be developed by using FOL.
Keywords existential import  negation  oppositions
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DOI 10.1080/01445340.2013.764962
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References found in this work BETA

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Citations of this work BETA

Logical Geometries and Information in the Square of Oppositions.Hans5 Smessaert & Lorenz6 Demey - 2014 - Journal of Logic, Language and Information 23 (4):527-565.
Logic in Opposition.Fabien Schang - 2013 - Studia Humana 2 (3):31-45.
Existential Import in Avicenna's Modal Logic.Saloua Chatti - 2016 - Arabic Sciences and Philosophy 26 (1):45-71.

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