Existential Import and Relations of Categorical and Modal Categorical Statements

Jiří Raclavský

DOI: http://dx.doi.org/10.12775/LLP.2017.026


I examine the familiar quadruple of categorical statements “Every F is/is not G.”, “Some F is/is not G.” as well as the quadruple of their modal versions “Necessarily, every F is/is not G.”, “Possibly, some F is/is not G.”. I focus on their existential import and its impact on the resulting Squares of Opposition. Though my construal of existential import follows modern approach, I add some extra details which are enabled by framing my definition of existential import within expressively rich higher-order partial type logic. As regards the modal categorical statements, I find that so-called void properties bring existential import to them, so they are the only properties which invalidate subalternation, and thus also contrariety and subcontrariety, in the corresponding Square of Opposition.


existential import; categorical statements; Square of Opposition; properties; quantified modal logic; partiality; type theory

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