Existential Import and Relations of Categorical and Modal Categorical Statements



Year of publication 2018
Type Article in Periodical
Magazine / Source Logic and Logical Philosophy
MU Faculty or unit

Faculty of Arts

Web http://apcz.umk.pl/czasopisma/index.php/LLP/article/view/LLP.2017.026
Doi http://dx.doi.org/10.12775/LLP.2017.026
Keywords existential import; categorical statements; Square of Opposition; properties; quantified modal logic; partiality; type theory
Description 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.
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