Empty Negations and Existential Import in Aristotle

Abstract

Aristotle draws what are, by our lights, two unusual relationships between predication and existence. First, true universal affirmations carry existential import. If ‘All humans are mortal’ is true, for example, then at least one human exists. And secondly, although affirmations with empty terms in subject position are all false, empty negations are all true: if ‘Socrates’ lacks a referent, then both ‘Socrates is well’ and ‘Socrates is ill’ are false but both ‘Socrates is not well’ and ‘Socrates is not ill’ are true. In this paper, I conjecture that for Aristotle predications have mereological truth conditions: for example, ‘Socrates is pale’ is true just in case Socrates is a part of the mereological sum of pale things. The existential import of universal affirmations and the semantic profile of empty negations follow from this mereological semantics.

La teoría del silogismo simpliciter en Las refutaciones sofísticas de Aristóteles

“…Finalmente, cabe destacar la importancia de la contradicción de las singulares para comprender el importe existencial de la lógica de Aristóteles, en virtud del realismo filosófico que soporta su lógica (cf. Corkum, 2018). La relación de la contradicción de las singulares con la existencia del sujeto se describe de esta manera en Cat 10.13b28-32:…”