Leeds, July 2017. “My future son is possibly alive. Existential import in Abelard’s modal logic”.

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Abstract:

The aim of this paper is to investigate the problem of existential import in Abelard’s modal logic, and to ask whether the system of logical relationships that he proposes for modal claims maintains its validity when some of the terms included in these claims are empty. In the following, I first argue that, just as in the case of non-modal propositions, Abelard interprets modal propositions as having existential import, so that it is a necessary condition for propositions like ‘It is possible for my future son to be alive’ or ‘it is necessary that all men are animals’ that their subjects’ referents exist. I then present the schemata of inferences that Abelard proposes to describe the logical behaviour of de rebus modal propositions, and I argue that this system of relations is only valid as long as all the terms contained in the formulas have an existing referent, while its validity is irremediably threatened if non-referring terms are admitted into the picture. I also claim that Abelard was aware of this difficulty (at least in the Logica Ingredientibus), and thus, that he explicitly decided to restrict the validity of his modal system to propositions that do not contain empty terms.

 

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