The article offers a generalpresentation ofAbelard's theory of negation, focusing in particular on his distinction between separative and extinctive negation and on the way this distinction is applied in his logic for simple and modal propositions. According to recent interpretations, Abelard is the first among medieval logicians to have a clear insight of propositionality and of propositional logic. As Christopher Martin has shown, Abelard's new approach to propositionality is clearly shown from his treatment of negation, and distinguishes his logicfrom that of his predecessors. In thefirst section of the article, I shall offer some reasons to support the interpretation of Abelard's extinctive negation as a propositional operator. Moreover, I will suggest that Abelard's new use of negation enables him to provide a logical system for non-modal claims that is valid even when some of the terms included in the formulas are empty, i.e. also in the case terms lack an existing referent. In the second section, I shall investigate Abelard's treatment of negation in his logic for modal propositions, and I mil highlight some inconsistencies concerning the way Abelard uses negation in this part of his logic. Finally, the third section deals with other medieval sources dating from the second quarter of the twelfth- century and poses the question of the impact that Abelard's theory of negation had on his successors.

Le teorie della negazione nel XII secolo e la riscoperta della logica proposizionale / Binini, I.. - In: VERIFICHE. - ISSN 0391-4186. - 46:2(2017), pp. 53-88.

Le teorie della negazione nel XII secolo e la riscoperta della logica proposizionale

Binini I.
2017

Abstract

The article offers a generalpresentation ofAbelard's theory of negation, focusing in particular on his distinction between separative and extinctive negation and on the way this distinction is applied in his logic for simple and modal propositions. According to recent interpretations, Abelard is the first among medieval logicians to have a clear insight of propositionality and of propositional logic. As Christopher Martin has shown, Abelard's new approach to propositionality is clearly shown from his treatment of negation, and distinguishes his logicfrom that of his predecessors. In thefirst section of the article, I shall offer some reasons to support the interpretation of Abelard's extinctive negation as a propositional operator. Moreover, I will suggest that Abelard's new use of negation enables him to provide a logical system for non-modal claims that is valid even when some of the terms included in the formulas are empty, i.e. also in the case terms lack an existing referent. In the second section, I shall investigate Abelard's treatment of negation in his logic for modal propositions, and I mil highlight some inconsistencies concerning the way Abelard uses negation in this part of his logic. Finally, the third section deals with other medieval sources dating from the second quarter of the twelfth- century and poses the question of the impact that Abelard's theory of negation had on his successors.
Le teorie della negazione nel XII secolo e la riscoperta della logica proposizionale / Binini, I.. - In: VERIFICHE. - ISSN 0391-4186. - 46:2(2017), pp. 53-88.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11381/2889553
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