Le teorie della negazione nel XII secolo e la riscoperta della logica proposizionale
Di Irene Binini
In: Negazione. Storia di un concetto XLVI , No. 2 ( 2017 )
Sezione Saggi / Articles
Keywords: medieval logic, peter abelard, 12th century logic, propositional ￼negation, square of opposition
The article offers a general presentation of Abelard’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 proposi- tions. 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 logic from that of his predecessors. In the first 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 will 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.