My current research on 12th century logic

My research focuses on medieval theories of modality and modal logic, with a particular attention to 12th century logical debates.

My doctoral thesis offers a major reassessment of Peter Abelard’s theory of necessity and possibility, presenting it as being far more uniform and consistent than was until now recognized, and providing a deeper understanding of the context in which this theory originated. The first part of the thesis offers a formal reconstruction of Abelard’s logic for modal and temporal propositions. Part II discusses Abelard’s theory of the nature and epistemology of modalities, investigating the many implications that modal notions have in his metaphysics and semantics. Part III offers a detailed analysis of Abelard’s theory of contingency, chance and free will, as well as a discussion of Abelard’s arguments against logical and theological determinism.

Many new results are offered in the thesis. First, I showed that the system of logical inferences that Abelard advances for modal propositions, which was considered as a valid system by recent interpreters, preserves its validity only under certain conditions, and particularly under the condition that no empty terms are included in modal claims. This result has been further developed in the article “My future son is possibly alive. Existential import and empty terms in Abelard’s modal logic”, published in 2018 by History and Philosophy of Logic. Second, I observed that Abelard’s discussion on the semantics of modal claims is grounded on a specific theory of the identity and persistence of substances, which had not yet been discussed by interpreters. This theory of identity, along with its connections to Abelard’s modal thought, is discussed in more length in my article “The role of differentiae in Abelard’s arguments for the identity and persistence of substances”, that is currently in publication. Third, I investigated Abelard’s treatment of negation and quantification within his logic for simple and modal proposition. In the article “12th century theories of negation and the re-discovery of propositional logic” (in Italian), I put this theory in comparison with other 12th and 13th century theories on the same subject.

My subsequent research into medieval modal theories has developed in three directions.

– First, I worked on various 12th century logical sources devoted to modal propositions, most of which are still unedited. This resulted in two articles, one dealing with 12th century strategies against logical determinism (currently under review by Vivarium); the other dealing with the origins and development of the de re/de dicto distinction, pre- and after Abelard (this article will be published in a special issue of Vivarium within the proceedings of the conference “The Known and the Unknown” held in Copenhagen in April 2018).

– Second, I compared the views on modality that Abelard expounds in his logical works with the ones he presents in his later theological and ethical works, especially on the topics of divine omnipotence and foreknowledge. This study resulted in one published article “Contingency and divine infallibility in Peter Abelard” (in Italian), presenting Abelard’s arguments against theological determinism and comparing his view with the one held by William of Champeaux.

– Third, I started to study the way in which 12th century modal views influenced later logicians and contributed to fund the notion of “logical possibility” in late 13th and 14th century.

I am currently in the process of integrating the results of my doctoral and postdoctoral research into a single-authored monograph in English, which will focus on 12th century theories of possibility and necessity. The monograph will offer new evidence on many logical sources which are yet unedited and unexplored.

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