Discussing modalities in the mid-twelfth century: An introductory study of the Introductiones Montane Maiores, the Summa Periermeneias and the Ars Meliduna on the de re/de dicto distinction

In this article, I bring attention to three interesting, still unexplored discussions on modalities that are found in some logical sources datable in the middle and the second half of the twelfth century. Through the examination of the ‘Introductiones Montane Maiores’, the ‘Summa Periermeneias’ and the ‘Ars Meliduna’, I retrace the different positions that masters of the time had on the syntactic structure of modal propositions and their use in modal syllogistic. My reconstruction particularly focuses on the distinction between de re and de dicto modalities, a distinction that authors in the second half of the century inherited from Abelard and his contemporaries, and further developed to support their grammatical and logical analysis of modals

Medieval Theories on the Conceivability of the Impossible: a Survey of Impossible Positio in Ars Obligatoria during the 13th-14th Centuries

During the 13th century, several logicians in the Latin medieval tradition showed a special interest in the nature of impossibility, and in the different kinds or ‘degrees’ of impossibility that could be distinguished. This discussion resulted in an analysis of the modal concept with a finesse of grain unprecedented in earlier modal accounts. Of the several divisions of the term ‘impossible’ that were offered, one became particularly relevant in connection with the debate on ars obligatoria and positio impossibilis: the distinction between ‘intelligible’ and ‘unintelligible’ impossibilities. In this article, I consider some 13th-century tracts on obligations that provide an account of the relation betweenimpossibility and intelligibility and discuss the inferential principles that are permissible when we reason from an impossible – but intelligible – premise. I also explore the way in which the 13th-century reflection on this topic survives, in a revised form, in some early 14th-century accounts of positio, namely, those of William of Ockham, Roger Swineshead and Thomas Bradwardine

Contingenza e Infallibilità Divina nei Testi Logici di Pietro Abelardo

Abelard takes the existence of contingent events as an evident and indubitable feature of the way things are. As any indeterminist, however, he must deal with several fatalist arguments, aiming to prove that the inevitability of all future events follows from the acceptance of some fundamental principles of logic and theology. In the article, I focus on the arguments for theological determinism that Abelard considers in the Dialectica and the Logica ingredientibus. The purpose of these argu- ments is to show that — because God has already established a providential plan for the world and knows everything that will occur — things cannot but happen in conformity to his knowledge, which is infallible, and according to his providential plan, which is unchangeable. Abelard rejects these arguments as sophistical, and strives to maintain the compatibility between God’s omniscience and the existence of chance and free will. Abelard’s strategy against theological determinism — which is deeply indebted to the one developed by his master, William of Champeaux — is built on a number of principles and rules of inference that are taken from his logic for modal propositions, such as the distinction between the de rebus and de sensu interpretations of modalities

La necessità della natura e la necessità dei dialettici. Un’analisi della distinzione tra necessità assoluta e necessità condizionata tra XI e XII secolo

This essay examines the way in which the modal concept of necessity was discussed and analyzed in some eleventh- and early twelfth-century sources, such as Peter Damian’s De divina omnipotentia, Anselm of Canterbury’s Cur deus homo and several anonymous commentaries on Aristotle’s De interpretatione that were presumably composed in the first two decades of the twelfth century by logicians connected to William of Champeaux’s and Peter Abelard’s milieu. My aim is to offer a comparison of these different sources with respect to their use of the Boethian distinction between two types or kinds of necessity, namely, the “absolute” or “simple” necessity that is involved in statements like “God is necessarily immortal” or “it is necessary for humans to be animals”, and the “conditional” or “temporal” necessity that is at stake when we say, for instance, that someone necessarily walks when he is walking

Riflessioni sul concetto di necessità nella prima metà del XII secolo

In this essay, I consider some logical treatises and commentaries from the first decades of the 12th century (many of which are still unedited) which contain a discussion on modalities and modal logic. After presenting a short catalogue of these sources and a description of their common features, I shall focus on some definitions of the modal term “necessarium” which are provided in them. As we will see, Abelard and logicians of his time advanced three different characterizations of this term: necessity was either defined in terms of unavoidability (ineuitabilitas), or in terms of immutability and omnitemporality (impermutabilitas, sempiternitas), or again in terms of absolute necessity as opposed to conditioned one (necessitas absoluta vs. determinata). I argue that the temporal understanding of necessity in terms of omnitemporality, inherited from ancient sources and extensively used by Abelard and others in the first years of the twelfth-century, started to disappear in texts datable from around the 1120, perhaps due to several difficulties that were related to this definition when applied in logical contexts. I also discuss how the notion of necessitas determinata was used by Abelard’s contemporaries to qualify the modal status of present and past events, which were generally believed to be necessary only in a “weak” and harmless sense that did not prevent them from being contingent

Pietro Abelardo

Questo profilo ripercorre la vita e le opere di Pietro Abelardo (1079-1142), logico francese del XII secolo, mettendo in risalto la profondità e originalità del suo pensiero filosofico, in particolare nei campi della logica e della metafisica. Ampio spazio sarà dato alle molte affinità – riscontrabili a livello sia di contenuto che di metodo filosofico – tra la riflessione di Abelardo e l’approccio analitico contemporaneo, in particolare rispetto al ruolo di rilievo dato alla logica e allo studio del rapporto tra linguaggio naturale e formale, nonché rispetto al rigore dell’argomentazione e all’interesse per gli ambiti di ontologia, semantica e filosofia del linguaggio.The following profile retraces the life and philosophical works of the 12th-century logician Peter Abelard (1079-1142), highlighting the relevance and originality of his thought in the fields of logic and metaphysics. The description particularly focuses on the many affinities that could be established between Abelard's approach to philosophy and the contemporary analytical approach, affinities that are found both at the level of content and at a methodological level. The main parallels that will be considered concern logical questions, and especially the relationship between natural and formal language, as well as the other questions in the fields of ontology, semantics and the philosophy of language

Riflessioni sul concetto di necessità nella prima metà del XII secolo

In this essay, I consider some logical treatises and commentaries from the first decades of the 12th century (many of which are still unedited) which contain a discussion on modalities and modal logic. After presenting a short catalogue of these sources and a description of their common features, I shall focus on some definitions of the modal term “necessarium” which are provided in them. As we will see, Abelard and logicians of his time advanced three different characterizations of this term: necessity was either defined in terms of unavoidability (ineuitabilitas), or in terms of immutability and omnitemporality (impermutabilitas, sempiternitas), or again in terms of absolute necessity as opposed to conditioned one (necessitas absoluta vs. determinata). I argue that the temporal understanding of necessity in terms of omnitemporality, inherited from ancient sources and extensively used by Abelard and others in the first years of the twelfth-century, started to disappear in texts datable from around the 1120, perhaps due to several difficulties that were related to this definition when applied in logical contexts. I also discuss how the notion of necessitas determinata was used by Abelard’s contemporaries to qualify the modal status of present and past events, which were generally believed to be necessary only in a “weak” and harmless sense that did not prevent them from being contingent

Focus on The History of Logical Reasoning

The history of logic – and more specifically the history of logical reasoning, on which the current issue of The Reasoner focuses – is nowadays facing methodological and disciplinary challenges similar to those that other historical studies are also confronting. Many of these challenges have to do with a reconsideration and redefinition of disciplinary boundaries, and thus call into question the very idea of the history of logic as a discipline. To this purpose I have solicited contributions from friends and colleagues, highlighting new research directions in this exciting field