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 fineness 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 between impossibility 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. (shrink)

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. -/- . (shrink)

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. (shrink)