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)

This book offers a major reassessment of Peter Abelard's modal logic and theory of modalities, presenting them as far more uniform and consistent than was until now recognized. Irene Binini offers new ways of connecting Abelard's modal views with other parts of his logic, semantics, metaphysics and theology. Further, the work also provides a comprehensive study of the logical context in which Abelard's theories originated and developed, by presenting fresh evidence about many 11th- and 12th-century sources that are still unpublished. (...) This analysis sheds new light on the relations between Abelard and ancient authors such as Aristotle, Boethius, and Priscian, as well as between Abelard and his contemporaries, such as Anselm of Canterbury, William of Champeaux, Joscelin of Soissons, and Alberic of Paris. (shrink)

The identification of two possible readings – de re and de dicto – of modal claims is considered one of the greatest achievements of Abelard’s logic. In the Dialectica and the Logica “Ingredientibus,” Abelard uses this distinction as a basis for his modal semantics and theory of modalities. Rather than focusing on Abelard’s own theory, the aim of this article is to pay attention to a number of sources that – like Abelard’s logical works – are datable to the first (...) decades of the twelfth century, to investigate whether the de re–de dicto distinction was already adopted and debated in them. It argues that, even if there is no systematic theorization of the distinction in these sources, Abelard’s contemporaries put forward a number of questions concerning the syntax and the signification of modal claims that contributed to set the stage for the distinction’s identification and later development. (shrink)

The aim of this paper is to investigate the problem of existential import in Abelard's modal logic, and to ask whether the system of logical relationships that he proposes for modal propositions ma...

Impossible antecedents entered the scene of medieval logic around the 1120s and soon started to dominate this scene, becoming one of the most debated issues from the second half of the twelfth century onwards. This article focuses on theories of counterpossibles from this period and aims to offer an overview of the different responses offered by twelfth-century logicians on whether everything, something, or nothing follows from an impossible statement. Rather than trying to historically reconstruct the positions of the different authors (...) – an operation that may be premature given the insufficient notions we still have of the authorship and dating of sources – I aim to provide a provisional map of the main arguments that were advanced in favour of or against the ex impossibili quodlibet principle. The article also aims to show that the strategies developed by twelfth-century logical schools in their approach to counterpossibles survive in logical discussions of the same topic during the thirteenth and the early fourteenth century, especially in the syncategoremata and sophistaria traditions. (shrink)

Thought experiments are fictional narratives that widen our cognitive horizons both in the sciences and in philosophy. In the present paper we argue that they can perform this function by bringing one’s perspective into view. Despite being traditionally conceived as devices that transmit true propositions to their readers, thought experiments are also particularly apt to express a specific theoretical perspective through the use of imagination. We suggest that this is a significant epistemic feature that is often overlooked in the debate. (...) After presenting our analysis of thought experiments (Section 2) and of the role that imagination plays in them (Section 3), we revisit Galileo Galilei’s use of imaginary cases in light of our account (Section 4). We show that the main aims of Galileo’s thought experiments are to highlight how different perspectives endorsed by fictional characters affect imagination and to invite readers to actively engage in perspectives that are different from their own. This results in a clash of perspectives which plays a crucial epistemic role (Section 5). Readers of thought experiments do not passively absorb information, but critically assess the other’s perspective. In the final part of the paper, we individuate different ways in which readers can react to thought experiments. (shrink)

This article investigates Abelard’s defence of the compatibility between universal bivalence and the existence of future contingent events. It first considers the standard strategy put forward by twelfth-century commentators to solve Aristotle’s dilemma in De Interpretatione 9, which fundamentally relies on Boethius’ distinction between definite and indefinite truth values. Abelard’s own position on the dilemma is then introduced, focusing on a specific deterministic argument considered in his logical works that aims to demonstrate that, given the determinacy of present-tense propositions such (...) as ‘“that Socrates will eat tomorrow” is true’, future contingent events such as that Socrates will eat tomorrow are determinate in advance. In addition to presenting Abelard’s reply to the argument, the article offers an analysis of his notions of contingency, determinacy, and future events, and a comparison between Abelard’s position and other twelfth-century discussions on future contingents. (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)

The notion of nature is central not only to Abelard’s theory of cognition and to his treatment of universals, but also to Abelard’s modal logic, to his discussion of future contingents and to his theory of conditionals. In this essay, I emphasize how the notion of nature—despite its pervasiveness in Abelard’s philosophy and despite the attention that has been paid to it—still raises puzzling questions to interpreters. One of these puzzles has to do with Abelard’s idea that different individuals may (...) be “of a same nature,” a claim that according to some is hardly compatible with the nominalist position he endorsed. Another interpretative issue is raised by Abelard’s claims in De Intellectibus that substances have more than one nature, and that we might consider things as being of a different nature depending on which of their properties we pay attention to. Given Abelard’s essentialist framework, his assertions on the multiplicity of natures associable to a single individual may sound perplexing. Other issues that I take into account are Abelard’s attribution of natures to non-existent things such as chimaeras or horned men, and his remarks concerning the accessibility of natures to our knowledge. (shrink)