Guido Alt

ABSTRACT In this article I propose an analysis of John Buridan's approach to demonstrations by reductio ad impossibilem, or indirect demonstrations. In distinction to categorical demonstrations, indirect demonstrations involve a conditional with an impossible antecedent. The article addresses the question of how Buridan’s analysis of indirect demonstrations relates to his notorious commitment to the ex impossibili quodlibet (EIQ) principle, as spelled out in his Tractatus de Consequentiis. The first two sections of the article (1-2) describe how Buridan approaches the inferential principles of indirect demonstrations, placing them in the context of his theory of logical consequence. In the remaining two sections (3-4), I investigate some key applications of this form of demonstration in Buridan’s commentary on the seventh book of Physics. The paper concludes that the distinction between counterpossibles about absolute impossibilities and counterpossibles about nomic impossibilities is central for the use of indirect demonstrations in Buridan’s sense.

Most nominalist logicians of the fifteenth and sixteenth centuries believed that we could conceive of and refer to impossible objects. The articulation of the semantics of impossibility that underlined this view is much less known than that of their fourteenth-century predecessors, and it may at first seem to conflict with that tradition’s core principle of theoretical parsimony. Here, I propose a first analysis of John Mair’s case and argue that a central part of that development concerns the theory of signification itself. I will examine his views on empty reference and imaginable impossibilities in relation to John Buridan, Marsilius of Inghen, and John Dorp of Leiden, as well as an anonymous work known as the Hagenau commentary. By doing so, I intend to show that his approach to empty reference is closely connected to issues of conceptual representation.

In his logical treatises, John Mair develops a method and a set of rules for the verification of modal propositions, which is in the spirit of his predecessors Ockham and Buridan, but ultimately goes beyond them. He calls this method positio de inesse. It is also by this method that the truth conditions for divided modal propositions are set out. There is a standard interpretation of it as a form of reductionist method, and scholars have been tempted to think that it was motivated by an implicit rejection of de re modal properties shared by Mair and other sixteenth- century nominalists. After presenting the background to Mair’s writings on the semantics of modal propositions, in this paper we revisit Mair's version of the method of positio de inesse. We argue that it is based on some basic semantic rules and contend that this procedure analyzes divided modal propositions into singular de re sentences referring to possible objects. Consequently, we conclude that this method does not reflect a reductionist approach to modal discourse. We instead provide an alternative interpretation.

O presente artigo investiga a conexão entre modalidade e tempo em dois mestres de artes Parisienses ativos na primeira metade do século 14, João Buridan (c.1290-c.1361) e João de Jandun (c.1286-c.1328). Busca-se elucidar a abordagem de ambos acerca da natureza dessa relação em um conjunto de textos pouco explorados nos debates sobre a interpretação de modalidades medievais, a saber, os comentários ao fim do primeiro livro do De Caelo de Aristóteles. A interpretação da relação entre o ‘necessário’ e o que ‘sempre é’ nesse texto recebera interpretações divergentes sobre a controversa assimilação de necessidade e omnitemporalidade em concepções pré-modernas das modalidades. Por meio da análise do debate em torno das passagens Aristotélicas do De Caelo, posto por ambos os filósofos pertencentes ao milieu da Faculdade de Artes em Paris, o artigo demonstra que tal assimilação não era consensual. Através do contraste entre as análises de Jandun e Buridan, conclui-se que, embora Buridan acomode a necessidade temporal pressuposta no De Caelo enquanto necessidade condicional, ele desenvolve uma crítica da validade geral dos argumentos de Aristóteles no que tange a modalidades absolutas.

This dissertation is a study of John Buridan's (c.1300-c.1361) conception of modalities. Modal concepts - concepts of necessity, possibility, impossibility, and contingency - describe the ways in which things could and could not be otherwise. These concepts became notoriously central for philosophical discourse in the late Middle Ages. In recent years, Buridan's philosophy and modal theory have received sophisticated scholarly attention. The main contribution of the dissertation is to show new ways in which Buridan's modal theory is embedded in its contextual practical aims, as providing methods for argumentation schemes and analysis used in his natural philosophy and metaphysics. The dissertation is divided into two parts. In Part I, I conduct a detailed analysis of Buridan's account of varieties of modality in logical contexts. In Chapter 2, I show that Buridan distinguishes between broad and restricted forms of necessity in his treatment of logical consequence. Moreover, I show how the distinction between these forms of necessity underpins his modal syllogistics. I argue in Chapter 3 that Buridan acknowledged a variety of modal concepts that are distinguished as a matter of degree. I identify the main modal concepts Buridan's theory reckons with, show how he motivates the distinctions among them, and clarify how they are logically related. Part II turns to applications of Buridan's modal analyses to natural philosophy. In Chapter 4, I address the relationship between necessity with sempiternal truth in Buridan's commentary on Aristotle's De Caelo and compare Buridan's treatment of a key passage in that commentary with the treatment by John of Jandun (c. 1285-1328), a near-contemporary master of arts at Paris. Chapter 5 focuses on Buridan's account of the relationship between power-based concepts of modality and his modal semantics. Chapter 6 describes Buridan's account of contingency in the Physics, and sets Buridan's account of the relationship between forms of contingency and chance against the background of a received debate between Avicenna's and Averroes' views on the subject. Finally, in Chapter 7, I analyse some important applications of Buridan's distinction between logical and metaphysical possibility in physical contexts. I conclude this section by showing how Buridan considered merely conceivable possibilities useful in natural philosophy, and draw further conclusions for investigating the connections between logic and natural philosophy in the later Middle Ages.

In his natural philosophy, John Buridan reinterprets Aristotelian conceptions of necessity using a framework derived from his logical writings. After a discussion of Buridan’s account of varieties of necessity, in this paper I shall approach some interpretative uses of that account where two natural philosophical concerns are involved. The first is connected with the relationship of modality and time in a question from the first book of his commentary to De Generatione et Corruptione addressing a consequence from possibilities of alteration to possibilities of generation. The content of that question hinges on the metaphysical connection between alteration and substantial changes. In the third section, I shall explore a quasi-definition of causal necessity and contingency Buridan discusses in the second book of his commentary to the Physics. Buridan’s discussion of alternative descriptions of causal necessity and contingency in that context reveals competing pictures of the role of essences in causal explanation associated with Avicenna and Averroes respectively.