Prologue

There was a very considerable development of modal logic within the mediaeval Latin tradition both before and rather soon after the translation of Aristotle's Prior Analytics. The subject was explored, largely without benefit of the Prior Analytics, by Abelard and his generation and with the Prior Analytics in hand by Kilwardby and his. By the early fourteenth century we find a good deal of reflection on just what was involved in a modal logic. In particular by this time there are a well-developed propositional logic and a well-developed syllogistic and the question of how modality interacted with each could be and was posed directly. In this chapter I hope first to present a sketch of the semantic and metaphysical foundation of modality as it appeared in the first half of the fourteenth century and then some of the nuts and bolts of modal logic as it was developed by Ockham.

Part I. The Foundation

Something between a Fable and a Fact

Once upon a time, perhaps by the mid- to late thirteenth century, the concept of possibility was intimately connected with that of power – some state of affairs was thought possible just in case it was thought there was some agent who could bring it about. For adherents of the Abrahamic religions the chief among these agents was an omnipotent God. Exactly what omnipotence meant is not entirely clear (it does not seem to require that God be able to make it true that Adam freely eats forbidden fruit, for example) but it at least entailed that if any agent could make or destroy a thing then God could make or destroy that thing. For the Latin West this picture had already been given a vivid and interesting formulation by Anselm of Canterbury and it had been developed in some earlier thirteenth century thinkers, Robert Grosseteste, for example. It remained central until the middle of the fourteenth century when a number of writers, Thomas Bradwardine and Gregory of Rimini notable among them, launched us on a path which broke the connection between possibility and power and eventually replaced it with a conception of possibility as a semantic or logical matter.

The Middle Ages inherited from antiquity an approach to metaphysics which supposed both that, to provide an account of being, one provides a theory of categories, and that a division into substance and accident is fundamental to such an account. During the thousand years between Boethius and Descartes, this fundamental division was subjected to careful scrutiny and modified dramatically. Eventually even the term ‘accident’ was partially eclipsed by a competing term, ‘mode,’ which bespoke a competing metaphysical picture; by the mid-seventeenth century Descartes was able to contrast his ontology of substances and modes with an ontology of substances and “real” accidents.

The doctrine of real accidents that Descartes rejects has two medieval roots. One lies in the related theological mysteries of the Eucharist and the Incarnation, and the other lies in the perceived need for real accidents to account for at least some physical phenomena. This chapter explores how these roots formed and developed, how accidents came to be “real,” and how real accidents came to be perceived as a philosophical mistake.

THE CATEGORIES FRAMEWORK

In his Categories chapter 4, Aristotle lists ten heads under which nouns and adjectives fall: Substance, Quality, Quantity, Relative, Place, Time, Situation, Habit, Action and Passion. Although there is little reason to think Aristotle was wedded to this list, it had special salience in the early medieval period, both because the Categories was translated and commented on by Boethius and because the list was also found in “On the Ten Categories” (De decem categoriae), a work attributed to Augustine (but likely from a hand influenced by Themistius).

Recent interest in John Duns Scotus’s modal theory derives largely from the suggestion that Scotus was the first in the Middle Ages, and perhaps the first ever, to employ a synchronic conception of modality, one that allowed for alternative possibilities at a given time, and from the debate about whether Scotus introduced a notion of logical possibility divorced from any question of what powers there are. These issues interact in the question of whether Scotus had any analogue of the notion of possible world in either the Leibnizian or the late twentieth-century sense. Late medieval interest in Scotus’s modal theory derived largely from its role in his account of divine and human freedom and from the debate about whether possibility itself depended in any way upon God. This discussion attempts to shed some light on these issues and to locate them in the context of the issues in the theory of modality with which Scotus and his contemporaries were themselves concerned.

It would be desirable in an essay of this kind to present a picture of the development of Scotus’s thought about modality, but in the current state of scholarship that is not possible. Despite nearly a century of work by the Scotus Commission and by a number of very able scholars outside it, our understanding of the textual tradition of Scotus’s works remains radically incomplete. In such a situation any hypothesis about the development of Scotus’s modal theory must be highly speculative. In what follows I will not attempt to trace such a development but will attempt to limn the modal theory with which Scotus seems to have been working at the end of his (unfortunately short) life.

Medieval logic begins for most purposes with the work of Boethius, who attempted a Latin rendering of the standard late-antique Greek logic course. As the Boethian treatises began to be more widely studied in the ninth and tenth centuries, an indigenous Latin tradition in logic developed that reached its zenith during the twelfth century in the work of figures like Peter Abelard. It was within this indigenous tradition that the major developments in the medieval theory of inference took place and that the foundations of later pictures of meaning were laid. As the work of the Byzantine grammarian Priscian became known in Western Europe, the grammatical and semantic theory embodied in it fused with the indigenous tradition. The resulting picture was then transformed by a flood of new translations of texts of Aristotle, of Greek commentaries, and of Islamic commentaries and treatises. The thirteenth and fourteenth centuries saw the digestion of this material and its integration into the already existing tradition. Some consequences of this were new theories of the semantic properties of terms (including theories of the analysis of sentences), the development of propositional logic more or less as we know it today, the working out of the theory of the categorical syllogism (including its modal extensions), the flowering of modal logic generally, and the development of a general theory of inference. By the mid-fourteenth century these developments were more or less complete. William Ockham is one of the greatest of the figures who completed them. He is in some ways an idiosyncratic logician, but his importance can hardly be overestimated.

One of the more striking differences between medieval and early modern philosophy is the status accorded the study of the theory of valid arguments. The study of this theory dominated the first two years of a medieval arts curriculum, and its influence permeated university life in the Middle Ages. There is nothing shocking about a medieval theologian who is discussing predestination or the creation of the world in time stopping his argument to spend a folio or two outlining some part of a logical system which he intends to use in resolving the question. It is partly this inter-penetration of logic and substantive philosophical discussion which makes much medieval philosophy seem so familiar to someone brought up in the twentieth-century Anglo-American tradition.

Within early modern philosophy the attitude is very different, an attitude exemplified by Descartes's discussion of the role of deduction in his Regulae: