History of Medieval Logic LEM/CNRS/ PSL, Paris Research University, France In the same manner as medieval philosophy, medieval logic includes a large range of cultures and languages in Byzantine, Syriac, Arabic, Hebrew and Latin traditions. It extends from the sixth century to the fifteenth century and beyond, as far as logic alone is concerned. Though challenged by Renaissance logics in the sixteenth century, especially in Reformed countries, and by new logics of discovery designed for the scientific revolution, it survived the collapse of the Aristotelian sciences up till the nineteenth century, under labels such as “scholastic logic”, “Aristotelian logic”, or “traditional logic”. Elaborating from the late ancient legacy accessible to them, that is few sketchy textbooks, some Neoplatonic commentaries to Aristotle’s Organon and a “peripatetized” version of Stoic logic, i.e. “hypothetical syllogistic”, medieval logicians have introduced many novelties nowhere found before and often still discussed today: a sophisticated conception of modalities, a general theory of consequences, the notion of a (contextual) reference, distinct from signification, a distinction between truth-bearers and truth-factors, a focus on the semantics of proper names and indexicals, a disputational, pragmatic, approach to logic, the distinction between the “form” and the “matter” of the arguments within a rich and varied conception of formality, etc. Even if schematic letters have been used, as they were already in Aristotle’s tracts, medieval theories are based upon a regimentation of already regimented natural languages, such as scholastic Latin.
Despite the wealth of discussions and logical innovations found in Arabic logic, the tutorials are essentially dedicated to Latin logicians. They use only English translations and terminology. They will explain and contextualize every reference to authors and texts. Everybody interested in the history of logic is welcome. A drastic selection of topics has been made in a rich history which extends over ten centuries. After a general presentation of medieval Latin logic in context (Session I), I will present only two aspects: theories of consequences (Session II), and theories of reference and truth (Session III).
I. General Presentation of Medieval Logic in Context
Medieval Latin logic can be roughly divided in five periods. They often correspond to a “Renaissance”, that is to a “re-discovery” of ancient texts not yet “available” (translated, circulated, taught, etc.). The High Middle Ages see the domination of a Roman logic (and grammar); the twelfth century witnesses a full Renaissance of logical inquiries based on Aristotle and Boethius (6th century AD) and focussed on “topical inferences”; the thirteenth century can be labelled a “Golden Age” of Aristotelian logic, with a strong focus on the recently rediscovered Prior and the Posterior Analytics; the fourteenth century is extremely innovative and introduces the notion of a general theory of inference; the fifteenth and the sixteenth centuries are a transitional period when the original text of Aristotle’s Organon is rediscovered, and scholastic logic reaches a (too?) high level of sophistication and formalization. It is challenged as “barbarous” and fruitless by Renaissance authors, and tentatively replaced by Renaissance logics. Seven features must be kept in mind when discovering the niceties of medieval logic, many of them closely connected: the exegetical dimension of medieval logic — a feature shared with medieval thought as a whole; the wide range of fields included in what was called “logic” by then (epistemology, philosophy of language, semantics, philosophy of science, etc.) and the strong connection to sister disciplines (rhetoric, grammar, metaphysic); the non-formality of medieval logic, even in its “formal” aspects; the philosophical and scientific orientation of logic as both an instrument for knowledge and a part of philosophy; the non-distinction between logic and philosophy of logic; the disputational approach to logic as a theory and a practice (the latter is also true of medieval university in general); last but not least, the major social and pedagogical role played by logic, before the rise of mathematics as a new standard in educational systems and sciences. This last aspect probably explains the existence of a fairly stable logical culture in the Middle Ages and pre-modern period.
II. Theories of Consequences
This tutorial studies some aspects of the transformation of the discussions about inferences (or “consequences”), deductions, syllogisms, arguments and proofs, from the twelfth to the fifteenth century. All the logicians of the Middle Ages shared an inclusive approach to logic where the study of formal reasoning is only a (small) portion of logic, even within this part of the logical teaching dedicated to the theory of inferences. Each period developed original approaches, which were based not only on a distinctive notion of what should be the basis of a successful inference, with a focus on the problem of relevance, but also on a specific conception of the relationship between inferences, deductions, syllogisms and proofs. In the twelfth century, the notion of “topical inference” means that all inferences, even formal ones, are based upon the topics and general rules derived from them, as described by Boethius (6th c. AD), a conception that survived long in the thirteenth century, despite Abelard (12th c. AD)’s fierce defence of the idea of a purely formal inference, i.e. based only on its form regardless of any content. In the thirteenth century, a “hylomorphic” conception of the syllogism as the subject matter of the Prior Analytics means that syllogistic studies as much the matter as the form of the syllogism. In the fourteenth century, great logicians such as Walter Burleigh, William of Occam, and John Buriban developed general theories of consequences and were very much divided about what can count as a definition of formal consequences. Not before the fourteenth century (with the notable exception of William of Occam) was the syllogism considered a formal inference only, rather than an argument or a proof based upon a formal inference studied regardless of its (particular) contents, a conception recovered at the end of the fifteenth century with the Renaissance rediscovery of Aristotle’s Organon . |
III. Semantic: Reference and Truth
From the twelfth century on, two important topics were discussed in medieval logic: the notion of reference, often contextually understood, and a vigorous debate about the truth-bearers, the propositions and their signification as distinct from that of the terms, as well as the truth-factors, facts and states of affairs. This last aspect underwent original reformulations in the thirteenth century, when the idea that (necessary) universal propositions had existential import was condemned, and in the fourteenth century, especially with Walter Burleigh, who promoted an “extreme realism” and the idea of “propositions in reality”. The medieval theory of reference of terms, called “supposition”, has known two canonical formulation in two distinctive periods, in the thirteenth century “terminist logic” and the famous Tractatus by Peter of Spain, with a strong realistic flavour, and in the fourteenth century in the new, nominalist, terminist logic, where a universal term do not have a referent distinct from the referent of each singular terms to which it corresponds, and where universal propositions do have existential import, though not necessarily for presently existing individuals. The various ways in which the propositions “every man is an animal” and “every man is white” are analysed will be taken as an example of the various approaches to reference, signification and truth in the period. Bibliography
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