Mediaeval and Renaissance Logic

Dov M. Gabbay, John Woods

• Publisher: North Holland
• Year: 2008
• eBook ISBN: 9780080560854
• Topic: History
• Subtopic: World History
• Index: History

Starting at the very beginning with Aristotle's founding contributions, logic has been graced by several periods in which the subject has flourished, attaining standards of rigour and conceptual sophistication underpinning a large and deserved reputation as a leading expression of human intellectual effort. It is widely recognized that the period from the mid-19th century until the three-quarter mark of the century just past marked one of these golden ages, a period of explosive creativity and transforming insights. It has been said that ignorance of our history is a kind of amnesia, concerning which it is wise to note that amnesia is an illness. It would be a matter for regret, if we lost contact with another of logic's golden ages, one that greatly exceeds in reach that enjoyed by mathematical symbolic logic. This is the period between the 11th and 16th centuries, loosely conceived of as the Middle Ages. The logic of this period does not have the expressive virtues afforded by the symbolic resources of uninterpreted calculi, but mediaeval logic rivals in range, originality and intellectual robustness a good deal of the modern record. The range of logic in this period is striking, extending from investigation of quantifiers and logic consequence to inquiries into logical truth; from theories of reference to accounts of identity; from work on the modalities to the stirrings of the logic of relations, from theories of meaning to analyses of the paradoxes, and more. While the scope of mediaeval logic is impressive, of greater importance is that nearly all of it can be read by the modern logician with at least some prospect of profit. The last thing that mediaeval logic is, is a museum piece.Mediaeval and Renaissance Logic is an indispensable research tool for anyone interested in the development of logic, including researchers, graduate and senior undergraduate students in logic, history of logic, mathematics, history of mathematics, computer science and AI, linguistics, cognitive science, argumentation theory, philosophy, and the history of ideas.- Provides detailed and comprehensive chapters covering the entire range of modal logic - Contains the latest scholarly discoveries and interpretative insights that answer many questions in the field of logic

The development of supposition theory in the later 12^th through 14^th centuries

Terence Parsons

Publisher Summary

This chapter presents an account of some of the main theories of this tradition, often called the “supposition theory.” For want of space, the commonest known themes will be treated, without extensive details of how the theories varied from author to author. The picture given here is then a kind of ideal framework of a large tradition. Supposition is a relation between an expression and what that expression stands for when the expression appears in a proposition. Much of the theory deals in some way with how changes in what a word supposits for affect the truth value of the sentence containing it. The chapter focuses on how changes in supposition can create divergences in truth conditions, and it is applied in analyzing fallacies of ambiguity; sometimes it is treated purely on its own, as a study of how language works. Although the theory is not formulated as a recursive theory of truth conditions, in many cases such a picture seems to lurk in the background.

INTRODUCTION

Soon after the time of Anselm (1033-1109) and Peter Abelard (1079-1142), universities began to be founded. Logic was taught pretty much as it had been before the year 500; it consisted of work from Aristotle’s Categories and On Interpretation, and material from the first few sections of his Prior Analytics. There was also material from the Stoics on propositional logic. In the early 1100’s, western scholars acquired Latin versions of additional work by Aristotle, including his Sophistical Refutations, which dealt extensively with fallacies. This inspired original new work by medieval scholars. Sometime in the 12^th century a number of original texts suddenly appeared containing a fairly extensive group of interrelated theories, usually employing the term ‘supposition’, which means pretty much what we mean by “reference” or “standing for". The texts were similar, expounding much the same doctrines, and often employing the same or closely similar examples. Clearly there was some common source, but the texts themselves contain no indication of the origin of the doctrines, and the early history of the topic is unknown. This essay is an account of some of the main theories of this tradition, often called Supposition Theory. For want of space, the commonest known themes will be treated, without extensive details of how the theories varied from author to author. The picture given here is then a kind of ideal framework of a large tradition.

Supposition is a relation between an expression and what that expression stands for when the expression appears in a proposition. Much of the theory deals in some way with how changes in what a word supposits for affects the truth value of the sentence containing it. It often focuses on how changes in supposition can create divergences in truth conditions, and it is applied in analyzing fallacies of ambiguity; sometimes it is treated purely on its own, as a study of how language works. Although the theory is not formulated as a recursive theory of truth conditions, in many cases such a picture seems to lurk in the background. One central theme is that authors often allude to structural considerations, such as scope, which we now see as a byproduct of a recursive semantics.

Medieval authors did not develop an artificial symbolism, as is the custom today.¹ Instead, they used Latin. But this was “regimented” Latin, which made the language under consideration serve many of the purposes of modern logical notation. For example, it was assumed (or perhaps stipulated) that the left-to-right ordering of signs corresponds to their semantic scope — so that ‘Every donkey not an animal is’ means that no donkey is an animal, and ‘Every donkey an animal not is’ means that for every donkey, there is an animal distinct from it. This was not how ordinary users of Latin understood their language, but it was very useful for logical theory. Also, because of the presence of inflections, Latin has a fairly free word order, so that the direct object can easily precede the subject in a sentence, as in ‘Every donkey some man owns’, giving it scope over the subject. Since English does not allow this, we need an artificial symbolism to permit various scope structures; medieval logicians already had this in their own Latin (properly, and artificially, understood).

Because this is a work on supposition theory, some important and interesting parts of medieval logic will not be addressed. Chief among these are the Insolubles (paradoxes), Obligations (rules for specialized debate), Consequences (general theory of inferences among arbitrary propositions), and Syncategoremata (individual studies of special words, such as ‘both’, ‘ceases’, ‘only’). These will be touched upon only as they bear on Supposition theory. Also, important earlier work, such as that by Abelard, will not be covered.

This essay is based entirely on Latin manuscripts that have been edited and published, and it is based mostly on those works among them that have been translated into English. Each reference to a medieval work is to book, volume, chapter, section, subsection, etc, followed by a page reference to the English translation. Unless otherwise stated, I use the English translations provided in the texts cited.

1 CORE ELEMENTS OF MEDIEVAL LOGIC

Medieval Logic is built on a foundation of logical terminology, principles, and methodology that was contained in the traditional liberal arts, in particular in that part of the Trivium called Logic or Dialectic. This material is mostly from the writings of Aristotle, including also the Stoics and Cicero, much of it as interpreted by Boethius.² This section is devoted to the fundamental parts of logic that medieval logicians accepted as the basis of their work.

I begin with an account of the forms of propositions that constitute the subject matter of Aristotle’s symbolic logic. In keeping with medieval terminology, I use the term ‘proposition’ to refer to what we today would call a meaningful sentence. It stands for a sentence, not for an abstract meaning expressed by a sentence which is named by a that-clause. So ‘Snow is white’ and ‘Scknee ist weiss’ are different propositions.³

1.1 Categorical Propositions

The simplest form of a proposition is a categorical proposition. In fundamental cases this consists of two nouns (the “subject” and the “predicate") separated by the copula (is), with perhaps some other signs (often quantifier words) which “modify” the nouns. Examples are:

Socrates — is — [an] animal.

Every animal — is — [a...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright page
• Preface
• Contributors
• The Latin Tradition of Logic to 1100
• Logic at the Turn of the Twelfth Century
• Peter Abelard and his Contemporaries
• The development of supposition theory in the later 12th through 14th centuries
• The Assimilation of Aristotelian and Arabic Logic up to the Later Thirteenth Century
• Logic and theories of meaning in the late 13th and early 14th century including the modistae
• The nominalist semantics of Ockham and Buridan: A “rational reconstruction”
• Logic in the 14th century after Ockham
• Medieval Modal Theories and Modal Logic
• Treatments of the paradoxes of self-reference
• Developments in the Fifteenth and Sixteenth Centuries
• Relational Logic of Juan Caramuel
• Port Royal: The Stirrings of Modernity
• Index