An early anonymous tract on consequences (Paris, BN, lat. 16130, ff. 118va-120vb), translation (original) (raw)
Related papers
The development of the medieval Parisian account of formal consequence
The concept of formal consequence is at the heart of logic today, and by extension, plays an important role in such diverse areas as mathematics, computing, philosophy, and linguistics. In this dissertation, I trace the roots of this concept in medieval logic from Pseudo-Scotus and John Buridan back to the earliest treatises on consequences, and provide translations of the three earliest known treatises on consequences - two anonymous, a third by Walter Burley. Chapter one introduces the reader to the dominant philosophical approaches to formal consequence from the turn of the twentieth century to today. After this, I introduce the account of formal consequence advanced by John Buridan, the medieval predecessor to the semantic account advocated by Tarski and his followers. The second chapter provides a detailed contrast of Buridan's account of formal consequence with those of Tarski, on the one hand, and later classical logic, on the other. Chapter three examines the account of formal consequence in Pseudo-Scotus. I show that Pseudo-Scotus' account is dependent on that of Buridan, and therefore most post-date it. Chapter four examines the account of divided modal consequence in William of Ockham. I show that Ockham's divided modalities are not fully assimilable to narrow-scope propositions of classical modal logic; formalize Ockham's account in an extension of first-order modal logic with restricted quantification; and provide a complete account of relations between two-term divided modal propositions on Ockham's account. Chapter five introduces Walter Burley's thinking about consequences, examining: Burley's division and enumeration of consequences; his distinction between principal and derivative rules licensing good consequences; the relation of the division of consequences into formal and material varieties to Burley's preferred division between natural and accidental consequences; the relation Burley's work bears to Buridan, to the Boethian reception of Aristotle's Topics, and to the earliest treatises on consequences. The final chapter concludes: highlighting the characteristic marks of medieval and modern approaches to consequences relative to each other; summarizing the various developments that led to the adoption of the account of formal consequence epitomized in Buridan's work; and suggesting prospects for recovering the most promising aspects of the medieval treatments of the topic.
Consequence and formality in the logic of Walter Burley
Vivarium, 2018
With William of Ockham and John Buridan, Walter Burley is often listed as one of the most significant logicians of the medieval period. Nevertheless, Burley’s contributions to medieval logic have received notably less attention than those of either Ockham or Buridan. To help rectify this situation, the author here provides a comprehensive examination of Burley’s account of consequences, first recounting Burley’s enumeration, organization, and division of consequences, with particular attention to the shift from natural and accidental to formal and material consequence, and then locating Burley’s contribution to the theory of consequences in the context of fourteenth-century work on the subject, detailing its relation to the earliest treatises on consequences, then to Ockham and Buridan.
Grounding medieval consequence
C. Normore, S. Schmid (eds.), Grounding in Medieval Philosophy (Springer), 2024
Developed out of earlier work on Aristotelian topics, syllogistic, and fallacies, by the early fourteenth century the medieval theory of consequence came to provide the first unified framework for the treatment of inference as such. With this development came the task of unifying the various justifications for inferences treated in earlier frameworks. Prior to the appearance of theories of consequences, the task of providing a real foundation, or grounding, for good inferences is shared between theories of demonstration, such as those provided in commentaries on Aristotle’s Posterior Analytics, and theories of topical inference, passed on to the medievals via Boethius. But by the time of the earliest consequentiae, most consequences were grounded in the theory of supposition, which began its own development in the twelfth century. Secondary literature on supposition has generally held that in the most common form of supposition, personal supposition, a term is taken to stand for individuals falling under it. In this paper, I show that for the earliest consequentiae this is false: prior to William of Ockham’s work, personal supposition could also involve descent to concepts or types falling under a term, previously thought to be the exclusive provision of simple supposition. As such, a greater variety of ways of grounding consequence exists in the period than has hitherto been recognized.
Introduction: Consequences in Medieval Logic
Vivarium, 2018
This paper summarizes medieval definitions and divisions of consequences and explains the import of the medieval development of the theory of consequence for logic today. It then introduces the various contributions to this special issue of Vivarium on consequences in medieval logic.
1. The limitations of Aristotelian syllogistic, and the need for non-syllogistic consequences Medieval theories of consequences are theories of logical validity, providing tools to judge the correctness of various forms of reasoning. Although Aristotelian syllogistic was regarded as the primary tool for achieving this, the limitations of syllogistic with regard to valid non-syllogistic forms of reasoning, as well as the limitations of formal deductive systems in detecting fallacious forms of reasoning in general, naturally provided the theoretical motivation for its supplementation with theories dealing with non-syllogistic, non-deductive, as well as fallacious inferences. We can easily produce deductively valid forms of inference that are clearly not syllogistic, as in propositional logic or in relational reasoning, or even other types of sound reasoning that are not strictly deductively valid, such as enthymemes, probabilistic arguments, and inductive reasoning, while we can just as easily provide examples of inferences that appear to be legitimate instances of syllogistic forms, yet are clearly fallacious (say, because of equivocation). For Aristotle himself, this sort of supplementation of his syllogistic was provided mostly in terms of the doctrine of " immediate inferences " 1 in his On Interpretation, various types of non-syllogistic or even non-deductive inferences in the Topics, and the doctrine of logical fallacies, in his On Sophistical Refutations. Taking their cue primarily from Aristotle (but drawing on Cicero, Boethius, and others as well), medieval logicians worked out in systematic detail various theories of non-syllogistic inferences, sometimes as supplementations of Aristotelian syllogistic, sometimes as merely useful devices taken to be reducible to syllogistic, and sometimes as more comprehensive theories of valid inference, containing syllogistic as a special, and important, case. 2. A brief survey of historical sources Accordingly, the characteristically medieval theories of non-syllogistic inferences were originally inspired by Aristotle's logical works other than his Analytics. Aristotle's relevant ideas were handed down to medieval thinkers by Boethius' translations of and commentaries on Porphyry's Isagoge and Aristotle's Categories and Peri Hermeneias, along with Boethius' own logical works, the most relevant to the development of consequences being his De Hypotheticis Syllogismis and De Topicis Differentiis. As Christopher Martin has convincingly argued, it was not until Abelard's " discovery of propositionality " , that is, the applicability of truth-functional logical operators (in particular, propositional negation and conjunction) to propositions of any complexity, that medieval logicians found the conceptual resources to develop what we would recognize as propositional logic. (Martin, 2009 and 2012) However, Abelard's own project, retaining certain elements of Boethius' non-truth-functional treatment of conditionals, was proven to be inconsistent by 1 In this chapter, I will use this phrase broadly, to refer to medieval doctrines covering logical relations between two categorical propositions sharing both of their terms, viz the doctrine of the Square of Opposition and its expansions as well as the doctrine of conversions.
The medieval theory of consequence
Synthese, 2008
The recovery of Aristotle’s logic during the twelfth century was a great stimulus to medieval thinkers. Among their own theories developed to explain Aristotle’s theories of valid and invalid reasoning was a theory of consequence, of what arguments were valid, and why. By the fourteenth century, two main lines of thought had developed, one at Oxford, the other at Paris. Both schools distinguished formal from material consequence, but in very different ways. In Buridan and his followers in Paris, formal consequence was that preserved under uniform substitution. In Oxford, in contrast, formal consequence included analytic consequences such as ‘If it’s a man, then it’s an animal’. Aristotle’s notion of syllogistic consequence was subsumed under the treatment of formal consequence. Buridan developed a general theory embracing the assertoric syllogism, the modal syllogism and syllogisms with oblique terms. The result was a thoroughly systematic and extensive treatment of logical theory and logical consequence which repays investigation.
John Buridan's Theory of Consequence and his Octagons of Opposition
One of the manuscripts of Buridan’s Summulae contains three figures, each in the form of an octagon. At each node of each octagon there are nine propositions. Buridan uses the figures to illustrate his doctrine of the syllogism, revising Aristotle's theory of the modal syllogism and adding theories of syllogisms with propositions containing oblique terms (such as ‘man’s donkey’) and with ‘propositions of non-normal construction’ (where the predicate precedes the copula). O-propositions of non-normal construction (i.e., ‘Some S (some) P is not’) allow Buridan to extend and systematize the theory of the assertoric (i.e., non-modal) syllogism. Buridan points to a revealing analogy between the three octagons. To understand their importance we need to rehearse the medieval theories of signification, supposition, truth and consequence.