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A selective background -- Broadly classical approaches -- Paracompleteness -- More on paracomplete solutions -- Paraconsistent dialetheism. |
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Of course we all know now that mathematics has proved that logic doesn't really make sense, but Etchemendy (philosophy, Stanford Univ.) goes further and challenges the received view of the conceptual underpinnings of modern logic by arguing that Tarski's model-theoretic analysis of logical consequences is wrong. He may have found the soft underbelly of the dead horse. Annotation copyrighted by Book News, Inc., Portland, OR. |
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This volume, the first dedicated and comprehensive companion to medieval logic, covers both the Latin and the Arabic traditions, and shows that they were in fact sister traditions, which both arose against the background of a Hellenistic heritage and which influenced one another over the centuries. A series of chapters by both established and younger scholars covers the whole period including early and late developments, and offers new insights into this extremely rich period in the history of logic. The volume (...) |
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We provide for the first time an exact translation into English of the Polish version of Alfred Tarski's classic 1936 paper, whose title we translate as ?On the Concept of Following Logically?. We also provide in footnotes an exact translation of all respects in which the German version, used as the basis of the previously published and rather inexact English translation, differs from the Polish. Although the two versions are basically identical, to an extent that is even uncanny, we note (...) |
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Much philosophy of logic is shaped, explicitly or implicitly, by the thought that logic is distinctively formal and abstracts from material content. The distinction between formal and material does not appear to coincide with the more familiar contrasts between a priori and empirical, necessary and contingent, analytic and synthetic—indeed, it is often invoked to explain these. Nor, it turns out, can it be explained by appeal to schematic inference patterns, syntactic rules, or grammar. What does it mean, then, to say (...) |
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An examination of the emergence of the phenomenon of deductive argument in classical Greek mathematics. |
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Central topics in medieval logic are here treated in a way that is congenial to the modern reader, without compromising historical reliability. The achievements of medieval logic are made available to a wider philosophical public then the medievalists themselves. The three genres of logica moderna arising in a later Middle Ages are covered: obligations, insolubles and consequences - the first time these have been treated in such a unified way. The articles on obligations look at the role of logical consistence (...) |
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Logical consequence is the relation that obtains between premises and conclusion(s) in a valid argument. Orthodoxy has it that valid arguments are necessarily truth-preserving, but this platitude only raises a number of further questions, such as: how does the truth of premises guarantee the truth of a conclusion, and what constraints does validity impose on rational belief? This volume presents thirteen essays by some of the most important scholars in the field of philosophical logic. The essays offer ground-breaking new insights (...) |
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HISTORICAL INTRODUCTION Although many of the details of the development of logic in the Middle Ages remain to be filled in, it is well known that between ... |
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_ Source: _Volume 56, Issue 3-4, pp 241 - 271 William of Ockham and John Buridan provide different accounts of the distinction between formal and material consequences. Some consequences – in particular, enthymemes – that Ockham would classify as formal would be classified as material by Buridan. This paper explains this taxonomical discrepancy. It identifies the root of the discrepancy not in a difference between Ockham’s and Buridan’s notions of propositional hylomorphism but rather in Ockham’s endorsement of relational characterizations of (...) |
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This chapter provides broad coverage of the notion of logical consequence, exploring its modal, semantic, and epistemic aspects. It develops the contrast between proof-theoretic notion of consequence, in terms of deduction, and a model-theoretic approach, in terms of truth-conditions. The main purpose is to relate the formal, technical work in logic to the philosophical concepts that underlie reasoning. |
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The paper investigates the propriety of applying the form versus matter distinction to arguments and to logic in general. Its main point is that many of the currently pervasive views on form and matter with respect to logic rest on several substantive and even contentious assumptions which are nevertheless uncritically accepted. Indeed, many of the issues raised by the application of this distinction to arguments seem to be related to a questionable combination of different presuppositions and expectations; this holds in (...) |
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_ Source: _Volume 56, Issue 3-4, pp 222 - 240 In medieval theories of consequence, we encounter several criteria of validity. One of these is known as the containment criterion: a consequence is valid when the consequent is contained or understood in the antecedent. The containment criterion was formulated most frequently in the thirteenth and fourteenth centuries, but it can be found in earlier writings as well. In _The Tradition of the Topics in the Middle Ages_, N.J. Green-Pedersen claimed that (...) |
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_ Source: _Volume 56, Issue 3-4, pp 340 - 366 The history of thinking about consequences in the Middle Ages divides into three periods. During the first of these, from the eleventh to the middle of the twelfth century, and the second, from then until the beginning of the fourteenth century, the notion of natural consequence played a crucial role in logic, metaphysics, and theology. The first part of this paper traces the development of the theory of natural consequence in (...) |
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v. 1. On the twelfth century theories of fallacy.--v. 2. The origin and early development of the theory of supposition. |
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_ Source: _Volume 56, Issue 3-4, pp 292 - 319 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 (...) |
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_ Source: _Volume 53, Issue 2-4, pp 353 - 371 While agreeing with Professor D’Ors’ thesis that the notion of logical consequence cannot be exhaustively characterized, I depart from Professor d’Ors’ conclusion that the very notion of good consequence is primitive and can only be identified with the set of acceptable rules of inference, and from his conviction that modal notions such as necessity and impossibility are equivocal and gain such clarity as they have by their interaction with rules of (...) |
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The first full-length study of Robert Kilwardby's commentary on Aristotle's Prior Analytics, based on a study of the medieval manuscripts. |
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_ Source: _Volume 56, Issue 3-4, pp 201 - 221 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. |
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This book presents the first study of the development of the theory of modal syllogistic in the Middle Ages. |
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_ Source: _Volume 56, Issue 3-4, pp 272 - 291 This paper offers an analysis of Marsilius of Inghen’s definition of _consequentia_ and of his treatment of logical validity as presented in the first book of his treatise on _Consequentiae_. Comparing Marsilius of Inghen’s, John Buridan’s, and Albert of Saxony’s theories, the author argues that Marsilius’ account is based on a conception of consequence as a relation of entailment among propositions rather than as a type of conditional sentence and, thus, (...) |
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