ABSTRACT: A comprehensive introduction to ancient (western) logic from earliest times to the 6th century CE, with a focus on issues that may be of interest to contemporary logicians and covering important topics in Post-Aristotelian logic that are frequently neglected (such as Peripatetic hypothetical syllogistic, the Stoic axiomatic system of propositional logic and various later ancient developments).
Truth, etc. is a wide-ranging study of ancientlogic based upon the John Locke lectures given by the eminent philosopher Jonathan Barnes in Oxford. The book presupposes no knowledge of logic and no skill in ancient languages: all ancient texts are cited in English translation; and logical symbols and logical jargon are avoided so far as possible. Anyone interested in ancient philosophy, or in logic and its history, will find much to learn and (...) enjoy here. (shrink)
"General Survey. The succession of thinkers and schools. The history of ancient philosophy covers about eleven centuries, from Thales who lived during the sixth century B.C. to Boethius and Simplicius who ﬂourished at the beginning of the sixth A.D. From the point of view of the history of formal logic this long epoch may be divided into three periods. (1) The pre-Aristotelian period, from the beginnings to the time at which Aristotle..
Clashes between bits of non-homogeneous theories inherited from antiquity were an important factor in the formation of medieval theories in logic and grammar, but the traditional categories of Aristotelianism, Stoicism and Neoplatonism are not quite adequate to describe the situation. Neoplatonism is almost irrelevant in logic and grammar, while there might be reasons to introduce a new category, LAS = Late Ancient Standard, with two branches: (1) logical LAS = Aristotle + Boethius, and (2) grammatical LAS (...) = Stoics &c. → Apollonius → Priscian. (shrink)
Susanne Bobzien (1996). Logic. In Simon Hornblower & A. Spawforth (eds.), The Oxford Classical Dictionary, 3rd edition. Oxford University Press.score: 54.0
ABSTRACT: A very brief summary presentation of western ancientlogic for the non-specialized reader, from the beginnings to Boethius. For a much more detailed presentation see my "AncientLogic" in the Stanford Encyclopedia of Philosopy (also on PhilPapers).
The ancient problems of bankruptcy, contested garment, and rights arbitration have generated many studies, debates, and controversy. The objective of this paper is to show that the Shapley value from game theory, measuring the power of each player in a game, may be consistently applied for getting the general one-step solution of all these three problems viewed as -person games. The decision making is based on the same tool, namely the game theory logic based on the use of (...) the Shapley value, but the specific games involved are slightly different in each problem. The kind of claims of the players, the relationship between the given claims and the given resources available, and the particular way of calculating the generalized characteristic function of the game determine the specific type of game which has to be solved in each of the three ancient problems mentioned. The iterative use of the Shapley value may also justify the well-known Aumann-Maschler step-by-step procedure for solving the bankruptcy problem. (shrink)
Machine generated contents note: Introduction; Part I. Truth, Falsehood and Self-Refutation: 1. Preliminaries; 2. A modern approach: Mackie on the absolute self-refutation of 'nothing is true'; 3. Setting the ancient stage: Dissoi Logoi 4.6; 4. Self-refutation and dialectic: Plato; 5. Speaking to Antiphasis: Aristotle; 6. Introducing peritroph: Sextus Empiricus; 7. Augustine's turn; 8. Interim conclusions; Part II. Pragmatic, Ad Hominem and Operational Self-Refutation: 9. Epicurus against the determinist: blame and reversal; 10. Anti-sceptical dilemmas: pragmatic or ad hominem self-refutations?; (...) 11. Must we philosophise? Aristotle's protreptic argument; 12. Augustine's 'Si fallor, sum': how to prove one's existence by Consequentia Mirabilis; 13. A step back: operational self-refutations in Plato; Part III. Scepticism and Self-Refutation: 14. Self-bracketing Pyrrhonism: Sextus Empiricus; 15. Scepticism and self-refutation: looking backwards; Conclusion. (shrink)
ABSTRACT: An introduction to Stoic logic. Stoic logic can in many respects be regarded as a fore-runner of modern propositional logic. I discuss: 1. the Stoic notion of sayables or meanings (lekta); the Stoic assertibles (axiomata) and their similarities and differences to modern propositions; the time-dependency of their truth; 2.-3. assertibles with demonstratives and quantified assertibles and their truth-conditions; truth-functionality of negations and conjunctions; non-truth-functionality of disjunctions and conditionals; language regimentation and ‘bracketing’ devices; Stoic basic principles of (...) propositional logic; 4. Stoic modal logic; 5. Stoic theory of arguments: two premisses requirement; validity and soundness; 6. Stoic syllogistic or theory of formally valid arguments: a reconstruction of the Stoic deductive system, which consisted of accounts of five types of indemonstrable syllogisms, which function as nullary argumental rules that identify indemonstrables or axioms of the system, and four deductive rules (themata) by which certain complex arguments can be reduced to indemonstrables and thus shown to be formally valid themselves; 7. arguments that were considered as non-syllogistically valid (subsyllogistic and unmethodically concluding arguments). Their validity was explained by recourse to formally valid arguments. (shrink)
ABSTRACT: Summary presentation of the surviving logic theories of Philo the Dialectician (aka Philo of Megara) and Diodorus Cronus, including some general remarks on propositional logical elements in their logic, a presentation of their theories of the conditional and a presentation of their modal theories, including a brief suggestion for a solution of the Master Argument.
ABSTRACT: A detailed presentation of Stoic theory of arguments, including truth-value changes of arguments, Stoic syllogistic, Stoic indemonstrable arguments, Stoic inference rules (themata), including cut rules and antilogism, argumental deduction, elements of relevance logic in Stoic syllogistic, the question of completeness of Stoic logic, Stoic arguments valid in the specific sense, e.g. "Dio says it is day. But Dio speaks truly. Therefore it is day." A more formal and more detailed account of the Stoic theory of deduction can (...) be found in S. Bobzien, Stoic Syllogistic, OSAP 1996. (shrink)
The sixteen essays written in honour of Jonathan Barnes for this volume reflect the impressive scope of his contributions to philosophy. Six are on knowledge, five on logic and metaphysics, five on ethics. The volume ranges widely over ancient philosophy, while also finding room for two contemporary papers on truth and vagueness. Aristotle is prominent in eight of the essays; Plato, Sextus Empiricus, the Stoics, the Epicureans, and ancient Greek medical writers are also discussed. The contributors include (...) some of the most distinguished scholars of our time. (shrink)
In this essay, I examine the nature of Chinese logic and Chinese sciences in the history of China. I conclude that Chinese logic is essentially analogical, and that the Chinese did not have theoretical sciences. I then connect these together and explain why the Chinese failed to develop theoretical sciences, even though they enjoyed an advanced civilization and great scientific and technological innovations. This is because a deductive system of logic is necessary for the development of theoretical (...) sciences, and analogical logic cannot provide the deductive connections between a theory and empirical observations required by a theoretical science. This also offers a more satisfactory answer to the long-standing Needham Problem. (shrink)
Original and penetrating, this book investigates of the notion of inference from signs, which played a central role in ancient philosophical and scientific method. It examines an important chapter in ancient epistemology: the debates about the nature of evidence and of the inferences based on it--or signs and sign-inferences as they were called in antiquity. As the first comprehensive treatment of this topic, it fills an important gap in the histories of science and philosophy.
Boethius, the Roman philosopher, was executed for treason and pilloried by modern scholars for misinterpreting Aristotle to the West. This book examines his semantics and logic, attempting to clear his name and lend him new credence.
ABSTRACT: ‘Aristotelian logic’, as it was taught from late antiquity until the 20th century, commonly included a short presentation of the argument forms modus (ponendo) ponens, modus (tollendo) tollens, modus ponendo tollens, and modus tollendo ponens. In late antiquity, arguments of these forms were generally classified as ‘hypothetical syllogisms’. However, Aristotle did not discuss such arguments, nor did he call any arguments ‘hypothetical syllogisms’. The Stoic indemonstrables resemble the modus ponens/tollens arguments. But the Stoics never called them ‘hypothetical syllogisms’; (...) nor did they describe them as ponendo ponens, etc. The tradition of the four argument forms and the classification of the arguments as hypothetical syllogisms hence need some explaining. In this paper, I offer some explanations by tracing the development of certain elements of Aristotle’s logic via the early Peripatetics to the logic of later antiquity. I consider the questions: How did the four argument forms arise? Why were there four of them? Why were arguments of these forms called ‘hypothetical syllogisms’? On what grounds were they considered valid? I argue that such arguments were neither part of Aristotle’s dialectic, nor simply the result of an adoption of elements of Stoic logic, but the outcome of a long, gradual development that begins with Aristotle’s logic as preserved in his Topics and Prior Analytics; and that, as a result, we have a Peripatetic logic of hypothetical inferences which is a far cry both from Stoic logic and from classical propositional logic, but which sports a number of interesting characteristics, some of which bear a cunning resemblance to some 20th century theories. (shrink)
ABSTRACT: Alexander of Aphrodisias’ commentaries on Aristotle’s Organon are valuable sources for both Stoic and early Peripatetic logic, and have often been used as such – in particular for early Peripatetic hypothetical syllogistic and Stoic propositional logic. By contrast, this paper explores the role Alexander himself played in the development and transmission of those theories. There are three areas in particular where he seems to have made a difference: First, he drew a connection between certain passages from Aristotle’s (...) Topics and Prior Analytics and the Stoic indemonstrable arguments, and, based on this connection, appropriated at least four kinds of Stoic indemonstrables as Aristotelian. Second, he developed and made use of a specifically Peripatetic terminology in which to describe and discuss those arguments – which facilitated the integration of the indemonstrables into Peripatetic logic. Third, he made some progress towards a solution to the problem of what place and interpretation the Stoic third indemonstrables should be given in a Peripatetic and Platonist setting. Overall, the picture emerges that Alexander persistently (if not always consistently) presented passages from Aristotle’s logical œuvre in a light that makes it appear as if Aristotle was in the possession of a Peripatetic correlate to the Stoic theory of indemonstrables. (shrink)
An argument for the existence of gods given by the Stoic Diogenes of Babylon and reported by Sextus Empiricus appears to be an ancient version of the ontological argument. In this paper I present a new reconstruction of Diogenes' argument that differs in certain important respects from the reconstruction presented by Jacques Brunschwig. I argue that my reconstruction makes better sense of how Diogenes' argument emerged as a response to an attack on an earlier Stoic argument presented by Zeno (...) of Citium. Diogenes' argument as reconstructed here is an example of a modal ontological argument that makes use of the concept of being of such a nature as to exist. I argue that this concept is a modal concept that is based on the Philonian definition of possibility, and thus that Diogenes' argument is a source of important evidence about the use of non-Stoic modalities in the post-Chrysippean Stoa. I conclude by arguing that the objections made against considering Diogenes' argument as ontological are unfounded and that Diogenes' argument clearly resembles modern versions of modal ontological arguments. (shrink)