Ancient philosophers -- The history of philosophy -- Philosophy within quotation marks? -- Anglophone attitudes -- Brentano's Aristotle -- Heidegger in the cave -- 'There was an old person from Tyre' -- The Presocratics in context -- Argument in ancient philosophy -- Philosophy and dialectic -- Aristotle and the methods of ethics -- Metacommentary -- An introduction to Aspasius -- Parmenides and the Eleatic One -- Reason and necessity in Leucippus -- Plato's cyclical argument -- Death and the philosopher -- (...) Aristotelian arithmetic -- The principle of plenitude -- 'Aristotle's opinion concerning destiny and what is up to us' -- 'Belief is up to us' -- The same again : the Stoics and eternal recurrence -- Bits and pieces -- Partial wholes -- 'Drei Sonnen sah ich ...' : Syrianus and astronomy -- Immaterial causes. (shrink)

Editorial preface to the fourth edition and modified translation -- The text of the Philosophische Untersuchungen -- Philosophische untersuchungen = Philosophical investigations -- Philosophie der psychologie, ein fragment = Philosophy of psychology, a fragment.

The ‘Dialectical school’ denotes a group of early Hellenistic philosophers that were loosely connected by philosophizing in the — Socratic — tradition of Eubulides of Megara and by their interest in logical paradoxes, propositional logic and dialectical expertise. . Its two best known members, Diodorus Cronus and Philo the Logician, made groundbreaking contributions to the development of theories of conditionals and modal logic. Philo introduced a version of material implication; Diodorus devised a forerunner of strict implication. Each developed a system (...) of modal notions that satisfies the basic logical requirements laid down by modern standard modal theories. In antiquity, Diodorus Cronus was famous for his so called Master Argument, which aims to prove that only the actual is possible. (shrink)

Following strict rules of interpretation, this book focuses on the ideas in Plato's early and middle dialogues that lie within the fields now called logic and methodology, specifically elenchus and dialectic and the method of hypothesis.

This book is intended to be used as a textbook by students of mathematics, and also within limitations as a reference work.

This book was designed primarily as a textbook; though the author hopes that it will prove to be of interests to others beside logic students. Part I of this book covers the fundamentals of the subject the propositional calculus and the theory of quantification. Part II deals with the traditional formal logic and with the developments which have taken that as their starting-point. Part III deals with modal, three-valued, and extensional systems.

De Interpretatione is among Aristotle's most influential and widely read writings; C. W. A. Whitaker presents the first systematic study of this work, and offers a radical new view of its aims, its structure, and its place in Aristotle's system. He shows that De Interpretatione is not a disjointed essay on ill-connected subjects, as traditionally thought, but a highly organized and systematic treatise on logic, argument, and dialectic.

This paper is an attempt so to construe the arguments of the Hippias Minor as to remove the justification for regarding it as unworthy of Plato either because of its alleged fallaciousness and Sophistic mode of argument or because of its alleged immorality. It focuses, therefore, only on the arguments and their conclusions, steering clear of the dialogue's dramatic and literary aspects. Whereas I do not wish to deny the importance of these aspects to a proper understanding of the dialogue (...) – on the contrary, in a dialogue so heavily laden with irony and caricature, these aspects are necessarily more significant than they are in other dialogues – I do think there is something to be gained from concentrating on the arguments themselves. Although there can be little doubt that Socrates is up to something in the Hippias Minor, the task of determining just what he is up to can only be simplified by clarifying the arguments first.The Hippias Minor has traditionally been thought to contain two independent arguments, each having its own paradoxical conclusion. The first argument begins, it is said, when Hippias characterizes the two Homeric heroes Achilles and Odysseus as the true man and the false man respectively. Through its discovery that both the false man and the true man have δύναμις, it results in the paradox that the false man and the true are identical. The second argument, on this view, leaves the subject of ⋯ ⋯ληθ⋯ς and ⋯ ψευδ⋯ς and compares instead all sorts of agents in intentional and unintentional action. Finding that the intentional agent is in every case better than the unintentional, the argument concludes that the intentional evil-doer is also better than the unintentional. Viewing the dialogue as thus containing two distinct topics treated in two self-sufficient arguments is perhaps not the best way to understand it. (shrink)

Putnam discusses each of the fifteen odes found in the book, studying the work both as a whole and as a series of interactive units.

Recently logic has shifted emphasis from static systems developed for purely theoretical reasons to dynamic systems designed for application to real world situations. The emphasis on the applied aspects of logic and reasoning means that logic has become a pragmatic tool, to be judged against the backdrop of a particular application. This shift in emphasis is, however, not new. A similar shift towards “interactive logic” occurred in the high Middle Ages. We provide a number of different examples of “interactive logic” (...) in the Middle Ages, all species of the disputation game obligatio. These games display a recognition of the importance of interaction in logical contexts and the way that interactive logic differs from single-agent inference. (shrink)

Published in 1987: The following essays form, as their title-page shows, only the first half of a collection which the writer hopes to complete in the course of a few months. Even when completed the whole work is designed to be merely preparatory to another on the interpretation of the Platonic Philosophy, and the materials brought together in the following pages, as well as those which, it is trusted, will form their continuation, were originally intended to appear in the Introduction (...) to that projected work. (shrink)

Introduction Since my work in medieval logic has concentrated on dialectic. I have tried to trace scholastic treatments of dialectic to discussions of it in ...

I consider the proper interpretation of the process of ecthesis which Aristotle uses several times in the Prior analytics for completing a syllogistic mood, i.e., showing how to produce a deduction of a conclusion of a certain form from premisses of certain forms. I consider two interpretations of the process which have been advocated by recent scholars and show that one seems better suited to most passages while the other best fits a single remaining passage. I also argue that ecthesis (...) for Aristotle really means ?setting out? the case to be proved using letters. Aristotle?s remarks about the use of letters in mathematical proofs suggest that he had some understanding of rules equivalent to universal generalization and existential instantiation; the ?proofs through ecthesis? are so called because they rest on the latter rule, with which use of letters is involved in a special way. (shrink)

Aristotle holds that it was Socrates who first made frequent, systematic use of epagôgç in his elenctic investigations of various definitions of the virtues . Plato and Xenophon also target epagôgç as an innovative, distinguishing mark of Socratic methodology when they have Socrates' interlocutors complain that Socrates prattles on far too much about "his favorite topic" —blacksmiths, cobblers, cooks, physicians, and other such tiresome craftspeople—in order to generate and test general principles concerning the alleged craft of virtue. It is remarkable, (...) then, how little secondary literature exists on this subject—moreover, several of the few accounts we do have naively assume that epagôgç is the same as modern inductive generalization. Others are in conflict as to whether, for example, we can find any legitimate instances of probabilistic inductive epagôgç in the Socratic dialogues. This paper addresses these and other issues by offering a new, critical account of Socratic epagôgç—one tied to its occurrences in several key Socratic elenchoi. (shrink)

After presenting the rules of Eleatic antilogic, i.e., dialectic, I argue that Zeno was a practitioner, and, on the basis of key passages from Plato’s Parmenides, that his paradoxes of divisibility and movement were notreductio ad absurdum, but simple derivation of impossibilities meant to ridicule Parmenides’ adversaries. Thus, Zeno did not try to prove that there is no motion, but simply derived this consequence from premises held by his opponents. I argue further that these paradoxes were devised, in accordance with (...) Eleatic antilogic, following a scheme that included hypotheses and their contradictories, within which the subject is to be treated both “in relation to itself,” and “in relation to other things”. (shrink)

In this paper, we study dialogue as a game, but not only in the sense in which there would exist winning strategies and a priori rules. Dialogue is not governed by game rules like for chess or other games, since even if we start from a priori rules, it is always possible to play with them, provided that some invariant properties are preserved. An important discovery of Ludics is that such properties may be expressed in geometrical terms. The main feature (...) of a dialogue is “convergence”. Intuitively, a dialogue “diverges” when it stops prematurely by some disruption, or a violation of the tacit agreed upon conditions of the discourse. It converges when the two speakers go together towards a situation where they agree at least on some points. As we shall see, convergence may be thought of through the geometrical concept of orthogonality . Utterances in a dialogue have as their content, not only the processes (similar to proofs) which lead to them from a monologic view, but also their interactions with other utterances. Finally, any utterance must be seen as co-constructed in an interaction between two processes. That is to say that it not only contains one speaker’s intentions but also his or her expectations from the other interlocutor. From our viewpoint, discursive strategies like narration , elaboration , topicalization may derive from such interactions, as well as speech acts like assertion, question and denegation. (shrink)

Formal dialectic has its roots in ancient dialectic. We can trace this influence in Charles Hamblin’s book on fallacies, in which he introduced his first formal dialectical systems. Earlier, Paul Lorenzen proposed systems of dialogical logic, which were in fact formal dialectical systems avant la lettre, with roles similar to those of the Greek Questioner and Answerer. In order to make a comparison between ancient dialectic and contemporary formal dialectic, I shall formalize part of the Aristotelian procedure for Academic debates. (...) The resulting system will be compared (1) with Van Eemeren and Grootendorst’s system of rules of Critical Discussion (the pragma-dialectical discussion procedure), which must, however, first itself be reconstructed as a formal dialectical system, and (2) with a Hamblin-type system, and (3) a Lorenzen-type system. When drawing comparisons, it will become clear that there is a line to be drawn from Aristotle to formal dialectic and pragma-dialectics, extending to contemporary computational models of argument. (shrink)

Nous montrons dans cet article comment les approches dynamiques en logique contemporaine ont retrouvé, quoique sous d ’ autres attendus, une configuration théorique qu ’ on peut attribuer à Aristote au moment de la rédaction des Topiques. Dans cette configuration, la logique et la rhétorique – ou au moins la dialectique – se complètent dans le cadre conceptuel homogène offert par la dialectique, entendue comme une certaine forme relativement codifiée de débat critique. L ’ idée principale est qu ’ aujourd (...) ’ hui, de même qu ’ alors, la dialectique est le cadre dans lequel il est possible de penser le rapport entre la logique et les formes générales de l ’ argumentation d ’ une part, et entre la logique et la théorie de la connaissance scientifique d ’ autre part. (shrink)

This work is an attempt to lay foundations for a theory of interactive computation and bring logic and theory of computing closer together. It semantically introduces a logic of computability and sets a program for studying various aspects of that logic. The intuitive notion of computational problems is formalized as a certain new, procedural-rule-free sort of games between the machine and the environment, and computability is understood as existence of an interactive Turing machine that wins the game against any possible (...) environment. The formalism used as a specification language for computational problems, called the universal language, is a non-disjoint union of the formalisms of classical, intuitionistic and linear logics, with logical operators interpreted as certain—most basic and natural—operations on problems. Validity of a formula is understood as being “always computable”, and the set of all valid formulas is called the universal logic. The name “universal” is related to the potential of this logic to integrate, on the basis of one semantics, classical, intuitionistic and linear logics, with their seemingly unrelated or even antagonistic philosophies. In particular, the classical notion of truth turns out to be nothing but computability restricted to the formulas of the classical fragment of the universal language, which makes classical logic a natural syntactic fragment of the universal logic. The same appears to be the case for intuitionistic and linear logics . Unlike classical logic, these two do not have a good concept of truth, and the notion of computability restricted to the corresponding two fragments of the universal language, based on the intuitions that it formalizes, can well qualify as “intuitionistic truth” and “linear-logic truth”. The paper also provides illustrations of potential applications of the universal logic in knowledgebase, resourcebase and planning systems, as well as constructive applied theories. The author has tried to make this article easy to read. It is fully self-contained and can be understood without any specialized knowledge of any particular subfield of logic or computer science. (shrink)

Exploring Aristotle's philosophical method and the merits of his conclusions, Irwin here shows how Aristotle defends dialectic against the objection that it cannot justify a metaphysical realist's claims. He focuses particularly on Aristotle's metaphysics, epistemology, philosophy of mind, and ethics, stressing the connections between doctrines that are often discussed separately.

Several of the so-called “fallacies” in Aristotle are not in fact mistaken inference-types, but mistakes or breaches of rules in the questioning games which were practiced in the Academy and in the Lyceum. Hence the entire Aristotelian theory of “fallacies” ought to be studied by reference to the author's interrogative model of inquiry, based on his theory of questions and answers, rather than as a part of the theory of inference. Most of the “fallacies” mentioned by Aristotle can in fact (...) be diagnosed by means of the interrogative model, including petitio principii, multiple questions, “babbling’, etc., and so can Aristotle's alleged anticipation of the fallacy of argumentum ad hominem. The entire Aristotelian conception of inquiry is an interrogative one. Deductive conclusions caught Aristotle's attention in the form of answers that every rational interlocutor must give, assuming only his own earlier answers. Several features of Aristotle's methodology can be understood by means of the interrogative model, including the role of endoxa in it. Theoretically, there is also considerable leeway as to whether “fallacies” are conceived of as mistakes in questioning or as breaches of the rules that govern questioning games. (shrink)

Peirce discusses the nature and structure of propositions in several manuscripts written in the 1890’s and during the first decade of this century. In this paper I shall outline the main features of Peirce’s theory of the proposition, especially his account of what may be called indeterminate indices in propositions.

Peirce discusses the nature and structure of propositions in several manuscripts written in the 1890’s and during the first decade of this century. In this paper I shall outline the main features of Peirce’s theory of the proposition, especially his account of what may be called indeterminate indices in propositions.

Logical Atomism is a philosophy that sought to account for the world in all its various aspects by relating it to the structure of the language in which we articulate information. In _The Philosophy of Logical Atomism,_ Bertrand Russell, with input from his young student Ludwig Wittgenstein, developed the concept and argues for a reformed language based on pure logic. Despite Russell’s own future doubts surrounding the concept, this founding and definitive work in analytical philosophy by one of the world’s (...) most significant philosophers is a remarkable attempt to establish a novel way of thinking. (shrink)

We present a setting in which the search for a proof of B or a refutation of B can be carried out simultaneously: in contrast, the usual approach in automated deduction views proving B or proving ¬B as two, possibly unrelated, activities. Our approach to proof and refutation is described as a two-player game in which each player follows the same rules. A winning strategy translates to a proof of the formula and a counter-winning strategy translates to a refutation of (...) the formula. The game is described for multiplicative and additive linear logic . A game theoretic treatment of the multiplicative connectives is intricate and our approach to it involves two important ingredients. First, labeled graph structures are used to represent positions in a game and, second, the game playing must deal with the failure of a given player and with an appropriate resumption of play. This latter ingredient accounts for the fact that neither player might win. (shrink)