Outstanding translations by leading contemporary scholars--many commissioned especially for this volume--are presented here in the first single edition to include the entire surviving corpus of works attributed to Plato in antiquity. In his introductory essay, John Cooper explains the presentation of these works, discusses questions concerning the chronology of their composition, comments on the dialogue form in which Plato wrote, and offers guidance on approaching the reading and study of Plato's works. Also included are concise introductions by Cooper and Hutchinson (...) to each translation, meticulous annotation designed to serve both scholar and general reader, and a comprehensive index. This handsome volume offers fine paper and a high-quality Smyth-sewn cloth binding in a sturdy, elegant edition. (shrink)

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)

This long-awaited study of the most enigmatic figure of Greek philosophy reclaims Socrates' ground-breaking originality. Written by a leading historian of Greek thought, it argues for a Socrates who, though long overshadowed by his successors Plato and Aristotle, marked the true turning point in Greek philosophy, religion and ethics. The quest for the historical figure focuses on the Socrates of Plato's earlier dialogues, setting him in sharp contrast to that other Socrates of later dialogues, where he is used as a (...) mouthpiece for Plato's often anti-Socratic doctrine. At the heart of the book is the paradoxical nature of Socratic thought. But the paradoxes are explained, not explained away. The book highlights the tensions in the Socratic search for the answer to the question 'How should we live?' Conceived as a divine mandate, the search is carried out through elenctic argument, and dominated by an uncompromising rationalism. The magnetic quality of Socrates' personality is allowed to emerge throughout the book. Clearly and forcefully written, philosophically sophisticated but entirely accessible to non-specialists, this book will be of major importance and interest to all those studying ancient philosophy and the history of Western thought. (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.

This presentation of Aristotle's natural deduction system supplements earlier presentations and gives more historical evidence. Some fine-tunings resulted from conversations with Timothy Smiley, Charles Kahn, Josiah Gould, John Kearns,John Glanvillle, and William Parry.The criticism of Aristotle's theory of propositions found at the end of this 1974 presentation was retracted in Corcoran's 2009 HPL article "Aristotle's demonstrative logic".

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)

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.

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)

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)

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.

This book presents novel formalizations of three of the most important medieval logical theories: supposition, consequence and obligations. In an additional fourth part, an in-depth analysis of the concept of formalization is presented - a crucial concept in the current logical panorama, which as such receives surprisingly little attention.Although formalizations of medieval logical theories have been proposed earlier in the literature, the formalizations presented here are all based on innovative vantage points: supposition theories as algorithmic hermeneutics, theories of consequence analyzed (...) with tools borrowed from model-theory and two-dimensional semantics, and obligations as logical games. For this reason, this is perhaps the first time that these medieval logical theories are made fully accessible to the modern philosopher and logician who wishes to obtain a better grasp of them, but who has always been held back by the lack of appropriate ‘translations' into modern terms.Moreover, the book offers a reflection on the very nature of logic, a reflection that is prompted by the comparisons between medieval and modern logic, their similarities and dissimilarities. It is thus a contribution not only to the history of logic, but also to the philosophy of logic, the philosophy of language and semantics.The analysis of medieval logic is also relevant for the modern philosopher and logician in that, being the unifying methodology used across all disciplines at that time, logic really provided unity to science. It thus presents a unified model of scientific investigation, where logic plays the aggregating role. (shrink)

In the present article we attempt to show that Aristotle's syllogistic is an underlying logiC which includes a natural deductive system and that it isn't an axiomatic theory as had previously been thought. We construct a mathematical model which reflects certain structural aspects of Aristotle's logic. We examine the relation of the model to the system of logic envisaged in scattered parts of Prior and Posterior Analytics. Our interpretation restores Aristotle's reputation as a logician of consummate imagination and skill. Several (...) attributions of shortcomings and logical errors to Aristotle are shown to be without merit. Aristotle's logic is found to be self-sufficient in several senses: his theory of deduction is logically sound in every detail. (His indirect deductions have been criticized, but incorrectly on our account.) Aristotle's logic presupposes no other logical concepts, not even those of propositional logic. The Aristotelian system is seen to be complete in the sense that every valid argument expressible in his system admits of a deduction within his deductive system: every semantically valid argument is deducible. (shrink)

Dialogical logic is a game-theoretical approach to logic. Logic is studied with the help of certain games, which can be thought of as idealized argumentations. Two players, the Proponent, who puts forward the initial thesis and tries to defend it, and the Opponent, who tries to attack the Proponent’s thesis, alternately utter argumentative moves according to certain rules. For a long time the dialogical approach had been worked out only for classical and intuitionistic logic. The seven papers of this dissertation (...) show that this narrowness was uncalled for. The initial paper presents an overview and serves as an introduction to the other papers. Those papers are related by one central theme. As each of them presents dialogical formulations of a different non-classical logic, they show that dialogical logic constitutes a powerful and flexible general framework for the development and study of various logical formalisms and combinations thereof. As such it is especially attractive to logical pluralists that reject the idea of “the single correct logic”. The collection contains treatments of free logic, modal logic, relevance logic, connexive logic, linear logic, and multi-valued logic. (shrink)

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

In his 1961 paper "Tithenai ta Phainomena",1 G. E. L. Owen addressed the problem of the relationship between science as preached in the Analytics and the practice of the Aristotelian treatises. However, he gave this venerable crux a novel twist by focusing on a different aspect of the issue. According to the Prior Analytics , it appears that the first premises of scientific demonstrations must be obtained from collections (historiai) of facts derived from empirical observation. However, many of the treatises (...) seem to make little use of empirical inquiry and instead concern themselves more with 'conceptual analysis.' This is especially true in the Metaphysics and the ethical treatises, but it is also very much characteristic of the Physics. How are these two kinds of inquiry related? (shrink)

Since the time of Aristotle's students, interpreters have considered Prior Analytics to be a treatise about deductive reasoning, more generally, about methods of determining the validity and invalidity of premise-conclusion arguments. People studied Prior Analytics in order to learn more about deductive reasoning and to improve their own reasoning skills. These interpreters understood Aristotle to be focusing on two epistemic processes: first, the process of establishing knowledge that a conclusion follows necessarily from a set of premises (that is, on the (...) epistemic process of extracting information implicit in explicitly given information) and, second, the process of establishing knowledge that a conclusion does not follow. Despite the overwhelming tendency to interpret the syllogistic as formal epistemology, it was not until the early 1970s that it occurred to anyone to think that Aristotle may have developed a theory of deductive reasoning with a well worked-out system of deductions comparable in rigor and precision with systems such as propositional logic or equational logic familiar from mathematical logic. When modern logicians in the 1920s and 1930s first turned their attention to the problem of understanding Aristotle's contribution to logic in modern terms, they were guided both by the Frege-Russell conception of logic as formal ontology and at the same time by a desire to protect Aristotle from possible charges of psychologism. They thought they saw Aristotle applying the informal axiomatic method to formal ontology, not as making the first steps into formal epistemology. They did not notice Aristotle's description of deductive reasoning. Ironically, the formal axiomatic method (in which one explicitly presents not merely the substantive axioms but also the deductive processes used to derive theorems from the axioms) is incipient in Aristotle's presentation. Partly in opposition to the axiomatic, ontically-oriented approach to Aristotle's logic and partly as a result of attempting to increase the degree of fit between interpretation and text, logicians in the 1970s working independently came to remarkably similar conclusions to the effect that Aristotle indeed had produced the first system of formal deductions. They concluded that Aristotle had analyzed the process of deduction and that his achievement included a semantically complete system of natural deductions including both direct and indirect deductions. Where the interpretations of the 1920s and 1930s attribute to Aristotle a system of propositions organized deductively, the interpretations of the 1970s attribute to Aristotle a system of deductions, or extended deductive discourses, organized epistemically. The logicians of the 1920s and 1930s take Aristotle to be deducing laws of logic from axiomatic origins; the logicians of the 1970s take Aristotle to be describing the process of deduction and in particular to be describing deductions themselves, both those deductions that are proofs based on axiomatic premises and those deductions that, though deductively cogent, do not establish the truth of the conclusion but only that the conclusion is implied by the premise-set. Thus, two very different and opposed interpretations had emerged, interestingly both products of modern logicians equipped with the theoretical apparatus of mathematical logic. The issue at stake between these two interpretations is the historical question of Aristotle's place in the history of logic and of his orientation in philosophy of logic. This paper affirms Aristotle's place as the founder of logic taken as formal epistemology, including the study of deductive reasoning. A by-product of this study of Aristotle's accomplishments in logic is a clarification of a distinction implicit in discourses among logicians--that between logic as formal ontology and logic as formal epistemology. (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.

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.

In previous articles, it has been shown that the deductive system developed by Aristotle in his "second logic" is a natural deduction system and not an axiomatic system as previously had been thought. It was also stated that Aristotle's logic is self-sufficient in two senses: First, that it presupposed no other logical concepts, not even those of propositional logic; second, that it is (strongly) complete in the sense that every valid argument expressible in the language of the system is deducible (...) by means of a formal deduction in the system. Review of the system makes the first point obvious. The purpose of the present article is to prove the second. Strong completeness is demonstrated for the Aristotelian system. (shrink)

Demonstrative logic, the study of demonstration as opposed to persuasion, is the subject of Aristotle's two-volume Analytics. Many examples are geometrical. Demonstration produces knowledge (of the truth of propositions). Persuasion merely produces opinion. Aristotle presented a general truth-and-consequence conception of demonstration meant to apply to all demonstrations. According to him, a demonstration, which normally proves a conclusion not previously known to be true, is an extended argumentation beginning with premises known to be truths and containing a chain of reasoning showing (...) by deductively evident steps that its conclusion is a consequence of its premises. In particular, a demonstration is a deduction whose premises are known to be true. Aristotle's general theory of demonstration required a prior general theory of deduction presented in the Prior Analytics. His general immediate-deduction-chaining conception of deduction was meant to apply to all deductions. According to him, any deduction that is not immediately evident is an extended argumentation that involves a chaining of intermediate immediately evident steps that shows its final conclusion to follow logically from its premises. To illustrate his general theory of deduction, he presented an ingeniously simple and mathematically precise special case traditionally known as the categorical syllogistic. (shrink)

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)

Scholars of classical philosophy have long disputed whether Aristotle was a dialectical thinker. Most agree that Aristotle contrasts dialectical reasoning with demonstrative reasoning, where the former reasons from generally accepted opinions and the latter reasons from the true and primary. Starting with a grasp on truth, demonstration never relinquishes it. Starting with opinion, how could dialectical reasoning ever reach truth, much less the truth about first principles? Is dialectic then an exercise that reiterates the prejudices of one's times and at (...) best allows one to persuade others by appealing to these prejudices, or is it the royal road to first principles and philosophical wisdom? In From Puzzles to Principles? May Sim gathers experts to argue both these positions and offer a variety of interpretive possibilities. The contributors' thoughtful reflections on the nature and limits of dialectic should play a crucial role in Aristotelian scholarship. (shrink)

This is a clear, accurate translation of Books I and VIII of Aristotle's Topics, with a philosophical commentary on these books and additional extracts from both Books II and III, and a related Aristotle work. It is ideal for students, especially those who do not know Greek.

Aristotle's treatise De Interpretatione is one of his central works; it continues to be the focus of much attention and debate. 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, basing this view upon a detailed chapter-by-chapter analysis.By treating the work systematically, rather than concentrating on certain selected passages, Whitaker is able to show that, contrary to traditional opinion, it forms (...) an organized and coherent whole. He argues that the De Interpretatione is intended to provide the underpinning for dialectic, the system of argument by question and answer set out in Aristotle's Topics; and he rejects the traditional view that the De Interpretatione concerns the assertion and is oriented towards the formal logic of the Prior Analytics. In doing so, he sheds valuable new light on some of Aristotle's most famous texts. (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 (127e-128e and 135d-136c), that his paradoxes of divisibility and movement were notreductio ad absurdum, but simple derivation of impossibilities (adunaton) 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)

Scholars of classical philosophy have long disputed whether Aristotle was a dialectical thinker. Most agree that Aristotle contrasts dialectical reasoning with demonstrative reasoning, where the former reasons from generally accepted opinions and the latter reasons from the true and primary. Starting with a grasp on truth, demonstration never relinquishes it. Starting with opinion, how could dialectical reasoning ever reach truth, much less the truth about first principles? Is dialectic then an exercise that reiterates the prejudices of one's times and at (...) best allows one to persuade others by appealing to these prejudices, or is it the royal road to first principles and philosophical wisdom? In From Puzzles to Principles? May Sim gathers experts to argue both these positions and offer a variety of interpretive possibilities. The contributors' thoughtful reflections on the nature and limits of dialectic should play a crucial role in Aristotelian scholarship. (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)

THE PHILOSOPHY which I advocate is generally regarded as a species of realism, and accused of inconsistency because of the elements in it which seem contrary to that doctrine. For my part, I do not regard the issue between realists and their opponents as a funda- mental one; I could alter my view on this issue without changing my mind as to any of the doctrines upon which I wish to lay stress. I hold that logic is what is fundamental (...) in philosophy, and that schools should be characterized rather by their logic than by their metaphysic. My own logic is atomic, and it is this aspect upon which I should wish to lay stress. Therefore I prefer to describe my philosophy as "logical atomism," rather than as "realism," whether with or without some prefixed adjective. (shrink)

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)