ABSTRACT: Recently a bold and admirable interpretation of Chrysippus’ position on the Sorites has been presented, suggesting that Chrysippus offered a solution to the Sorites by (i) taking an epistemicist position1 which (ii) made allowances for higher-order vagueness. In this paper I argue (i) that Chrysippus did not take an epistemicist position, but − if any − a non-epistemic one which denies truth-values to some cases in a Sorites-series, and (ii) that it is uncertain whether and how he made allowances (...) for higher-order vagueness, but if he did, this was not grounded on an epistemicist position. (shrink)

Paul Boghossian defends a meaning‐based approach to the apriority of the propositions of logic. His model is based on the idea that the logical constants are implicitly defined by some of the axioms and inference rules in which they are involved, thereby offering an alternative to those theories that deny that grasp of meaning can contribute to the explanation of a thinker's entitlement to a particular type of transition or belief.

Excerpt from A History of Formal Logic In this edition of the most considerable history Of formal logic yet published, the Opportunity has Of course been taken to make some adjustments seen to be necessary in the original, with the author's full concurrence. Only in 36, however, has the numeration of cited passages been altered owing to the introduction of new matter. Those changes are as follows. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. (...) Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

This book traces the development of formal logic from its origins inancient Greece to the present day. The authors first discuss the work oflogicians from Aristotle to Frege, showing how they were influenced by thephilosophical or mathematical ideas of their time. They then examinedevelopments in the present century.

Formal methods are changing how epistemology is being studied and understood. A Critical Introduction to Formal Epistemology introduces the types of formal theories being used and explains how they are shaping the subject. Beginning with the basics of probability and Bayesianism, it shows how representing degrees of belief using probabilities informs central debates in epistemology. As well as discussing induction, the paradox of confirmation and the main challenges to Bayesianism, this comprehensive overview covers objective chance, peer disagreement, the concept of (...) full belief, and the traditional problems of justification and knowledge. Subjecting each position to a critical analysis, it explains the main issues in formal epistemology, and the motivations and drawbacks of each position. Written in an accessible language and supported study questions, guides to further reading and a glossary, positions are placed in an historic context to give a sense of the development of the field. As the first introductory textbook on formal epistemology, A Critical Introduction to Formal Epistemology is an invaluable resource for students and scholars of contemporary epistemology. (shrink)

Jennifer Fisher's ON THE PHILOSOPHY OF LOGIC explores questions about logic often overlooked by philosophers. Which of the many different logics available to us is right? How would we know? What makes a logic right in the first place? Is logic really a good guide to human reasoning? An ideal companion text for any course in symbolic logic, this lively and accessible book explains important logical concepts, introduces classical logic and its problems and alternatives, and reveals the rich and interesting (...) philosophical issues that arise in exploring the fundamentals of logic. (shrink)

In virtue of what are we justified in employing the rule of inference Modus Ponens? One tempting approach to answering this question is to claim that we are justified in employing Modus Ponens purely in virtue of facts concerning meaning or concept-possession. In this paper, we argue that such meaning-based accounts cannot be accepted as the fundamental account of our justification.

"One of the most careful and intensive among the introductory texts that can be used with a wide range of students. It builds remarkably sophisticated technical skills, a good sense of the nature of a formal system, and a solid and extensive background for more advanced work in logic.... The emphasis throughout is on natural deduction derivations, and the text's deductive systems are its greatest strength. Lemmon's unusual procedure of presenting derivations before truth tables is very effective." --Sarah Stebbins, The (...) Journal of Symbolic Logic. (shrink)

It is often taken for granted by writers who propose--and, for that matter, by writers who oppose--'justifications' of inductions, that deduction either does not need, or can readily be provided with, justification. The purpose of this paper is to argue that, contrary to this common opinion, problems analogous to those which, notoriously, arise in the attempt to justify induction, also arise in the attempt to justify deduction.

The Philosophy of Chrysippus is a reconstruction of the philosophy of an eminent Stoic philosopher, based upon the fragmentary remains of his voluminous writings. Chrysippus of Cilicia, who lived in a period that covers roughly the last three-quarters of the third century B.C., studied philosophy in Athens and upon Cleanthes’ death became the third head of the Stoa, one of the four great schools of philosophy of the Hellenistic period. Chrysippus wrote a number of treatises in each of the major (...) departments of philosophy, logic, physics, and ethics. Much of his fame derived from his acuteness as a logician, but his importance for Stoic philosophy generally was acknowledged in antiquity in the saying, “Had there been no Chrysippus, there would be no Stoa.” Previous accounts of Chrysippus’ philosophy, including Émile Bréhier’s study, the only work in this century which had sought to deal with Chrysippus’ philosophy alone, blurred the distinctive contributions of Chrysippus to Stoic philosophy and failed to bring to light the peculiar features in his thought. The vagueness in these accounts resulted in large measure from the assumption that if an ancient author ascribed a doctrine to “the Stoics” or “Stoicism”, one could infer that the doctrine belonged to Chrysippus. Professor Gould works from the more circumspect methodological principle that unless an ancient author explicitly ascribes a doctrine to Chrysippus, his testimony cannot be used in reconstructing Chrysippus’ philosophy. Working with those of the fragments in Hans von Arnim’s collection, Stoicorum Veterum Fragmenta, which are explicitly Chrysippean in the sense suggested, Mr. Gould has worked out an account of Chrysippus’ views in the fields of logic, natural philosophy, and ethics. In order that Chrysippus’ thought might be viewed in context Mr. Gould provides a background picture by describing the third century milieu in which the Stoic philosopher worked. This follows an account of Chrysippus’ life and reputation in antiquity and a description of modern assessments of Chrysippus’ position in the Stoa. In his account of Chrysippus’ philosophy Mr. Gould frequently introduces comparisons and contrasts with Plato and Aristotle to help emphasize the continuity between Hellenic and early Hellenistic philosophy. Finally, in a concluding chapter, the author shows that the dominant themes in Chrysippus’ philosophy, while not exhibiting a thoroughly well-knit system, nevertheless are woven together into a remarkably comprehensive whole, which must have been extraordinarily impressive in antiquity. (shrink)

Pendant cinq siecles, de 300 av. J.C. jusqu'au crepuscule de Marc Aurele, la philosophie stoicienne domina la culture antique. Encore aujourd'hui, notre grammaire, notre logique et notre linguistique sont les heritieres plus ou moins conscientes de l'une des trois parties de cette philosophie, la dialectique, qui fut, dans sa forme classique, l'oeuvre de Chrysippe (280-204 av. J.C.). Ce livre est la premiere reconstruction synthetique de la dialectique stoicienne dans son ensemble. Son point de vue est en outre entierement nouveau. En (...) effet, pour l'auteur, les stoiciens n'avaient pas une logique au sens moderne du terme, mais une dialectique, c'est-a-dire une technique de l'argumentation dialoguee. Sa conception complexe, a premiere vue multiple et equivoque, recoit ainsi un eclairage inedit, qui permet de comprendre son originalite et d'en reinterpreter la place dans l'ensemble du systeme. Cela nous permet aussi de mieux comprendre le sens des disciplines qui en sont les heritieres infideles. (shrink)

In Rationality and Logic, Robert Hanna argues that logic is intrinsically psychological and that human psychology is intrinsically logical. He claims that logic is cognitively constructed by rational animals and that rational animals are essentially logical animals. In order to do so, he defends the broadly Kantian thesis that all rational animals possess an innate cognitive "logic faculty." Hanna 's claims challenge the conventional philosophical wisdom that sees logic as a fully formal or "topic-neutral" science irreconcilably separate from the species- (...) or individual-specific focus of empirical psychology.Logic and psychology went their separate ways after attacks by Frege and Husserl on logical psychologism--the explanatory reduction of logic to empirical psychology. Hanna argues, however, that--despite the fact that logical psychologism is false--there is an essential link between logic and psychology. Rational human animals constitute the basic class of cognizers or thinkers studied by cognitive psychology; given the connection between rationality and logic that Hanna claims, it follows that the nature of logic is significantly revealed to us by cognitive psychology. Hanna 's proposed "logical cognitivism" has two important consequences: the recognition by logically oriented philosophers that psychologists are their colleagues in the metadiscipline of cognitive science; and radical changes in cognitive science itself. Cognitive science, Hanna argues, is not at bottom a natural science; it is both an objective or truth-oriented science and a normative human science, as is logic itself. (shrink)