in die operative Logik und Mathematik Zweite Auflage Springer-Verlag Berlin Heidelberg New York 1969 Paul Lorenzen o. Prof. der Philosophie an der Universitat Erlangen Geschaftsfilhrende Herausgeber: Prof. Dr. B. Eckmann Eidgenossische Technische Hochschule Zurich Prof. Dr. B. L. van cler Waerclen Mathematisches Institut der Universitat ZUrich ISBN 978-3-642-86519-0 ISBN 978-3-642-86518-3 (eBook) DOl 10.1007/978-3-642-86518-3 Aile Rechte vorbehalten. Kein Teil dieses Buches darf ohne schriftliche Genehmigung des Springer-Verlages ubersetzt oder in irgendeiner Form vervielfaltigt werden © by Springer-Verlag Berlin· Heidelberg 1955 und 1969 (...) Softcover reprint of the hardcover 2nd edition 1969 Library of Congress Catalog Card Number 73-76724 Titel-Nr. 5061 Vorwort zur zweiten Auflage. Fiir die Neuauflage ist der Text nur unwesentlich geandert worden. Es ist - neben der Korrektur einiger Ungenauigkeiten - vor allem die Terminologie und Symbolik an meine spateren Arbeiten angeglichen. Obwohl ich - verstandlicherweise - jetzt die Ansatze der spateren Arbeiten fiir "sachgemaBer" halte, z. B. eine Logik der Dialoge statt einer Logik der Kalkiile, die Verwendung indefiniter Quantoren statt einer expliziten Konstruktion von Sprachschichten, enthalt diese Neu­ auflage den Inhalt der 1. Auflage unverandert. Der Leser kann also einen Vergleich mit meinen spateren Arbeiten (vgl. Literaturverzeichnis) seIber durchfiihren. Mein Dank gilt wiederum dem Verlag fiir seine entgegenkommende Mitarbeit bei der Vorbereitung dieser Neuauflage. Erlangen, den 1. November I968. PAUL LORENZEN. Vorwort zur ersten Auflage. (shrink)

The extensive research in logic conducted by using concepts and methods of game theory as documented in this collection of papers, allows to see dialogue logic in a number of new perspectives. This situation may gain further clarity by looking back to the inception of dialogue logic in the late fifties and early sixties.

The extensive research in logic conducted by using concepts and methods of game theory as documented in this collection of papers, allows to see dialogue logic in a number of new perspectives. This situation may gain further clarity by looking back to the inception of dialogue logic in the late fifties and early sixties.

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)

I present a semantics for the language of first-order additive-multiplicative linear logic, i.e. the language of classical first-order logic with two sorts of disjunction and conjunction. The semantics allows us to capture intuitions often associated with linear logic or constructivism such as sentences = games, SENTENCES = resources or sentences = problems, where “truth” means existence of an effective winning strategy.The paper introduces a decidable first-order logic ET in the above language and gives a proof of its soundness and completeness (...) with respect to this semantics. Allowing noneffective strategies in the latter is shown to lead to classical logic.The semantics presented here is very similar to Blass's game semantics. Although there is no straightforward reduction between the two corresponding notions of validity, my completeness proof can likely be adapted to the logic induced by Blass's semantics to show its decidability, which was the main problem left open in Blass's paper.The reader needs to be familiar with classical logic and arithmetic. (shrink)

We describe a logic which is the same as first-order logic except that it allows control over the information that passes down from formulas to subformulas. For example the logic is adequate to express branching quantifiers. We describe a compositional semantics for this logic; in particular this gives a compositional meaning to formulas of the 'information-friendly' language of Hintikka and Sandu. For first-order formulas the semantics reduces to Tarski's semantics for first-order logic. We prove that two formulas have the same (...) interpretation in all structures if and only if replacing an occurrence of one by an occurrence of the other in a sentence never alters the truth-value of the sentence in any structure. (shrink)

[Wilfrid Hodges] During the last forty or so years it has become popular to offer explanations of logical notions in terms of games. There is no doubt that many people find games helpful for understanding various logical phenomena. But we ask whether anything is really 'explained' by these accounts, and we analyse Paul Lorenzen's dialogue foundations for constructive logic as an example. The conclusion is that the value of games lies in their ability to provide helpful metaphors and representations, rather (...) than in any true conceptual analysis. In fact some of the standard explanations of logical notions in terms of competitive games simply don't work. /// [Erik C. W. Krabbe] In an attempt to redeem the Lorenzen-type dialogues from their detractors, it is perhaps best first to provide a survey of the various benefits these dialogues have been supposed to yield. This will be done in Section I. It will not be possible, within the confines of this paper, to scrutinize them all, but in Section II we shall delve deeper into the capacity of this type of dialogue to yield a model for the immanent criticism of philosophical positions. Section III will extend the concept of a dialogue in such a way as to conform better with our intuitive conceptions of what a rational discussion of a position should contain. This will be followed up by a concept of 'winning a dialogue' that takes position midway between the old conception of 'winning one play' and that of the full-fledged presentation of a winning strategy. Concepts of 'rational discussion' are thus shown to be, plausibly, more fundamental than those of proof. In Section IV, I shall discuss the specific problems about dialogical foundations put forward by Wilfrid Hodges. (shrink)

This book, written by one of philosophy's pre-eminent logicians, argues that many of the basic assumptions common to logic, philosophy of mathematics and metaphysics are in need of change. It is therefore a book of critical importance to logical theory. Jaakko Hintikka proposes a new basic first-order logic and uses it to explore the foundations of mathematics. This new logic enables logicians to express on the first-order level such concepts as equicardinality, infinity, and truth in the same language. The famous (...) impossibility results by Gödel and Tarski that have dominated the field for the last sixty years turn out to be much less significant than has been thought. All of ordinary mathematics can in principle be done on this first-order level, thus dispensing with the existence of sets and other higher-order entities. (shrink)

Extending the project of analysis -- Elaborating abilities : the expressive role of logic -- Artificial intelligence and analytic pragmatism -- Modality and normativity : from Hume and Quine to Kant and Sellars -- Incompatibility, modal semantics, and intrinsic logic -- Intentionality as a pragmatically mediated semantic relation -- Afterword : philosophical analysis and analytic philosophy.

Robert Brandom's latest book, the product of his John Locke lectures in Oxford in 2006, is a return to the philosophy of language and is easily read as a continuation and development of the views defended in Making it Explicit. The text of the lectures is presented much as they were delivered, but it contains an ‘Afterword’ of more than 30 pages which responds to questions raised when he gave the lectures, and also when they were subsequently delivered in Prague (...) the following year. The published text also contains relatively technical appendices to two of the lectures.The individual lectures engage with some important and difficult issues, often ones that were explored in detail in the earlier book. However, these discussions are located within a broader meta-philosophical context, and it says something about the abstract and difficult character of these views that they provide the main subject matter of the Afterword. This framework affects how we should understand the relations between this book and Making It Explicit too. Although most of the detailed discussions happily belong within the general project of the earlier book, they are offered as illustrations of a framework that is independent of this project. Indeed, Brandom suggests that defenders of the semantic views of David Lewis, for example, could embrace his main message as well as those who favour Brandom's own form of pragmatism.Neo-pragmatist philosophers such as Brandom's teacher, Richard Rorty, often present themselves as rejecting the analytic tradition in philosophy. When Brandom describes the ‘pragmatist challenge’ to the ‘classical project of analysis’, he appeals to the criticisms found in the work of Wittgenstein and Sellars that are often appealed to by the critics of the analytic tradition. The message of the new book is that the views he has built on this …. (shrink)

This new work provides an approachable introduction to the complex system that Making It Explicit mapped out.

We present a game semantics in the style of Lorenzen for Girard's linear logic . Lorenzen suggested that the meaning of a proposition should be specified by telling how to conduct a debate between a proponent P who asserts and an opponent O who denies . Thus propositions are interpreted as games, connectives as operations on games, and validity as existence of a winning strategy for P. We propose that the connectives of linear logic can be naturally interpreted as the (...) operations on games introduced for entirely different purposes by Blass . We show that affine logic, i.e., linear logic plus the rule of weakening, is sound for this interpretation. We also obtain a completeness theorem for the additive fragment of affine logic, but we show that completeness fails for the multiplicative fragment. On the other hand, for the multiplicative fragment, we obtain a simple characterization of game-semantical validity in terms of classical tautologies. An analysis of the failure of completeness for the multiplicative fragment leads to the conclusion that the game interpretation of the connective is weaker than the interpretation implicit in Girard's proof rules; we discuss the differences between the two interpretations and their relative advantages and disadvantages. Finally, we discuss how Gödel's Dialectica interpretation , which was connected to linear logic by de Paiva , fits with game semantics. (shrink)

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...) position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many. (shrink)

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...) position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many. (shrink)

Albert approaches critical rationalism as an alternative to other philosophical standpoints dominant in Germany: the conceptions of the Frankfurt School, hermeneutical thinking as represented by Gadamer, analytic philosophy, and logical empiricism. The author's purpose is to find a way out of the foundationalism of classical philosophy without falling back on the skeptical views so prevalent in today's philosophical thinking. Originally published in 1985. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the (...) distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

Translated from the author's unpublished manuscript. Includes bibliographical references and index.

Such a conception, says Dummett, will form "a base camp for an assault on the metaphysical peaks: I have no greater ambition in this book than to set up a base ...

What is essential to language? Two thinkers active in Vienna in the 1930's, Karl Bühler and Ludwig Wittgenstein, gave apparently incompatible answers to this question. I compare what Wittgenstein says about language and reference at the beginning of his Philosophical Investigations with some aspects of the descriptive analysis of language worked out by Bühler between 1907 and 1934, a systematic development of the philosophies of mind and language of such heirs of Brentano as Martinak, Marty, Meinong, Landgrebe and Husserl. Y (...) a-Uil quelque chose qui est essentiel au langage? Deux penseurs actifs à Vienne dans les années trente, Karl Bühler et Ludwig Wittgenstein, donnent à cette question des réponses qui sont apparemment incompatibles. Je compare ce que Wittgenstein dit du langage et de la référence au début de ses Investigations Philosophiques avec quelques aspects de l'analyse descriptive élaborée par Bühler entre 1907 et 1934, un développement systématique des philosophies de l'esprit et du langage des héritiers de Brentano tels que Martinak, Marty, Meinong, Landgrebe et Husserl. (shrink)

In this book, which remained unfinished at his death, Husserl attempts to forge a union between phenomenology and existentialism.

This volume examines the notion of an analytic proof as a natural deduction, suggesting that the proof's value may be understood as its normal form--a concept with significant implications to proof-theoretic semantics.

This book, written by one of philosophy's pre-eminent logicians, argues that many of the basic assumptions common to logic, philosophy of mathematics and metaphysics are in need of change. It is therefore a book of critical importance to logical theory. Jaakko Hintikka proposes a new basic first-order logic and uses it to explore the foundations of mathematics. This new logic enables logicians to express on the first-order level such concepts as equicardinality, infinity, and truth in the same language. The famous (...) impossibility results by Gödel and Tarski that have dominated the field for the last sixty years turn out to be much less significant than has been thought. All of ordinary mathematics can in principle be done on this first-order level, thus dispensing with the existence of sets and other higher-order entities. (shrink)

I LOGIC IN PHILOSOPHY— PHILOSOPHY OF LOGIC i. On the relation of logic to philosophy I n this book, the consequences of certain logical insights for ...

Presents for the first time in English, this 1967 text which came to be known as the 'bible' of a new movement in German philosophy of language, the 'Erlanger School.' This school of linguistic philosophy's treatment of language is rooted in the tradition of transcendentalism, and bases its system on Kant and his Continental successors. For the Erlanger School, 'language is not just a fact we discover...but a human cultural accomplishment whose construction reason can and should be controlled.' An influential (...) work which will be a valuable resource for students of philosophy, particularly philosophy of language and transcendentalism. (shrink)

Collected here in a single volume for the first time, On Liberty, Utilitarianism, Considerations on Representative Government, and The Subjection of Women show Mill applying his liberal utilitarian philosophy to a range of issues that remain vital today - issues of the nature of ethics, the scope and limits of individual liberty, the merits of and costs of democratic government, and the place of women in society. In his Introduction John Gray describes these essays as applications of Mill's doctrine of (...) the Art of Life, as set out in A System of Logic. Using the resources of recent revisionist scholarship, he shows Mill's work to be far richer and subtler than traditional interpretations allow. (shrink)

ONE Methodical Thinking Motto: When we teach men how to think, instead of what to think, then we also reduce misunderstanding. ...

The idea to produce the current volume was conceived by Jiirgen Mittelstrass and Robert E. Butts in 1978. Idealist philosophers are wrong about one thing: the temporal gap separating idea and reality can be very long indeed - even ten or so years! Problems of timing were joined by personal problems and by the pressure of other professional commitments. Fortunately, James Brown agreed to cooperate in the editing of the volume; the infusion of his usual energy, good judgement and good-natured (...) promptness saved the volume and made its produc tion possible. Despite the delays, the messages of the papers included in the book have not gone stale. An extremely worthwhile exercise in international philosophical cooperation has come to fruition; the German constructivist philosophical position is here represented in papers in English that will make its contemporary importance available to a larger audience. The editors owe thanks to many persons. All involved in the project owe much to the interest and support of Nicholas Rescher, a friend of the undertaking from the time of its inception. My review of the translations was helped immensely by Andrea Purvis' careful copy editing of the typescript. Most of all, however, we owe gratitude and admiration for the tireless efforts on behalf of this enterprise to Jiirgen Mittelstrass. (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)