Frege, Gottlob (1848–1925)

Abstract

Nathan Salmon is Professor of Philosophy at the University of California, Santa Barbara, where he has taught since 1984. His research focuses on the philosophy of language and metaphysics, but he has written in many other areas of philosophy, including the philosophy of mind, epistemology, the philosophy of mathematics, and the philosophy of logic. He is perhaps best known for his work on direct reference theory and modality. In addition to numerous papers, Salmon has written several books: Reference and Essence (1981, 2005 with new appendices); Frege’s Puzzle (1986, 1991); Metaphysics, Mathematics, and Meaning: Philosophical Papers Volume I (2006); Content, Cognition, and Communication: Philosophical Papers Volume 2 (2007). Together with Scott Soames, Salmon co-edited Propositions and Attitudes in 1988. This interview was conducted for the Yale Philosophy Review by Leslie F. Wolf, a graduate student in the Department of Philosophy at Yale University.

Model theory is used in every theoretical branch of analytic philosophy: in philosophy of mathematics, in philosophy of science, in philosophy of language, in philosophical logic, and in metaphysics. But these wide-ranging appeals to model theory have created a highly fragmented literature. On the one hand, many philosophically significant results are found only in mathematics textbooks: these are aimed squarely at mathematicians; they typically presuppose that the reader has a serious background in mathematics; and little clue is given as to their philosophical significance. On the other hand, the philosophical applications of these results are scattered across disconnected pockets of papers. The first aim of this book, then, is to consider the philosophical uses of model theory, focusing on the central topics of reference, realism, and doxology. Its second aim is to address important questions in the philosophy of model theory, such as: sameness of theories and structure, the boundaries of logic, and the classification of mathematical structures. Philosophy and Model Theory will be accessible to anyone who has completed an introductory logic course. It does not assume that readers have encountered model theory before, but starts right at the beginning, discussing philosophical issues that arise even with conceptually basic model theory. Moreover, the book is largely self-contained: model-theoretic notions are defined as and when they are needed for the philosophical discussion, and many of the most philosophically significant results are given accessible proofs.

Preface. Abbreviations. Part 1: Philosophy of Language. The Social Aspect of Language D. Davidson. Singular Terms B. Hale. Philosophical Theorizing and Particularism: Michael Dummett on Wittgenstein's Later Philosophy of Language D. Pears. Convention and Assertion E. Picardi. Meaning Theory and Anti-Realism D. Prawitz. Part 2: Philosophy of Mathematics. Anti-Realism and the Philosophy of Mathematics G. Oliveri. Dummett and Wittgenstein's Philosophy of Mathematics C. Penco. Vestiges of Realism G. Sundholm. About 'the Philosophical Significance of Godel's Theorem': Some Issues C. Wright. Part 3: Philosophy of Mind, Time and Religion. Dummett, Realism and Other Minds A. Bilgrami. Truth, Time and Deity B.F. McGuinness. Leaving the Past Where it Belongs J. Schulte. Part 4: Dummett's Replies. Reply to Davidson. Reply to Hale. Reply to Pears. Reply to Picardi. Reply to Prawitz. Reply to Oliveri. Reply to Penco. Reply to Sundholm. Reply to Wright. Reply to Bilgrami. Reply to McGuinness. Reply to Schulte. Bibliography. Index.

This handbook provides a systematic survey of the central areas of philosophical logic. It is divided into four volumes, each devoted to a major sub-field within the disciplines. The articles should be of value to general philosophers, linguists, logicians, mathematicians and computer scientists. Volume 1, Elements of Classical Logic, deals with the background to what has come to be considered the standard formulation of predicate logic - both as far as its semantics and proof theory are concerned. The central chapter on predicate logic is followed by chapters outlining various alternative, but essentially equivalent ways of constructing the semantics for first-order logic as well as its proof theory. In addition, this volume contains a discussion of higher-order extensions of first-order logic and a compendium of the algorithmic and decision-theoretic prerequisites in the study of logical systems. Volume 2, Extensions of Classical Logic, surveys the most significant extensions of predicate logic and their applications to various philosophical fields of inquiry. The 12 chapters in this volume together provide a succinct introduction to a variety of intensional frameworks, a discussion of the most well-known logical systems, as well as an overview of major applications and of the open problems in the respective fields. Volume 3, Alternatives to Classical Logic, consists of a series of surveys of some of the alternatives to the basic assumptions of classical logic. These include many-valued logic, partial logic, free logic, relevance and entailment logics, dialogue logic, quantum logic and intuitionism. Volume 4, Topics in the Philosophy of Language, presents a panorama of the applications of logical tools and methods in the formal analysis of natural language. Since a number of developments in philosophical logic were originally stimulated by concern arising in the semantic analysis of natural language discourse, the chapters in this volume provide some criteria of evaluation of the applications of work in philosophical logic. In revealing both the adequacies and inadequacies of logical investigations in the semantic structures of natural discourse, these chapters also point the way to future developments in philosophical logic in general and thus close again the circle of inquiry relating logic and language.

_Russell_ journal (home office): E:CPBRRUSSJOURTYPE2501\REVIEWS.251 : 2005-09-14 19:58  Reviews RUSSELL’S INFLUENCE ON INGEMAR HEDENIUS S A Theology and Religious Studies / U. of Lund  , Lund, Sweden @. Svante Nordin. Ingemar Hedenius. En filosof och hans tid [Ingemar Hedenius. A philosopher and his time]. Stockholm: Natur och Kultur, . Pp. ;  photos.  kr. en years ago I wrote a review article about Gunnar Fredriksson’s book Tabout Bertrand Russell for Russell called “Russell’s Influence in Sweden”. In it I mentioned two Swedish philosophers who introduced and established analytic philosophy in Sweden. The oldest, Ingemar Hedenius (–), was professor in practical philosophy in Uppsala from  to ; the younger, Anders Wedberg (–), was professor in theoretical philosophy in Stockholm from  to . Together they had an enormous influence on the development of Swedish philosophy, since—among other things—they had the  See the review of Bertrand Russell: en intellektuelli i politiken, Russell, n.s.  (): –. _Russell_ journal (home office): E:CPBRRUSSJOURTYPE2501\REVIEWS.251 : 2005-09-14 19:58 Reviews  power to influence most of the new professors in philosophy. And they can both be called disciples of Bertrand Russell. The formal division between theoretical and practical philosophy goes back to Aristotle and Kant and consists in a distinction between the philosophy of thinking and the philosophy of acting. In practice it means that the former subject includes metaphysics, epistemology, philosophy of language and philosophy of mathematics and logic, while the latter deals with ethics, aesthetics, social philosophy and philosophy of religion. It was Wedberg who introduced Russell as a logician and a philosopher of mathematics and for a long time theoretical philosophers primarily wrote about logic and tried to apply the symbols of mathematical logic to classical philosophical problems. Russell’s influence on Hedenius was of a more general character that showed itself in his writings on ethics and religion, but also in his general attitude to life. In  Hedenius published a collection of essays called Tro och Vetande [Faith and Knowledge] that started a public discussion about the truth of Christianity that went on for years. The book was an undisguised attack on Swedish theology and Swedish theologians that caused a lot of hard feelings and undermined the reputation of theology as a legitimate academic subject. It was such a knock out that still today many Swedish theologians suffer from a “Hedenius complex”. (One could call it a “Russell complex”.) There is only one reference to Russell in Hedenius’ book and that is to Sceptical Essays, where Russell writes: “I wish to propose for the reader’s favourable consideration a doctrine which may, I fear, appear wildly paradoxical and subversive. The doctrine in question is this: that it is undesirable to believe a proposition when there is no ground whatever for supposing it true” (SE, p. ). Of course, Russell was not the first philosopher to endorse such a doctrine, which can be traced back to the spirit of Socrates and the old Greek sceptical philosophers, but Hedenius seems to have been impressed by Russell’s humorous and elegant way of formulating it. He took it to his heart and called it “den intellektuella moralens maxim”, which translates into “the maxim of intellectual morality” and sounds like an echo of Kingdon Clifford, although Hedenius might not have heard of him. Anyway, Hedenius thought that it was morally wrong to believe any proposition without having good reasons. With this maxim in mind he examined the major tenets of Christianity and found that very few—if any—passed the test, although he never seems to have doubted that Jesus existed, which he might have done, if he had examined the reasons for believing so more critically. From now on Hedenius was the best known and feared philosopher in Sweden. Another professor in Uppsala with a big sense of humour said: “There is no God and Ingemar Hedenius is his prophet.” Hedenius took an active part _Russell_ journal (home office): E:CPBRRUSSJOURTYPE2501\REVIEWS.251 : 2005-09-14 19:58  Reviews in many public discussions and wrote hundreds of newspaper articles, essays and close to  books that could be read by anyone. The influence of Russell is obvious in many of them, although he is seldom...

A distinguished international group of philosophers contribute new essays on central issues in philosophy of language and logic, in honour of Michael Dummett, one of the most influential philosophers of the late twentieth century. The essays are focused on areas particularly associated with Professor Dummett. Five are contributions to the philosophy of language, addressing in particular the nature of truth and meaning and the relation between language and thought. Two contributors discuss time, in particular the reality of the past. The last four essays focus on Frege and the philosophy of mathematics. The volume represents some of the best work in contemporary analytical philosophy.

This introduction discusses the development of Quine’s system over time and the centrality of structure to it. It explains the contributions made in this volume to our understanding of Quine’s thought on structure and ontology, especially with respect to philosophical logic, philosophy of language, history of philosophy, mathematics, philosophy of time, and set theory. Chapters by Michael Resnik, Frederique Janssen-Lauret and Fraser MacBride, John Collins, Jaroslav Peregrin, and Paul Gregory explore whether Quine’s structuralism is epistemological, language-based, or ontological. Greg Frost-Arnold, Robert Sinclair, and Gary Kemp and Andrew Lugg explore Quine’s views on structure from a historical point of view. Nathan Salmón, Gila Sher, Marianna Antonutti Marfori, and Natalja Deng consider Quine’s views on the structure of logic, language, and theories in relation to contemporary philosophy, specifically ontology, the philosophy of logic and mathematics, philosophy of set theory, and philosophy of time.

Gottlob Frege (1848–1925) was unquestionably one of the most important philosophers of all time. He trained as a mathematician, and his work in philosophy started as an attempt to provide an explanation of the truths of arithmetic, but in the course of this attempt he not only founded modern logic but also had to address fundamental questions in the philosophy of language and philosophical logic. Frege is generally seen (along with Russell and Wittgenstein) as one of the fathers of the analytic method, which dominated philosophy in English-speaking countries for most of the twentieth century. His work is studied today not just for its historical importance but also because many of his ideas are still seen as relevant to current debates in the philosophies of logic, language, mathematics and the mind. The Cambridge Companion to Frege provides a route into this lively area of research.

Walter Dubislav (1895–1937) was a leading member of the Berlin Group for scientific philosophy. This “sister group” of the more famous Vienna Circle emerged around Hans Reichenbach’s seminars at the University of Berlin in 1927 and 1928. Dubislav was to collaborate with Reichenbach, an association that eventuated in their conjointly conducting university colloquia. Dubislav produced original work in philosophy of mathematics, logic, and science, consequently following David Hilbert’s axiomatic method. This brought him to defend formalism in these disciplines as well as to explore the problems of substantiating (Begründung) human knowledge. Dubislav also developed elements of general philosophy of science. Sadly, the political changes in Germany in 1933 proved ruinous to Dubislav. He published scarcely anything after Hitler came to power and in 1937 committed suicide under tragic circumstances. The intent here is to pass in review Dubislav’s philosophy of logic, mathematics, and science and so to shed light on some seminal yet hitherto largely neglected currents in the history of philosophy of science.

In this path-breaking study Christopher Norris proposes a transformed understanding of the much-exaggerated differences between analytic and continental philosophy. While keeping the analytic tradition squarely in view, his book focuses on the work of Jacques Derrida and Alain Badiou, two of the most original and significant figures in the recent history of ideas. Norris argues that these thinkers have decisively reconfigured the terrain of contemporary philosophy and, between them, pointed a way beyond some of those seemingly intractable issues that have polarised debate on both sides of the notional rift between the analytic and continental traditions. In particular his book sets out to show - against the received analytic wisdom - that continental philosophy has its own analytic resources and is capable of bringing some much-needed fresh insight to bear on problems in philosophy of language, logic and mathematics. Norris provides not only a unique comparative account of Derrida's and Badiou's work but also a remarkably wide-ranging assessment of their joint contribution to philosophy's current - if widely resisted - potential for self-transformation.

In his later works, the great logician and mathematician Kurt Gödel concentrates his focus on the philosophical problems such as the implications of set theory, the grammar and philosophy of language, objectivity and relativity, the ontological proof of God’s existence, and phenomenology as an exact method. This essay explores how Gödel reads the philosophy (of logic and mathematics) of his time and why he turns his attention to Husserl’s phenomenology for describing the foundations of mathematics. To begin with, Gödel employs Husserl’s significant distinction between Weltanschauung (worldview) philosophy and philosophy as rigorous science: According to the Weltanschauung philosophy, the spirit of time constantly changes so that the ideas discussed and goals attempted are meant to be temporal, and not for the sake of eternal truths, but for that of their own perfection; philosophy as rigorous science, on the other hand, is supratemporal so that its aim is to discover absolute and timeless values. As for the worldview of his time, Gödel sees the development of philosophy and mathematics leaned toward skepticism, pessimism, and positivism. The antinomies of set theory, for instance shaked the grounds on which mathematics and logic are founded. Gödel, too, uses these paradoxes in his incompleteness theorems in order to prove that there are some statements which can neither be proved nor disproved within a system. That also means that arithmetic is not eligible to prove its own consistency. From this, however, Gödel does not come to a conclusion for a nihilism in mathematics and logic: These mere antinomies of set theory do not “necessarily” lead us to logical positivism, and neither to such a materialism, nor to any kind of pessimistic theory of knowledge. The incompleteness theorems assert that there are arithmetical propositions that are true but neither provable nor unprovable within its own calculus, so that arithmetic is intrinsically incomplete. However, instead of Alfred Tarski’s pathological view of examining the detections within the faulty system and then reforming the system all together, Gödel holds that we need to change our methods to find new patterns that describe the antinomies pointing to the unrecoverable reality of the mathematical world. Thus, Gödel does not follow any variation of the Weltanschauung philosophy of his time, either attempting to reduce mathematical realities to mathematical proofs in order to get rid of antinomies, or endeavoring to rescue a complete system of truths by a closed formal system, both Weltanschauung philosophies fail to set forth a realistic method. In this context, Gödel finds the task of phenomenology analogous to what he pursues in terms of a systematic framework for the foundations of mathematics. Husserl’s phenomenology, in Gödel’s account, proliferates the intuition of (mathematical) essences and provides a clarification of meaning of undefinable concepts, such as the antinomies of set theory. Applying the phenomenological reduction to the objective reality of the mathematical world, Gödel believes one obtains a clear experiential reality of the essential characteristics of (mathematical and logical) concepts. Briefly put, what Gödel finds in Husserl’s phenomenology that corresponds to his way of mathematical realism is a thoroughly designated method giving us mathematical essences back again.

This book defends a version of linguistic idealism, the thesis that the world is a product of language. In the course of defending this radical thesis, Gaskin addresses a wide range of topics in contemporary metaphysics, philosophy of language, philosophical logic, and syntax theory. Starting from the context and compositionality principles, and the idea of a systematic theory of meaning in the Tarski–Davidson tradition, Gaskin argues that the sentence is the primary unit of linguistic meaning, and that the main aspects of meaning, sense and reference, are themselves theoretical posits. Ontology, which is correlative with reference, emerges as language-driven. This linguistic idealism is combined with a realism that accepts the objectivity of science, and it is accordingly distinguished from empirical pragmatism. Gaskin contends that there is a basic metaphysical level at which everything is expressible in language; but the vindication of linguistic idealism is nuanced inasmuch as there is also a derived level, asymmetrically dependant on the basic level, at which reality can break free of language and reach into the realms of the unnameable and indescribable. Language and World will be of interest to scholars and advanced students working in metaphysics, philosophy of language, and linguistics.

The paper focuses on the review of current literature on formal philosophy. Special attention is paid to the review of the book «Introduction to Formal Philosophy» [Hansson, Hendricks, 2018]. The book is a consistent introduction to the problems of formal philosophy, a research tradition that relies on the precise mathematical tools in order to study traditional philosophical problems. The methods of formal philosophy are successfully applied not only to the problems of ontology, epistemology and philosophy of language but also relevant for the problems of ethics, axiology and social philosophy. The book demonstrates that it is not correct to identify formal philosophy with another area of study – philosophical logic, since formal philosophy uses not only logical methods of analysis, but also uses the tools of game theory, decision theory, probability theory, Bayesian statistics, and other theories. Although the book has a propaedeutic character, it also contains some open problems. These problems include the aggregation of the opinions of the group under the condition of a conflicting base of premises in the theory of public choice, there are still open problems in the interpretation of Arrow’s impossibility theorem and others. Certainly, formalization in itself is not a general solution to the particular philosophical problem, but only a tool that allows to formulate a problem in a more rigorous and precise way, which sometimes allows to reveal some unexpected consequences, some implicit contradictions and new solutions. Despite the importance of the concept of coherence in ethics, decision theory, philosophy of law, Bayesian epistemology, philosophy of science, the existing formalizations of the concept of coherence are highly specialized for epistemology, researchers recognize the lack of the relevant explanatory models. Overall, the book is an excellent introduction in to the field of formal philosophy, which provides a general overview of different aspects of formal philosophy and the opportunity to study particular research topics by means of an extensive bibliography accompanying each of the chapters.

In Philosophical Logic, the Liar Paradox has been used to motivate the introduction of both truth value gaps and truth value gluts. Moreover, in the light of "revenge Liar" arguments, also higher-order combinations of generalized truth values have been suggested to account for so-called hyper-contradictions. In the present paper, Graham Priest's treatment of generalized truth values is scrutinized and compared with another strategy of generalizing the set of classical truth values and defining an entailment relation on the resulting sets of higher-order values. This method is based on the concept of a multilattice. If the method is applied to the set of truth values of Belnap's "useful four-valued logic", one obtains a trilattice, and, more generally, structures here called Belnap-trilattices. As in Priest's case, it is shown that the generalized truth values motivated by hyper-contradictions have no effect on the logic. Whereas Priest's construction in terms of designated truth values always results in his Logic of Paradox, the present construction in terms of truth and falsity orderings always results in First Degree Entailment. However, it is observed that applying the multilattice-approach to Priest's initial set of truth values leads to an interesting algebraic structure of a "bi-and-a-half" lattice which determines seven-valued logics different from Priest's Logic of Paradox.