Philosophy and Model Theory

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.

Model theory for universal classes with the amalgamation property: A study in the foundations of model theory and algebra

Frege, Gottlob (1848–1925)

From the Editors Charles Chihara is the most senior of the philosophers contributing to this book. He appears to be genuinely interested in having his philosophy of mathematics be one that is acceptable to mathematicians. One would think that this is requisite; what is the point of a philosophy of X that people who work in X view as absurd? But there has not been much interaction between the two communities (mathematicians and philosophers of mathematics) in the last half century. As he notes in his chapter, Charles Chihara started out as a mathematician and has both a brother and a niece who are mathematicians. He thus has a better feel for what will make sense to a mathematician than do many philosophers of mathematics. His writings are normally quite accessible to mathematicians, and this one is especially so . His chapter walks a rather delicate line. Since Chihara is a nominalist, he is not willing t commit to the existence of any mathematical objects, including structures. Yet it is important from his viewpoint that we do have mathematical knowledge. Chihara's solution is a sort of structuralism, but without a commitment to the existence of structures. It is a rather delicate balance, but it is certainly a thoughtful one . Charles Chihara is an Emeritus Professor of Philosophy at the University of California, Berkeley (sophos.berkeley.edu/chihara/). Chihara has published nearly fifty articles in his principal areas of interest: philosophy of mathematics and philosophy of logic. He has also published widely in the philosophy of science and confirmation theory, as well as on the philosophies of Wittgenstein, Russell, Quine, Goodman and Davidson .

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.

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.

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.

During his long career, Rudolf Carnap held various different views about the concept of truth and its philosophical significance. As a good logical empiricist, he insisted on the distinction between logical and factual statements, and employed his technical powers to give rigorous characterizations of the notions of logical, analytic, and factual truth. The development of Carnap’s views reflected his ability to quickly absorb new influences and his broad interests ranging from logic to epistemology, philosophy of language, and philosophy of science (Sections 1 and 2). Carnap was the co-founder of logical semantics with Alfred Tarski (Section 3), and therefore it is especially interesting to see how Carnap’s work was related to Tarski’s early definition of truth and to the later Tarskian model theory (Section 4). In Section 5, we discuss some difficulties in Carnap’s liberally empiricist treatment of scientific theories. The final section 6 makes some remarks on Carnap’s contemporary relevance.

Abstract

This chapter attacks the belief that metaphor is needed in order to think, express, communicate, or discover certain things. This claim is dubbed the ‘Indispensability Thesis’. This thesis is accepted by a variety of metaphysicians, philosophers of language, philosophers of science, philosophers of mathematics, and philosophers of religion. Some aestheticians appeal to it to explain metaphor’s prevalence in critics’ descriptions of artworks and of our responses to them. The chapter argues that recent arguments for metaphor’s indispensability, by Stephen Yablo, Richard Boyd, Elisabeth Camp, and Berys Gaut, are unconvincing. It provides an explanation of why the Indispensability Thesis seems plausible. It also distinguishes it from several related claims about metaphor. Some of these other claims are plausible, and the Indispensability Thesis acquires an air of plausibility when not clearly distinguished from them. The chapter concludes that the thesis is far from obviously true, and has not been supported by convincing arguments.

_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.

Mary Kate McGowanAssistant Professor of Philosophy at Wellesley College. She works in metaphysics, philosophy of language and philosophy of science. Forthcoming articles include ‘Gruesome Connections’ in Philosophical Quarterly and ‘Privileging Properties’ in Philosophical Studies.Anthony SkillenRecently retired as lecturer in the Philosophy Department of the University of Kent at Canterbury.Charles D. TarltonProfessor of Political Science at the University of Albany. In recent years he has written on Locke, Machiavelli, and Hobbes. He is currently engaged in an analysis of the structural ambiguities of Rousseau's Discours sur l'origine et les fondaments de l'inegalité parmi les hommes.Stephen J. BoulterSenior Lecturer in Philosophy at Oxford Brookes University. His research areas include the philosophy of language, the philosophy of science and medieval philosophy.Gabriele De AnnaA tutor in the Philosophy Department at St Andrews and research fellow at the University of Padua, Italy. He has published papers in American, British and Italian journals and is the author of the forthcoming book, Realismo Metafisico e Rappresentazione Mentale (Padua: Il Poligrafo).Roy SorensenRoy Sorensen seeks Fame and Fortune as a Dartmouth College philosophy professor. He is the author of Blindspots, Thought Experiments and Pseudo-Problems, and most recently Vagueness and Contradiction.David BeiseckerAssistant Professor of Philosophy at the University of Nevada, Las Vegas. He has published articles in the philosophy of mind and language, with an eye towards writing a book on the metaphysics of mind and meaning.

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.

Volume I: 1. Idealist Origins: 1920s and Before by Martin Davies and Stein Helgeby.- 2. John Anderson Arrives: 1930s by Mark Weblin.- 3. The Influence of Wittgenstein: 1940s by Graeme Marshall.- 4. Reconstruction and Enthusiasm by Brian F. Scarlett.- 5. Political Polarisation: 1960s by John Burnheim and Paul Crittenden.- 6. Turbulent Times: 1970s by Aubrey Townsend.- 7. Achievements of the 1980s by Lynda Burns.- 8. The Canberra Plan and the Diversification of Australasian Philosophy: 1990s by John Quilter.- 9. Philosophers in Schools: 2000s by Graham Oppy. Volume II: 10. From Conventionalism to Scientific Metaphysics by Brian Ellis.- 11. Metaphysics by John Bigelow.- 12. Epistemology by Stephen Hetherington.- 13. Philosophy of Language by Frederick Kroon with Appendix: The University of Melbourne, Philosophy of Language, and the Oxford Connection by Denis Robinson.- 14. Philosophy of Religion in Australasia: Philosophy of Religion in Australia by Peter Forrest and Philosophy of Religion in New Zealand by John Bishop & Ken Perszyk.- 15. Aesthetics and Philosophy of Music in Australasia: Aesthetics in Australasia: 1945-2005 by Ismay Barwell and Philosophy of Music in Australasia by Justine Kingsbury.- 16. Moral Philosophy in Australasia by Justin Oakley.- 17. Environmental Philosophy by Freya Matthews.- 18. Feminist Philosophy by Catriona Mackenzie.- 19. Black Swan: A History of Continental Philosophy in Australia and New Zealand by Robert Sinnerbrink & Matheson Russell.- 20. Logic by Ross Brady & Chris Mortensen.- 21. History and Philosophy of Science by Brian Ellis, Rod Home, David Oldroyd, Robert Nola, Howard Sankey, Keith Hutchison, Neil Thomason, John Wilkins, John Forge, Philip Catton & Ruth Barton.- 22. Philosophy of Mind and Cognitive Science since 1980 by Elizabeth Schier & John Sutton.