This paper argues that Carnap both did not view and should not have viewed Frege's project in the foundations of mathematics as misguided metaphysics. The reason for this is that Frege's project was to give an explication of number in a very Carnapian sense — something that was not lost on Carnap. Furthermore, Frege gives pragmatic justification for the basic features of his system, especially where there are ontological considerations. It will be argued that even on the question of the (...) independent existence of abstract objects, Frege and Carnap held remarkably similar views. I close with a discussion of why, despite all this, Frege would not accept the principle of tolerance. (shrink)

Carnap's position on mathematical truth in The Logical Syntax of Language has been attacked from two sides: Kreisel argues that it is formalistic but should not be, and Friedman argues that it is not formalistic but needs to be. In this paper I argue that the Carnap of Syntax does not eliminate our ordinary notion of mathematical truth in favour of a formal analogue; so Carnap's notion of mathematical truth is not formalistic. I further argue that there is no conflict (...) between Carnap's use of informal notions and his principle of tolerance; so Carnap's definition of mathematical truth need not be formalistic. CiteULike Connotea Del.icio.us What's this? (shrink)

From 1953 to 1959 Gödel worked on a response to Carnap’s philosophy of mathematics. The drafts display Gödel’s familiarity with Carnap’s position from The Logical Syntax of Language, but they received a dismissive reaction on their eventual, posthumous, publication. Gödel’s two principal points, however, will here be defended. Gödel, though, had wished simply to append a few paragraphs to show that the same arguments apply to Carnap’s later views. Carnap’s position, however, had changed significantly in the intervening years, and to (...) a significant extent, this mature position realizes much of what Gödel himself wanted out of a philosophy of mathematics. (shrink)

This paper will deal with three questions regarding Carnap's transition from the position he held at the time of writing Syntax to the doctrines he held during his semantic phase: (1) What was Carnap's attitude towards truth at the time of writing Syntax? (2) What was Carnap's position regarding questions of reference and ontology at the time of writing Syntax? (3) Was Carnap's acceptance of Tarski's analysis of truth and reference detrimental to his philosophical project? Section 1 of this paper (...) will deal with the first of these questions. Special attention will be paid to identifying what it was that prevented Carnap from defining a truth predicate for descriptive languages in Syntax. Section 2 of this paper will deal with the question of Carnap's attitude towards reference and ontology in Syntax. It will be shown that the attempt in Syntax to address ontological questions is seriously defective. Section 3 of this paper addresses the last of the questions posed above. It is argued that in the light of what is established in Sections 1 and 2, Carnap could not have retained the position of Syntax with respect to truth and reference. (shrink)

This paper investigates the relation between Carnap and Quine’s views on analyticity on the one hand, and their views on philosophical analysis or explication on the other. I argue that the stance each takes on what constitutes a successful explication largely dictates the view they take on analyticity. I show that although acknowledged by neither party (in fact Quine frequently expressed his agreement with Carnap on this subject) their views on explication are substantially different. I argue that this difference not (...) only explains their differences on the question of analyticity, but points to a Quinean way to answer a challenge that Quine posed to Carnap. The answer to this challenge leads to a Quinean view of analyticity such that arithmetical truths are analytic, according to Quine’s own remarks, and set theory is at least defensibly analytic. (shrink)

Carnap’s ‘Empiricism, Semantics, and Ontology’ (Carnap (1950a), ESO hereafter) is certainly a classic of twentieth century analytic philosophy. For decades now, most undergraduates are expected to read it at some point in their studies. Lately, it is being seen as the inspiration for a host of positions in the field of metaontology. Despite the widespread agreement on the importance of the paper, there is a lack of agreement on what Carnap attempts to do in the paper. My main aim in (...) this chapter is to defend an interpretation of ESO by displaying its relation to Carnap’s earlier works. My secondary goal will be to draw a lesson from this discussion for Carnap’s later work on unobservable entities in science. (shrink)

Abstract At the time of The Logical Syntax of Language (Syntax), Quine was, in his own words, a disciple of Carnap’s who read this work page by page as it issued from Ina Carnap’s typewriter. The present paper will show that there were serious problems with how Syntax dealt with ontological claims. These problems were especially pronounced when Carnap attempted to deal with higher order quantification. Carnap, at the time, viewed all talk of reference as being part of the misleading (...) material mode of speech, and as such dismissed, rather than addressed, ontological problems. Central to the analysis in the present paper is the concept of an explication, which was seen by both Carnap and Quine as being of great philosophical importance. It will be shown that the concept of explication played a significant role in how each formulated their mature position on ontology. Both these final positions on ontology can also be seen as a evolving in reaction to Carnap’s flawed handling of ontological matters at the time of Syntax. Carnap, influenced by Tarski’s work on semantics, comes to believe that the concept of reference can be given an acceptable explication, and that by doing so we can see reference to abstract objects as unobjectionable. As a result, Carnap develops a position very different from the one presented in Syntax. Quine strongly rejected the instrumentalism of Syntax, and sought to give an explication of ontological questions that was language independent. This paper closes with a discussion of each’s understanding of the other’s position. (shrink)

This paper puts forward and defends an account of mathematical truth, and in particular an account of the truth of mathematical axioms. The proposal attempts to be completely nonrevisionist. In this connection, it seeks to satisfy simultaneously both horns of Benacerrafs work on informal rigour. Kreisel defends the view that axioms are arrived at by a rigorous examination of our informal notions, as opposed to being stipulated or arrived at by trial and error. This view is then supplemented by a (...) Fregean account of the objectivity and our knowledge of abstract objects. It is then argued that the resulting view faces no insurmountable metaphysical or epistemic obstacles. (shrink)

Gregory Lavers gives us a timeline of Waismann’s career, an overview of Waismann’s most significant publications in this later period and a detailed walkthrough from the first to the last paper of Waismann’s series on analyticity, “Analytic - Synthetic”. Lavers closes his paper with comparisons of Waismann and Quine as well as Waismann and Carnap. Both Waismann and Quine argue that the concept of analyticity is vague and both reject reductionism. However, behind these superficial similarities we find (...) fundamentally different epistemologies. According to Lavers, the web of inferential relations, spanning from every experience to any item of scientific knowledge, that supports the outlook suggested by Quine, is rejected as manifestly wrong by Waismann. Conversely, Lavers shows that despite superficial contrasts between Waismann and Carnap—Waismann being interested in the subtleties of natural language, Carnap in replacing these through explication—the two do not really oppose each other’s’ views on analyticity and necessary truth. (shrink)

In this paper I examine the fundamental views on the nature of logical and mathematical truth of both Frege and Carnap. I argue that their positions are much closer than is standardly assumed. I attempt to establish this point on two fronts. First, I argue that Frege is not the metaphysical realist that he is standardly taken to be. Second, I argue that Carnap, where he does differ from Frege, can be seen to do so because of mathematical results proved (...) in the early twentieth century. The differences in their views are, then, not primarily philosophical differences. Also, it might be thought that Frege was interested in analyzing our ordinary mathematical notions, while Carnap was interested in the construction of arbitrary systems. I argue that this is not the case: our ordinary notions play, in a sense, an even more important role in Carnap’s philosophy of mathematics than they do in Frege’s. Finally, I address Tyler Burge’s interpretation of Frege which is in opposition to any Carnapian reading of Frege. (shrink)

This paper argues that Frege is not the metaphysical platonist about mathematics that he is standardly taken to be. It is shown that Frege’s project has two distinct stages: the identification of what is true of our ordinary notions, and then the provision of a systematic account that shares the identified features. Neither of these stages involves much metaphysics. The paper criticizes in detail Dummett’s interpretation of §§55-61 of Grundlagen. These sections fall under the heading ‘Every number is a self-subsistent (...) object’ and are described by Dummett as containing the worst arguments put forward by Frege. It is argued that essentially all of Dummett’s interpretive points are mistaken. Finally, I show that Frege’s claims about the independence of mathematics from humans and their activities does not commit him to any particularly metaphysical position either. (shrink)

Quine’s ‘Two Dogmas of Empiricism’ is generally seen as overturning Carnap’s epistemological picture of mathematics and the sciences. However, I wish to stress how this paper grew out of arguments not having anything to do with large-scale epistemological concerns, but ones originally presented against quantified modal logic. Quine thought he could demonstrate the impossibility of adding anything like ordinary quantification to modal logic, but Barcan Marcus did exactly this. In fact, as I will argue, ‘Two Dogmas ...’ can be seen (...) as growing out of a 1947 paper of Quine’s where Barcan Marcus is the explicit target. Later, in certain exchanges with Quine, Barcan Marcus puts forward and defends a consistent and interesting position on matters of ontology and the philosophy of language. This chapter will examine Barcan Marcus’s role in both the debate over analyticity and the debate on (meta-)ontology. (shrink)

Of Zeno’s book of forty paradoxes, it was the first that attracted Socrates’ attention. This is the paradox of the like and the unlike. On contemporary assessments, this paradox is largely considered to be Zeno’s weakest surviving paradox. All of these assessments, however, rely heavily on reconstructions of the paradox. It is only relative to these reconstructions that there is nothing paradoxical involved, or that there is some rather obvious mistake being made. This paper puts forward and defends a novel (...) interpretation of this paradox, according to which the concept of a unit plays a central role. There is every reason to think the paradox turns on the concept of a unit: after the presentation of the paradox the text of the Parmenides immediately turns to a discussion of units, and the concept of a unit is also central to the Greek conception of a plurality. If this interpretation is correct then the paradox that Zeno presented was the same as one discussed and solved in Frege’s Grundlagen. (shrink)

This book has two main goals: first, to show that Quine's New Foundations set theory is better motivated than often assumed; and second, to defend Quine's philosophy of set theory. It is divided into three parts. The first concerns the history of set theory and argues against readings that see the iterative conception of set being the dominant notion of set from the very beginning. The second part concerns Quine's philosophy of set theory. Part 3 is a contemporary assessment of (...) the philosophical status of NF. Here one of the central targets is Boolos's defense of the iterative conception of set and his dismissal of NF as completely unnatural.As this is a very short review, I will avoid specific points and... (shrink)

Øystein Linnebo*. Philosophy of Mathematics. Princeton University Press, 2017. ISBN: 978-0-691-16140-2 ; 978-1-40088524-4. Pp. xviii + 203.

In this paper, I explain the curious role played by the Argument from Absolute Terms in Peter Unger's book Ignorance, I provide a critical presentation of the argument, and I consider some outstanding issues and the argument’s contemporary significance.

Virtually all historical treatments of just war recognize the importance of the account given by Thomas Aquinas in Summa theologiae II-II, q. 40, ?De bello?, where he outlines three conditions ? legitimate authority, just cause, and right intention ? for a justifiable use of armed force. It is, however, less well known that within the same section of the work (q. 50, a. 4) Aquinas extended his reflection on just war into a theory of military prudence. By placing generalship under (...) the category of ?prudence?, rather than ?art? or ?science?, he held that military command involves more than a morally neutral skill with victory as its sole aim. Building on the premise that service to the common good constitutes the overarching purpose of the military profession, Aquinas showed how the virtue of prudence provides an inner compass for decision-making amid the uncertainty and confusion of the battlefield. (shrink)

Henry Kyburg’s lottery paradox (1961, p. 197) arises from considering a fair 1000 ticket lottery that has exactly one winning ticket. If this much is known about the execution of the lottery it is therefore rational to accept that one ticket will win. Suppose that an event is very likely if the probability of its occurring is greater than 0.99. On these grounds it is presumed rational to accept the proposition that ticket 1 of the lottery will not win. Since (...) the lottery is fair, it is rational to accept that ticket 2 won’t win either—indeed, it is rational to accept for any individual ticket i of the lottery that ticket i will not win. However, accepting that ticket 1 won’t win, accepting that ticket 2 won’t win, . . . , and accepting that ticket 1000 won’t win entails that it is rational to accept that no ticket will win, which entails that it is rational to accept the contradictory proposition that one ticket wins and no ticket wins. (shrink)

Stoicism, a philosophy and set of practices developed in ancient times, commands ever-growing interest. Its present day, students, practitioners, teachers, and scholars adapt it to the challenges of modern life. This third volume brings together fifty pieces previously published in the Stoicism Today blog, ranging from personal essays to conference presentations, from bits of practical advice to history and interpretation, from polemics to symposia grappling with controversies, key issues, and central concepts. There is something for everyone in this volume. The (...) selections in this volume range over a vast array of topics. You will encounter authors applying Stoicism to parenting, medicine, psychotherapy, culinary arts, time-management, exercise and fitness, the emotions, relationships, the workplace, and the environment. Some selections examine useful practices, the nature and scope of the virtues, how to develop equanimity, resilience, and happiness. Comparative studies bring Stoicism into connection with Buddhism, mindfulness, self-help and productivity authors, and modalities of psychotherapy. This book bridges the gaps between philosophical reflection and practical wisdom, between study and interpretation of Stoicism, and its application to present-day issues and problems. The essays in this volume speak to anyone intending to start or to deepen a thoughtful Stoic life in the modern world. (shrink)

_Evolution and Human Culture_ surveys disciplines of evolutionary studies to posit that hominin evolved moral sentiments have been integral to the development of artistic culture.

Now in its twentieth year of publication, this rich collection, popular among teachers and students alike, provides an in-depth look at major cases that have shaped the field of medical ethics. The book presents each famous (or infamous) case using extensive historical and contextual background, and then proceeds to illuminate it by careful discussion of pertinent philosophical theories and legal and ethical issues.

The purpose of this article is to explore the close link between technology and death in the philosophical writings of Lewis Mumford. Mumford famously argued that throughout the history of western civilization we find intertwined two competing forms of technics; the democratic biotechnic form and the authoritarian monotechnic form. The former technics were said to be strongly compatible with an organic form of life while the latter were said to be allied to a mechanical power complex. What is perhaps less (...) well known is the extent to which Mumford characterizes the authoritarian technical form as being a technics of death. This article will argue that the connection between death and technics is a key theme in Mumford’s philosophy of technology. In addition to elaborating this theme and detailing how it informs Mumford’s other positions on the nature of technology, this article will also argue that Mumford’s theory of a technics of death bears witness, both implicitly and explicitly, to the influence of Sigmund Freud’s theory of the death instinct. Freud’s account of the death instinct will be outlined briefly and its influence on Mumford’s writings will be explained. Death, in Mumford’s technological writings, has a generally negative function and serves to warn humanity of the perilous course that its technological civilization is set upon. However it also has a positive function in that it encourages man to transcend its biological existence in acts of creativity and purpose. Death, in this positive sense, serves the purpose of life whereas, in the negative sense, it hinders it. The role of death, in both aspects, will be explored and related to Mumford’s overall perspective on technics and life. It is argued that Mumford’s philosophy of technology cannot be fully understood without an awareness of his views on death and its role in the life of technological society. (shrink)

This chapter contains sections titled: The Non‐Darwinian Revolution 1870–1880: The Struggle for Existence and Cultural Evolution 1880–1882: Nietzsche contra Spencer 1883–1888: The Will to Power as Bildungstrieb Conclusion.

ArgumentContrary to common portrayals of social Darwinism as a transference of laissez-faire values, the widely read evolutionism of Japan's foremost Darwinist of the early twentieth-century, Oka Asajirō (1868–1944), reflects a statist outlook that regards capitalism as the beginning of the nation's degeneration. The evolutionary theory of orthogenesis that Oka employed in his 1910 essay, “The Future of Humankind,” links him to a pre-Darwinian idealist tradition that depicted the state as an organism that develops through life-cycle stages. For Oka, laissez-faire capitalism (...) marked the moment when the state began to decline toward extinction due to the orthogenetic overdevelopment of hitherto subordinate individual egos. Because conservative bureaucrat-intellectuals had been drawing upon this same organicist-developmental tradition since the 1880s in an attempt to forestall the social ills of industrialism, Oka's call for statist measures, including eugenics, to lessen and delay the atomizing, enervating, and corrupting influence of capitalism articulated the political vision of officialdom. Statist evolutionism, not social Darwinism, might be the term that best describes Oka's approach. (shrink)

In 2020, it is clear that racism must be a moral priority for white American Catholics, as for all white Americans. To face racism maturely, our consciences need more robust formation than we received as children preparing for First Reconciliation—or as adolescents at Confirmation, when we were instructed that we must be prepared to act boldly to defend our commitment to Christ. One way to build a racially-mature conscience is to seek feedback from anti-racism accountability partners, as the author did. (...) Another is to explore the distinction in Catholic moral theology between invincible and vincible ignorance—what we can know and what we cannot—in order to discern whether an action or inaction is moral. Much of what liberal whites claim we can’t know without input from Blacks is readily available if we have ears to hear. (shrink)

This chapter contains sections titled: Vasconcelos and Essentialist Conceptions of Mestizaje Gloria Anzaldúa: The New Mestizaje María Lugones: Mestizaje and Hybridity The New Mestizaje and Race Mestizaje and Pan‐Hispanic Identity References Further Reading.

The Nicomachean Ethics is generally thought to be a “dialectical” work, aimed at resolving aporia in a set of endoxa, which it takes as its starting-point. I argue that Aristotle’s aim in the treatise is, rather, to produce definitions of key ethical terms, and that his starting-points are limited to evaluative and discriminative judgments of a certain sort, which are demanded by the nature of the discipline and are not endoxa. I discuss also how the definitions are reached (focusing on (...) the cases of the virtues of character) and the roles that aporiai do play in the process. (shrink)

Given its title, one might expect Ayn Rand's Introduction to Objectivist Epistemology (ITOE) to outline her positions on the issues normally covered in introductory courses and texts on epistemology. In particular, one might expect to find discussions of epistemic justification- i.e., "our right to the beliefs we have" (Dancy 2005, 263). Justification and the nature of knowledge are widely regarded as the essential subject matter of the field, and, as we will see, Rand effectively agrees with this consensus. 1 Yet (...) her monograph says little directly on these subjects. Rather, it is devoted entirely to the presentation of a theory of concepts. My subject in this essay is how a theory of concepts can be an introduction to an epistemology. More specifically, I will show how Rand's theory and the view of consciousness that it embodies relate to some concerns about justification that are familiar from the contemporary, analytic literature on epistemology. Though I will present some exegesis of Rand and some arguments in support of her positions and related theses of my own, this essay is not primarily exegetical or argumentative. My aim is, rather, to sketch the outlines of an epistemology in a way that brings out the relations between a seldom studied theory of concepts and some much debated questions about justification. I hope in doing so to shed light both on the theory and on the questions. I hope this paves the way for others to argue in greater detail for (or against) the theses I sketch here, and to do so in a way that engages more substantially with the analytic literature. In my view, the chief obstacle to work of this kind has been the lack of a big-picture account of the relation between the subject matter of ITOE and the central concern of analytic epistemology. This is the lack that I aim to remove. (shrink)

When the Origins of Species was published on 24 November 1859, its author, Charles Darwin, was near the end of a nine-week stay in the remote Yorkshire village of Ilkley. He had come for the 'water cure' - a regime of cold baths and wet sheets - and for relaxation. But he used his time in Ilkley to shore up support, through extensive correspondence, for the extraordinary theory that the Origin would put before the world: evolution by natural selection. In (...) Darwin in Ilkley, Mike Dixon and Gregory Radick bring to life Victorian Ilkley and the dramas of body and mind that marked Darwin's visit. (shrink)

Reinhold Niebuhr (1892-1971) may have been the most influential and insightful American thinker of the twentieth century. In dealing with the intricacies of human nature, society, politics, ethics, theology, racism and international relations, Niebuhr the teacher, preacher, philosopher, social critic and ethicist, was highly influential and difficult to ignore during the Second World War and Cold War eras because of his intellectual heft and the novel manner in which he addressed the economic, spiritual, social and political problems of his time. (...) This book distils Niebuhr's disparate and now difficult to access work into one volume, making it more easily accessible than ever before, at the same time bringing his work into the twenty first century. It argues that if he were alive today Niebuhr would be a champion of the U.N, a supporter of globalization, a fierce opponent of America's 2003 Iraq War (for all the reasons he opposed the Vietnam War), an advocate of the Responsibility to Protect, and a pragmatic hawk on China as it rises today. It also highlights his many contributions to international relations theory, from Realism to Liberalism to existentialism to the English School to constructivism. This is the first book that focuses exclusively on the international relations thought of Reinhold Niebuhr, one of Classical Realism's most important figures, one whom diplomat and Realist George Kennan called, "the father of us all.". (shrink)

A new translation of the 6th-century Taoist text Bai Yao Lu (Statutes of the Hundred Remedies), with practical commentary. Explains how the Hundred Remedies of the Bai Yao Lu offer a practical guide to what enlightened or sagely behavior looks like. Shows how each short verse of the Hundred Remedies presents a spiritual precept as a solution to the problems encountered in daily life and on the spiritual path. Provides insightful commentary for each of the Hundred Remedies, showing how they (...) relate to meditation practice and can help us navigate emotional and social challenges. (shrink)

Remapping Biology with Goethe, Schelling, and Herder recruits a Romantic philosophy of biology into contemporary debates to both integrate the theoretical implications of ecology, evolution, and development, and to contextualize the successes of the Modern Evolutionary Synthesis's gene's-eye-view of biology. The dominant philosophy of biology in the twentieth century was one developed within and for the Modern Evolutionary Synthesis. As biologists like those developing an Extended Evolutionary Synthesis have pushed the limits of this paradigm, fresh philosophical approaches have become necessary. (...) This book makes the case that an organicism developed by the 19th century figures Goethe, Schelling, and Herder offers surprising resources to navigate the contemporary biological and evolutionary terrain. This "metamorphic organicism" resonates with present trends in biological theory that emphasize process, organismal dynamics, ecology, and agency. It also proposes strategies for reintegrating reductive and mechanistic maps of biology, like those of the Modern Evolutionary Synthesis, into richer theoretical representations of life. Drawing from cutting-edge biology, Romantic history, and perspectival pluralist literatures, this integrated history-and-philosophy-of-biology will be of interest to students and scholars interested in the genesis of current theoretical tensions in evolutionary biology, and to those seeking constructive ways to resolve those tensions, including practicing biologists and educators. (shrink)