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

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)

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)

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)

In Complicity and Moral Accountability, Gregory Mellema presents a philosophical approach to the moral issues involved in complicity. Starting with a taxonomy of Thomas Aquinas, according to whom there are nine ways for one to become complicit in the wrongdoing of another, Mellema analyzes each kind of complicity and examines the moral status of someone complicit in each of these ways. Mellema's central argument is that one must perform a contributing action to qualify as an accomplice, and that it (...) is always morally blameworthy to perform such an action. Additionally, he argues that an accomplice frequently bears moral responsibility for the outcome of the other's wrongdoing, but he distinguishes this case from cases in which the accomplice is tainted by the wrongdoing of the principal actor. He further distinguishes between enabling, facilitating, and condoning harm, and introduces the concept of indirect complicity. Mellema tackles issues that are clearly important to any case of collective and shared responsibility, yet rarely discussed in depth, always presenting his arguments clearly, concisely, and engagingly. His account of the nonmoral as well as moral qualities of complicity in wrongdoing--especially of the many and varied ways in which principles and accomplices can interact--is highly illuminating. Liberally sprinkled with helpful and nuanced examples, Complicity and Moral Accountability vividly illustrates the many ways in which one may be complicit in wrongdoing. "In Complicity and Moral Accountability, Gregory Mellema has made an immensely important contribution to the discussion of group morality and collective responsibility both within and far beyond professional academic philosophy. His clearly written book will be essential reading." --Fergus Kerr, Honorary Fellow, University of Edinburgh. (shrink)

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.

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)

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.

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)

Death is the destiny we all share, and this will not change. Yet the way we die, which had remained the same for many generations, has changed drastically in a relatively short time for those in developed countries with access to healthcare. For generations, if people were lucky enough to reach old age, not having died in infancy or childhood, in childbirth, in war, or by accident, they would take to bed, surrounded by loved ones who cared for them, and (...) fade into death. Most likely, they would have seen their parents and grandparents die the same way, and so this manner of dying would be familiar: it was part of the natural cycle of life. Now less than 25 per cent of Americans die at home, having reached much older ages than people would have dreamed of in past generations, often after surviving many illnesses and even diseases that would have been terminal for their grandparents. We are fortunate to live (and die) today, supported by myriad scientific, medical, and technological advancements, however we also face new problems as a result of the new way in which we die. We can no longer anticipate a peaceful waning at home with family. We know our lives will likely end in hospitals likely after we have endured grueling treatments to prolong life. We have to decide what decisions we want our loved ones, or care-givers, to make when we cannot choose for ourselves. We have to think about whether in any circumstances we would seek physician-assisted death. We know we face other questions as well, but we may not even know where to start. In the face of these decisions, we can feel daunted and afraid. The best remedy is information and planning. In this book, Gregory Eastwood - a physician who has cared for dying patients, served as an ethics consultant, and taught end of life issues to medical and other health profession students - draws from his substantial experience with patients and families to provide the information that will help us think clearly about the choices and issues we will face at the end of our own lives, and when faced with the deaths of our loved ones. With sensitivity and profound insight, Eastwood guides us through all the important questions about death and dying in straightforward, clear language, enhanced by real-life stories. Throughout, he shows us how we can take ownership of the way we want to die, when we must die, and feel more in control as death approaches. (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)

Preliminary Abstract: -/- The late Mary Midgley (1919-2018) was one of the most relevant and wide-ranging moral philosophers of the last century. For over forty years, she drew attention to the necessity of philosophy in everyday life while making significant contributions on such topics as human nature, ethics, animals and the environment, science, religion, and other real-world issues. Midgley’s remarkable career saw the publication of over 250 books, journal articles, pamphlets, and other materials, concluding with the publication of What Is (...) Philosophy For? at age 99, just one month before her death. This work was the last in a series of publications late in Midgley’s career that underscored her reputation as a singular thinker and a shining example of the significant presence of women in philosophy. -/- Mary Midgley on What Matters offers a window into this noteworthy period late in Midgley’s career. This volume invites the reader into a series of visits and conversations between Gregory McElwain and Mary Midgley at her home in Newcastle from 2011-2018. Framed and thematically curated by McElwain, these conversations present Midgley’s thoughts, reminiscences, and concerns on life and the topics for which she is best known, with special emphasis on her influential perspective on animals and the environment. Midgley’s witty and lively voice is emphasized throughout this accessbile book, engaging the reader with one of the more vibrant philosophers in living memory. (shrink)

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 collection of new essays addresses emotion in relation to the arts. The essays consider such topics as the paradox of fiction, emotion in the pure and abstract arts, and the rationality and ethics of emotional responses to art.

This book offers a philosophical approach to religion that acknowledges both the diversity of religions and the many and varied dimensions of the religious life. Rather than restricting itself to Christian theism, it covers a wide range of religious traditions, examining their beliefs in the context of the actual practice of the religious life. After outlining the aims of religion, the book focuses on claims to knowledge. What kinds of knowledge do religions purport to offer? In what idiom is it (...) couched? From what sources do devotees draw their claims to knowledge? Are these sources reliable? Rather than trying to settle age-old questions about religious belief, the book offers its readers a set of criteria with which they can make informed decisions in matters of faith. Gregory W. Dawes is Associate Professor in Philosophy at the University of Otago, New Zealand. He completed his first graduate degree at the Pontifical Biblical Institute in Rome before returning to New Zealand to complete PhD degrees in both biblical studies and philosophy. His previous books include The Historical Jesus Question, Theism and Explanation, and Galileo and the Conflict between Religion and Science. (shrink)

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)

This chapter contains sections titled: Cheerful Resignation Self‐Sufficiency Murphy was an Optimist: Negative Visualization Agency and Control Fate, Freedom, and Sailing.

This chapter contains sections titled: Classical Theories of Success Morris's 3‐D Approach to Life Lance Discovers His Positive Talents Lance Develops His Talents: Pre‐Cancer Lance Develops His Talents: Post‐Cancer Lance Deploys His Talents Notes.

This chapter focuses on one of the common fallacies in Western philosophy, appeal to ridicule. An appeal to ridicule is closely related to an ad hominem argument because both attack the person. There is a similarity between an appeal to ridicule and an appeal to emotion in that both attempt to bypass rational assessment of a point of view and elicit an emotional reaction from the audience. An appeal to ridicule may be an attempt to elicit humor at another's expense, (...) or it may be an attempt to elicit enmity, playing on the fears and prejudices of the group. The difference between a reductio ad absurdum and an appeal to ridicule is that the former uses good evidence while the latter does not. Perhaps the best way to avoid this fallacy is to cultivate an attitude of respect for other points of view. (shrink)

This chapter contains sections titled: Warning: Plot Spoiler! Mediums: The Seen and the Felt Competing Messages: “Man was in the Forest” vs. “There is Another” Challenging Bambi Bambi's Counter‐Charge Re‐gifting Bambi Notes.

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.