The eight pieces constituting this Meeting Report are summaries of presentations made during a panel session at the 2011 Association for Practical and Professional Ethics (APPE) annual meeting held between March 3rd and 6th in Cincinnati. Lisa Newton organized the session and served as chair. The panel of eight consisted both of pioneers in the field and more recent arrivals. It covered a range of topics from how the field has developed to where it should be going, from identification of (...) issues needing further study to problems of training the next generation of engineers and engineering-ethics scholars. (shrink)
Fixing Frege is one of the most important investigations to date of Fregean approaches to the foundations of mathematics. In addition to providing an unrivalled survey of the technical program to which Frege’s writings have given rise, the book makes a large number of improvements and clariﬁcations. Anyone with an interest in the philosophy of mathematics will enjoy and beneﬁt from the careful and well informed overview provided by the ﬁrst of its three chapters. Specialists will ﬁnd the book an (...) indispensable reference and an invaluable source of insights and new results. Although Frege is widely regarded as the father of analytic philosophy, his work on the foundations of mathematics was for a long time rather peripheral to the ongoing research. The main reason for this is no doubt Russell’s discovery in 1901 that the paradox now bearing his name can be derived in Frege’s logical system. But recent decades have seen a huge surge of interest in Fregean approaches to the foundations of mathematics. (The work of George Boolos, Kit Fine, Bob Hale, Richard Heck, Stewart Shapiro, and Crispin Wright is singled out for particular attention in the present monograph.) A variety of consistent theories have been discovered that can be salvaged from Frege’s inconsistent system, and foundational and philosophical claims have been made on behalf of many of these theories. Burgess claims quite plausibly that the signiﬁcance of any such modiﬁed Fregean theory will in large part depend on how much of ordinary mathematics it enables us to develop.1 His.. (shrink)
Numbers and other mathematical objects are exceptional in having no locations in space or time or relations of cause and effect. This makes it difficult to account for the possibility of the knowledge of such objects, leading many philosophers to embrace nominalism, the doctrine that there are no such objects, and to embark on ambitious projects for interpreting mathematics so as to preserve the subject while eliminating its objects. This book cuts through a host of technicalities that have obscured previous (...) discussions of these projects, and presents clear, concise accounts of a dozen strategies for nominalistic interpretation of mathematics, thus equipping the reader to evaluate each and to compare different ones. The authors also offer critical discussion, rare in the literature, of the aims and claims of nominalistic interpretation, suggesting that it is significant in a very different way from that usually assumed. (shrink)
The form of nominalism known as 'mathematical fictionalism' is examined and found wanting, mainly on grounds that go back to an early antinominalist work of Rudolf Carnap that has unfortunately not been paid sufficient attention by more recent writers.
Quine correctly argues that Carnap's distinction between internal and external questions rests on a distinction between analytic and synthetic, which Quine rejects. I argue that Quine needs something like Carnap's distinction to enable him to explain the obviousness of elementary mathematics, while at the same time continuing to maintain as he does that the ultimate ground for holding mathematics to be a body of truths lies in the contribution that mathematics makes to our overall scientific theory of the world. Quine's (...) arguments against the analytic/synthetic distinction, even if fully accepted, still leave room for a notion of pragmatic analyticity sufficient for the indicated purpose. (shrink)
What is the simplest and most natural axiomatic replacement for the set-theoretic definition of the minimal fixed point on the Kleene scheme in Kripke’s theory of truth? What is the simplest and most natural set of axioms and rules for truth whose adoption by a subject who had never heard the word "true" before would give that subject an understanding of truth for which the minimal fixed point on the Kleene scheme would be a good model? Several axiomatic systems, old (...) and new, are examined and evaluated as candidate answers to these questions, with results of Harvey Friedman playing a significant role in the examination. (shrink)
Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel’s incompleteness theorems, but also a large number of optional topics, from Turing’s theory of computability to Ramsey’s theorem. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a new and simpler treatment of the representability of recursive functions, a (...) traditional stumbling block for students on the way to the Godel incompleteness theorems. (shrink)
One textbook may introduce the real numbers in Cantor’s way, and another in Dedekind’s, and the mathematical community as a whole will be completely indifferent to the choice between the two. This sort of phenomenon was famously called to the attention of philosophers by Paul Benacerraf. It will be argued that structuralism in philosophy of mathematics is a mistake, a generalization of Benacerraf’s observation in the wrong direction, resulting from philosophers’ preoccupation with ontology.
This paper re-examines the question of whether quirks of early human foetal development tell against the view (conceptionism) that we are human beings at conception. A zygote is capable of splitting to give rise to identical twins. Since the zygote cannot be identical with either human being it will become, it cannot already be a human being. Parallel concerns can be raised about chimeras in which two embryos fuse. I argue first that there are just two ways of dealing with (...) cases of fission and fusion and both seem to be available to the conceptionist. One is the Replacement View according to which objects cease to exist when they fission or fuse. The other is the Multiple Occupancy View – both twins may be present already in the zygote and both persist in a chimera. So, is the conceptionist position tenable after all? I argue that it is not. A zygote gives rise not only to a human being but also to a placenta – it cannot already be both a human being and a placenta. Neither approach to fission and fusion can help the conceptionist with this problem. But worse is in store. Both fission and fusion can occur before and after the development of the inner cell mass of the blastocyst – the entity which becomes the embryo proper. The idea that we become human beings with the arrival of the inner cell mass leads to bizarre results however we choose to accommodate fission and fusion. (shrink)
Recent philosophy of language has been profoundly impacted by the idea that mainstream, model-theoretic semantics is somehow incompatible with deflationary accounts of truth and reference. The present article systematizes the case for incompatibilism, debunks circularity and “modal confusion” arguments familiar in the literature, and reconstructs the popular thought that truth-conditional semantics somehow “presupposes” a correspondence theory of truth as an inference to the best explanation. The case for compatibilism is closed by showing that this IBE argument fails to rule out (...) two kinds of deflationism: the position Field famously accused Tarski of having; and a less familiar version of the view that defines reference in terms of a deflated notion of truth. Finally, the distinction between unifying and constitutive explanation is used to forestall the response that correspondence theory is literally part of mainstream semantics. (shrink)
I aim to show how and why some definitions can be benignly circular. According to Lloyd Humberstone, a definition that is analytically circular need not be inferentially circular and so might serve to illuminate the application-conditions for a concept. I begin by tidying up some problems with Humberstone's account. I then show that circular definitions of a kind commonly thought to be benign have inferentially circular truth-conditions and so are malign by Humberstone's test. But his test is too demanding. The (...) inferences we actually use to establish the applicability of, e.g., colour concepts are designed to establish warranted assertability and not truth. Understood thus, dispositional analyses are not inferentially circular. (shrink)
A new axiomatization of set theory, to be called Bernays-Boolos set theory, is introduced. Its background logic is the plural logic of Boolos, and its only positive set-theoretic existence axiom is a reflection principle of Bernays. It is a very simple system of axioms sufficient to obtain the usual axioms of ZFC, plus some large cardinals, and to reduce every question of plural logic to a question of set theory.
There are three general ways to approach reconciliation: from the side of nonfactualism, from the side of deflationism, or from both sides at once. To approach reconciliation from a given side, as I will use the expression, just means to attend in the first instance to the details of that side’s position. (It will be important to keep in mind that the success of an approach from one side may ultimately require concessions from the other side.) The only attempts at (...) reconciliation in the literature of which I am aware fall in to the first of these three categories. Such writers argue that the tension between our –isms can be resolved by paying sufficiently close attention to the nature of nonfactualism. While I have nothing against this approach in principle, I do have reservations about the particular proposals that have been made in its pursuit. The first section of the present paper briefly develops a line of objection against one such proposal, in order to motivate the approach to reconciliation from the side of deflationism. In section two, I argue that the deflationist can and should reject the inference from (2) to (3) above. Section three addresses a special problem of reconciliation for the nonfactu- alist who continues to use the discourse she takes to be factually defective. By paying close attention to the details of deflationism about reference, I show how a deflationist about truth might avoid this problem. I conclude that deflationism can be developed in a way that renders it compatible with nonfactualism. (shrink)
One thousand stones, suitably arranged, might form a heap. If we remove a single stone from a heap of stones we still have a heap; at no point will the removal of just one stone make sufficient difference to transform a heap into something which is not a heap. But, if this is so, we still have a heap, even when we have removed the last stone composing our original structure. So runs the Sorites paradox. Similar paradoxes can be constructed (...) with any predicate which, like 'heap', displays borderline vagueness. Although I have frequently heard it said that there is no completely credible and satisfying dissolution of the paradoxes of the Sorites family; and although there is no possible approach to dissolution which has not been at least partially explored, philosophers continue glibly to use vague language as though it were entirely unproblematic. Since no argument has ever been produced which would justify our ignoring the para~doxes, this situation is extremely unsatisfactory. (shrink)
Appointment as a director of a company board often represents the pinnacle of a management career. Worldwide, it has been noted that very few women are appointed to the boards of directors of companies. Blame for the low numbers of women of company boards can be partly attributed to the widely publicized "glass ceiling". However, the very low representation of women on company boards requires further examination. This article reviews the current state of women's representation on boards of directors and (...) summarizes the reasons as to why women are needed on company boards. Given that more women on boards are desirable, the article then describes how more women could be appointed to boards, and the actions that organizations and women could take to help increase the representation of women. Finally, the characteristics of those women that have succeeded in becoming members of company boards are described from an international perspective. Unfortunately, answers to the vexing question of whether these women have gained board directorships in their own right as extremely competent managers, or whether they are mere token female appointments in a traditional male dominated culture, remains elusive. (shrink)
Saul Kripke has made fundamental contributions to a variety of areas of logic, and his name is attached to a corresponding variety of objects and results. 1 For philosophers, by far the most important examples are ‘Kripke models’, which have been adopted as the standard type of models for modal and related non-classical logics. What follows is an elementary introduction to Kripke’s contributions in this area, intended to prepare the reader to tackle more formal treatments elsewhere.2 2. WHAT IS A (...) MODEL THEORY? Traditionally, a statement is regarded as logically valid if it is an instance of a logically valid form, where a form is regarded as logically valid if every instance is true. In modern logic, forms are represented by formulas involving letters and special symbols, and logicians seek therefore to define a notion of model and a notion of a formula’s truth in a model in such a way that every instance of a form will be true if and only if a formula representing that form is true in every model. Thus the unsurveyably vast range of instances can be replaced for purposes of logical evaluation by the range of models, which may be more tractable theoretically and perhaps practically. Consideration of the familiar case of classical sentential logic should make these ideas clear. Here a formula, say (p & q) ∨ ¬p ∨ ¬q, will be valid if for all statements P.. (shrink)
This paper aims to make three contributions to decision theory. First there is the hope that it will help to re-establish the legitimacy of the problem, pace various recent analyses provided by Maitzen and Wilson, Slezak and Priest. Second, after pointing out that analyses of the problem have generally relied upon evidence that is conditional on the taking of one particular option, this paper argues that certain assumptions implicit in those analyses are subtly flawed. As a third contribution, the piece (...) aims to draw attention to an important similarity between Newcomb’s problem and the toxin puzzle. In short, both problems illustrate the fact that you can have a reason to intend to φ without having a reason to actually φ. (shrink)
Metalinguistic descriptivism is the view that proper names are semantically equivalent to descriptions featuring their own quotations (e.g., ?Socrates? means ?the bearer of ?Socrates??). The present paper shows that Millians can actually accept an inferential version of this equivalence thesis without running afoul of the modal argument. Indeed, they should: for it preserves the explanatory virtues of more familiar forms of descriptivism while avoiding objections (old and new) to Kent Bach's nominal description theory. We can make significant progress on Frege's (...) puzzle and Plato's beard without committing ourselves one way or the other on the semantic values of proper names. The view on offer can also be motivated by analogy with Tarski's schema T, inviting the idea that the equivalence between a name and the associated nominal description has more to do with the semantics of representational locutions than it does with names per se. My response to the modal argument exploits the Kripkean distinction between reference at a world and reference in a world, and can be accepted by metalinguistic descriptivists and Millians alike. (shrink)
A revision of a sermon on the evils of calling model theory “semantics”, preached at Notre Dame on Saint Patrick’s Day, 2005. Provisional version: references remain to be added. To appear in Mathematics, Modality, and Models: Selected Philosophical Papers, coming from Cambridge University Press.
The argument from potential has been hard to assess because the versions presented by friends and those presented by enemies have born very little resemblance to each other. I here try to improve this situation by attempting to bring both versions into enforced contact. To this end, I sketch a more detailed analysis of the modern concept of potential than any hitherto attempted. As one would expect, arguments from potential couched in terms of that notion are evident non-starters. I then (...) ask how the modern notion of potential needs to be supplemented in order to produce a more convincing argument. I then enquire whether the supplementations utilised in the most distinguished recent presentations of the argument have anything better than an ad hoc role to play in contemporary metaphysics. I conclude that the rehabilitation of the argument is unlikely; in any event, the onus of proof seems to be on the friend of that argument to show that it is uncontrived. Finally, I argue that the (modern) notion of potential has an important role to play in any plausible account of foetal value. (shrink)
Dummett's case against platonism rests on arguments concerning the acquisition and manifestation of knowledge of meaning. Dummett's arguments are here criticized from a viewpoint less Davidsonian than Chomskian. Dummett's case against formalism is obscure because in its prescriptive considerations are not clearly separated from descriptive. Dummett's implicit value judgments are here made explicit and questioned. ?Combat Revisionism!? Chairman Mao.
There are statements of the form “There are no Fs” that we would like to count as true, yet it is hard to see how they could be true (at least, operating within the semantic framework of structured propositions). The relevant Fs are general terms that we take to be semantically fundamental or primitive, especially those native to metaphysical discourse. A case can be made the problem is no less difficult than the corresponding problem for singular terms.
The question, "Which modal logic is the right one for logical necessity?," divides into two questions, one about model-theoretic validity, the other about proof-theoretic demonstrability. The arguments of Halldén and others that the right validity argument is S5, and the right demonstrability logic includes S4, are reviewed, and certain common objections are argued to be fallacious. A new argument, based on work of Supecki and Bryll, is presented for the claim that the right demonstrability logic must be contained in S5, (...) and a more speculative argument for the claim that it does not include S4.2 is also presented. (shrink)
: Decisions about funding health services are crucial to controlling costs in health care insurance plans, yet they encounter serious challenges from intellectual property protection—e.g., patents—of health care services. Using Myriad Genetics' commercial genetic susceptibility test for hereditary breast cancer (BRCA testing) in the context of the Canadian health insurance system as a case study, this paper applies concepts from social contract theory to help develop more just and rational approaches to health care decision making. Specifically, Daniels's and Sabin's "accountability (...) for reasonableness" is compared to broader notions of public consultation, demonstrating that expert assessments in specific decisions must be transparent and accountable and supplemented by public consultation. (shrink)
The discovery of the note cards for Quine’s previously unpublished 1946 lecture on nominalism provides an obvious occasion for commenting on the differences between the issue of nominalism as Quine first publicized it to a wide philosophical audience and the issue of nominalism as debated among Quine’s successors today. Yet as I read and reread the text of Quine’s lecture, I found myself struck less by the differences between Quine’s position there and the positions of present-day writers than by differences (...) between Quine’s position there and the positions of Quine himself in later writings — and not his writings from many years later but his writings from the next few years, and especially one of his writings from the very next year, his notorious joint paper with Goodman. (shrink)
In this era when results of empirical scientific research are being appealed to all across philosophy, when we even find moral philosophers invoking the results of brain scans, many profess to practice "naturalized epistemology," or to be "epistemological naturalists." Such phrases derive from the title of a well-known essay by Quine, but Paul Gregory's thesis in the work under review is that there is less connection than is usually assumed between Quine's variety of naturalized epistemology and what is today taken, (...) by opponents and proponents alike, to constitute epistemological naturalism. To put it bluntly, as Gregory does in the opening sentence of his introduction, Quine "has not been well understood." If there is less connection between the Quinian and other epistemological naturalisms than there has often been taken to be, on Gregory's account there is also much more connection between Quine's position on epistemology and his positions on other contentious issues. (shrink)
The source, status, and significance of the derivation of the necessity of identity at the beginning of Kripke’s lecture “Identity and Necessity” is discussed from a logical, philosophical, and historical point of view.