The central question which I address is whether appeal to a hypothetical contract between moral persons is acceptable as a method for justifying basic ethical principles. ;My first two substantive chapters concern general issues in metaethics, particularly the shortcomings of both standard naturalist and noncognitivist theories of evaluative language; some conditions of acceptability for methods of moral justification are proposed and supported as well. Firth's and Hare's methods fail to satisfy these criteria, while Brandt's present approach and Rawls' method (...) of reflective equilibrium largely succeed. Rawls, quite correctly, intends his contract argument to apply only within the framework of this more basic method. ;Major aspects of Rawls' contract theory are examined at length in Chapter IV. My central concern is with the reasons Rawls gives for regarding his interpretation of the initial contract situation as the "rationally preferred" one. The concepts of impartiality, neutrality, and fairness are discussed at the outset. I then proceed to explain and criticize Rawls' reasons for imposing a "thick veil of ignorance" on the contractors. The argument that natural assets and social contingencies are "morally arbitrary" and hence should not influence the choice of principles of justice is found to be open to serious objection and to rest upon a specific type of egalitarian moral commitment. Rawls' "Kantian" argument is shown to lack sufficient support and to involve an unwarranted exclusion of certain deontological, perfectionist, and other teleological theories from serious consideration. ;Grice's contract theory, which omits the "veil," is examined in Chapter V, together with his account of prudential reasoning and his argument for a necessary connection between moral obligation and rationality. His type of contract approach is demonstrated to be unworkable due to vague description of the initial situation. Moreover, it has unacceptable implications and cannot serve as an appropriate basis for moral justification in any case. ;I conclude that the ideal contract method is at best a very conditional procedure of moral justification, far more suitable for some types of moral conceptions than for others. It seems unlikely, furthermore, that achievement of wide reflective equilibrium or "full rationality" in Brandt's sense would result in a consensus favoring any one description of the initial contract situation. (shrink)

"The availability of a paperback version of Boyle's philosophical writings selected by M. A. Stewart will be a real service to teachers, students, and scholars with seventeenth-century interests. The editor has shown excellent judgment in bringing together many of the most important works and printing them, for the most part, in unabridged form. The texts have been edited responsibly with emphasis on readability.... Of special interest in connection with Locke and with the reception of Descarte's Corpuscularianism, to students of (...) the Scientific Revolution and of the history of mechanical philosophy, and to those interested in the relations among science, philosophy, and religion. In fact, given the imperfections in and unavailability of the eighteenth-century editions of Boyle’s works, this collection will benefit a wide variety of seventeenth-century scholars." --Gary Hatfield, University of Pennsylvania. (shrink)

The computations involved in statistical learning have long been debated. Here, we build on work suggesting that a basic memory process, chunking, may account for the processing of statistical regularities into larger units. Drawing on methods from the memory literature, we developed a novel paradigm to test statistical learning by leveraging a robust phenomenon observed in serial recall tasks: that short‐term memory is fundamentally shaped by long‐term distributional learning. In the statistically induced chunking recall (SICR) task, participants are exposed to (...) an artificial language, using a standard statistical learning exposure phase. Afterward, they recall strings of syllables that either follow the statistics of the artificial language or comprise the same syllables presented in a random order. We hypothesized that if individuals had chunked the artificial language into word‐like units, then the statistically structured items would be more accurately recalled relative to the random controls. Our results demonstrate that SICR effectively captures learning in both the auditory and visual modalities, with participants displaying significantly improved recall of the statistically structured items, and even recall specific trigram chunks from the input. SICR also exhibits greater test–retest reliability in the auditory modality and sensitivity to individual differences in both modalities than the standard two‐alternative forced‐choice task. These results thereby provide key empirical support to the chunking account of statistical learning and contribute a valuable new tool to the literature. (shrink)

It feels like there’s two of you inside—like there’s another half of you, which is my anorexia, and then there’s the real K [own name], the real me, the logic part of me, and it’s a constant battle between the two. The anorexia almost does become part of you, and so in order to get it out of you I think you do have to kind of hurt you in the process. I think it’s almost inevitable. We came to the (...) concept of authenticity belatedly, one might say. We had been talking to people who had a diagnosis of anorexia nervosa about their experiences of living with their condition, and though we had not raised issues of authenticity or identity ourselves, they often did. They struggled with questions of .. (shrink)

This chapter provides broad coverage of the notion of logical consequence, exploring its modal, semantic, and epistemic aspects. It develops the contrast between proof-theoretic notion of consequence, in terms of deduction, and a model-theoretic approach, in terms of truth-conditions. The main purpose is to relate the formal, technical work in logic to the philosophical concepts that underlie reasoning.

This paper uses neo-Fregean-style abstraction principles to develop the integers from the natural numbers (assuming Hume’s principle), the rational numbers from the integers, and the real numbers from the rationals. The first two are first-order abstractions that treat pairs of numbers: (DIF) INT(a,b)=INT(c,d) ≡ (a+d)=(b+c). (QUOT) Q(m,n)=Q(p,q) ≡ (n=0 & q=0) ∨ (n≠0 & q≠0 & m⋅q=n⋅p). The development of the real numbers is an adaption of the Dedekind program involving “cuts” of rational numbers. Let P be a property (of (...) rational numbers) and r a rational number. Say that r is an upper bound of P, written P≤r, if for any rational number s, if Ps then either s<r or s=r. In other words, P≤r if r is greater than or equal to any rational number that P applies to. Consider the Cut Abstraction Principle: (CP) ∀P∀Q(C(P)=C(Q) ≡ ∀r(P≤r ≡ Q≤r)). In other words, the cut of P is identical to the cut of Q if and only if P and Q share all of their upper bounds. The axioms of second-order real analysis can be derived from (CP), just as the axioms of second-order Peano arithmetic can be derived from Hume’s principle. The paper raises some of the philosophical issues connected with the neo-Fregean program, using the above abstraction principles as case studies. (shrink)

Meaning, Understanding, and Practice is a selection of the most notable essays of an eminent contemporary philosopher on a set of central topics in analytic philosophy. Barry Stroud offers penetrating studies of meaning, understanding, necessity, and the intentionality of thought, with particular reference to the thought of Wittgenstein.

This paper investigates Locke’s views about materialism, by looking at the discussion in Essay IV.x. There Locke---after giving a cosmological argument for the existence of God---argues that God could not be material, and that matter alone could never produce thought. In discussing the chapter, I pay particular attention to some comparisons between Locke’s position and those of two other seventeenth-century philosophers, René Descartes and Ralph Cudworth. -/- Making use of those comparisons, I argue for two main claims. The first is (...) that the important argument of Essay IV.x.10 is fundamentally an argument about the causation of perfections. Indeed, Locke gives multiple such arguments in the chapter. My second main claim is that my proposed reading of IV.x is not merely consistent with what Locke says elsewhere about superaddition, but also provides reasons to favor a particular understanding of what superaddition is. (shrink)

There is a parallel between the debate between Gottlob Frege and David Hilbert at the turn of the twentieth century and at least some aspects of the current controversy over whether category theory provides the proper framework for structuralism in the philosophy of mathematics. The main issue, I think, concerns the place and interpretation of meta-mathematics in an algebraic or structuralist approach to mathematics. Can meta-mathematics itself be understood in algebraic or structural terms? Or is it an exception to the (...) slogan that mathematics is the science of structure? (shrink)

This is a new release of the original 1924 edition.

At the beginning of Die Grundlagen der Arithmetik [1884], Frege observes that “it is in the nature of mathematics to prefer proof, where proof is possible”. This, of course, is true, but thinkers differ on why it is that mathematicians prefer proof. And what of propositions for which no proof is possible? What of axioms? This talk explores various notions of self-evidence, and the role they play in various foundational systems, notably those of Frege and Zermelo. I argue that both (...) programs are undermined at a crucial point, namely when self-evidence is supported by holistic and even pragmatic considerations. (shrink)

The purpose of this paper is to assess the prospects for a neo‐logicist development of set theory based on a restriction of Frege's Basic Law V, which we call (RV): ∀P∀Q[Ext(P) = Ext(Q) ≡ [(BAD(P) & BAD(Q)) ∨ ∀x(Px ≡ Qx)]] BAD is taken as a primitive property of properties. We explore the features it must have for (RV) to sanction the various strong axioms of Zermelo–Fraenkel set theory. The primary interpretation is where ‘BAD’ is Dummett's ‘indefinitely extensible’.1 Background: what (...) and why?2 Framework3 GOOD candidates, indefinite extensibility4 The framework of (RV) alone, or almost alone5 The axioms6 Brief closing. (shrink)

The subject of this paper is the philosophical problem of accounting for the relationship between mathematics and non-mathematical reality. The first section, devoted to the importance of the problem, suggests that many of the reasons for engaging in philosophy at all make an account of the relationship between mathematics and reality a priority, not only in philosophy of mathematics and philosophy of science, but also in general epistemology/metaphysics. This is followed by a (rather brief) survey of the major, traditional philosophies (...) of mathematics indicating how each is prepared to deal with the present problem. It is shown that (the standard formulations of) some views seem to deny outright that there is a relationship between mathematics and any non-mathematical reality; such philosophies are clearly unacceptable. Other views leave the relationship rather mysterious and, thus, are incomplete at best. The final, more speculative section provides the direction of a positive account. A structuralist philosophy of mathematics is outlined and it is proposed that mathematics applies to reality though the discovery of mathematical structures underlying the non-mathematical universe. (shrink)

The purpose of this article is to explore the extent to which mathematics is subject to open texture and the extent to which mathematics resists open texture. The resistance is tied to the importance of proof and, in particular, rigor, in mathematics.

We look at some interesting and important episodes in the life of early modern Epicureanism, focusing on natural philosophy. We begin with two early moderns who had a great deal to say about ancient Epicureanism: Pierre Gassendi and Ralph Cudworth. Looking at how Gassendi and Cudworth conceived of Epicureanism gives us a sense of what the early moderns considered important in the ancient tradition. It also points us towards three main themes of early modern Epicureanism in natural philosophy, which we (...) then discuss at greater length: atomism, materialism about the mind or soul, and the denial of providence, which was often accompanied by deflationary explanations of religious belief. (shrink)

Ethical codes have been hailed as an explicit vehicle for achieving more sustainable and defensible organizational practice. Nonetheless, when legal compliance and corporate governance codes are conflated, codes can be used to define organizational interests ostentatiously by stipulating norms for employee ethics. Such codes have a largely cosmetic and insurance function, acting subtly and strategically to control organizational risk management and protection. In this paper, we conduct a genealogical discourse analysis of a representative code of ethics from an international corporation (...) to understand how management frames expectations of compliance. Our contribution is to articulate the problems inherent in codes of ethics, and we make some recommendations to address these to benefit both an organization and its employees. In this way, we show how a code of ethics can provide a foundation for ethical sustainability, while addressing management intentions and employees’ ethical satisfaction. (shrink)

The answers to the questions in the title depend on the kind of pluralism one is talking about. We will focus here on our own views. The purpose of this article is to trace out some possible connections between these kinds of pluralism. We show how each of them might bear on the other, depending on how certain open questions are resolved.

Over the last few decades Michael Dummett developed a rich program for assessing logic and the meaning of the terms of a language. He is also a major exponent of Frege's version of logicism in the philosophy of mathematics. Over the last decade, Neil Tennant developed an extensive version of logicism in Dummettian terms, and Dummett influenced other contemporary logicists such as Crispin Wright and Bob Hale. The purpose of this paper is to explore the prospects for Fregean logicism within (...) a broadly Dummettian framework. The conclusions are mostly negative: Dummett's views on analyticity and the logical/non-logical boundary leave little room for logicism. Dummett's considerations concerning manifestation and separability lead to a conservative extension requirement: if a sentence S is logically true, then there is a proof of S which uses only the introduction and elimination rules of the logical terms that occur in S. If basic arithmetic propositions are logically true-as the logicist contends-then there is tension between this conservation requirement and the ontological commitments of arithmetic. It follows from Dummett's manifestation requirements that if a sentence S is composed entirely of logical terminology, then there is a formal deductive system D such that S is analytic, or logically true, if and only if S is a theorem of D. There is a deep conflict between this result and the essential incompleteness, or as Dummett puts it, the indefinite extensibility, of arithmetic truth. (shrink)

χαιρέτω ἡμέτερος βασιλεὺς σωτήρ τε πατήρ τε·ἡμῖν δὲ κρητῆρ’ οἰνοχόοι θέραπεςκιρνάντων προχύταισιν ἐν ἀργυρέοις· †ὁ δὲ χρυσὸςοἶνον ἔχων χειρῶν νιζέτω εἰς ἔδαφος.†σπένδοντες δ’ ἁγνῶς Ἡρακλεῖ τ’ Ἀλκμήνηι τε,Προκλεῖ Περσείδαις τ’ ἐκ Διὸς ἀρχόμενοιπίνωμεν, παίζωμεν· ἴτω διὰ νυκτὸς ἀοιδή,ὀρχείσθω τις· ἑκὼν δ’ ἄρχε φιλοφροσύνης.ὅντινα δ’ εὐειδὴς μίμνει θήλεια πάρευνος,κεῖνος τῶν ἄλλων κυδρότερον πίεται.May our king rejoice, our saviour and father; let the attendant cup-bearers mix for us a crater from silver urns; †Let the golden one with wine in his hands wash (...) to the base† Pouring libations piously to Heracles and Alcmene, Procles and the sons of Perseus and Zeus first of all, let us drink, let us play, let our song rise through the night. Dance someone, willingly begin the festivities. And anyone who has a fair girl waiting to share his bed will drink more like a man than all the others.(Ion, fr. 27 West = fr. 90 Leurini). (shrink)

This chapter provides an overview of second-order logic and higher-order logic generally. It provides the basic formal languages, deductive systems, and model-theoretic semantics, including a brief account of George Boolos’s interpretation of second-order languages in terms of the plural construction. It then goes into some of the arguments in favor of second-order logic.

Hawe et al. raise concerns about Human Research Ethics Committees (HRECs) taking a risk-averse and litigation-sensitive approach to ethical review of research proposals. HRECs are tasked with reviewing proposals for compliance with the National Statement on Ethical Conduct in Human Research for the purpose of promoting the welfare of participants. While these guidelines intentionally include a significant degree of discretion in HREC decision making, there is also evidence that HRECs sometimes request changes that go beyond the guidance provided by the (...) National Statement. When HRECs request changes outside their remit, inconsistencies between individual HRECs become more common, contributing to delays in ethical review and reducing the quality of HREC decision making. Improvements to the HREC regulatory system are needed to promote transparency and accountability. (shrink)

A typical interpreted formal language has (first‐order) variables that range over a collection of objects, sometimes called a domain‐of‐discourse. The domain is what the formal language is about. A language may also contain second‐order variables that range over properties, sets, or relations on the items in the domain‐of‐discourse, or over functions from the domain to itself. For example, the sentence ‘Alexander has all the qualities of a great leader’ would naturally be rendered with a second‐order variable ranging over qualities. Similarly, (...) the sentence ‘there is a property that holds of all and only the prime numbers’ has a variable ranging over properties of natural numbers. Third‐order variables range over properties of properties, sets of sets, functions from properties to sets, etc. For example, according to some logicist accounts, the number 4 is the property shared by all properties that apply to exactly four objects in the domain. Accordingly, the number 4 is a third‐order item. Fourth‐order variables, and beyond, are characterized similarly. The phrase ‘higher‐order variable’ refers to the variables beyond first‐order. (shrink)

The purpose of this note is to examine the relationship between the practice of mathematics and the philosophy of mathematics, ontology in particular. One conclusion is that the enterprises are (or should be) closely related, with neither one dominating the other. One cannot 'read off' the correct way to do mathematics from the true ontology, for example, nor can one ‘read off’ the true ontology from mathematics as practiced.

In lieu of an abstract, here is a brief excerpt of the content:Response to CommentariesLauren Freeman (bio) and Heather Stewart (bio)We are grateful and humbled that this esteemed group of scholars and healthcare practitioners have dedicated the time to read and engage with our book. Their thoughtful, critical comments have given us new ways of reflecting on our own work, compelled us to develop and expand some of our claims, and have also nudged us to move in new directions (...) that we hope to explore in future research. In what follows, we reply to each of the commentaries, focusing on what we take to be the most central insights, critiques, and areas for further exploration from each contribution.Catherine Sherron (2024) offers an expansive commentary on chapter 4, "Epistemic Microaggressions," focusing on the nature of epistemic agency, situating epistemic agency within the bioethical context of the principle of autonomy, considering epistemic microaggressions and the phenomenon of silencing of patients, asking whose evidence counts when making claims within medical contexts, and questioning how we might develop a system of reward and admonishment to healthcare professionals who respectively mitigate and commit microaggressions. She presents far more content than we can adequately respond to here. We have chosen to focus on Sherron's specific point about why certain patients experience epistemic microaggressions and what they can do about it. Her line of reasoning echoes an argument found in popular articles about women's health and healthcare that, while seemingly reasonable at first glance, is fraught with problematic assumptions and implications that we would like to draw out and reflect on. Doing so helps pinpoint where the locus of our attention should be in our aim to diminish microaggressions in medical contexts, without placing that burden on the very people who experience and are harmed by them.Within the context of discussing possible contributing factors that perpetuate epistemic microaggressions for patients, Sherron mentions the reality that "patients often don't have good scientific or medical literacy, or education generally, so they might not be in a position to advocate for themselves as epistemic [End Page 169] agents" (150). We surmise that Sherron's more complete argument runs something like this. Many patients lack scientific or medical literacy, postsecondary and postgraduate education, and the language, concepts, and frameworks to be fully empowered epistemic agents and best communicate with healthcare professionals on their terms. As a consequence—and combined with other factors pertaining to their identities and the accompanying stereotypes and biases that healthcare professionals (and all of us) hold—patients who are members of marginalized groups are often not treated as epistemic equals or epistemic peers by healthcare professionals; they are also unable to best advocate for themselves or to speak up in the aftermath of experiencing microaggressions (or macroaggressions) in medical contexts. Thus, if patients were more literate, educated, and able to speak the language of healthcare professionals, they would be able to better advocate for themselves, and they would be better positioned to speak up and respond when epistemic microaggressions (and other injustices and harms) occur. As a result, their situation and relationships with healthcare professionals, their epistemic credibility, and consequently, their care (and maybe even their health outcomes) would improve. Thus, the line o argument implies that we ought to focus our attention on empowering patients: helping them learn how to better educate and advocate for themselves so that they can improve their epistemic situation and, consequently, receive better medical care.This line of argument is common in popular books and articles about women's health (see Dusenbery [2018], who criticizes the argument and Gainty [2023], Jacqueline [2024], Lichtman et al. [2015], Onque [2022], and Singh [2015] where the argument is promoted). The consensus seems to be that yes, there is a problem: women and members of marginalized groups are not getting adequate healthcare, and if only they took better control of and responsibility for their care, they could and would receive better care. We are highlighting this line of reasoning because it is commonplace, problematic, and dangerous.Such an argument is worrisome for at least two reasons. First, the suggested solution—that members of marginalized groups just need to become better advocates for themselves—is not only a form of (unintentional... (shrink)

Several defences, viewed in this study as specifications or 'offspring' of the 'parent' greater-good defence, have been formulated in response to the charge that Christianity is untenable because God's existence is incompatible with evil's existence. In this first book-length study of the parent defence, Stewart begins with careful definitions of the omni-attributes central to the dispute: omnipotence, omniscience, omnibenevolence. The parent defence is traced to tenets of theism and variant accounts of the defence considered. Plantinga's modal free-will defence and (...) Hick's and Yandell's soul-growth specifications are carefully analyzed and several difficulties resolved. An original formulation of a redemption specification and an original account of the origin of moral evil are offered. Stewart argues that the defences are rightly viewed as a family of defences falling under the greater-good heading, and that they comprise a complementary apologetic complex that refutes the claim of inconsistency. (shrink)

Since virtually every mathematical theory can be interpreted in Zermelo-Fraenkel set theory, it is a foundation for mathematics. There are other foundations, such as alternate set theories, higher-order logic, ramified type theory, and category theory. Whether set theory is the right foundation for mathematics depends on what a foundation is for. One purpose is to provide the ultimate metaphysical basis for mathematics. A second is to assure the basic epistemological coherence of all mathematical knowledge. A third is to serve mathematics, (...) by lending insight into the various fields and suggesting fruitful techniques of research. A fourth purpose of a foundation is to provide an arena for exploring relations and interactions between mathematical fields. While set theory does better with regard to some of these and worse with regard to others, it has become the de facto arena for deciding questions of existence, something one might expect of a foundation. Given the different goals, there is little point to determining a single foundation for all of mathematics. (shrink)

Famously, Michael Dummett argues that considerations concerning the role of language in communication lead to the rejection of classical logic in favor of intuitionistic logic. Potentially, this results in massive revisions of established mathematics. Recently, Neil Tennant (“The law of excluded middle is synthetic a priori, if valid”, Philosophical Topics 24 (1996), 205-229) suggested that a Dummettian anti-realist can accept the law of excluded middle as a synthetic, a priori principle grounded on a metaphysical principle of determinacy. This article shows (...) that the for the anti-realist, the law of excluded middle entails that humans have wildly implausible abilities. The proposed synthesis between anti-realism and classical mathematics thus fails. (shrink)