Set-theoretic pluralism is an increasingly influential position in the philosophy of set theory (Balaguer [1998], Linksy and Zalta [1995], Hamkins [2012]). There is considerable room for debate about how best to formulate set-theoretic pluralism, and even about whether the view is coherent. But there is widespread agreement as to what there is to recommend the view (given that it can be formulated coherently). Unlike set-theoretic universalism, set-theoretic pluralism affords an answer to Benacerraf’s epistemological (...) challenge. The purpose of this paper is to determine what Benacerraf’s challenge could be such that this view is warranted. I argue that it could not be any of the challenges with which it has been traditionally identified by its advocates, like of Benacerraf and Field. Not only are none of the challenges easier for the pluralist to meet. None satisfies a key constraint that has been placed on Benacerraf’s challenge. However, I argue that Benacerraf’s challenge could be the challenge to show that our set-theoretic beliefs are safe – i.e., to show that we could not have easily had false ones. Whether the pluralist is, in fact, better positioned to show that our set-theoretic beliefs are safe turns on a broadly empirical conjecture which is outstanding. If this conjecture proves to be false, then it is unclear what the epistemological argument for set-theoretic pluralism is supposed to be. (shrink)

Much of the discussion of set-theoretic independence, and whether or not we could legitimately expand our foundational theory, concerns how we could possibly come to know the truth value of independent sentences. This paper pursues a slightly different tack, examining how we are ignorant of issues surrounding their truth. We argue that a study of how we are ignorant reveals a need for an understanding of set-theoretic explanation and motivates a pluralism concerning the adoption of foundational theory.

First we review highlights of the ongoing debate about foundations of category theory, beginning with Fefermantop-down” approach, where particular categories and functors need not be explicitly defined. Possible reasons for resisting the proposal are offered and countered. The upshot is to sustain a pluralism of foundations along lines actually foreseen by Feferman (1977), something that should be welcomed as a way of resolving this long-standing debate.

In this article, we discuss a simple argument that modal metaphysics is misconceived, and responses to it. Unlike Quine's, this argument begins with the simple observation that there are different candidate interpretations of the predicate ‘could have been the case’. This is analogous to the observation that there are different candidate interpretations of the predicate ‘is a member of’. The argument then infers that the search for metaphysical necessities is misguided in much the way the ‘set-theoretic pluralist’ claims that (...) the search for the true axioms of set theory is. We show that the obvious responses to this argument fail. However, a new response has emerged that purports to prove, from higher-order logical principles, that metaphysical possibility is the broadest kind of possibility applying to propositions, and is to that extent special. We distill two lines of reasoning from the literature, and argue that their import depends on premises that any ‘modal pluralist’ should deny. Both presuppose that there is a unique typed hierarchy, which is what the modal pluralist, in the context of higher-order logic, should disavow. In other words, both presupposes that there is a unique candidate for what higher-order claims could mean. We consider the worry that, in a higher-order setting, modal pluralism faces an insuperable problem of articulation, collapses into modal monism, is vulnerable to the Russell-Myhill paradox, or even contravenes the truism that there is a unique actual world, and argue that these worries are misplaced. We also sketch the bearing of the resulting ‘Higher-Order Pluralism’ on the theory of content. One theme of the discussion is that, if Higher-Order Pluralism is correct, then there is no fixed metatheory from which to characterize higher-order reality. (shrink)

Pluralist mathematical realism, the view that there exists more than one mathematical universe, has become an influential position in the philosophy of mathematics. I argue that, if mathematical pluralism is true (and we have good reason to believe that it is), then mathematical realism cannot (easily) be justified by arguments from the indispensability of mathematics to science. This is because any justificatory chain of inferences from mathematical applications in science to the total body of mathematical theorems can cover at (...) most one mathematical universe. Indispensability arguments may thus lose their central role in the debate about mathematical ontology. (shrink)

This chapter contains sections titled: Pluralistic Ignorance Modal Operator Epistemology Agents and Inquiry Methods Multimodal Systems Knowledge Transmissibility Knowledge Transmissibility and Public Announcement Knowledge Transmissibility and Pluralistic Ignorance References.

Pluralism about truth is the view that there are many properties, not just one, in virtue of which things are true. Pluralists hope to dodge the objections that face traditional monistic substantive views of truth, as well as those facing deflationary theories of truth. More specifically, pluralists hope to advance an explanatorily potent understanding of truth that can capture the subtleties of various realist and anti-realist domains of discourse, all while avoiding the scope problem. I offer a new objection (...) to pluralism that challenges its fundamental commitment to there being a set of alethic properties in virtue of which claims are true. In its place I offer an alternative view that merges standard truthmaker theory with a primitivist conception of truth. This combination of views satisfies the theoretical desires that pluralists claim for themselves, but without taking on pluralism's host of challenges and problems. (shrink)

Scientific pluralism has become a household position within the philosophy of science literature. There are numerous accounts of plurality within various research fields. Most scientific pluralists, however, focus on the plurality of theories, explanations, or mechanisms, while other potential targets of plurality that the philosophy of scientific practice has particularly emphasized have so far not received extensive treatment. How should we approach such practice-based candidates of plurality? And what are potential pluralist positions concerning the objects of scientific practice? In (...) this article, I set out to answer these questions. I combine approaching a widely influential topic within the philosophy of science, scientific pluralism, with social science methodology. Using interview data combined with sociological analysis, I provide a nuanced picture of the dynamics of one particular research field that displays plurality. Focusing on how sociological configurations resonate with intellectual commitments within a research field, I disentangle practice-based from theoretical plurality. I consider how these empirical results should feedback on the scientific pluralism literature. (shrink)

This volume explores the inherent pluralism of Hinduism through ethnographic and philosophical evidence as presented in the Journal of Anthropological Society of Bombay. The essays dated 1886-1936, represent a period that marked the emergence of a European-educated native intelligentsia with a rationalist outlook. The essays cover a wide range of topics from Tree Worship in Mohenjo Daro, the origin of the Hindu Trimurti, interpretation of Avestic and Vedic Texts; to a second set of more localized papers that cover the (...) Muhammadan Castes of Bengal, the Tenets and Practices of a Certain Class of Faqirs in Bengal, the Theoretical History of the Goddess Yellamma, and much more. Written during a particular historical as well as intellectual period that reflected certain key patterns - a period just following the Bengal Renaissance of the nineteenth century that ushered in the ideologies of a reformative Hinduism - this volume highlights how religions of all denominations have influenced each other and appear to have mingled beliefs and practices from multiple sources. It shows how tolerance and inclusiveness along with syncretism have been part of India's religious and social history. This book will be of interest to students and researchers of religions, history, anthropology, sociology, political science, and sociology of religion. It will also be useful to those interested in inter-religious dialogues and civil society. (shrink)

Mathematical pluralism can take one of three forms: (1) every consistent mathematical theory consists of truths about its own domain of individuals and relations; (2) every mathematical theory, consistent or inconsistent, consists of truths about its own (possibly uninteresting) domain of individuals and relations; and (3) the principal philosophies of mathematics are each based upon an insight or truth about the nature of mathematics that can be validated. (1) includes the multiverse approach to set theory. (2) helps us to (...) understand the significance of the distinguished non‐logical individual and relation terms of even inconsistent theories. (3) is a metaphilosophical form of mathematical pluralism and hasn't been discussed in the literature. In what follows, I show how the analysis of theoretical mathematics in object theory exhibits all three forms of mathematical pluralism. (shrink)

Set-theoretic and category-theoretic foundations represent different perspectives on mathematical subject matter. In particular, category-theoretic language focusses on properties that can be determined up to isomorphism within a category, whereas set theory admits of properties determined by the internal structure of the membership relation. Various objections have been raised against this aspect of set theory in the category-theoretic literature. In this article, we advocate a methodological pluralism concerning the two foundational languages, and provide a theory that (...) fruitfully interrelates a `structural' perspective to a set-theoretic one. We present a set-theoretic system that is able to talk about structures more naturally, and argue that it provides an important perspective on plausibly structural properties such as cardinality. We conclude the language of set theory can provide useful information about the notion of mathematical structure. (shrink)

The main claim of this thesis is that value-judgments should play a profound role in the construction and evaluation of species classifications. The arguments for this claim will be presented over the course of five chapters. These are divided into two main parts; part one, which consists of the two first chapters, presents an argument for a radical form of species pluralism; part two, which comprises the remaining chapters, discusses the implications of radical species pluralism for the role (...) of values in species classification. The content of the five chapters is as follows. Chapter 1 starts with a discussion of the theoretical assumptions concerning species and natural kinds that form the broad framework within which the arguments of the thesis are placed. The aim of this chapter is to introduce a set of relatively uncontroversial assumptions that frame the rest of the thesis. On the basis of these assumptions, chapter 2 presents an argument for radical species pluralism. The chapter substantiates this argument with a broad range of examples, and compares this position to other forms of species pluralism. Chapter 3 returns to the main interest of the thesis, namely, the role of values in species classification. It introduces the notion of values and presents an argument for the value-ladenness of taxonomy on the basis of the considerations in the first two chapters. It then sketches three important views on values in science in the literature. Chapter 4 argues that the case presented in chapter 3 provides strong support for one of these views, called the ‘Aims View’, and against two other prominent views, called the ‘Epistemic Priority View’ and the ‘Value-Free Ideal’. The resulting view, in line with the Aims View, is that value-judgments should play a particularly substantial role in species classification. Chapter 5 then considers the popular assumption that these value-judgments in taxonomy commonly take the shape of generally accepted classificatory norms, and argues that this assumption is not tenable. Finally, a brief concluding chapter points at some implications of the claims and arguments in this thesis. (shrink)

When talking about truth, we ordinarily take ourselves to be talking about one-and-the-same thing. Alethic monists suggest that theorizing about truth ought to begin with this default or pre-reflective stance, and, subsequently, parlay it into a set of theoretical principles that are aptly summarized by the thesis that truth is one. Foremost among them is the invariance principle.

The themes of citizenship and community are today at the center of a fierce debate as both left and right try to mobilize them for their cause. For the left such notions are crucial in all the current attempts to redefine political struggle through extending and deepening democracy. But, argue the contributors to this volume, these concepts need to be made compatible with the pluralism that marks modern democracy. Rather than reject the liberal tradition, they argue, the aim should (...) be to radicalize it. These essays set out to examine what types of “citizen” and “community” might be required by such a radical and plural democracy. From a range of disciplines and a fruitful diversity of theoretical perspectives, the contributors help us to address the following challenge: how to defend the greatest possible pluralism without destroying the very framework of the democratic political community. Despite their differences, a vision emerges from these essays which is sharply at odds both with the universalistic and rationalistic conception to be found in the work of Habermas, and with postmodern celebrations of absolute heterogeneity. For this book is an exploration of politics—of a politics where power, conflict and antagonism will always play a central role. (shrink)

IntroductionScientific pluralism is generally understood in the backdrop of scientific monism. So is mathematical pluralism. Though there are many culture-dependent mathematical practices, mathematical concepts and theories are generally taken to be culture invariant. We would like to explore in this paper whether mathematical pluralism is admissible or not.Materials and methodsMathematical pluralism may be approached at least from five different perspectives. 1. Foundational: The view would claim that different issues within mathematics need support of different foundations, apparently (...) incompatible with one another. 2. Ontological: The world itself is dappled—the mathematical counterpart of which can be traced to the admission of non-Euclidean spaces and also in simultaneous acceptance of set-theoretic and category theoretic entities in the ontology of mathematics. 3. The third route is epistemological. It follows from the view that the nature of reality is so complex that different aspects of it require alternative modes of representation and explanation sometimes severally, sometimes simultaneously, e.g., classical, constructivist, computer-aided and different finitist mathematics can be used depending on the knowledge situation. 4. The fourth route is semantic. Fuzzy mathematics, we know, gives up bivalence in theory of truth, and ascribes truth to mathematical propositions in degrees. 5. The last one is Programmatic: for some, mathematical pluralism is a stance, a programme. It provides a framework which strikes at the root of cultural hegemony and nourishes a climate of intellectual humility and tolerance. It is not my intention to hold the brief of any of these versions. I just want to present to the readers a more or less complete picture of the scenario, though not an exhaustive one. ConclusionUnlike monism, mathematical pluralism does not rule out any possibility—even the possibility of having a unitary over-arching framework of interpretation remains as an open option. This paper highlights the fact that motivations for upholding pluralism in mathematics have been many and one can be a pluralist just by subscribing to any of the views listed above. (shrink)

Despite the common use of the concept of emergence, no uncontroversial theoretical framework has been yet formulated in this regard. In this paper, I examine what this circumstance suggests about the significance and usefulness of this concept. I first trace a brief history of the notion of emergence from its first formulation among the British Emergentists to its contemporary uses. Then, I outline its most common features and examine three examples of emergent phenomena, namely particle decay, free will, and division (...) of labour in ant colonies. These three cases of emergence exhibit different features and imply criteria which only partially overlap. I then suggest that the multiplicity of features and criteria recognised as defining emergence, rather than being a threat to the tenability of the concept, should encourage the assumption of a pluralist attitude that is consistent with both the employment of this idea in different sciences and the recognition of emergent phenomena across different levels of organisation. Finally, I propose that emergence can be approached in a similar way to how Richard Boyd approached the problem of natural kinds, namely by identifying an open cluster of properties, rather than a set of necessary and sufficient conditions. (shrink)

Most theories of slurs fall into one of two families: those which understand slurring terms to involve special descriptive/informational content (however conveyed), and those which understand them to encode special emotive/expressive content. Our view is that both offer essential insights, but that part of what sets slurs apart is use-theoretic content. In particular, we urge that slurring words belong at the intersection of a number of categories in a sociolinguistic register taxonomy, one that usually includes [+slang] and [+vulgar] and (...) always includes [-polite] and [+derogatory]. Thus, e.g., what distinguishes ‘Chinese’ from ‘chink’ is neither a peculiar sort of descriptive nor emotional content, but rather the fact that ‘chink’ is lexically marked as belonging to different registers than ‘Chinese’. It is, moreover, partly such facts which makes slurring ethically unacceptable. (shrink)

Moral diversity is a fundamental reality of today’s world, but moral theorists have difficulty responding to it. Some take it as evidence for skepticism – the view that there are no moral truths. Others, associating moral reasoning with the search for overarching principles and unifying values, see it as the result of error. In the former case, moral reasoning is useless, since values express individual preferences; in the latter, our reasoning process is dramatically at odds with our lived experience. Moral (...) Reasoning in a Pluralistic World takes a different approach, proposing an alternative way of thinking about moral reasoning and progress by showing how diversity and disagreement are compatible with theorizing and justification. Patricia Marino demonstrates that, instead of being evidence for skepticism and error, moral disagreements often arise because we value things pluralistically. This means that although people share multiple values such as fairness, honesty, loyalty, and benevolence, we interpret and prioritize those values in various ways. Given this pluralistic evaluation process, preferences for unified single-principle theories are not justified. Focusing on finding moral compromises, prioritizing conflicting values, and judging consistently from one case to another, Marino elaborates her ideas in terms of real-life dilemmas, arguing that the moral complexity and conflict we so often encounter can be part of fruitful and logical moral reflection. Aiming to draw new connections and bridge the gap between theoretical ethics and applied ethics, Moral Reasoning in a Pluralistic World offers a sophisticated set of philosophical arguments on moral reasoning and pluralism with real world applications. (shrink)

THE INAPPLICABILITY THESIS There is a gap between the idea of distributive justice and the many factors that are morally relevant for decision making on economic issues. Only to a degree can this gap be attributed to the distance between “ideal reach” and “practical grasp,” to the legitimate difference in detail between an abstractly delineated economic scenario and a concrete set of circumstances, and to the disparate idioms and metaphors of theoretical and practical discourse. Rather, the gap indicates a fundamental (...) problem with the concept of distributive justice. The problem, that is here termed the “inapplicability thesis,” is that even if distributive justice in abstract formulation were to be accepted as a value, its application in economic decision making is indeterminate. (shrink)

In the field of bioethics, scholars have begun to consider carefully the impact of structural issues on global population health, including socioeconomic and political factors influencing the disproportionate burden of disease throughout the world. Human rights and social justice are key considerations for both population health and biomedical research. In this paper, I will briefly explore approaches to human rights in bioethics and review guidelines for ethical conduct in international health research, focusing specifically on health research conducted in resource-poor settings. (...) I will demonstrate the potential for addressing human rights considerations in international health research with special attention to the importance of collaborative partnerships, capacity building, and respect for cultural traditions. Strengthening professional knowledge about international research ethics increases awareness of ethical concerns associated with study design and informed consent among researchers working in resource-poor settings. But this is not enough. Technological and financial resources are also necessary to build capacity for local communities to ensure that research results are integrated into existing health systems. Problematic issues surrounding the application of ethical guidelines in resource-poor settings are embedded in social history, cultural context, and the global political economy. Resolving the moral complexities requires a commitment to engaged dialogue and action among investigators, funding agencies, policy makers, governmental institutions, and private industry. (shrink)

Scientific specialties are the key unit of analysis in Kuhn’s theory of scientific change. Kuhn believed that scientific specialties, in their normal phases, are characterized by theoretical monism. This is what makes scientists so efficient in realizing their epistemic goals. Recent work in the philosophy of scientific practice raises questions about the extent to which there is or needs to be consensus in science, thus challenging a key dimension of Kuhn’s view. Hasok Chang has been a leader in this project, (...) focusing attention on the benefits of pluralism. I argue that Chang and other pluralists are overcorrecting. I argue that a variety of types of pluralism can be reconciled with theoretical monism, and that theoretical monism serves significant functions, aiding scientists in the effective pursuit of their epistemic goals. Thus, I aim to set limits to pluralism. I argue that Kuhn’s theoretical monism not only has room for the sort of pluralism that Chang and others aims to defend, I also show that it presupposes such forms of pluralism. (shrink)

The debate on probabilistic measures of coherence flourishes for about 15 years now. Initiated by papers that have been published around the turn of the millennium, many different proposals have since then been put forward. This contribution is partly devoted to a reassessment of extant coherence measures. Focusing on a small number of reasonable adequacy constraints I show that (i) there can be no coherence measure that satisfies all constraints, and that (ii) subsets of these adequacy constraints motivate two different (...) classes of coherence measures. These classes do not coincide with the common distinction between coherence as mutual support and coherence as relative set-theoretic overlap. Finally, I put forward arguments to the effect that for each such class of coherence measures there is an outstanding measure that outperforms all other extant proposals. One of these measures has recently been put forward in the literature, while the other one is based on a novel probabilistic measure of confirmation. (shrink)

In today’s pluralistic society, clinical ethics consultation cannot count on a pre-given set of rules and principles to be applied to a specific situation, because such an approach would deny the existence of different and divergent backgrounds by imposing a dogmatic and transcultural morality. Clinical ethics support (CES) needs to overcome this lack of foundations and conjugate the respect for the difference at stake with the necessity to find shared and workable solutions for ethical issues encountered in clinical practice. We (...) argue that a pragmatist approach to CES, based on the philosophical theories of William James, John Dewey, and Charles Sanders Peirce, can help to achieve the goal of reaching practical solutions for moral problems in the context of today’s clinical environment, characterized by ethical pluralism. In this article, we outline a pragmatist theoretical framework for CES. Furthermore, we will show that moral case deliberation, making use of the dilemma method, can be regarded an example of a pragmatist approach to CES. (shrink)

Available from UMI in association with The British Library. Requires signed TDF. ;My aim has been to present an abstract model for the acquisition of knowledge, to develop its consequences, and to compare these consequences with science$\sp1$. ;My intention has been to take this remark seriously. I hope to demonstrate that the papers which Feyerabend wrote between 1955 and the mid-1960's can most profitably be understood as a contribution to this project. The first three chapters lay the groundwork of Feyerabend's (...) earlier epistemology. They pick out the themes in his model for the acquisition of 'knowledge'. Chapter One sets out Feyerabend's rather unorthodox conception of scientific or theoretical realism, which has not received the attention which I believe it deserves. I detail Feyerabend's objections to some anti-realist positions and outline the formidable structure of his central argument for realism. I then consider a vital and problematic part of his epistemology, the 'pragmatic theory of observation'. ftn$\sp1$'Reply To Criticism: Comments on Smart, Sellars and Putnam', reprinted in Feyerabend's Philosophical Papers volume I, p.104. (shrink)

Psychologists increasingly support the development of a methodological pluralism for research applications. Methodological pluralism, particularly as conceptualized by William James, can provide important benefits, such as a shift away from the totalizing hegemony of the received view of science and the formulation of deeper, more clear accounts of psychological life. Before such a methodological pluralism can be viable, however, psychologists must secure a theoretically coherent set of methods and an indigenous epistemology. Failure to address these concerns not (...) only decreases the likelihood that psychologists will formulate a coherent account of psychological life, but also increases the likelihood that psychology will suffer from increased fragmentation and perhaps dissolution as an autonomous discipline. (shrink)

The author reviews recent books by Alasdair MacIntyre and Garrett Barden that critique the impulse to foundational theory and transhistorical argumentation in moral theory; these arguments are then set in relation to books by Franklin Gamwell and Karl-Otto Apel that seek, in new ways, to defend that impulse. Although far more sympathetic to the latter perspective, the author maintains that all four of these second-order theoretical discussions lack an appropriate understanding of and engagement with the post-Enlightenment tradition of moral theorizing.

The existence of fundamental moral disagreements is a central problem for moral realism and has often been contrasted with an alleged absence of disagreement in mathematics. However, mathematicians do in fact disagree on fundamental questions, for example on which set-theoretic axioms are true, and some philosophers have argued that this increases the plausibility of moral vis-à-vis mathematical realism. I argue that the analogy between mathematical and moral disagreement is not as straightforward as those arguments present it. In particular, I (...) argue that pluralist accounts of mathematics render fundamental mathematical disagreements compatible with mathematical realism in a way in which moral disagreements and moral realism are not. 11. (shrink)

This paper analyses the hidden use of new axioms in set-theoretic practice with a focus on large cardinal axioms and presents a general overview of set-theoretic practices using large cardinal axioms. The hidden use of a new axiom provides extrinsic reasons in support of this axiom via the idea of verifiable consequences, which is especially relevant for set-theoretic practitioners with an absolutist view. Besides that, the hidden use has pragmatic significance for further important sub-groups of the set- (...) class='Hi'>theoretic community---set-theoretic practitioners with a pluralist view and set-theoretic practitioners who aim for ZFC-proofs. By describing this, the paper gives a more complete picture of new axioms in set-theoretic practice. These observations, for instance, show that set-theoretic practitioners interested in ZFC-proofs use tools that go beyond ZFC. The analysis is based on empirical data that was collected in an extensive interview study with set-theoretic practitioners. (shrink)

Alethic pluralists argue truth is a metaphysically robust higher-order property that is multiply realized by a set of diverse and domain-specific subvening alethic properties. The higher-order truth property legitimizes mixed inferences and accounts for a univocal truth predicate. Absent of this higher-order property, pluralists lack an account of the validity of mixed inferences and an adequate semantics for the truth predicate and thereby appear forced to abandon the central tenets of alethic pluralism. I argue the use of many-valued logics (...) to support pluralism fails to address the pluralist’s metaphysical problem regarding mixed inferences and mixed truth functional connectives. The high degree of heterogeneity of the alethic realizers challenges the plausibility of a single higher-order functional property. A functional property with such a heterogeneous base cannot be projectable at a theoretically significant level. The problem with mixed inferences and truth functions is but one symptom of the deeper projectability problem. (shrink)

This chapter sets out a theory of how to weigh alethic and pragmatic (non-alethic) reasons for belief, or more precisely, to say how alethic and non-alethic considerations jointly determine what one ought to believe. It replaces my earlier (2008) weighing account. It is part of _The true and the good: a new theory of theoretical reason_, which develops a view, welfarist pluralism, which comprises central two theses. One is that there are both irreducibly alethic or epistemic reasons for belief (...) and irreducibly pragmatic (and non-alethic) reasons for belief. The other is that despite this, the source of all normativity is pragmatic in a particular way, i.e. that all reasons are reasons in virtue of their being conducive to wellbeing. The pluralist theory of reasons emerges from the irreducibly plural nature of the components of wellbeing, on of which is being in a positively-valenced epistemic state. This view also offers some insight into outstanding problems concerning the scope, chronicity, and normativity of the requirements of theoretical rationality as well. (Updated 10 May 2022). (shrink)

Starting from a proof-theoretic perspective, where meaning is determined by the inference rules governing logical operators, in this paper we primarily aim at developing a proof-theoretic alternative to the model-theoretic meaning-invariant logical pluralism discussed in Beall and Restall. We will also outline how this framework can be easily extended to include a form of meaning-variant logical pluralism. In this respect, the framework developed in this paper—which we label two-level proof-theoretic pluralism—is much broader in (...) scope than the one discussed in Beall and Restall’s book. (shrink)

The multiverse view in set theory, introduced and argued for in this article, is the view that there are many distinct concepts of set, each instantiated in a corresponding set-theoretic universe. The universe view, in contrast, asserts that there is an absolute background set concept, with a corresponding absolute set-theoretic universe in which every set-theoretic question has a definite answer. The multiverse position, I argue, explains our experience with the enormous range of set-theoretic possibilities, a phenomenon (...) that challenges the universe view. In particular, I argue that the continuum hypothesis is settled on the multiverse view by our extensive knowledge about how it behaves in the multiverse, and as a result it can no longer be settled in the manner formerly hoped for. (shrink)

In his paper "Are There Set Theoretic Possible Worlds?", Selmer Bringsjord argued that the set theoretic definition of possible worlds proffered by, among others, Robert Adams and Alvin Plantinga is incoherent. It is the purpose of this note to evaluate that argument. The upshot: these set theoretic accounts can be preserved, but only by abandoning the power set axiom.

This is a survey of work on set-theoretical invariance criteria for logicality. It begins with a review of the Tarski-Sher thesis in terms, first, of permutation invariance over a given domain and then of isomorphism invariance across domains, both characterized by McGee in terms of definability in the language L∞,∞. It continues with a review of critiques of the Tarski-Sher thesis, and a proposal in response to one of those critiques via homomorphism invariance. That has quite divergent characterization results depending (...) on its formulation, one in terms of FOL, the other by Bonnay in terms of L∞,∞, both without equality. From that we move on to a survey of Bonnay’s work on similarity relations between structures and his results that single out invariance with respect to potential isomorphism among all such. Turning to the critique that calls for sameness of meaning of a logical operation across domains, the paper continues with a result showing that the isomorphism invariant operations that are absolutely definable with respect to KPU−Inf are exactly those definable in full FOL; this makes use of an old theorem of Manders. The concluding section is devoted to a critical discussion of the arguments for set-theoretical criteria for logicality. (shrink)

The national standards for clinical ethics consultation set forth by the American Society for Bioethics and Humanities endorse an “ethics facilitation” approach, which characterizes the role of the ethicist as one skilled at facilitating consensus within the range of ethically acceptable options. To determine the range of ethically acceptable options, ASBH recommends the standard model of decision-making, which is grounded in the values of autonomy, beneficence, nonmaleficence, and justice. H. Tristram Engelhardt Jr. has sharply criticized the standard model for presuming (...) contentful moral claims in circumscribing the range of ethically acceptable options, which, he argues, cannot be rationally justified in a pluralistic context. Engelhardt’s solution is a secular clinical ethics based on a contentless principle of permission. The first part of this article lays out Engelhardt’s negative claim, that reason cannot establish contentful moral claims, and his positive claim, that secular clinical ethics ought to be based on a contentless principle of permission. The second part critiques these negative and positive claims. The purpose of this paper is to defend secular clinical ethics expertise—defined as the ability of ethicists to offer justified moral recommendations grounded in consensus positions endorsed by the American Society for Bioethics and Humanities—from the radical critiques of Engelhardt, who argues that no moral or metaphysical claims, and hence no bioethical consensus, can be rationally justified. Engelhardt’s critiques have caused some to worry that secular clinical ethics is in a state of theoretical crisis; this article concludes that Engelhardt’s view is an unstable basis for that worry. (shrink)

A prominent philosophical debate concerns whether we should accept causal decision theory or evidential decision theory as our best theory of rational choice. However, instead of accepting one of these theories at the expense of the other, an alternative would be to accept that both theories play a partial role in the true account of rational choice. In this paper, I defend a pluralist account of this sort. In particular, I argue that rational permissibility is an indeterminate notion, with EDT (...) and CDT each corresponding to one sharpening of this notion. (shrink)

Psychological essentialism is a cognitive bias through which human beings conceive the entities around them as having inner essences and basic natures. Social scientists routinely generate flawed inferences because their methods require the truth of psychological essentialism. This article develops set-theoretic analysis as a scientific-constructivist approach that overcomes the bias of psychological essentialism. With this approach, the “sets” of set-theoretic analysis are mental phenomena that establish boundaries and identify similarities and differences among entities whose natural kind composition is (...) not known. The approach is illustrated through a consideration of research on intelligence, race, and poverty in the United States. (shrink)

The author reviews recent books by Alasdair MacIntyre and Garrett Barden that critique the impulse to foundational theory and transhistorical argumentation in moral theory; these arguments are then set in relation to books by Franklin Gamwell and Karl-Otto Apel that seek, in new ways, to defend that impulse. Although far more sympathetic to the latter perspective, the author maintains that all four of these second-order theoretical discussions lack an appropriate understanding of and engagement with the post-Enlightenment tradition of moral theorizing.

My aim in this paper is to propose what seems to me a distinctive approach to set theoretic methodology. By ‘methodology’ I mean the study of the actual methods used by practitioners, the study of how these methods might be justified or reformed or extended. So, for example, when the intuitionist's philosophical analysis recommends a wholesale revision of the methods of proof used in classical mathematics, this is a piece of reformist methodology. In contrast with the intuitionist, I will (...) focus more narrowly on the methods of contemporary set theory, and, more importantly, I will certainly recommend no sweeping reforms. Rather, I begin from the assumption that the methodologist's job is to account for set theory as it is practiced, not as some philosophy would have it be. This credo lies at the very heart of the so-called ‘naturalism’ to be described here.A philosopher looking at set theoretic practice from the outside, so to speak, might notice any number of interesting methodological questions, beginning with the intuitionist's ‘why use classical logic?’, but this sort of question is not a live issue for most practicing set theorists. One central question on which the philosopher's and the practitioner's interests converge is this: what is the status of independent statements like the continuum hypothesis (CH)? A number of large questions arise in its wake: what criteria should guide the search for new axioms? For that matter, what reasons support our adoption of the old axioms? (shrink)

In this article we study several reduction principles in the context of Simpson’s set theory ATR0S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ATR_{0}^{S}$$\end{document} and Kripke-Platek set theory KP (with infinity). Since ATR0S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ATR_{0}^{S}$$\end{document} is the set-theoretic version of ATR0 there is a direct link to second order arithmetic and the results for reductions over ATR0S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ATR_{0}^{S}$$\end{document} are as expected and more or (...) less straightforward. However, over KP we obtain several interesting new results and are lead to some open questions. (shrink)

We consider a set-theoretic version of mereology based on the inclusion relation ⊆ and analyze how well it might serve as a foundation of mathematics. After establishing the non-definability of ∈ from ⊆, we identify the natural axioms for ⊆-based mereology, which constitute a finitely axiomatizable, complete, decidable theory. Ultimately, for these reasons, we conclude that this form of set-theoretic mereology cannot by itself serve as a foundation of mathematics. Meanwhile, augmented forms of set-theoretic mereology, such as (...) that obtained by adding the singleton operator, are foundationally robust. (shrink)

Insights from social science are increasingly used in the field of applied ethics. However, recent insights have shown that the empirical branch of business ethics lacks thorough theoretical grounding. This article discusses the use of the Rawlsian methods of wide reflective equilibrium and overlapping consensus in the field of applied ethics. Instead of focussing on one single comprehensive ethical doctrine to provide adequate guidance for resolving moral dilemmas, these Rawlsian methods seek to find a balance between considered judgments and intuitions (...) concerning particular cases on the one hand and general principles and theories on the other. In business ethics this approach is promissing because it enables decision-making in a pluralist context with different stakeholders who often endorse different or even conflicting cultural and moral frameworks without giving priority to any of them. Moreover, the method is well founded in political theory. A taxonomy of different kinds of applications is developed, and classified according to the purpose, the content, and the type of justification. On the basis of this taxonomy an inventory of 12 recent applications is made. In terms of the purpose and content of the method the applications are rather diverse. Two conceptual obstacles for applying Rawlsian methods are identified, viz. inclusiveness and the communitarian objection that people have to become detached from their personal life. It is found that methodological questions, such as the question how to retrieve the relevant empirical data, are scarcely addressed in the literature. To advance the use of empirical approaches in general, and that of Rawlsian approaches in particular, it is important not only to use empirical data but to use methodological insights from social sciences in order to further advance the field of empirical ethics. It is recommended that stakeholders be given a more active role in the assessment and justification of these methods. (shrink)

Recent discussions of how axioms are extrinsically justified have appealed to abductive considerations: on such accounts, axioms are adopted on the basis that they constitute the best explanation of some mathematical data, or phenomena. In the first part of this paper, I set out a potential problem caused by the appeal made to the notion of mathematical explanation and suggest that it can be remedied once it is noted that all the justificatory work is done by appeal to the theoretical (...) virtues. In the second part of the paper, I appeal to the theoretical virtues account of axiom justification to provide an argument that judgements of theoretical virtuousness, and therefore of extrinsic justification, are subjective in a substantive sense. This tells against a recent claim by Penelope Maddy that such justification is “wholly objective”. (shrink)