In many ways set theory lies at the heart of modern mathematics, and it does powerful work both philosophical and mathematical – as a foundation for the subject. However, certain philosophical problems raise serious doubts about our acceptance of the axioms of set theory. In a detailed and original reassessment of these axioms, Sharon Berry uses a potentialist approach to develop a unified determinate conception of set-theoretic truth that vindicates many of our intuitive expectations regarding set theory. (...) class='Hi'>Berry further defends her approach against a number of possible objections, and she shows how a notion of logical possibility that is useful in formulating Potentialist set theory connects in important ways with philosophy of language, metametaphysics and philosophy of science. Her book will appeal to readers with interests in the philosophy of set theory, modal logic, and the role of mathematics in the sciences. (shrink)

In this article, I discuss a trivialization worry for Hartry Field’s official formulation of the access problem for mathematical realists, which was pointed out by Øystein Linnebo. I argue that various attempted reformulations of the Benacerraf problem fail to block trivialization, but that access worriers can better defend themselves by sticking closer to Hartry Field’s initial informal characterization of the access problem in terms of general epistemic norms of coincidence avoidance.

In this article, I discuss a trivialization worry for Hartry Field’s official formulation of the access problem for mathematical realists, which was pointed out by Øystein Linnebo (and has recently been made much of by Justin Clarke-Doane). I argue that various attempted reformulations of the Benacerraf problem fail to block trivialization, but that access worriers can better defend themselves by sticking closer to Hartry Field’s initial informal characterization of the access problem in terms of (something like) general epistemic norms of (...) coincidence avoidance. (shrink)

It’s sometimes suggested that we can (in a sense) settle the truth-value of some statements in the language of number theory by stipulation, adopting either φ or ¬φ as an additional axiom. For example, in Clarke-Doane (2020b) and a series of recent APA presentations, Clarke-Doane suggests that any Σ01 sound expansion of our current arithmetical practice would express a truth. In this paper, I’ll argue that (given a certain popular assumption about the model-theoretic representability of languages like ours) we can’t (...) know ourselves to have any such freedom. (shrink)

In this paper, I will attempt to develop and defend a common form of intuitive resistance to the companions in guilt argument. I will argue that one can reasonably believe there are promising solutions to the access problem for mathematical realism that don’t translate to moral realism. In particular, I will suggest that the structuralist project of accounting for mathematical knowledge in terms of some form of logical knowledge offers significant hope of success while no analogous approach offers such hope (...) for moral realism. (shrink)

Since Benacerraf’s ‘What Numbers Could Not Be, ’ there has been a growing interest in mathematical structuralism. An influential form of mathematical structuralism, modal structuralism, uses logical possibility and second order logic to provide paraphrases of mathematical statements which don’t quantify over mathematical objects. These modal structuralist paraphrases are a useful tool for nominalists and realists alike. But their use of second order logic and quantification into the logical possibility operator raises concerns. In this paper, I show that the work (...) of both these elements can be done by a single natural generalization of the logical possibility operator. (shrink)

ABSTRACT It is currently fashionable to take Putnamian model-theoretic worries seriously for mathematics, but not for discussions of ordinary physical objects and the sciences. However, I will argue that merely securing determinate reference to physical possibility suffices to rule out the kind of nonstandard interpretations of our number talk Putnam invokes. So, anyone who accepts determinate reference to physical possibility should not reject determinate reference to the natural numbers on Putnamian model-theoretic grounds.

In this paper I will draw attention to an important route to external world skepticism, which I will call confidence skepticism. I will argue that we can defang confidence skepticism (though not a meeker ‘argument from might’ which has got some attention in the 20th century literature on external world skepticism) by adopting a partially psychologistic answer to the problem of priors. And I will argue that certain recent work in the epistemology of mathematics and logic provides independent support for (...) such psychologism. (shrink)

In this paper I will argue that (principled) attempts to ground a priori knowledge in default reasonable beliefs cannot capture certain common intuitions about what is required for a priori knowledge. I will describe hypothetical creatures who derive complex mathematical truths like Fermat’s last theorem via short and intuitively unconvincing arguments. Many philosophers with foundationalist inclinations will feel that these creatures must lack knowledge because they are unable to justify their mathematical assumptions in terms of the kind of basic facts (...) which can be known without further argument. Yet, I will argue that nothing in the current literature lets us draw a principled distinction between what these creatures are doing and paradigmatic cases of good a priori reasoning (assuming that the latter are to be grounded in default reasonable beliefs). I will consider, in turn, appeals to reliability, coherence, conceptual truth and indispensability and argue that none of these can do the job. (shrink)

Mathematical knowledge and moral knowledge (or normative knowledge more generally) can seem intuitively puzzling in similar ways. For example, taking apparent human knowledge of either domain at face value can seem to require accepting that we benefited from some massive and mysterious coincidence. In the mathematical case, a pluralist partial response to access worries has been widely popular. In this paper, I will develop and address a worry, suggested by some works in the recent literature like (Clarke-Doane, 2020), that connections (...) between ought facts and action prevent us from giving a similarly pluralist response to moral access worries. (shrink)

In this paper I will argue that Tait’s axiomatic conception of mathematics implies that it is in principle impossible to be justified in believing a mathematical statement without being justified in believing that statement to be provable. I will then show that there are possible courses of experience which would justify acceptance of a mathematical statement without justifying belief that this statement is provable.

It's currently fashionable to take Putnamian model theoretic worries seriously for mathematics, but not for discussions of ordinary physical objects and the sciences. But I will argue that (under certain mild assumptions) merely securing determinate reference to physical possibility suffices to rule out nonstandard models of our talk of numbers. So anyone who accepts realist reference to physical possibility should not reject reference to the standard model of the natural numbers on Putnamian model theoretic grounds.

A range of current truth-value realist philosophies of mathematics allow one to reduce the Benacerraf Problem to a problem concerning mathematicians' ability to recognize which conceptions of pure mathematical structures are coherent – in a sense which can be cashed out in terms of logical possibility. In this paper I will clarify what it takes to solve this `residual' access problem and then present a framework for solving it.

This note points out a conflict between some common intuitions about metaphysical possibility. On the one hand, it is appealing to deny that there are robust counterfactuals about how various physically impossible substances would interact with the matter that exists at our world. On the other hand, our intuitions about how concepts like MOUNTAIN apply at other metaphysically possible worlds seem to presuppose facts about ‘solidity’ which cash out in terms of these counterfactuals. I consider several simple attempts to resolve (...) this conflict and note they all fall short. (shrink)

Invoking a form of quantifier variance promises to let us explain mathematicians’ freedom to introduce new kinds of mathematical objects in a way that avoids some problems for standard platonist and nominalist views. In this paper I’ll note that, despite traditional associations between quantifier variance and Carnapian rejection of metaphysics, Siderian realists about metaphysics can naturally be quantifier variantists. Unfortunately a variant on the Quinean indispensability argument concerning grounding seems to pose a problem for philosophers who accept this hybrid. However (...) I will charitably reconstruct this problem and then argue for optimism about solving it. (shrink)

The three papers which make up this dissertation form part of a larger project, which aims to solve the `access problem' for realism about mathematics by providing a clear and plausible example of what a satisfying explanation of human accuracy about objective mathematical facts could look like. They fit into this project as follows.

Across countries and throughout society, it is not uncommon to find individuals espousing incompatible and/or immovable positions in regard the perceived duality between science and religion. Many scholars in these domains propose other ways of thinking about science and religion, arguing for more nuanced understandings about how they might relate to each other. Children can be exposed to elements of either ‘side’ of such debate in their home life which may or may not include faith-based instruction, through the media and (...) throughout their schooling. Few teachers are likely to have the in-depth understanding and the confidence to help their students to appreciate that there is a range of ways of thinking about how science and religion relate including positive ways. Having an insight into student’s initial ideas is a key step in developing the confidence and understanding needed to engage with the issues they raise or that emerge in their education. This chapter reports on research undertaken collaboratively by researchers from the University of Reading, UK, and the University of Tasmania, Australia, looking at ways in which primary students perceive science and religion and the relationship between them. The research highlights particular challenges faced by teachers in Australian schools who are required to teach science and address students’ doubts about religion and its relationship with science. (shrink)

Human genomics is a translational field spanning research, clinical care, public health, and direct-to-consumer testing. However, law differs across these domains on issues including liability, consent, promoting quality of analysis and interpretation, and safeguarding privacy. Genomic activities crossing domains can thus encounter confusion and conflicts among these approaches. This paper suggests how to resolve these conflicts while protecting the rights and interests of individuals sequenced. Translational genomics requires this more translational approach to law.

This book offers a foundation for mathematics grounded in a collection of axioms for logical possibility in a first-order language. The offered foundation is ar.

Creatures inveterately wrong in their inductions have a pathetic but praiseworthy tendency to die before reproducing their kind.— Quine (1969).

This paper explores two questions in moral philosophy that might at first seem unrelated. The first question is practical. While it’s not a truth we like to contemplate, each of us faces the eventual loss of everyone and everything we love. Is there a way to live in full awareness of that fact without falling into anxiety or depression, or resorting to one form or another of forgetfulness, denial or numbing out? The second question is metaethical. Is it possible to (...) vindicate a strong form of ethical objectivity without positing anything metaphysically or epistemologically mysterious? In this paper, I sketch a partially Buddhist-inspired metaethical view that would, if it could be made to work, give a positive answer to both questions. The overall view is too much to defend in one paper, so I focus on developing one limited part of it. I begin by characterizing the general constructivist strategy for vindicating the objectivity of ethics. After briefly discussing Christine Korsgaard’s Kantian implementation of the strategy, I suggest an alternative implementation. I explore the idea that every agent necessarily faces what I call the problem of attachment and loss. I close with some speculative remarks about why, even though the problem of attachment and loss presents itself in a different substantive guise to each individual agent, it is still possible that the best solution to the problem is universal, and involves taking up an ethical perspective on the world. (shrink)

This chapter outlines a case for why liminality is of educational and not only of pedagogical concern, building on James Conroy's notion of the liminal imagination and his emphasis on the importance of metaphor for calling our attention to the ontological spaces that make up educational practice. It then turns to developing how different metaphors may be mobilised to signify the particularly relational quality of becoming, drawing on Luce Irigaray's work to explore more closely the corporeal and spiritual aspects of (...) becoming in relation. The chapter also presents a more fulsome discussion of the significance of approaching pedagogical relationships in education in this way and what this signifies for the teacher‐student encounter in particular. Finally, it argues that exploring the existential dimensions of pedagogical relationships between body and spirit similarly requires a language of in‐betweenness, or liminality, that gives full weight to the complex processes of human becoming. (shrink)

Contemporary realist theories of value claim to be compatible with natural science. In this paper, I call this claim into question by arguing that Darwinian considerations pose a dilemma for these theories. The main thrust of my argument is this. Evolutionary forces have played a tremendous role in shaping the content of human evaluative attitudes. The challenge for realist theories of value is to explain the relation between these evolutionary influences on our evaluative attitudes, on the one hand, and the (...) independent evaluative truths that realism posits, on the other. Realism, I argue, can give no satisfactory account of this relation. On the one hand, the realist may claim that there is no relation between evolutionary influences on our evaluative attitudes and independent evaluative truths. But this claim leads to the implausible skeptical result that most of our evaluative judgements are off track due to the distorting pressure of Darwinian forces. The realist’s other option is to claim that there is a relation between evolutionary influences and independent evaluative truths, namely that natural selection favored ancestors who were able to grasp those truths. But this account, I argue, is unacceptable on scientific grounds. Either way, then, realist theories of value prove unable to accommodate the fact that Darwinian forces have deeply influenced the content of human values. After responding to three objections, the third of which leads me to argue against a realist understanding of the disvalue of pain, I conclude by sketching how antirealism is able to sidestep the dilemma I have presented. Antirealist theories of value are able to offer an alternative account of the relation between evolutionary forces and evaluative facts —
an account that allows us to reconcile our understanding of evaluative truth with our understanding of the many non-rational causes that have played a role in shaping our evaluative judgements. (shrink)

The impact of Nietzsche's engagement with the Greek skeptics has never before been systematically explored in a book-length work - an inattention that belies the interpretive weight scholars otherwise attribute to his early career as a professor of classical philology and to the fascination with Greek literature and culture that persisted throughout his productive academic life. Jessica N. Berry fills this gap in the literature on Nietzsche by demonstrating how an understanding of the Pyrrhonian skeptical tradition illuminates Nietzsche's own (...) reflections on truth, knowledge, and ultimately, the nature and value of philosophic inquiry. This entirely new reading of Nietzsche's epistemological and ethical views promises to make clear and render coherent his provocative but often opaque remarks on the topics of truth and knowledge and to grant us further insight into his ethics-since the Greek skeptics, like Nietzsche, take up the position they do as a means of promoting well-being and psychological health. In addition, it allows us to recover a portrait of Nietzsche as a philologist and philosophical psychologist that has been too often obscured by commentaries on his thought. "The book addresses a number of central issues in Nietzsche's philosophy, including perspectivism and his conception of truth. The idea that his views in these areas owe much to the ancient Pyrrhonists casts them in an important new light, and is well supported by the texts. A lot of people from a lot of different areas in philosophy will have good reason to take notice." - Richard Bett, Johns Hopkins University. (shrink)

Most agree that when it comes to so-called 'first-order' normative ethics and political philosophy, constructivist views are a powerful family of positions. When it comes to metaethics, however, there is serious disagreement about what, if anything, constructivism has to contribute. In this paper I argue that constructivist views in ethics include not just a family of substantive normative positions, but also a distinct and highly attractive metaethical view. I argue that the widely accepted 'proceduralist characterization' of constructivism in ethics is (...) inadequate, and I propose what I call the 'practical standpoint characterization' in its place. I then offer a general taxonomy of constructivist positions in ethics. Since constructivism's standing as a family of substantive normative positions is relatively uncontested, I devote the remainder of the paper to addressing skeptics' worries about the distinctiveness of constructivism understood as a metaethical view. I compare and contrast constructivism with three other standard metaethical positions with which it is often confused or mistakenly thought to be compatible: realism; naturalist reductions in terms of an ideal response; and expressivism. In discussing the contrast with expressivism, I explain the sense in which, according to the constructivist, the distinction between substantive normative ethics and metaethics breaks down. I conclude by distinguishing between two importantly different debates about the mind-dependence of value. I argue that a failure to make this distinction is part of what explains why the possibility of constructivism as a metaethical view is often overlooked. (shrink)

In Science as Social Knowledge, Helen Longino offers a contextual analysis of evidential relevance. She claims that this "contextual empiricism" reconciles the objectivity of science with the claim that science is socially constructed. I argue that while her account does offer key insights into the role that values play in science, her claim that science is nonetheless objective is problematic.

Advocates of “Mendelism” early on stressed the usefulness of Mendelian principles for breeders. Ever since, that usefulness—and the favourable opinion of Mendelism it supposedly engendered among breeders—has featured in explanations of the rapid rise of Mendelian genetics. An important counter-tradition of commentary, however, has emphasized the ways in which early Mendelian theory in fact fell short of breeders’ needs. Attention to intellectual property, narrowly and broadly construed, makes possible an approach that takes both the tradition and the counter-tradition seriously, by (...) enabling a more complete description of the theory-reality shortfall and a better understanding of how changing practices, on and off the Mendelians’ experimental farms, functioned to render that shortfall unproblematic. In the case of plant breeding in Britain, a perennial source of lost profits and disputes over ownership was the appearance of individual plants departing from their varietal types—so-called “rogues.” Mendelian plant varieties acquired a reputation for being rogue-free, and so for demonstrating the correctness of Mendelian principles , at a time when Mendelians were gradually taking control of the means for distributing their varieties. Mendelian breeders protected their products physically from rogue-inducing contamination in such a way that when rogues did appear, the default explanation—that contamination had somehow occurred—ensured that there was no threat to Mendelian principles. (shrink)

There are many touch points between the work of Jacques Derrida and René Girard. To me, as a student of literature, these two writers particularly stand out as great readers or great exegetes.1 The way they handle and combine texts, the way they dare to break with reading conventions, has proved to be really fruitful.Some time ago I watched a documentary about Derrida, made by Kirby Dick and Amy Ziering Kofman, published in 2002, carrying the simple title Derrida.2 I found (...) that this experimental documentary at the same time reflected Derrida’s many reservations, not to say his skepticism, as to the possibility of making portraits—and—proved to be far more revealing, even intimate, than a conventional documentary... (shrink)

Next SectionAn attempt to resolve the controversy regarding the solution of the Sleeping Beauty Problem in the framework of the Many-Worlds Interpretation led to a new controversy regarding the Quantum Sleeping Beauty Problem. We apply the concept of a measure of existence of a world and reach the solution known as ‘thirder’ solution which differs from Peter Lewis’s ‘halfer’ assertion. We argue that this method provides a simple and powerful tool for analysing rational decision theory problems.

This chapter accepts for the sake of argument Ronald Dworkin’s point that the only viable form of normative skepticism is internal, and develops an internal skeptical argument directed specifically at normative realism. There is a striking and puzzling coincidence between normative judgments that are true, and normative judgments that causal forces led us to believe—a practical/theoretical puzzle to which the constructivist view has a solution. Normative realists have no solution, but are driven to conclude that we are probably hopeless at (...) recognizing the independent normative truths they posit. Since this is an unacceptable conclusion, we must conclude that normative realism is false. Drawing on evolutionary considerations, it is explained why this internal skeptical argument does not carry over to our knowledge of objects in our manifest surroundings, and why the challenge does not depend on any assumption that the epistemology of the normative domain must be a causal one. (shrink)

The way a rational agent changes her belief in certain propositions/hypotheses in the light of new evidence lies at the heart of Bayesian inference. The basic natural assumption, as summarized in van Fraassen's Reflection Principle, would be that in the absence of new evidence the belief should not change. Yet, there are examples that are claimed to violate this assumption. The apparent paradox presented by such examples, if not settled, would demonstrate the inconsistency and/or incompleteness of the Bayesian approach, and (...) without eliminating this inconsistency, the approach cannot be regarded as scientific. The Sleeping Beauty Problem is just such an example. The existing attempts to solve the problem fall into three categories. The first two share the view that new evidence is absent, but differ about the conclusion of whether Sleeping Beauty should change her belief or not, and why. The third category is characterized by the view that, after all, new evidence is involved. My solution is radically different and does not fall into either of these categories. I deflate the paradox by arguing that the two different degrees of belief presented in the Sleeping Beauty Problem are in fact beliefs in two different propositions, i.e., there is no need to explain the change of belief. The Sleeping Beauty Problem The Problem Deflated 2.1 From contradiction to consistency 2.2 The inanimate version 2.3 Back to SB Summary CiteULike Connotea Del.icio.us What's this? (shrink)

Unlike most texts in critical thinking, _Reason in the Balance_ focuses broadly on the practice of critical inquiry, the process of carefully examining an issue in order to come to a reasoned judgment. Although analysis and critique of individual arguments have an important role to play, this text goes beyond that dimension to emphasize the various aspects that go into the practice of inquiry, including identifying issues and relevant contexts, understanding competing cases, and making a comparative judgment._ Distinctive Features of (...) the Text:_ Emphasis on applying critical thinking to complex issues with competing arguments Inclusion of chapters on inquiry in specific contexts Attention to the dialogical aspects of inquiry, including sample dialogues Emphasis on the spirit of inquiry _The Second Edition Features:_ Updated examples and items of current interest New dialogues on vaccination, prostitution, and climate change New material on biases in reasoning, including emotional, psychological, social, and cognitive _The _Reason in the Balance_ Website includes:_ An Appendix on Logic Exercises Quizzes. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Pyrrhonian Revival in Montaigne and NietzscheJessica N. BerryMichel de Montaigne occupies a unique place in Nietzsche's history of ideas. He is one of a very few figures for whom Nietzsche expresses deep admiration and about whom he has virtually nothing critical to say. This is a rare enough mark of distinction; but contrary to what it might lead us to expect, the relationship between Montaigne and Nietzsche has (...) seldom been carefully examined. There has yet to be a book-length study devoted solely to Montaigne and Nietzsche,1 and article-length treatments of the relationship between their works and thought have been surprisingly scarce. What discussions there have been tend to locate the connections between Nietzsche and Montaigne mainly in matters of either literary or personal style,2 but studies that examine Montaigne's influence on Nietzsche with an eye toward philosophical rather than literary or stylistic issues have been almost non-existent.3 This dearth of treatments can be explained, at least in part, by the fact that, while Montaigne is rightly recognized for the literary merits of his work and for its subsequent influence on later prose stylists (and not only in French), his work on the whole has seldom been appreciated as having any philosophical value in its own right. Small wonder, then, that the connection between Montaigne and Nietzsche has [End Page 497] appeared more significant to commentators on Montaigne who are interested in tracing his influence on later thinkers than to scholars of Nietzsche—even those Nietzsche scholars who take an acute interest in his intellectual heritage. What I will argue here is that Montaigne makes a more concrete and philosophically more substantive contribution to Nietzsche's thought than has generally been appreciated; specifically, by giving impetus to the naturalism that develops in Human, All Too Human as an antidote to Schopenhauer's pessimistic metaphysics of will.In this essay, I present a two-fold thesis about Montaigne's influence on Nietzsche's early work. First, I will argue that the "naturalistic turn" in Human, All Too Human reflects Nietzsche's engagement with Montaigne during a crucial moment in the development of his thought. Second, I will demonstrate that the naturalism Nietzsche adopts from Montaigne has roots in the tradition of Pyrrhonian skepticism that Montaigne carries forward into the Renaissance. In the end, a better understanding of the skeptical ancestry of Nietzsche's naturalism should help us make better sense of Human, All Too Human and its immediate successors in Nietzsche's oeuvre, which cultivate what otherwise seems to be an uneasy partnership between naturalism and skepticism.I. It is by now widely accepted that Nietzsche's estimation of the value of the techniques and methods of the natural sciences undergoes radical revision in the period culminating in the first volume of Human, All Too Human (HAH),4 a book sometimes described as inaugurating a "positivist" phase in Nietzsche's work. From the first of its nine major sections, "Of First and Last Things," HAH narrates a struggle between science on the one hand and philosophy on the other. It is important to note the breadth of the extension of the term "science" (Wissenschaft), which includes not only what we think of as the "hard" or physical sciences (physics, chemistry, and the like) but also areas of inquiry we now consider "behavioral sciences" such as psychology and sociology—and, Nietzsche would say, philology as well. "Philosophy," by contrast is specified more narrowly. As Nietzsche uses the term throughout HAH, "philosophy" is usually shorthand for "metaphysical philosophy" and singles out for criticism the discourse of metaphysics that has dominated the philosophical landscape at least since Plato.In the sense in which Nietzsche worries about it "metaphysical philosophy" promotes speculation about such supra-sensible entities as Platonic forms, Descartes's "immaterial substances," and Kantian things-in-themselves. That its contributions include, for instance, theories about the existence and immortality of the soul accounts for Nietzsche's grouping "metaphysical philosophy" [End Page 498] together with religion and art as "arts of narcosis."5 Consciously or not they endeavor to comfort us by assuaging our fear of death, our existential anxieties about the purposelessness of... (shrink)

New biotechnologies have propelled the question of what it means to be human - or posthuman - to the forefront of societal and scientific consideration. This volume provides an accessible, critical overview of the main approaches in the debate on posthumanism, and argues that they do not adequately address the question of what it means to be human in an age of biotechnology. Not because they belong to rival political camps, but because they are grounded in a humanist ontology that (...) presupposes a radical separation between human subjects and technological objects. The volume offers a comprehensive mapping of posthumanist discourse divided into four broad approaches-two humanist-based approaches: dystopic and liberal posthumanism, and two non-humanist approaches: radical and methodological posthumanism. The author compares and contrasts these models via an exploration of key issues, from human enhancement, to eugenics, to new configurations of biopower, questioning what role technology plays in defining the boundaries of the human, the subject and nature for each. Building on the contributions and limitations of radical and methodological posthumanism, the author develops a novel perspective, mediated posthumanism, that brings together insights in the philosophy of technology, the sociology of biomedicine, and Michel Foucault's work on ethical subject constitution. In this framework, technology is neither a neutral tool nor a force that alienates humanity from itself, but something that is always already part of the experience of being human, and subjectivity is viewed as an emergent property that is constantly being shaped and transformed by its engagements with biotechnologies. Mediated posthumanism becomes a tool for identifying novel ethical modes of human experience that are richer and more multifaceted than current posthumanist perspectives allow for. The book will be essential reading for students and scholars working on ethics and technology, philosophy of technology, poststructuralism, technology and the body, and medical ethics. (shrink)