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 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)

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)

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)

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)

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)

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.

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 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)

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)

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.

In management research, theory testing confronts a paradox described by Meehl in which designing studies with greater methodological rigor puts theories at less risk of falsification. This paradox exists because most management theories make predictions that are merely directional, such as stating that two variables will be positively or negatively related. As methodological rigor increases, the probability that an estimated effect will differ from zero likewise increases, and the likelihood of finding support for a directional prediction boils down to a (...) coin toss. This paradox can be resolved by developing theories with greater precision, such that their propositions predict something more meaningful than deviations from zero. This article evaluates the precision of theories in management research, offers guidelines for making theories more precise, and discusses ways to overcome barriers to the pursuit of theoretical precision. (shrink)

The intellectual history of Germany in the late eighteenth and nineteenth centuries is sometimes compared to the philosophical achievement of Athens at the very height of the classical age. Both were tremendously fruitful periods, which saw the birth of revolutionary philosophical systems that inspired a fantastic intellectual commerce among new and rival schools of thought. The plenitude of references to Greek mythology in literary works from Goethe and Lessing to Schiller, Novalis, and Hölderlin; the burgeoning interest in classical philology and (...) the translation and transmission of works of antiquity; and the growing interest in the history of skepticism in ancient Greece; all are instances of a widespread preoccupation with Hellenic thought and culture that persisted throughout the nineteenth and into the twentieth century. The intellectual associations between many seminal thinkers during this time make it easy to trace the transmission of this enthusiasm from one figure or group to another. (shrink)

By illuminating the striking affinity between the most innovative aspects of postmodern thought and religious mystical discourse, Shadow of Spirit challenges the long established assumption that western thought is committed to nihilism. This collection of essays by internationally recognized scholars explores the implications of the fascination with the "sacred," "divine" or "infinite" which characterizes much contemporary thought. It shows how these concerns have surfaced in the work of Derrida, Baudrillard, Lyotard, Kristeva, Irigaray and others. Examining the connection between this postmodern (...) "turn" and the current search for a new discourse of ethics and politics, it also stresses the contribution made by feminist thought to this unexpected intellectual direction. (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)

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)

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)

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)

This chapter contains sections titled: The Nature of Critical Thinking Critical Thinking: Skills/Abilities and Dispositions Critical Thinking and the Problem of Generalizability The Relationship Between Critical Thinking and Creative Thinking “Critical Thinking” and Other Terms Referring to Thinking Critical Thinking and Education Critiques of Critical Thinking Conclusion.

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.

Analysis of sites of newly integrated DNA in cellular genomes is important to several fields, but methods for analyzing and visualizing these datasets are still under development. Here, we describe tools for data analysis and visualization that take as input integration site data from our INSPIIRED pipeline. Paired-end sequencing allows inference of the numbers of transduced cells as well as the distributions of integration sites in target genomes. We present interactive heatmaps that allow comparison of distributions of integration sites to (...) genomic features and that support numerous user-defined statistical tests. To summarize integration site data from human gene therapy samples, we developed a reproducible report format that catalogs sample population structure, longitudinal dynamics, and integration frequency near cancer-associated genes. We also introduce a novel summary statistic, the UC50, which provides a single number summarizing possible clonal expansion. Using these tools, we characterize ongoing longitudinal characterization of a patient from the first trial to treat severe combined immunodeficiency-X1, showing successful reconstitution for 15 years accompanied by persistence of a cell clone with an integration site near the cancer-associated gene CCND2. Software is available at https://github.com/BushmanLab/INSPIIRED. (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)

Feminist philosophy of science appears to present problems for the ideal of value-free science. These difficulties also challenge a traditional understanding of the objectivity of science. However, feminist philosophers of science have good reasons for desiring to retain some concept of objectivity. The present essay considers several recent and influential feminist approaches to the role of social and political values in science, with particular focus on feminist empiricism and feminist standpoint theory. The similarities and difference, as well as the strengths (...) and weaknesses of these approaches are explored. The essay concludes with suggestions for future research in the area of feminist epistemology and philosophy of science. (shrink)

A newly revised edition of the International Best-Seller, Making the Brain/Body Connection hit the book stores in June. This book has people raving about its user friendly approach and its solid research based information. Explore and experience how your brain, body and senses interrelate. Sharon Promislow's approach makes the brain research almost fun. Learn about your body's defence mechanism for stress and how you can adapt them to defuse stress instead of allowing it to accumulate into a full blown (...) stress attack. In her lively and entertaining book, Sharon blends cutting edge stress and brain research with practical exercises and techniques that have you moving beyond your current limitations and into a life you only imagined you could have. Her Quick Six stress buster techniques can be used on the street, in the board room, wherever you are when stress hits.Follow along with this step-by-step guide as she leads you through a model for change that unlocks hidden "stress circuits." Clear away mental, emotional and physical blocks to success with simple movements from the 10 Step Change Process, that make change fun. Illustrated with humorus new cartoon characters by Cathrine Levan. (shrink)

Plato's account of an important dialogue on the nature of love between Phaedrus, Pausanias, Eryximachus, Aristophanes, Agathon, Socrates and Alcibiades. English translation with notes and introduction.

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)