This chapter offers an opinionated introduction to higher-order formal languages with an eye towards their applications in metaphysics. A simply relationally typed higher-order language is introduced in four stages: starting with first-order logic, adding first-order predicate abstraction, generalizing to higher-order predicate abstraction, and finally adding higher-order quantification. It is argued that both β-conversion and Universal Instantiation are valid on the intended interpretation of this language. Given these two principles, it is then shown how we can use pure higher-order logic to (...) ask, and begin to answer, metaphysical questions with non-trivial implications. In particular, while we must reject the popular idea that structural differences between sentences correspond to parallel distinctions in the logical structure of extra-linguistic reality, it may still be possible to give a purely logical characterization of objectual aboutness and related notions. (shrink)

Some propositions are true, and it is true that some propositions are true. Each of these facts looks like an impeccable ground of the other. But they cannot both ground each other, since grounding is asymmetric. This paper explores two new diagnoses of this much discussed puzzle. The tools of higher-order logic are used to show how both diagnoses can be fleshed out into strong and consistent theories of grounding. These theories of grounding in turn demand new theories of the (...) granularity of propositions, properties, and relations. Even those who are uninterested in grounding should take seriously these pictures of reality’s logical structure, which are in many ways reminiscent of Russell’s and Wittgenstein’s logical atomism. (shrink)

This volume collects two lectures by Jeremy Waldron that were originally given as Berkeley Tanner Lectures along with responses to the lectures from Wai Chee Dimock, Don Herzog, and Michael Rosen; a reply to the responses by Waldron; and an introduction by Meir Dan-Cohen.

Picturing is a poorly understood element of Sellars’s philosophical project. We diagnose the problem with picturing as follows: on the one hand, it seems that it must be connected with action in order for it to do its job. On the other hand, the representational states of a picturing system are characterized in descriptive and seemingly static terms. How can static terms be connected with action? To solve this problem, we adopt a concept from recent work in Sellarsian metaethics: the (...) idea of a material practical inference, which (we argue) features centrally in how we picture. The key distinction is that the picturing of nonhuman animals involves only Humean material practical inference, in which representational states are corrected only by feedback from the environment and not from discursive interactions. The resulting view shows that Sellars’s contributions to practical philosophy (especially theory of action and metaethics) cannot be separated from his contributions to philosophy of mind, language, and cognitive science. Further, the view makes it clear that picturing is neither a version of the Given, nor is it a fifth wheel to inferential role in explaining representation, but is essential to Sellars’s model of how animals—including humans—represent their environment. (shrink)

In this paper, I introduce a version of perdurantism called Priority Perdurantism, according to which perduring, four-dimensional objects are ontologically fundamental and the temporal parts of those objects are ontologically derivative, depending for their existence and their identity on the four-dimensional wholes of which they are parts. I argue that by switching the order of the priority relations this opens up new solutions to the too-many-thinkers problem and the personite problem – solutions that are more ontologically robust than standard maximality (...) solutions. I then consider and respond to two initial objections to the view: that it no longer counts as a perdurantist theory and that it reintroduces the problem of temporary intrinsics. I conclude by offering two further advantages of priority perdurantism: that it is consistent with hunky time and with the existence of irreducibly temporally-extended actions, such as those pertaining to deliberative agency. (shrink)

Scholars have wrestled with "consciousness", a major scholar calling it the "hard problem". Some thirty-plus years after the Towards a Science of Consciousness, we do not seem to be any closer to an answer to "What is consciousness?". Seemingly irresolvable metaphysical problems are addressed by bootstrapping, provisional assumptions, not unlike those used by logicians and mathematicians. I bootstrap with the same ontology and epistemology applicable to everything we apprehend. Here, I argue for a version of the unity of opposites, a (...) form of neutral monism. Something exists because of what it is not; nothing can exist by itself, singularities (analogous to monads), expressing the model. Applying this most fundamental law to the consciousness problem, the physical (movement) comes into being simultaneously as the mental (stasis), each displayed by a field that is variegated (ranging from creative to entropic processes). Such is in keeping with how the singularity emerged as our universe, the same form that may account for sub-Planck-scale phenomena. Overall, like the most fundamental law, deep structures are imminent in our universe, both as objects and processes. (shrink)

Decision-making capacity (DMC) is, in many ways, a central organizing concept of modern health care ethics. Patients with DMC have the moral—if not always the legal—authority to make all manner of...

This is a concise and profound book from one of the world's leading political and legal philosophers about a major theme, equality, and the proposition that humans are all one another's equals. Jeremy Waldron explores the implications of this fundamental tenet for law, politics, society and economy in the company of John Locke, whose work Waldron regards 'as well-worked-out a theory of basic equality as we have in the canon of political philosophy'. Throughout the text, which is based on (...) the Carlyle Lectures given in Oxford in 1999, Jeremy Waldron discusses contemporary approaches to equality and rival interpretations of Locke, and this dual agenda gives the whole an unusual degree of accessibility and intellectual excitement, of interest to philosophers, political theorists, lawyers and theologians around the world. (shrink)

The epsilon calculus is a logical formalism developed by David Hilbert in the service of his program in the foundations of mathematics. The epsilon operator is a term-forming operator which replaces quantifiers in ordinary predicate logic. Specifically, in the calculus, a term εx A denotes some x satisfying A(x), if there is one. In Hilbert's Program, the epsilon terms play the role of ideal elements; the aim of Hilbert's finitistic consistency proofs is to give a procedure which removes such terms (...) from a formal proof. The procedures by which this is to be carried out are based on Hilbert's epsilon substitution method. The epsilon calculus, however, has applications in other contexts as well. The first general application of the epsilon calculus was in Hilbert's epsilon theorems, which in turn provide the basis for the first correct proof of Herbrand's theorem. More recently, variants of the epsilon operator have been applied in linguistics and linguistic philosophy to deal with anaphoric pronouns. (shrink)

This outstanding collection offers a thorough and diverse philosophical exploration of habit from the classical period to the modern day. Essential reading for students and researchers in the history of philosophy, ethics, phenomenology, philosophy of action and pragmatism.

An enduring theme of Western philosophy is that we are all one another’s equals. Yet the principle of basic equality is woefully under-explored in modern moral and political philosophy. What does it mean to say we are all one another’s equals? Jeremy Waldron confronts this question fully and unflinchingly in a major new multifaceted account.

"Arguing that debates over legitimacy, political violence, freedom, and justice would benefit greatly from cross-tradition theorizing, this book shows how putting analytic and continental political theory in conversation would help us to overcome these intractable problems"--.

This is a review of Hossenfelder’s book, Lost in Math: How Beauty Leads Physics Astray. The book gives a breezy exposition of the present situation in fundamental physics, and raises important questions: both about the content of the physics, and the way physics research is organized. I first state my main disagreements. Then, I mostly praise the book: I concentrate on Hossenfelder’s discussion of supersymmetry, naturalness and the multiverse.

Biomedical and behavioral research may affect strongly held social values and thereby create significant controversy over whether such research should be permitted in the first place. Institutional review boards responsible for protecting the rights and welfare of participants in research are sometimes faced with review of protocols that have significant implications for social policy and the potential for negative social consequences. Although IRB members often raise concerns about potential long-term social implications in protocol review, federal regulations strongly discourage IRBs from (...) considering them in their decisions. Yet IRBs often do consider the social implications of research protocols and sometimes create significant delays in initiating or even prevent such research. The social implications of research are important topics for public scrutiny and professional discussion. This article examines the reasons that the federal regulations preclude IRBs from assessing the social risks of research, and examines alternative approaches that have been used with varying success by national advisory groups to provide such guidance. The article concludes with recommendations for characteristics of a national advisory group that could successfully fulfill this need, including sustainability, independence, diverse and relevant expertise, and public transparency. (shrink)

In _Nonsense upon Stilts¸_ first published in 1987, Waldron includes and discusses extracts from three classic critiques of the idea of natural rights embodied in the 1789 Declaration of the Rights of Man and the Citizen. Each text is prefaced by an historical introduction and an analysis of its main themes. The collection as a whole in introduced with an essay tracing the philosophical background to the three critiques as well as the eighteenth-century idea of natural rights which they attacked. (...) But the point of reproducing these works is not merely historical. Modern attacks on ‘rights-based’ political philosophy mirror the concerns of Bentham, Burke and Marx. Jeremy Waldron has therefore added an extensive concluding essay which relates these classic texts to the modern discussion of rights and re-examines the idea of rights in the light of contemporary critiques. This text provides an invaluable teaching tool for courses in politics and philosophy. (shrink)

Every branch of mathematics has its subject matter, and one of the distinguishing features of logic is that so many of its fundamental objects of study are rooted in language. The subject deals with terms, expressions, formulas, theorems, and proofs. When we speak about these notions informally, we are talking about things that can be written down and communicated with symbols. One of the goals of mathematical logic is to introduce formal definitions that capture our intuitions about such objects and (...) enable us to reason about them precisely. At the most basic level, syntactic objects can be viewed as strings of symbols. For concreteness, we can identify symbols with particular set-theoretic objects, but for most purposes, it doesn't matter what they are; all that is needed is that they are distinct from one another. (shrink)

A rigorous, authoritative new anthology which brings together some of the most significant contemporary scholarship on the theory of knowledge Carefully-calibrated and judiciously-curated, this strong and contemporary new anthology builds upon Epistemology: An Anthology, Second Edition (Wiley Blackwell, 2008) by drawing a concise and well-balanced selection of higher-level readings from a large, diverse, and evolving body of research. Includes 17 readings that represent a broad and vital part of contemporary epistemology, including articles by female philosophers and emerging thought leaders Organized (...) into seven thoughtful and distinct sections, including virtue epistemology, practical reasons for belief, and epistemic dysfunctions among others Designed to sit alongside the highly-successful anthology of canonical essays, Epistemology: An Anthology, Second Edition (Wiley Blackwell, 2008) Edited by a distinguished editorial team, including Ernie Sosa, one of the most influential active epistemologists Highlights cutting edge methodologies and contemporary topics for advanced students, instructors, and researchers. (shrink)

"With its wide-ranging analyses, this book offers insights of interest to scholars of religion, philosophers, art historians, and students of French ...

We describe a model-theoretic approach to ordinal analysis via the finite combinatorial notion of an α-large set of natural numbers. In contrast to syntactic approaches that use cut elimination, this approach involves constructing finite sets of numbers with combinatorial properties that, in nonstandard instances, give rise to models of the theory being analyzed. This method is applied to obtain ordinal analyses of a number of interesting subsystems of first- and second-order arithmetic.

Philosophical concerns rarely force their way into the average mathematician’s workday. But, in extreme circumstances, fundamental questions can arise as to the legitimacy of a certain manner of proceeding, say, as to whether a particular object should be granted ontological status, or whether a certain conclusion is epistemologically warranted. There are then two distinct views as to the role that philosophy should play in such a situation. On the first view, the mathematician is called upon to turn to the counsel (...) of philosophers, in much the same way as a nation considering an action of dubious international legality is called upon to turn to the United Nations for guidance. After due consideration of appropriate regulations and guidelines (and, possibly, debate between representatives of different philosophical factions), the philosophers render a decision, by which the dutiful mathematician abides. Quine was famously critical of such dreams of a ‘first philosophy.’ At the opposite extreme, our hypothetical mathematician answers only to the subject’s internal concerns, blithely or brashly indifferent to philosophical approval. What is at stake to our mathematician friend is whether the questionable practice provides a proper mathematical solution to the problem at hand, or an appropriate mathematical understanding; or, in pragmatic terms, whether it will make it past a journal referee. In short, mathematics is as mathematics does, and the philosopher’s task is simply to make sense of the subject as it evolves and certify practices that are already in place. In his textbook on the philosophy of mathematics (Shapiro, 2000), Stewart Shapiro characterizes this attitude as ‘philosophy last, if at all.’. (shrink)

Using a slight generalization, due to Palmgren, of sheaf semantics, we present a term-model construction that assigns a model to any first-order intuitionistic theory. A modification of this construction then assigns a nonstandard model to any theory of arithmetic, enabling us to reproduce conservation results of Moerdijk and Palmgren for nonstandard Heyting arithmetic. Internalizing the construction allows us to strengthen these results with additional transfer rules; we then show that even trivial transfer axioms or minor strengthenings of these rules destroy (...) conservativity over HA. The analysis also shows that nonstandard HA has neither the disjunction property nor the explicit definability property. Finally, careful attention to the complexity of our definitions allows us to show that a certain weak fragment of intuitionistic nonstandard arithmetic is conservative over primitive recursive arithmetic. (shrink)

We consider the extent to which one can compute bounds on the rate of convergence of a sequence of ergodic averages. It is not difficult to construct an example of a computable Lebesgue measure preserving transformation of [0, 1] and a characteristic function f = χA such that the ergodic averages Anf do not converge to a computable element of L2([0, 1]). In particular, there is no computable bound on the rate of convergence for that sequence. On the other hand, (...) we show that, for any nonexpansive linear operator T on a separable Hilbert space and any element f , it is possible to compute a bound on the rate of convergence of Anf from T , f , and the norm f ∗ of the limit. In particular, if T is the Koopman operator arising from a computable ergodic measure preserving transformation of a probability space X and f is any computable element of L2 (X ), then there is a computable bound on the rate of convergence of the sequence Anf. (shrink)

Acentral promise of human embryonic stem cell research is the potential to develop viable therapeutic approaches to a range of devastating diseases and conditions. Despite excitement over such advances, there are scientific and medical reasons to be cautious as stem cells and their products are introduced into patients. In response to such concerns, the International Society for Stem Cell Research as well as ad hoc groups and individuals have offered approaches to governance of this research. While there are similarities among (...) these governance models and they are in principle easily endorsable, in this paper I raise a set of concerns related to their implementation, suggesting areas where gathering data may facilitate more appropriate oversight. Next, I suggest areas that seem to have been neglected as these governance models have been developed so that they may be on the agendas of those seeking to revise these models in the future. Finally, I describe how some of the concerns that have arisen in considering the appropriate governance of stem cell research may be useful in science and translational research more broadly. (shrink)

The presidency of Donald Trump saw the rise of a new kind of conspiracy in QAnon. The internet-assembled meta-conspiracy has grown to include elements of other growing conspiracies such as the anti-mask movement and anti-vaxxers. As it has grown, QAnon has attracted significant support for its beliefs from white evangelicals who also supported Trump in huge numbers in both 2016 and 2020. In this integrative review of literature, I explore the reasons that QAnon has performed so well so quickly, finding (...) justification for conspiracy theory support among evangelicals in the theory of cognitive dissonance. QAnon has found a foothold in evangelical circles during worldwide pandemic, which has left many evangelicals unmoored from their spiritual family and susceptible to other realms of community online. The conspiracy theory has infiltrated evangelicalism by using the language and concerns of Christianity in its messaging and by attempting to justify evangelical support of Donald Trump. Although traditional media are quick to point out the theory’s inconsistencies and failed prophecies, this paper finds that the harm QAnon has done to the evangelical community may only be undone through spiritual connection and practice. (shrink)

Among the many obscure sects of sexual fetishism, few remain as perplexing as that of the “crush freaks,” who are aroused by the sight of an insect exploded beneath a human foot. Moving beyond the glib discussions of those entomologists and sexologists who classify this fetish as a subset of foot worship and/or macrophilia, I propose an analysis of the crush freaks through the writings of French thinker Georges Bataille. Employing Bataille’s notions of sacrificial eroticism and mysticism to approach the (...) religio-sexual dimensions of crush freakism, I argue that these practices are best understood as ambivalent manifestations of technophilia . More specifically, crush freakism, I submit, devolves on a violent literalization of the analogies between insects and machines. (shrink)

Negative Ecstasies discusses the contribution and significance of the work of Georges Bataille to the contemporary study of religion and theology, collecting essays that examine specific case studies and make connections to other significant scholars in the field.

Genetic roots: Lonergan's understanding of love, 1943/1964 -- Developing the shift to interiority: 1965 to November, 1972 -- The emergence & clarification of the fifth level of consciousness: December, 1972, to November, 1984 -- "What was going forward" in Lonergan's development on love: a history of Lonergan's development -- The scholarly discussion on love and the fifth level of consciousness in Lonergan -- Love as a fifth level of consciousness.

The philosophy of mathematics has long been concerned with deter- mining the means that are appropriate for justifying claims of mathemat- ical knowledge, and the metaphysical considerations that render them so. But, as of late, many philosophers have called attention to the fact that a much broader range of normative judgments arise in ordinary math- ematical practice; for example, questions can be interesting, theorems important, proofs explanatory, concepts powerful, and so on. The as- sociated values are often loosely classied as (...) aspects of \mathematical understanding." Meanwhile, in a branch of computer science known as \formal ver- ication," the practice of interactive theorem proving has given rise to software tools and systems designed to support the development of com- plex formal axiomatic proofs. Such eorts require one to develop models of mathematical language and inference that are more robust than the the simple foundational models of the last century. This essay explores some of the insights that emerge from this work, and some of the ways that these insights can inform, and be informed by, philosophical theories of mathematical understanding. (shrink)

If we accept that at least some kinds of nonhuman animals are persons, a variety of paradoxes emerge in our ethical relations with them, involving apparently unavoidable disrespect of their personhood. We aim to show that these paradoxes are legitimate but can be illuminatingly resolved in the light of an adequate understanding of the nature of persons. Drawing on recent Western, Daoist, and Zen Buddhist thought, we argue that personhood is already paradoxical in the same way as these aspects of (...) our ethical relations with nonhuman animals, and in fact is the source of their paradoxical character. In both contexts, depth and shallowness turn out to be internal to or crucial parts of each other, with logically anomalous consequences. We try to show that the character of this paradoxical relation between depth and shallowness in the nature of personhood involves a crucial inflection in the case of nonhuman animal persons that allows us to make sense of and resolve these ethical paradoxes. (shrink)

This paper gives a technically elementary treatment of some aspects of Hamilton -Jacobi theory, especially in relation to the calculus of variations. The second half of the paper describes the application to geometric optics, the optico-mechanical analogy and the transition to quantum mechanics. Finally, I report recent work of Holland providing a Hamiltonian formulation of the pilot-wave theory.

Criticisms of the traditional clinical research pathway and its extensive oversight often focus on proposals for deregulation or assert that as in clinical treatment, clinical research should always offer benefit to patient-subjects. Proponents of medical innovation take a different, middle path, arguing that innovation is distinguishable from both research and treatment. This article considers this third pathway by examining stem cell-based innovation.Stem cell-based medical innovation is one pathway toward clinical translation. In fact, such an approach was taken in developing umbilical (...) cord blood transplantation, which is now widely viewed as a safe and effective means for treating a range of malignant and non-malignant conditions. While the Guidelines for the Clinical Translation of Stem Cells created by the International Society for Clinical Research provide an approach to clinical translation that involves “responsible innovation” as an alternative to clinical research, there are at least four sets of unanswered questions regarding the use of an innovation pathway in this context that warrant careful attention. (shrink)

From proofs in any classical first-order theory that proves the existence of at least two elements, one can eliminate definitions in polynomial time. From proofs in any classical first-order theory strong enough to code finite functions, including sequential theories, one can also eliminate Skolem functions in polynomial time.

Since his death in 1986, Michel de Certeau's reputation as a thinker has steadily grown both in France and throughout the English-speaking world. His work is extraordinarily innovative and wide-ranging, cutting across issues in historiography, literary and cultural studies, anthropology, sociology, theology, philosophy and psychoanalysis. This book represents the first full-length study of Certeau's thought. It is organized around the central theme of interpretation and alterity, which Ahearne uses to illuminate Certeau's work as a whole. The author also examines Certeau's (...) theory and practice of historiography; his reflection on the relations between changing historical forms of writing, reading and orality; and his distinction between the "strategic" programmes of the politically powerful and the "tactics" of the relatively powerless. Ahearne places Certeau's work in its general intellectual context, relating it to the views of important contemporary thinkers, such as Pierre Bourdieu and Michel Foucault, and demonstrating the decisive importance to Certeau's thought of the writings of the early modern mystics and travellers. This book constitutes an excellent critical introduction to Certeau's work, while also providing a comprehensive and nuanced reading for those already familiar with his thought. (shrink)

This paper develops some ideas from previous work (coauthored, mostly with C.J.Isham). In that work, the main proposal is to assign as the value of a physical quantity in quantum theory (or classical physics), not a real number, but a certain kind of set (a sieve) of quantities that are functions of the given quantity. The motivation was in part physical---such a valuation illuminates the Kochen-Specker theorem; in part mathematical---the valuations arise naturally in the theory of presheaves; and in part (...) conceptual---the valuations arise from applying to propositions about the values of physical quantities some general axioms governing partial truth for any kind of proposition. In this paper, I give another conceptual motivation for the proposal. I develop (in Sections 2 and 3) the notion of a topos (of which presheaves give just one kind of example); and explain how this notion gives a satisfactory general framework for making sense of the idea of partial truth. Then I review (in Section 4) how our proposal applies this framework to the case of physical theories. (shrink)

We use model-theoretic methods described in [3] to obtain ordinal analyses of a number of theories of first- and second-order arithmetic, whose proof-theoretic ordinals are less than or equal to Γ0.

A Humean Critique of David Hume's Theory of Knowledge provides the first full-length Aristotilian-Thomistic critique of Hume's most mature and familiar work. While giving Hume proper respect and appreciation for his achievement, Jeremy White engages in a thoughtful critique through an approach based in Hume's own method.