The law within each legal system is a function of the practices of some social group. In short, law is a kind of socially grounded norm. H.L.A Hart famously developed this view in his book, The Concept of Law, by arguing that law derives from a social rule, the so-called “rule of recognition.” But the proposition that social facts play a foundational role in producing law is a point of consensus for all modern jurisprudents in the Anglo-American tradition: not just (...) Hart and his followers in the positivist school, most prominently Joseph Raz and Jules Coleman, but also the anti-positivist Ronald Dworkin, who argues that law necessarily synthesizes moral considerations with social facts. But which group’s practices ground each legal system? In particular, which group’s practices undergird U.S. law? Positivists since Hart have universally pointed to either officials or judges as the “recognitional community” (my term): the group such that its rules, conventions, cooperative activities, or practices in some other sense are the social facts from which the law of a given legal system derives. So Hart and all other positivists would identify either U.S. officials or U.S. judges as the recognitional community for U.S. law. This Article grapples with the tension between the positivist’s official- or judge-centered account of the recognitional community and the “popular constitutionalism” now so widely defended by constitutional scholars such as Larry Kramer, Robert Post, Reva Siegel, Mark Tushnet, Jeremy Waldron, and many others. Surely the popular constitutionalist would want to claim that U.S. citizens, not judges or officials, are the recognitional community for U.S. law. I term this position “deep popular constitutionalism.” Indeed, it turns out that Dworkin’s account of law, in its ambition to generate associative moral obligations for the citizenry as a whole, implies deep popular constitutionalism. Here there is a disagreement, hitherto unnoticed, between Dworkin and the positivists. My solution to this disagreement – to the debate between deep popular constitutionalists and deep official or judicial supremacists -- is to dissolve it by providing a group-relative account of law. Social norms, such as norms of dress or eating, are clearly group-relative. A particular dressing or eating behavior may be socially appropriate relative to one group’s norms, yet socially inappropriate relative to another’s. This Article extends the group-relative view from social norms to law itself, with a particular focus on U.S. law and constitutionalism. Part I surveys the jurisprudential literature. It shows how Hart and successor positivists identify the rule of recognition as a social practice engaged in by officials or some subset of officials (judges), rather than citizens generally, and argues that Dworkin by contrast sees the citizenry as a whole as his recognitional community. Parts II and III defend a group-relative account of law. Part II argues, with reference to the U.S. experience, that multiple groups can simultaneously instantiate the kind of social fact that undergirds law, be it a convention, a social norm, a “shared cooperative activity” (SCA), or something else. At many points in U.S. constitutional history, multiple official or citizen groups, defined along departmental, partisan, regional, state-federal, religious, or other lines, have accepted competing rules of recognition for U.S. law. Part III argues that “law” functions, primarily, as either an explanatory or a normative construct, and that insisting on a single recognitional community for each legal system would be arbitrary, both for explanatory purposes and for normative purposes. Part IV considers the many implications of the group-relative account for U.S. constitutional theory – in particular, for popular constitutionalism. (shrink)

Introduction: the age of reflexion Part I. Romanticism: 1. Romanticism and the sciences David Knight 2. Schelling and the origins of his Naturphilosophie S. R. Morgan 3. Romantic philosophy and the organization of the disciplines: the founding of the Humboldt University of Berlin Elinor S. Shaffer 4. Historical consciousness in the German Romantic Naturforschung Dietrich Von Engelhardt 5. Theology and the sciences in the German Romantic period Frederick Gregory 6. Genius in Romantic natural philosophy Simon Shaffer Part II. Sciences of (...) the Organic: 7. Doctors contra clysters and feudalism: the consequences of a Romantic revolution Nelly Tsouyopoulos 8. Morphotypes and the historical-genetic method in Romantic biology Timothy Lenoir 9. ’Metaphorical mystifications’: the Romantic gestation of nature in British biology Evelleen Richards 10. Transcendental anatomy Philip F. Rehbock 11. Romantic thought and the origins of cell theory L. S. Jacyna 12. Alexander von Humbolt and the geography of vegetation Malcolm Nicholson Part III. Sciences of the Inorganic: 13. Goethe, colour, and the science of seeing Dennis L. Sepper 14. Johann Wilhelm Ritter: Romantic physics in Germany Walter D. Wetzels 15. The power and the glory: Humphrey Davy and Romanticism Christopher Lawrence 16. Oersted’s discovery of electromagnetism H. A. M. Snelders 17. Caves, fossils and the history of the earth Nicholas A. Rupke Part IV. Literature and the Sciences: 18. Goethe’s use of chemical theory in his Elective Affinities Jeremy Adler 19. Kleist’s bedlam: abnormal psychology and psychiatry in the works of Heinrich von Kleist Nigel Reeves 20. Coleridge and the sciences Trevor H. Levere 21. Nature’s book: the language of science in the American Renaissance David van Leer 22. The shattered whole: Georg Buchner and Naturphilosophie John Reddick. (shrink)

Thomas Hobbes’ Lebensaufgabe besteht in einer wissenschaftlichen Staatsphilosophie. Dabei stellt er sich den drei Herausforderungen seiner Epoche: methodisch dem Beweisideal der Mathematik, politisch der blutigen Wirklichkeit der Kriege und Bürgerkriege und moralisch dem Schwinden gemeinsamer Überzeugungen. Weil er sich allen drei Herausforderungen stellt, zugleich sie miteinander verbindet, schafft er das die Tradition stürzende Argumentationsmuster der politischen Moderne, die Vertragstheorie. Mit ihr bringt er eine der größten Staatsphilosophien der abendländischen Geistesgeschichte hervor. In De cive / Vom Bürger (1642), das noch vor (...) dem Leviathan (1651) entstand, finden sich bereits zahlreiche von Hobbes’ zentralen Gedanken zur politischen Philosophie. Diese Schrift wird hier durchgängig von international renommierten Autoren kommentiert. Mit Beiträgen von Jeremy Adler, Ronald Asch, Dirk Brantl, Franz Hespe, Moritz Hildt, Otfried Höffe, Heiner Klemme, Elif Özmen, Dietrich Schotte, Peter Schröder, Patricia Springborg, Tom Sorell und Lothar Waas. (shrink)

I show that locality, as it occurs in EPR arguments for the incompleteness of quantum mechanics, can be construed as causal independence understood in terms of Lewis' counterfactual analysis of causation. This construal has two benefits. It supplements recent analyses, which have not treated locality in detail. And it clarifies the relation between two EPR arguments that have recently been distinguished. It shows that the simpler of the two is more complex than has been thought; and that the other argument (...) does not need 'counterfactual definiteness'. (shrink)

Of all the demands that mathematics imposes on its practitioners, one of the most fundamental is that proofs ought to be correct. It has been common since the turn of the twentieth century to take correctness to be underwritten by the existence of formal derivations in a suitable axiomatic foundation, but then it is hard to see how this normative standard can be met, given the differences between informal proofs and formal derivations, and given the inherent fragility and complexity of (...) the latter. This essay describes some of the ways that mathematical practice makes it possible to reliably and robustly meet the formal standard, preserving the standard normative account while doing justice to epistemically important features of informal mathematical justification. (shrink)

The pandemic creates unprecedented challenges to society and to health care systems around the world. Like all crises, these provide a unique opportunity to rethink the fundamental limiting assumptions and institutional inertia of our established systems. These inertial assumptions have obscured deeply rooted problems in health care and deflected attempts to address them. As hospitals begin to welcome all patients back, they should resist the temptation to go back to business as usual. Instead, they should retain the more deliberative, explicit, (...) and transparent ways of thinking that have informed the development of crisis standards of care. The key lesson to be learned from those exercises in rational deliberation is that justice must be the ethical foundation of all standards of care. Justice demands that hospitals take a safety‐net approach to providing services that prioritizes the most vulnerable segments of society, continue to expand telemedicine in ways that improve access without exacerbating disparities, invest in community‐based care, and fully staff hospitals and clinics on nights and weekends. (shrink)

On a traditional view, the primary role of a mathematical proof is to warrant the truth of the resulting theorem. This view fails to explain why it is very often the case that a new proof of a theorem is deemed important. Three case studies from elementary arithmetic show, informally, that there are many criteria by which ordinary proofs are valued. I argue that at least some of these criteria depend on the methods of inference the proofs employ, and that (...) standard models of formal deduction are not well-equipped to support such evaluations. I discuss a model of proof that is used in the automated deduction community, and show that this model does better in that respect. (shrink)

This is an excellent book, by one of the philosophy of quantum theory's brightest stars. It combines a clear presentation of determinism, probability and non-locality in several current interpretations of quantum theory, with a good deal of detailed analysis, both reporting other people's and Dickson's own results, and developing his own ideas|which are often heterodox, but always well-defended and thought-provoking. The treatment is often concise, especially when reporting standard material or others' results. There are also frequent changes of gear; both (...) because the issues are complexly related to each other, and because Dickson sensibly does not aim for a de nitive treatment of issues that are at present so controversial|accordingly, he weaves about, not forcing his material into some single line of argument. So this is a monograph, not a textbook for teaching or a treatise summing up a conquered eld. But the style is clear and vigourous; the book is packed with information (sometimes about ancillary issues); and as we shall see, Dickson does have some provocative main claims, if not an overarching single line of argument. In this short space, I can only praise the book's general virtues and state some of the main claims. (shrink)

Despite a significant amount of literature debating the efficiency of high-risk pools in health insurance, dramatically less has been written about their normative implications. The present article takes the route less traveled by setting aside the question of efficiency to argue that the use of high-risk pools creates some serious normative concerns. The article explores these concerns by dividing them on two fronts. First, as regards the social-recognitional status of those who are forced into the high-risk pool. Second, as regards (...) a general concern of distributive justice, namely fairness in access to resources. The author argues that regardless of the veracity of arguments which laud the efficiency of high-risk pools, their use in health insurance is unjust because of the herein explained implications for social recognition and distributive justice. (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)

A general method of interpreting weak higher-type theories of nonstandard arithmetic in their standard counterparts is presented. In particular, this provides natural nonstandard conservative extensions of primitive recursive arithmetic, elementary recursive arithmetic, and polynomial-time computable arithmetic. A means of formalizing basic real analysis in such theories is sketched.

“Now, in calm weather, to swim in the open ocean is as easy to the practised swimmer as to ride in a spring-carriage ashore. But the awful lonesomeness is intolerable. The intense concentration of self in the middle of such a heartless immensity, my God! who can tell it? Mark, how when sailors in a dead calm bathe in the open sea—mark how closely they hug their ship and only coast along her sides.” (Herman Melville, Moby Dick, Chapter 94).

This is a discussion of some themes in Max Tegmark’s recent book, Our Mathematical Universe. It was written as a review for Plus Magazine, the online magazine of the UK’s national mathematics education and outreach project, the Mathematics Millennium Project. Since some of the discussion---about symmetry breaking, and Pythagoreanism in the philosophy of mathematics---went beyond reviewing Tegmark’s book, the material was divided into three online articles. This version combines those three articles, and adds some other material, in particular a brief (...) defence of quidditism about properties. It also adds some references, to other Plus articles as well as academic articles. But it retains the informal style of Plus. (shrink)

A number of classical theories are interpreted in analogous theories that are based on intuitionistic logic. The classical theories considered include subsystems of first- and second-order arithmetic, bounded arithmetic, and admissible set theory.

We present a simple propositional proof system which consists of a single axiom schema and a single rule, and use this system to construct a sequence of combinatorial tautologies that, when added to any Frege system, p-simulates extended-Frege systems.

As idealized descriptions of mathematical language, there is a sense in which formal systems specify too little, and there is a sense in which they specify too much. On the one hand, formal languages fail to account for a number of features of informal mathematical language that are essential to the communicative and inferential goals of the subject. On the other hand, many of these features are independent of the choice of a formal foundation, so grounding their analysis on a (...) particular choice of a formal system introduces unnecessary specificity. This chapter begins to map out the design features of mathematical language without descending to the level of formal implementation, drawing on examples from the mathematical literature and insights from the design of computational proof assistants and their libraries. (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.

Working in homotopy type theory, we provide a systematic study of homotopy limits of diagrams over graphs, formalized in the Coq proof assistant. We discuss some of the challenges posed by this approach to the formalizing homotopy-theoretic material. We also compare our constructions with the more classical approach to homotopy limits via fibration categories.

We re-express our theorem on the strong-normalisation of display calculi as a theorem about the well-foundedness of a certain ordering on first-order terms, thereby allowing us to prove the termination of systems of rewrite rules. We first show how to use our theorem to prove the well-foundedness of the lexicographic ordering, the multiset ordering and the recursive path ordering. Next, we give examples of systems of rewrite rules which cannot be handled by these methods but which can be handled by (...) ours. Finally, we show that our method can also prove the termination of the Knuth-Bendix ordering and of dependency pairs. Keywords: rewriting, termination, well-founded ordering, recursive path ordering.. (shrink)

In recent years ever-increasing concerns about ethical dimensions of fieldwork practice have forced anthropologists and other social scientists to radically reconsider the nature, process, and outcomes of fieldwork: what should we be doing, how, for whom, and to what end? In this volume, practitioners from across anthropological disciplines-social and biological anthropology and primatology-come together to question and compare the ethical regulation of fieldwork, what is common to their practices, and what is distinctive to each discipline. Contributors probe a rich variety (...) of contemporary questions: the new, unique problems raised by conducting fieldwork online and via email; the potential dangers of primatological fieldwork for locals, primates, the environment, and the fieldworkers themselves; the problems of studying the military; and the role of ethical clearance for anthropologists involved in international health programs. The distinctive aim of this book is to develop of a transdisciplinary anthropology at the methodological, not theoretical, level. (shrink)

In 1837, Dirichlet proved that there are infinitely many primes in any arithmetic progression in which the terms do not all share a common factor. We survey implicit and explicit uses ofDirichlet characters in presentations of Dirichlet’s proof in the nineteenth and early twentieth centuries, with an eye toward understanding some of the pragmatic pressures that shaped the evolution of modern mathematical method.

An efficient variant of the double-negation translation explains the relationship between Shoenfield’s and G¨odel’s versions of the Dialectica interpretation.

Algebraic proofs of the cut-elimination theorems for classical and intuitionistic logic are presented, and are used to show how one can sometimes extract a constructive proof and an algorithm from a proof that is nonconstructive. A variation of the double-negation translation is also discussed: if ϕ is provable classically, then ¬(¬ϕ)nf is provable in minimal logic, where θnf denotes the negation-normal form of θ. The translation is used to show that cut-elimination theorems for classical logic can be viewed as special (...) cases of the cut-elimination theorems for intuitionistic logic. (shrink)

This contribution explores the potential value of a postcolonial approach for teaching Mark’s gospel. Investigating a number of texts from the gospel, it asks to what extent a postcolonial optic implies a different approach to the gospel, what it adds and where challenges exist. Teaching with a postcolonial optic entails framing the gospel in its 1st-century imperial context and focusing on the ambivalence and ambiguity of imperial rule, investigating texts with attention to hybridity and mimicry in particular. Teaching the Gospel (...) of Mark through a postcolonial optic opens up new possibilities for interpretation and contextualisation, but at the same time poses certain challenges, pedagogically and otherwise. (shrink)

A seminal theorem due to Weyl [14] states that if $(a_n)$ is any sequence of distinct integers, then, for almost every $x \in \mathbb{R}$, the sequence $(a_n x)$ is uniformly distributed modulo one. In particular, for almost every $x$ in the unit interval, the sequence $(a_n x)$ is uniformly distributed modulo one for every computable sequence $(a_n)$ of distinct integers. Call such an $x$ UD random. Here it is shown that every Schnorr random real is UD random, but there are (...) Kurtz random reals that are not UD random. On the other hand, Weyl's theorem still holds relative to a particular effectively closed null set, so there are UD random reals that are not Kurtz random. (shrink)

This paper asks how we should regard the laws and customs of armed conflict, and specifically the rule prohibiting the targeting of civilians. What view should we take of the moral character and significance of such rules? Some philosophers have suggested that they are best regarded as useful conventions. This view is sometimes motivated by a "deep moral critique" of the rule protecting civilians: Jeff McMahan believes for example that the existing rules protect some who ought to be liable to (...) attack (on account of their having voluntarily contributed to the injustice or aggression being resisted). He thinks we would be better off with a different principle of discrimination in warfare. But McMahan acknowledges that for the time being we must stick with the rules that we have. The present paper does five things: (1) it explores and takes further some of McMahan's insights about the importance of existing positive law in this area; (2) it argues that some of the features that philosophers find problematic with the rule offering blanket protection to all civilians have to do with administrability; (3) it raises some questions about whether the rule protecting civilians can really be regarded as a convention (and it argues that certainly it cannot be regarded as a "Lewis-convention" in a strict sense); (4) to the extent that the rule can be regarded as conventional, the paper argues that it remains a deadly serious moral rule, partly because of the circumstances of death and destruction in which it operates and which it tries to ameliorate, and partly on account of its fragility. The fifth point is the most important. (5) The rule protecting civilians does not operate in circumstances in which, apart form positive law, civilians like everyone would be liable to attack. The rule operates against a moral background in which all deliberate killing is to be regarded as murder; some deliberate killings (of combatants) are privileged in warfare; but the rule about civilians reflects the fact that this is a strictly limited privilege and that those who target civilians do not get the benefit of it. Changing our view of the default position in this way enables us to better understand the distinctive work that this rule does. (shrink)

Deacon’s approach to resolving mechanism/semiotic duality exemplifies an innovative methodology for imposing greater rigor on abductive assumptions in biosemiotics and beyond. His approach specifies interpretive agents and their responsive effort as the categories of phenomena to be explained. Implicit in his approach are five standards for imposing greater rigor on abduction or categorization, here named and described by the author.

In this article, I try to do two things. First I analyse critically the suggestion that the principles of criminal culpability can be explained by reference to a single, all-encompassing concept, such as “defiance of the law”. I then go on to explain the foundations of criminal culpability by reference to three interlocking theories — the capacity theory, the character theory, and the agency theory. I conclude that even these three theories may not be sufficient to explain the complex structure (...) of culpability, which is shaped as much by shared cultural understanding as by moral theory. (shrink)

Ballantyne correctly notes the need for clarification as to the standard of fairness that should guide nonexploitative international research on human subjects. When accounts of exploitation are applied to pharmaceutical development (as well as other areas), there is too often an uncritical acceptance that exploitation involves a form of unfairness. Moreover, these authors typically fail to produce an account of fairness by which exploitation should be identified. Ballantyne should be applauded for her attempt to inject greater clarity into these debates. (...) Her preferred standard of fairness is problematic, however. Ballantyne fails to distinguish between at least two forms of exploitation, tied to two distinct forms of unfairness, that can take place in international research on human subjects. As I argue here, the first form of exploitation derives from transactional unfairness where researchers take special unfair advantage of research subjects. The second form of exploitation occurs when researchers take advantage of background injustices that disadvantage research subjects. As a result of this failure to differentiate between different forms of exploitation, Ballantyne misidentifies the requirements of fairness for engaging in nonexploitative international human subject research. (shrink)