Background Outbreaks of infectious disease cause serious and costly health and social problems. Two new technologies – pathogen whole genome sequencing and Big Data analytics – promise to improve our capacity to detect and control outbreaks earlier, saving lives and resources. However, routinely using these technologies to capture more detailed and specific personal information could be perceived as intrusive and a threat to privacy. Method Four community juries were convened in two demographically different Sydney municipalities and two regional cities in (...) New South Wales, Australia to elicit the views of well-informed community members on the acceptability and legitimacy of: making pathogen WGS and linked administrative data available for public health researchusing this information in concert with data linkage and machine learning to enhance communicable disease surveillance systems Fifty participants of diverse backgrounds, mixed genders and ages were recruited by random-digit-dialling and topic-blinded social-media advertising. Each jury was presented with balanced factual evidence supporting different expert perspectives on the potential benefits and costs of technologically enhanced public health research and communicable disease surveillance and given the opportunity to question experts. Results Almost all jurors supported data linkage and WGS on routinely collected patient isolates for the purposes of public health research, provided standard de-identification practices were applied. However, allowing this information to be operationalised as a syndromic surveillance system was highly contentious with three juries voting in favour, and one against by narrow margins. For those in favour, support depended on several conditions related to system oversight and security being met. Those against were concerned about loss of privacy and did not trust Australian governments to run secure and effective systems. Conclusions Participants across all four events strongly supported the introduction of data linkage and pathogenomics to public health research under current research governance structures. Combining pathogen WGS with event-based data surveillance systems, however, is likely to be controversial because of a lack of public trust, even when the potential public health benefits are clear. Any suggestion of private sector involvement or commercialisation of WGS or surveillance data was unanimously rejected. (shrink)

Abstract:This paper investigates whether, in theoretical terms, corporations can be citizens. The argument is based on the observation that the debate on “corporate citizenship” (CC) has only paid limited attention to the actual notion of citizenship. Where it has been discussed, authors have either largely left the concept of CC unquestioned, or applied rather unidimensional and decontextualized notions of citizenship to the corporate sphere. The paper opens with a critical discussion of a major contribution to the CC literature, the work (...) of Logsdon and Wood (Wood and Logsdon 2001; Logsdon and Wood 2002). It continues with a consideration of the nature and role of metaphors for business and of the contestable nature of the political concept of citizenship. It evaluates corporations as citizens through a four-dimensional framework of democratic citizenship offered by Stokes (2002). The analysis suggests that corporations do not easily fit the “liberal minimalist” model of citizenship. It finds, however some possibilities for fit with the three more participatory models. The paper concludes by cautioning against basing corporate citizenship on legal and administrative status or identity, and mapping out specific criteria by which we might determine whether corporations could be considered as citizens by virtue of their participation in processes of governance. (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)

Debates about the ethics and effects of placebos and whether ‘placebos’ in clinical trials of complex treatments such as acupuncture are adequate rage. Yet there is currently no widely accepted definition of the ‘placebo’. A definition of the placebo is likely to inform these controversies. Grünbaum’s characterization of placebos and placebo effects has been touted by some authors as the best attempt thus far, but has not won widespread acceptance largely because Grünbaum failed to specify what he means by a (...) therapeutic theory and because he does not stipulate a special role for expectation effects. Grünbaum claims that placebos are treatments whose ‘characteristic features’ do not have therapeutic effects on the target disorder. I show that with four modifications, Grünbaum’s definition provides a defensible account of placebos for the purpose of constructing placebo controls within clinical trials. The modifications I introduce are: adding a special role for expectations, insisting that placebo controls control for all and only the effects of the incidental treatment features, relativizing the definition of placebos to patients, and introducing harmful interventions and nocebos to the definitional scheme. I also provide guidance for classifying treatment features as characteristic or incidental. (shrink)

In a wide range of fields, the word “modular” is used to describe complex systems that can be decomposed into smaller systems with limited interactions between them. This essay argues that mathematical knowledge can fruitfully be understood as having a modular structure and explores the ways in which modularity in mathematics is epistemically advantageous.

“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).

We show that certain model-theoretic forcing arguments involving subsystems of second-order arithmetic can be formalized in the base theory, thereby converting them to effective proof-theoretic arguments. We use this method to sharpen the conservation theorems of Harrington and Brown-Simpson, giving an effective proof that WKL+0 is conservative over RCA0 with no significant increase in the lengths of proofs.

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.

Achieving social equality has been an important aim of modern democratic societies. Yet the process has engendered debate about the nature of equality and the consequences of its application. Why is equality valuable? What kind of equality should be aimed for? When is inequality justified? Should a principle of equality apply globally? The book assesses and links the different dimensions of equality and asks whether recent writing on the topic has the philosophical substance and political force traditionally associated with egalitarian (...) thought. (shrink)

We show that the theory ATR 0 is equivalent to a second-order generalization of the theory $\widehat{ID}_{ . As a result, ATR 0 is conservative over $\widehat{ID}_{ for arithmetic sentences, though proofs in ATR 0 can be much shorter than their $\widehat{ID}_{ counterparts.

A notion called Herbrand saturation is shown to provide the model-theoretic analogue of a proof-theoretic method, Herbrand analysis, yielding uniform model-theoretic proofs of a number of important conservation theorems. A constructive, algebraic variation of the method is described, providing yet a third approach, which is finitary but retains the semantic flavor of the model-theoretic version.

is a fragment of first-order aritlimetic so weak that it cannot prove the totality of an iterated exponential fimction. Surprisingly, however, the theory is remarkably robust. I will discuss formal results that show that many theorems of number theory and combinatorics are derivable in elementary arithmetic, and try to place these results in a broader philosophical context.

Having the emotion of pride requires taking oneself to stand in some special relation to the object of pride. According to agency accounts of this pride relation, the self and the object of pride are suitably related just in case one is morally responsible for the existence or excellence of the object of one's pride. I argue that agency accounts fail. This argument provides a strong prima facie defence of an alternate account of pride, according to which the self and (...) the object of pride are suitably related just in case one's relation to the object of pride indicates that one's life accords with some of one's personal ideals. I conclude that the pride relation, though distinct from the relation of moral responsibility, is nonetheless a relation of philosophical interest that merits further attention. (shrink)

Paul Cohen’s method of forcing, together with Saul Kripke’s related semantics for modal and intuitionistic logic, has had profound effects on a number of branches of mathematical logic, from set theory and model theory to constructive and categorical logic. Here, I argue that forcing also has a place in traditional Hilbert-style proof theory, where the goal is to formalize portions of ordinary mathematics in restricted axiomatic theories, and study those theories in constructive or syntactic terms. I will discuss the aspects (...) of forcing that are useful in this respect, and some sample applications. The latter include ways of obtaining conservation results for classical and intuitionistic theories, interpreting classical theories in constructive ones, and constructivizing model-theoretic arguments. (shrink)

In the following reply to Joe Frank Jones, Ill's "Analysis, Phenomenology and the Travails of Ontology," I argue that skepticism about method plays an important critical role in philosophical thinking. I further suggest that it may be time for philosophy to rehabilitate metaphysics rather than simply ceding it to the natural sciences.

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)

In Section 2, I survey some of the ways that computers are used in mathematics. These raise questions that seem to have a generally epistemological character, although they do not fall squarely under a traditional philosophical purview. The goal of this article is to try to articulate some of these questions more clearly, and assess the philosophical methods that may be brought to bear. In Section 3, I note that most of the issues can be classified under two headings: some (...) deal with the ability of computers to deliver appropriate “evidence” for mathematical assertions, a notion that is explored in Section 4, while others deal with the ability of computers to deliver appropriate mathematical “understanding,” a notion that is considered in Section 5. Final thoughts are provided in Section 6. (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.

A critical appraisal of Chiara Bottici’s influential work on imaginal politics, this collection uses this rich theoretical framework for incisive analysis, within critical theory and political philosophy, psychoanalysis and sociology.

This anthology provides a set of distinctive selections that explore both Western and Eastern views of lying and truthfulness, including selections from Augustine, Grotius, Aristotle, the _Mahabharata_, Confucius, Kant, Plato, Sunzi, Han Feizi, Aquinas, the _Lotus Sutra_, Hobbes, Hume, Locke, Bacon, Nietzsche, and more. Hackett Readings in Philosophy is a versatile series of compact anthologies, each devoted to a topic of traditional interest in philosophy or political theory. Selections are chosen for their accessibility, significance, and ability to stimulate thought and (...) discussion. (shrink)

Les sociétés démocratiques sont confrontées à l'émergence d'enjeux environnementaux décisifs qui concernent tant les modes de production, d'échange et de consommation que l'habitat, les transports, l'agriculture, l'industrie et même nos modes de vie. La prise en charge de ces enjeux ne saurait s'opérer simplement par des mesures ponctuelles ou locales. Elle doit aujourd'hui être repensée la temporalité de l'action politique, confrontée à une urgence qui ne cessera de s'accroître dans les prochaines années.

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)

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.

We analyze the pointwise convergence of a sequence of computable elements of L1 in terms of algorithmic randomness. We consider two ways of expressing the dominated convergence theorem and show that, over the base theory RCA0, each is equivalent to the assertion that every Gδ subset of Cantor space with positive measure has an element. This last statement is, in turn, equivalent to weak weak Königʼs lemma relativized to the Turing jump of any set. It is also equivalent to the (...) conjunction of the statement asserting the existence of a 2-random relative to any given set and the principle of Σ2 collection. (shrink)

The 1-consistency of arithmetic is shown to be equivalent to the existence of fixed points of a certain type of update procedure, which is implicit in the epsilon-substitution method.

The evidence of high cognitive abilities in cetaceans does not stand up to close scrutiny under the standards established by laboratory researchers. This is likely to lead to a sterile debate between laboratory and field researchers unless fresh ways of taking the debate forward are found. A few suggestions as to how to do this are proposed.

As the sciences of biotechnology, synthetic biology, and nanotechnology develop, questions about liability for harms caused by self-replicating inventions will arise increasingly often. Although negligence, nuisance, and other torts may be relevant in such circumstances, trespass may be the more appropriate cause of action. First, the author explores doctrinal hurdles facing plaintiffs alleging biotrespass. To overcome concerns about the metaphysicality of molecular biotrespass, the author draws analogies to “cybertrespass.” To confront the problem of suing patent licensors for the actions of (...) their licensees, the author makes reference to principles of landlord-tenant law. Well-established laws concerning wandering animals shed light on the policies underlying biotrespass. In the second part, the author examines such policies in further detail and considers the purpose of transporting property metaphors into bio/nanospace. The article concludes that biotrespass can be a viable cause of action, if crafted carefully and understood properly. (shrink)

This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes that we view mathematics as a system of conventions and norms that is designed to help us make sense of the world and reason efficiently. Like any designed system, it can perform well or poorly, and the philosophy of mathematics has a role to play in helping (...) us understand the general principles by which it serves its purposes well. (shrink)

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)

We develop fundamental aspects of the theory of metric, Hilbert, and Banach spaces in the context of subsystems of second-order arithmetic. In particular, we explore issues having to do with distances, closed subsets and subspaces, closures, bases, norms, and projections. We pay close attention to variations that arise when formalizing definitions and theorems, and study the relationships between them.

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)

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)

Extending Gödel's Dialectica interpretation, we provide a functional interpretation of classical theories of positive arithmetic inductive definitions, reducing them to theories of finite-type functionals defined using transfinite recursion on well-founded trees.

We discuss the development of metamathematics in the Hilbert school, and Hilbert’s proof-theoretic program in particular. We place this program in a broader historical and philosophical context, especially with respect to nineteenth century developments in mathematics and logic. Finally, we show how these considerations help frame our understanding of metamathematics and proof theory today.

Although construct measurement is critical to explanatory research and intervention efforts, rigorous measure development remains a notable challenge. For example, though the primary theoretical model for understanding health disparities among sexual minority (e.g., lesbian, gay, bisexual) adolescents is minority stress theory, nearly all published studies of this population rely on minority stress measures with poor psychometric properties and development procedures. In response, we developed the Sexual Minority Adolescent Stress Inventory (SMASI) with N = 346 diverse adolescents ages 14–17, using a (...) comprehensive approach to de novo measure development designed to produce a measure with desirable psychometric properties. After exploratory factor analysis on 102 candidate items informed by a modified Delphi process, we applied item response theory techniques to the remaining 72 items. Discrimination and difficulty parameters and item characteristic curves were estimated overall, within each of 12 initially derived factors, and across demographic subgroups. Two items were removed for excessive discrimination and three were removed following reliability analysis. The measure demonstrated configural and scalar invariance for gender and age; a three-item factor was excluded for demonstrating substantial differences by sexual identity and race/ethnicity. The final 64-item measure comprised 11 subscales and demonstrated excellent overall (α = 0.98), subscale (α range 0.75–0.96), and test–retest (scale r > 0.99; subscale r range 0.89–0.99) reliabilities. Subscales represented a mix of proximal and distal stressors, including domains of internalized homonegativity, identity management, intersectionality, and negative expectancies (proximal) and social marginalization, family rejection, homonegative climate, homonegative communication, negative disclosure experiences, religion, and work domains (distal). Thus, the SMASI development process illustrates a method to incorporate information from multiple sources, including item response theory models, to guide item selection in building a psychometrically sound measure. We posit that similar methods can be used to improve construct measurement across all areas of psychological research, particularly in areas where a strong theoretical framework exists but existing measures are limited. (shrink)

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)

The metamathematical tradition, tracing back to Hilbert, employs syntactic modeling to study the methods of contemporary mathematics. A central goal has been, in particular, to explore the extent to which infinitary methods can be understood in computational or otherwise explicit terms. Ergodic theory provides rich opportunities for such analysis. Although the field has its origins in seventeenth century dynamics and nineteenth century statistical mechanics, it employs infinitary, nonconstructive, and structural methods that are characteristically modern. At the same time, computational concerns (...) and recent applications to combinatorics and number theory force us to reconsider the constructive character of the theory and its methods. This paper surveys some recent contributions to the metamathematical study of ergodic theory, focusing on the mean and pointwise ergodic theorems and the Furstenberg structure theorem for measure preserving systems. In particular, I characterize the extent to which these theorems are nonconstructive, and explain how proof-theoretic methods can be used to locate their "constructive content.". (shrink)

The material in this volume constitutes a philosophical commonplace book, compiled by Bentham in the mid-1770s, in which he worked out the foundational ideas for his new science of legislation. One of Bentham's central concerns was the development of an adequate ontological and epistemological basis for legal terminology, and the replacement of the traditional terminology of English law with that of universal jurisprudence. Preparatory Principles constitutes a remarkable record of the evolving ideas of a major legal philosopher at a formative (...) stage of his career. (shrink)

To identify motivational factors linked to child health status that affected the likelihood of parents’ allowing their child to participate in pediatric research.