Ethics as a field should, we argue, pay more attention to the (eco)system. Van Rensselaer Potter, one of the pillars of contemporary bioethics, advocated for a global “bios” ethics that literally and metaphorically bridges the gap between biological knowledge and ethical reflection. However, a Potterian Bio-Ethics faces a major obstacle: its acentric focus. Consequently, Global Bio-Ethics remains opaque for those trained under the anthropocentric biomedical ethics that instrumentalizes the environment. This paper aims to demystify two key concepts—Globality and Complexity—and (...) show how a Potterian Bio-Ethics can effectively bridge the gap between knowledge-building in ecology and policy-making in the context of medical and environmental practices. Drawing on an experience in Québec, Canada, to mitigate the threat of antimicrobial resistance using a biosurveillance system, we show the utility of having ethics as an integral part of ecosystem(ic) approaches to bridge health and environment. We conclude by arguing that bioethics (and bioethicists) should become a locus for cascading communication, collaboration, and translation by co-constructing biosurveillance data governance. (shrink)

The concept of regulatory ‘checkpoints’ in the eukaryotic cycle has proved to be a fruitful one. Here, its applicability to the bacterial cell cycle is examined. A primitive DNA damage checkpoint operates in E. coli such that, after exposure to ultraviolet light, while excision repair occurs, chromosome replication continues very slowly with the production of discontinuous daughter strands. The slower the rate of excision of photoproducts, the greater the delay before the normal rate of DNA replication is restored, the additional (...) time for repair ensuring that normal survival is maintained. A model is proposed in which replication rate is controlled by the ratio of RecAcoated to uncoated single stranded regions of DNA in the replication fork. There are also two cell division inhibitors SulA (=SfiA) and SfiC under the control of the SOS system and sensitive to DNA damage, but they are irrelevant to the survival of wild‐type bacteria under normal conditions. In strains where SulA and SfiC do not operate, inhibition is not influenced by the rate of excision repair and so fails one of the criteria for a DNA damage checkpoint, namely the monitoring of the DNA for the level of residual damage. (shrink)

There is growing evidence that mutations can arise in non‐dividing cells (both bacterial and mammalian) in the absence of chromosomal replication. The processes that are involved are still largely unknown but may include two separate mechanisms. In the first, DNA lesions resulting from the action of endogenous mutagens may give rise to RNA transcripts with miscoded bases. If these confer the ability to initiate DNA replication, the DNA lesions may have an opportunity to miscode during replication and thus could give (...) rise to apparently ‘adaptive’ mutations. A second mechanism is suggested by recent work in starved bacteria, showing that there is much more turnover of chromosomal DNA than has been previously thought. This could permit polymerase errors to lead to mutations in non‐dividing cells. Such cryptic DNA synthesis, which may essentially replace existing DNA rather than duplicating it, could, in principle, act as an additional source of variability on which selection may act, initially in the absence of cell division. In mammals such processes would undoubtedly have implications for germ cell mutagenesis and carcinogenesis. (shrink)

Surveillance programs supporting the management of One Health issues such as antibiotic resistance are complex systems in themselves. Designing ethical surveillance systems is thus a complex task (retroactive and iterative), yet one that is also complicated to implement and evaluate (e.g., sharing, collaboration, and governance). The governance of health surveillance requires attention to ethical concerns about data and knowledge (e.g., performance, trust, accountability, and transparency) and empowerment ethics, also referred to as a form of responsible self-governance. Ethics in reflexive governance (...) operates as a systematic critical-thinking procedure that aims to define its value: What are the “right” criteria to justify how to govern “good” actions for a “better” future? The objective is to lay the foundations for a methodological framework in empirical bioethics, the rudiments of which have been applied to a case study to building reflexive governance in One Health. This ongoing critical thinking process involves “mapping, framing, and shaping” the dynamics of interests and perspectives that could jeopardize a “better” future. This paper proposes to hybridize methods to combine insights from collective deliberation and expert evaluation through a reflexive governance functioning as a community-based action-ethics methodology. The intention is to empower individuals and associations in a dialogue with society, which operation is carried out using a case study approach on data sharing systems. We based our reasoning on a feasibility study conducted in Québec, Canada (2018–2021), envisioning an antibiotic use surveillance program in animal health for 2023. Using the adaptive cycle and governance techniques and perspectives, we synthesize an alternative governance model rooted in the value of empowerment. The framework, depicted as a new “research and design (R&D)” practice, is linking operation and innovation by bridging the gap between Reflexive, Evaluative, and Deliberative reasonings and by intellectualizing the management of democratizing critical thinking locally (collective ethics) by recognizing its context (social ethics). Drawing on the literature in One Health and sustainable development studies, this article describes how a communitarian and pragmatic approach can broaden the vision of feasibility studies to ease collaboration through public-private-academic partnerships. The result is a process that “reassembles” the One Health paradigm under the perspective of global bioethics to create bridges between the person and the ecosystem through pragmatic ethics. (shrink)

Our brains are us. But we are neither happy, fulfilled, nor all that we 'should' (or maybe could) be. We have everything previous generations could have dreamed of, but it seems it's never quite enough. What's going on? Has it anything to do with the way those brains have developed, by any chance? Gillian Bridge takes us on a journey through time, history and the mysterious labyrinth that is the brain, investigating strange happenings and unlikely people on the way. The (...) Significance Delusion is a challenging explanation of our species' peculiar vulnerability to disorders of both thinking and social cohesion. It is a power pack of research, ideas, facts and fascinating real life stories which explores our species' obsession with meaning and significance. What does it all mean for me? What do I mean to you? The Significance Delusion is humorous as well as deeply serious, and it is the must read compilation of lifestyle advice for tomorrow's well-adjusted people. It is a book about what it takes to thrive and survive as an individual human and as a society. From it you will learn the meaning of life, and your place in the world. For parents, educators, thinkers, psychologists, psychotherapists and policy makers. (shrink)

Two classically equivalent, but constructively inequivalent, strict convexity properties of a preference relation are discussed, and conditions given under which the stronger notion is a consequence of the weaker. The last part of the paper introduces uniformly rotund preferences, and shows that uniform rotundity implies strict convexity. The paper is written from a strictly constructive point of view, in which all proofs embody algorithms. MSC: 03F60, 90A06.

It is shown that in any model of constructive mathematics in which a certain omniscience principle is false, for strongly extensional functions on an interval the distinction between sequentially continuous and regulated disappears. It follows, without the use of Markov's Principle, that any recursive function of bounded variation on a bounded closed interval is recursively sequentially continuous.

This is an introduction to, and survey of, the constructive approaches to pure mathematics. The authors emphasise the viewpoint of Errett Bishop's school, but intuitionism. Russian constructivism and recursive analysis are also treated, with comparisons between the various approaches included where appropriate. Constructive mathematics is now enjoying a revival, with interest from not only logicans but also category theorists, recursive function theorists and theoretical computer scientists. This account for non-specialists in these and other disciplines.

One of the chief aims of Donald Davidson's later work was to show that participation in a certain causal nexus involving two creatures and a shared environment–Davidson calls this nexus “triangulation”–is a metaphysically necessary condition for the acquisition of thought. This doctrine, I suggest, is aptly regarded as a form of what I call transcendental externalism. I extract two arguments for the transcendental-externalist doctrine from Davidson's writings, and argue that neither succeeds. A central interpretive claim is that the arguments are (...) primarily funded by a particular conception of the nature of non-human animal life. This conception turns out to be insupportable. The failure of Davidson's arguments presses the question of whether we could ever hope to arrive at far-reaching claims about the conditions for thought if we deny, as does Davidson, the legitimacy of the naturalistic project in the philosophy of mind. (shrink)

Cultures of low aspirations, and more particularly young people's adaptation to them, are often presented as the major obstacle to an economic development agenda which requires more higher-level skills and a social agenda which is about enabling people from ‘non-traditional’ backgrounds to go to university. The article analyses and discusses some of the different sorts of constraints on the choices which we make and which may become unconsciously internalised and so constitute our adaptive preference. It argues, however, that all choice (...) is significantly adaptive and has its roots in a self which neither in its development nor in its current agency is detached from the social context in which it has been constructed, with which it identifies and from which that identity itself derives many of its features. Finally the article discusses briefly the grounds on which intervention in the life of such a chooser might be justified and some implications for interventionist strategies which are sensitive to such a socially embedded view of the self. (shrink)

We prove constructively that, in order to derive the uniform continuity theorem for pointwise continuous mappings from a compact metric space into a metric space, it is necessary and sufficient to prove any of a number of equivalent conditions, such as that every pointwise continuous mapping of [0, 1] into R is bounded. The proofs are analytic, making no use of, for example, fan-theoretic ideas.

Constructive mathematics – mathematics in which ‘there exists’ always means ‘we can construct’ – is enjoying a renaissance. Fifty years on from Bishop’s groundbreaking account of constructive analysis, constructive mathematics has spread out to touch almost all areas of mathematics and to have profound influence in theoretical computer science. This handbook gives the most complete overview of modern constructive mathematics, with contributions from leading specialists surveying the subject’s myriad aspects. Major themes include: constructive algebra and geometry, constructive analysis, constructive topology, (...) constructive logic and foundations of mathematics, and computational aspects of constructive mathematics. A series of introductory chapters provides graduate students and other newcomers to the subject with foundations for the surveys that follow. Edited by four of the most eminent experts in the field, this is an indispensable reference for constructive mathematicians and a fascinating vista of modern constructivism for the increasing number of researchers interested in constructive approaches. (shrink)

This book seeks to salvage liberalism, as a form of political association and as a unique culture, from the wreck of the Enlightenment.

Relying on more expansive criteria for defining “mass shootings” than much existing research, we examine a subset of a unique dataset incorporating 7,048 news documents covering 2,170 shootings in the United States between 2013 and 2019. We analyze the descriptive language used to describe incidents and perpetrators and discover significant racial disparities in representation. This research enables a critical examination of the explanatory frames utilized by news media to tell the public who mass shooters are and journalistic attempts to explain (...) why they occur. Data were analyzed utilizing a mixed methods approach, relying on content analysis to inductively code emergent categories of descriptions of shooters and binary logistic regressions to analyze the preponderance of descriptive categories when comparing news articles reporting on shootings committed by differently racialized shooters. Our results confirm some recent research showing that mass shooters racialized as white are more likely to be described with kind and compassionate language. With our larger sample, however, we also find that mass shooters racialized as white are additionally more likely to be described with negative language as “bad” or “evil” in comparison to shooters of color. We discuss how these data demonstrate that media reports present a more complex picture of white mass shooters for the public than shooters of color. (shrink)

In the informal setting of Bishop-style constructive reverse mathematics we discuss the connection between the antithesis of Specker’s theorem, Ishihara’s principle BD-N, and various types of equicontinuity. In particular, we prove that the implication from pointwise equicontinuity to uniform sequential equicontinuity is equivalent to the antithesis of Specker’s theorem; and that, for a family of functions on a separable metric space, the implication from uniform sequential equicontinuity to uniform equicontinuity is equivalent to BD-N.

Ethical mysticism, by S. Coit.--The ethical import of history, by D. S. Muzzey.--The tragic and heroic in life, by W. M. Salter.--Distinctive features of the ethical movement, by A. W. Martin.--Ethical experience as the basis of religious education, by H. Neumann.--"All men are created equal," by G. E. O'Dell.--How far is art an aid to religion? by P. Chubb.--Evolution and the uniqueness of man, by H. J. Bridges.--The spiritual outlook on life, by H. J. Golding.--The ethics of Abu'l Ala (...) al Ma'arri, by N. Schmidt.--Life's unused moral force, by H. Snell.--Is the ideal real? by G. A. Smith.--Some ethical tendencies in the professions, by R. D. Kohn.--On the art of living, by W. Boerner.--The relation of the ethical ideal to social reform, by J. L. Elliott.--Concerning tolerance, by R. F. Dewey.--Ethical culture in Germany after the war, by R. Penzig.--A confession of faith, by S. B. Weston.--"Hearing the witnesses," by J. Gutmann. (shrink)

This paper explores the political potential of digital failure as a refusal to work in service of today’s dataveillance society. Moving beyond criticisms of flawed digital systems, this paper traces the moments of digital failure that seek to break, rather than fix, existing systems. Instead, digital failure is characterized by pesky data that sneaks through the cracks of digital capitalism and dissipates into the unproductive; it supports run-away data prone to misidentifications by digital marketers, coders, and content moderators; and it (...) celebrates data predisposed to “back-talk” with playful irreverence toward those that seek to bring order through normative categorization and moderation. I call these data entropic, fugitive, and queer and explore their mischievous practices through three case studies: the unaccountable data in identity resolution, public shaming of the ImageNet training data, and reading practices of sex worker and influencer, @Charlieshe. Together these case studies articulate the political potential of digital failure as a process of unbecoming the good data subject by pushing past the margins of legibility, knowability, and thinkability, to reveal what is made illegible, unknowable, and unthinkable to data’s seeing eye. As predictive analytics, automated decision-systems, and artificial intelligence take on increasingly central roles in public governance, digital failure reveals how data itself is a flawed concept prone to political abuse and social engineering to protect the interests of the powerful, while keeping those marginalized over-surveilled and underrepresented. (shrink)

Recent initiatives from the Employment Department in the UK have promoted ‘enterprise education’. This paper discusses the relationship of enterprise education to the more established notion of a liberal education. It is argued that enterprise education should be understood not as replacing the aspirations of a liberal education, but rather as supporting or extending them. It does this (i) by helping pupils to understand what is arguably a significant form of life; (ii) by developing understanding of the economic conditions of (...) our social functioning; and (iii) by developing personal qualities which equip us practically to pursue our chosen paths in a competitive and sometimes hostile world. (shrink)

© The Authors 2017. Published by Oxford University Press on behalf of The Analysis Trust. All rights reserved. For Permissions, please email: [email protected] Blome-Tillmann’s Knowledge and Presuppositions proposes and defends a novel form of epistemological contextualism. As the title would suggest, the view’s novelty lies in its deployment of the pragmatic-theoretic concept of a conversational presupposition to delineate a role for context in shaping the meaning of our knowledge claims. Over the course of six dense, argument-filled chapters, Blome-Tillmann brings his (...) approach into focus and claims for it several advantages. While existing varieties of contextualism can account for widely shared intuitions about the truth values of knowledge ascriptions in various familiar thought experiments, the distinctive flexibility of Presuppositional Epistemological Contextualism, Blome-Tillmann argues, enables it to account as well for cases in which our intuitions diverge. This flexibility also allows for especially satisfying analyses of scepticism... (shrink)

This article is centrally concerned with the sort of knowledge that can and should inform educational policy—and it treats this as an epistemological question. It distinguishes this question from the more extensively explored question of what sort of knowledge in what form policy-makers do in fact commonly take into account. The article examines the logical and rhetorical character of policy and the components of policy decisions and argues that policy demands a much wider range of information than research typically provides. (...) Either the research task or commission has to be substantially extended or the gap will be filled by information or thinking that is not derived from research. One of the gaps between research of an empirical kind and policy is the normative gap. In the final section the article points to the inescapably normative character of educational policy. Of course the values that inform policy can be investigated empirically, but this kind of enquiry cannot tell us what we should do. There is a role for research/scholarship and more rather than less intelligent and critical argumentation in addressing these normative questions as well as the empirical questions that underpin policy. (shrink)

This book evaluates the increasingly wide variety of intellectual resources for research methods and methodologies and investigates what constitutes good educational research. Written by a distinguished international group of philosophers of education Questions what sorts of research can usefully inform policy and practice, and what inferences can be drawn from different kinds of research Demonstrates the critical engagement of philosophers of education with the wider educational research community and illustrates the benefits that can accrue from such engagement.

A critique of attempts by Charles Travis and others to read contextualism back into Philosophical Investigations. The central interpretive claim is that this reading is not only unsupported; it gets Wittgenstein's intent, in the parts of the text at issue, precisely backwards. The focus of the chapter is on Wittgenstein's treatment of explanation, understanding, proper names, and family-resemblance concepts.

This publication arises in a context in which policy makers and educational researchers are increasingly vocal in their demands that educational policy and prac.

It is shown, within constructive mathematics, that the unit ball B1 of the set of bounded operators on a Hilbert space H is weak-operator totally bounded. This result is then used to prove that the weak-operator continuity of the mapping T → AT on B1 is equivalent to the existence of the adjoint of A.

The first part of the paper introduces the varieties of modern constructive mathematics, concentrating on Bishop's constructive mathematics. it gives a sketch of both Myhill's axiomatic system for BISH and a constructive axiomatic development of the real line R. The second part of the paper focusses on the relation between constructive mathematics and programming, with emphasis on Martin-L6f 's theory of types as a formal system for BISH.

On the Arbitrary Nature of Things approaches Hegel's Phenomenology of Spirit through a paradigm of agnosticism developed from Hegel's own critique of systems of knowledge. This work traces Hegel's descriptions of the movements of Spirit with equal measures of charity and skepticism. It provokes one to question the level of agnosticism that should be taken toward our various systems of human understanding, both in Hegel's Phenomenology and in our contemporary world. With respect to our contemporary world, Bridges questions whether (...) the nature of things is ultimately arbitrary and finds that phenomena such as the placebo effect and the use of sensoriums in phenomenological anthropology add credence to the position of agnosticism toward the arbitrary nature of things. (shrink)

Cultural capital and hegemonic masculinity are two concepts that have received intense attention. While both have received serious consideration, critique and analysis, the context or field-specificity of each is sometimes ignored. They have been used in a diversity of ways. Using ethnographic and interview data from a US male bodybuilding community, this study highlights one useful employment. Hegemonic masculinity takes different shapes in different fields of interaction, acting as a form of cultural capital: gender capital. Inherent in this discussion are (...) the cultural contradictions apparent among individuals striving for either physical or ideological embodiments of gender capital. Individuals can attempt to embody hegemonic idealizations, but bodies are not only inscribed with gender, inscriptions are read, and read differently by different social actors and in different settings. The capacity of gender capital to remain elusive is precisely what enables gender practices and projects like bodybuilding to retain passionate participation. (shrink)

This paper offers an interpretation of the later Wittgenstein's handling of the idea of an "essence of human language", and examines in particular his treatment of the 'Augustinean' vision of reference as constituting this "essence". A central theme of the interpretation is the perennial philosophical desire to impose upon linguistic meaning conceptual templates drawn from outside the forms of thought about meaning in which we engage when we exercise our capacity to speak and understand a language. The paper closes with (...) a consideration of ways in which Donald Davidson's generally congenial work on interpretation may diverge from Wittgenstein's thinking in this vicinity. (shrink)

This paper notes the critical response that the ‘competence movement’ has received from writers in philosophy of education and argues for a more positive assessment of what it offers in relation to: (i) the place of practical competence in a liberal education, (ii) the meritocratic principles underlying the competence movement, (iii) the ‘transparency’ of expectations in assessment, and even (iv) the element of practical competence in moral performance. It emphasises, however, that not all versions of ‘competence’ can be defended in (...) these terms and that this requires a more generic and cognitively laden concept of personal and professional competence. (shrink)

The desire to use established corporate law skill sets in the pro bono context has lead some lawyers to extend pro bono services to charitable and non-profit organisations. But does the provision of free legal services to well-funded organisations constitute pro bono work, and how can providers of pro bono legal services best prioritise among competing organisations? The author surveys various sources of formal and informal regulation in Singapore and selected Asian and other common law jurisdictions and suggests that when (...) distinguishing between non-profit organisations with different levels of funding, a coherent guideline would evaluate whether the payment of legal fees would deplete economic resources to the extent of significantly impairing organisation programmes. (shrink)

Explores the central role in Wittgenstein's later work of his opposition to a 'mechanistic' conception of understanding. Offers a diagnosis of Kripke's skeptical paradox on this basis.

In this paper, I argue that informational semantics, the most well-known and worked-out naturalistic account of intentional content, conflicts with a fundamental psychological principle about the conditions of belief-formation. Since this principle is an important premise in the argument for informational semantics, the upshot is that the view is self-contradictory??indeed, it turns out to be guilty of a sophisticated version of the fallacy famously committed by Euthyphro in the eponymous Platonic dialogue. Criticisms of naturalistic accounts of content typically proceed piecemeal (...) by narrowly constructed counterexamples, but I argue that the current result is more robust. It affects a broad family of accounts, and provokes a wider doubt about the possibility of successful execution of the naturalistic project. (shrink)

Working within Bishop-style constructive mathematics, we derive a number of results relating the nonconstructive LPO and sequential compactness property on the one hand, and the intuitionistically reasonable anti-Specker property on the other.

Uniform sequential continuity, a property classically equivalent to sequential continuity on compact sets, is shown, constructively, to be a consequence of strong continuity on a metric space. It is then shown that in the case of a separable metric space, uniform sequential continuity implies strong continuity if and only if one adopts a certain boundedness principle that, although valid in the classical, recursive and intuitionistic setting, is independent of Heyting arithmetic.

We propose a natural definition of what it means in a constructive context for a Banach space to be reflexive, and then prove a constructive counterpart of the Milman-Pettis theorem that uniformly convex Banach spaces are reflexive.

This paper starts from the point in the early 1970s at which educational theory and research was temporarily structured under the ‘foundation’ disciplines of psychology, sociology, philosophy and history of education. It observes the way the intellectual resources of educational research have become enlarged and enriched and these disciplines themselves fragmented and hybridised to a degree that prompts talk not just of interdisciplinarity but of ‘postdisciplinarity’. The paper argues, however, that without discipline, in the sense of a shared language, a (...) rule governed structure of enquiry—something ‘systematic’—we lose the conditions that make a community of arguers possible. Further, we lose the basis for the special claim which research might otherwise make on our attention and on our belief. (shrink)

This chapter examines criticisms made by or on behalf of ‘disempowered’ groups against outsider research into their experience: that outsiders cannot properly understand and represent their experience and are exploitative and disrespectful, and that having outsiders articulate your views for you is intrinsically disempowering. I argue that ‘outsider research’ can contribute to the better understanding of the researcher, of the community engaged in the research and of the wider community. Nevertheless the claim ‘nothing about us without us’ expresses an ethical (...) and epistemological truth in educational research: as a statement about the kind of relationship which should obtain between researcher and participants. (shrink)

This book evaluates the increasingly wide variety of intellectual resources for research methods and methodologies and investigates what constitutes good educational research. Written by a distinguished international group of philosophers of education Questions what sorts of research can usefully inform policy and practice, and what inferences can be drawn from different kinds of research Demonstrates the critical engagement of philosophers of education with the wider educational research community and illustrates the benefits that can accrue from such engagement.

The central question addressed in this paper is about the ethics of engaging with educational development in countries perceived as undemocratic or as failing to respect human rights. More particularly, it examines the nature of the arguments that are brought to bear on this issue. It suggests that these are essentially consequentialist in character and hence fall prey to many of the limitations of such consequentialism, including the unpredictability of what will unfold, the indeterminacy of the consequences and the complex (...) balance sheet of benefits and loss that might be anticipated. The paper also suggests some unease about the way judgements of the acceptability or otherwise of political processes are made across international boundaries and the presumptions of a ‘democratic’ western perspective. The observation of these complexities of principle and fact take the argument into the territory of case-based ethical judgement and the world of casuistry. (shrink)

The constructive functional calculus for a sequence of commuting selfadjoint operators on a separable Hilbert space is shown to be independent of the orthonormal basis used in its construction. The proof requires a constructive criterion for the absolute continuity of two positive measures in terms of test functions.

The focus of this paper is on a variety of practices associated with the transfer of educational policy and practice from one national education system to another – practices sometimes referred to as ‘policy borrowing’. Its concern is with the ethical and political issues raised by these practices. In particular, it discusses concerns that these practices might be practically inappropriate, that they might be culturally insensitive or inappropriate, and that they might be impositional, exploitative perhaps or even oppressive. Such concerns (...) arise particularly in contexts in which the transfer is from relatively rich and powerful countries to relatively poor and less powerful countries. But policy transfer is a feature of relations between the rich and powerful too, and to some extent the issues are then turned on their head. Those engaged in the business of transfer become more clearly identified as service providers and they have to ask questions about to whom and under what conditions they might provide this service. Finally, the paper considers policy transfer as a form of pedagogy and asks whether the kind of ethical considerations which underpin any properly educational transaction might not provide a guide to behaviour by the agents of policy transfer. (shrink)

A critique of attempts by Charles Travis and others to read contextualism back into Philosophical Investigations. The central interpretive claim is that this reading is not only unsupported; it gets Wittgenstein's intent, in the parts of the text at issue, precisely backwards. The focus of the chapter is on Wittgenstein's treatment of explanation, understanding, proper names, and family-resemblance concepts.

Fred Dretske’s teleofunctional theory of content aims to simultaneously solve two ground-floor philosophical puzzles about mental content: the problem of naturalism and the problem of epiphenomenalism. It is argued here that his theory fails on the latter score. Indeed, the theory insures that content can have no place in the causal explanation of action at all. The argument for this conclusion depends upon only very weak premises about the nature of causal explanation. The difficulties Dretske’s theory encounters indicate the severe (...) challenges involved in arriving at a robust naturalistic understanding of content. (shrink)

The notions of linear and metric independence are investigated in relation to the property: if U is a set of n+1 independent vectors, and X is a set of n independent vectors, then adjoining some vector in U to X results in a set of n+1 independent vectors. It is shown that this property holds in any normed linear space. A related property – that finite-dimensional subspaces are proximinal – is established for strictly convex normed spaces over the real or (...) complex numbers. It follows that metric independence and linear independence are equivalent in such spaces. Proofs are carried out in the context of intuitionistic logic without the axiom of countable choice. (shrink)

In this chapter, which has evolved over the last ten years to what I hope will be its perfect Platonic form, I shall first discuss those features of constructive mathematics that distinguish it from its traditional, or classical, counterpart, and then illustrate the practice of that distinction in aspects of complex analysis whose classical treatment ought to be familiar to a beginning graduate student of pure mathematics.

Working within Bishop-style constructive mathematics, we examine some of the consequences of the anti-Specker property, known to be equivalent to a version of Brouwer's fan theorem. The work is a contribution to constructive reverse mathematics.

In education issues to do with insider and outsider understanding arise in debates about religious education and about certain areas of research, and in argument about education for international understanding. Here I challenge the dichotomy between insider and outsider, arguing that a more collectivist view of human identity combined with elements of 'the self which we share with our fellows' means that we always stand in part as an insider and in part as an outsider in relation to others. I (...) argue further that 'understanding' needs always to be thought of in the plural, as a matter of 'understanding s ', since members of any community, and even any one individual, have different understandings at different times. Against what may seem the strong case in favour of the superiority or exclusivity of insider understanding, I note the force of claims in a variety of theoretical traditions (expressed notably in the Marxist tradition in the notion of 'false consciousness' and in psychoanalytic attention to the unconscious) concerning the limitations of the exclusively insider perspective and in contrast the particular authority of the outsider perspective. Finally, I acknowledge the discomfort with which people respond to outsiders' claims to understand them, especially where such understanding fails to support their own self-understanding, and identify ethical considerations, which might shape sensitive negotiation between insider and outsider perspectives. (shrink)

The minimax theorem of matrix game theory is examined from a constructive point of view. It is then shown that the existence of solutions for matrix games cannot be proved constructively, but that a 2-by-2 game with at most one solution has a constructible solution.

This is the second of two Special Issues, the first of which appeared as Volume 40, Issue 2 of this year. In the first Issue, our contributors were particularly inclined to question two assumptions that colour thinking about educational research. The first is that educational research is essentially a ‘scientific’ exercise, reaching its apogee in randomised control trials, as if medical research were the ideal to which all other kinds of research should attempt to measure up, and as if education (...) were a process largely analogous to that of administering drugs in order to enhance performance. The second, related assumption is that educational research is to be understood as, at heart, a matter of discovering ‘what works’. This is the background—also explored in other recent publications such as Smeyers and Depaepe (2006)—against which this second Special Issue should be seen. (shrink)