The existence of either a maximum or a minimum for a uniformly continuous mapping f of a compact interval into ${\mathbb{R}}$ is established constructively under the hypotheses that f′ is sequentially continuous and f has at most one critical point.

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.

It is argued that Hellman's arguments purporting to demonstrate that constructive mathematics cannot cope with unbounded operators on a Hilbert space are seriously flawed, and that there is no evidence that his thesis is correct.

In lieu of an abstract, here is a brief excerpt of the content:A Bridge From Analysis to Action:Psychodynamic Analyses of Religion and Michael S. Hogue's American ImmanenceAJ Turner (bio)I. IntroductionThe purpose of this essay is to work constructively with Michael S. Hogue's groundbreaking American Immanence: Democracy for an Uncertain World to demonstrate how psychodynamic analyses of religion are essential theoretical allies in the fight for resilient democracy. The "revolution in mind"1 that psychodynamic approaches contribute, especially in their analyses of religion, (...) both complements and complicates socio-political theory as a whole. In the improvisational spirit of "yes-and," the goal here is not to identify and decry the failures and shortcomings of Hogue's theopolitical vision but rather to inspire the recovery of a sibling discourse—a kind of "rebirth of a forgotten alternative"2—that also draws deeply from the American immanental tradition in order to add psychodynamic depth to Hogue's timely and important analysis. Psychodynamic theories of religion shed light on how symbolic identifications, including and especially ultimate concerns, structure personal and collective experience. By engaging religion and theology sympathetically, constructively, and creatively, theorists such as Rollo May, Gordon Allport, Karen Horney, Erich Fromm, and Ernest Becker departed from the skepticism, reductionism, and dismissal that characterized psychoanalytic analyses of religion in the wake of Freud.3 Each of these figures, and especially Becker whose work will be a focus in this essay, are noteworthy interlocutors for extending Hogue's theopolitical theorizing of resilient democracy, particularly in how they drew unique inspiration from the American immanental tradition [End Page 44] in their social analyses. In this respect, they provide a more robust theorization of the psychosocial conditions of the associational ethos needed to connect Hogue's conception of resilient democracy with forms of agonistic organization and democratic activism. Briefly stated, psychodynamic approaches are a helpful bridge for connecting these proposals to strategies of organization, their impediments, and collective action.In this way, both psychodynamic analyses of religion and Hogue's theopolitical innovation insist that no revolutionary political change is possible, and certainly not of the kind or scale needed to counter our wickedly entangled global crises, without a deep engagement with theological imaginaries. They differ, however, in their theoretical aims. Whereas Hogue compellingly argues for the political upshot of a theology deriving from the American immanental tradition, psychodynamic analysts of religion focus on the function of ultimate concerns in individual and collective life. In other words, American Immanence rests on a methodology of analyzing the philosophical and theological assumptions that have contributed to our climate crises and then presenting clear and compelling articulation of an alternative paradigm meant to open up new ways of being. In contrast psychodynamic analyses leverage conceptual clarity of psychic reality for the fundamentally therapeutic aim of transformation. At their best, both approaches share what could be called an etiological orientation to ontological questions in order to provide liberative alternatives through rational understanding and clarification, but the terrain, and thus the problems they hope to mitigate in their analyses are focused differently. Extending the visual metaphor, they are different lenses highlighting different areas of the same landscape. Furthermore, it must be said that neither are sufficient in themselves, but the psychodynamic theorists of religion to be highlighted in this essay share deeply with Hogue's heading in American Immanence.II. A Problematic AssumptionIn emphasizing and attempting to explain4 the role of non-rational processes in the both individual and social processes of perception and organization of experience, psychodynamic theories confound a widely held and problematic assumption that the triumph of rational analysis is the hallmark for building the society to which we should aspire. Political theory in general, [End Page 45] especially as it has taken its cues from a rationalist legacy about the inherently liberating force of Reason, has been weighted toward an assumption that its task of exposing the mystifications of power would suffice in inspiring more "rational" and therefore necessarily equitable social organization. This speaks to the longstanding socio-political interest in "consciousness raising" tactics, which are often meant to dispel "false consciousness." It even comes across in the emphases of Deweyan pragmatists on education. Psychologists of all stripes point out that this approach... (shrink)

Continuing the study of apartness in lattices, begun in [8], this paper deals with axioms for a product a-frame and with their consequences. This leads to a reasonable notion of proximity in an a-frame, abstracted from its counterpart in the theory of set-set apartness.

The anti-Specker property, a constructive version of sequential compactness, is used to prove constructively that a pointwise continuous, order-dense preference relation on a compact metric space is uniformly sequentially continuous. It is then shown that Ishihara's principle BD-ℕ implies that a uniformly sequentially continuous, order-dense preference relation on a separable metric space is uniformly continuous. Converses of these two theorems are also proved.

The theory and methods of cultural psychology begin with the assumption that psychological processes are socioculturally and historically grounded. As such, they offer a new approach for understanding the diversity of human functioning because they (a) question the presumed neutrality of the majority group perspective; (b) take the target’s point-of-view (i.e., what it means to be a person in a particular context); (c) assume that there is more than one viable way of being a competent or effective person; and (d) (...) provide a road map for understanding and reducing social inequities. As illustrated in this essay, a cultural psychological approach provides a bridge between anthropology and the cognitive sciences, and in so doing it offers an alternative set of explanations and interventions for group differences. (shrink)

It is shown how, under certain circumstances and within Bishop‐style constructive mathematics, one can construct a product of two a‐frames (the structures underlying the constructive theory of apartness on frames).

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.

We examine, from a constructive perspective, the relation between the complements of S, T, and S ∩ T in X, where X is either a metric space or a normed linear space. The fundamental question addressed is: If x is distinct from each element of S ∩ T, if s ϵ S, and if t ϵ T, is x distinct from s or from t? Although the classical answer to this question is trivially affirmative, constructive answers involve Markov's principle and (...) the completeness of metric spaces. (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.

Previous chapters considered value theories of psychology, sociology, anthropology, and philosophy. These disciplines can benefit and learn from one another, and closer interaction between disciplines will lead to better value theory. To facilitate an interdisciplinary understanding of value, this chapter will highlight the overlap between the different disciplines and what they can learn from one another. Each section of this chapter compares two disciplines and highlights overlaps, similarities, and differences. The hope is that this constructive comparison will build a bridge (...) between disciplines, which helps to advance the theory development within the disciplines and brings theoretical blind spots into focus. Bringing disciplines together is the first step towards crossing disciplinary boundaries, resolving conceptual differences, and increasing interdisciplinary communication. (shrink)

Though there is a vast literature on performances of drag, performances of gender and sexual transgressions outside of drag clubs are less studied. This case study of men’s marches protesting violence against women—“Walk a Mile in Her Shoes” marches— examines the politics of such transgressions. Cross-dressing to various degrees is strategically utilized at these events in an attempt to encourage men to become empathetic allies. This article suggests, however, that context is critical to the political potential of performances of drag. (...) The author’s observations of the interactions at the marches suggest that drag at “Walk a Mile” marches often symbolically reproduces gender and sexual inequality despite good intentions. At these marches, feminism is gendered when performances of politics and protest are contextually framed as gender and/or sexual transgressions when “feminism” is understood as “feminine.”. (shrink)

A characterisation of a type of weak-operator continuous linear functional on certain linear subsets of B, where H is a Hilbert space, is derived within Bishop-style constructive mathematics.

The main result of this paper is a weak constructive version of the uniform continuity theorem for pointwise continuous, real-valued functions on a convex subset of a normed linear space. Recursive examples are given to show that the hypotheses of this theorem are necessary. The remainder of the paper discusses conditions which ensure that a sequentially continuous function is continuous. MSC: 03F60, 26E40, 46S30.

This paper is dedicated to Prof. Dr. Günter Asser, whose work in founding this journal and maintaining it over many difficult years has been a major contribution to the activities of the mathematical logic community.At first sight it appears highly unlikely that Urysohn's Lemma has any significant constructive content. However, working in the context of an apartness space and using functions whose values are a generalisation of the reals, rather than real numbers, enables us to produce a significant constructive version (...) of that lemma. (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)

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.

The little-known story of the architectural project that lay at the heart of Paine's grand political vision for the United States. Thomas Jefferson praised Tom Paine as the greatest political writer of the age. The author of 'Common Sense' and Rights of Man, Paine helped make revolutions in America and France. But beyond his inspiring calls to action, Paine harbored a deeper political vision for his adopted country. It was embodied in an architectural project that he spent decades planning: an (...) iron bridge to span the Schuylkill River at Philadelphia. The bridge was Paine's answer to the political puzzle of the new nation: how to sustain a republic as large and geographically fragmented as the United States. Among its patrons were other giants of the time, including Benjamin Franklin and Edmund Burke, Paine's ideological opponent. Set against the background of the American Revolution, the story of his iron bridge reveals a new Tom Paine and connects this revolutionary to the vast program of internal improvements that soon transformed America"--Provided by publisher. (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)

A popular goal in psychological science is to understand human cognition and behavior in the ‘real-world.’ In contrast, researchers have typically conducted their research in experimental research settings, a.k.a. the ‘psychologist’s laboratory.’ Critics have often questioned whether psychology’s laboratory experiments permit generalizable results. This is known as the ‘real-world or the lab’-dilemma. To bridge the gap between lab and life, many researchers have called for experiments with more ‘ecological validity’ to ensure that experiments more closely resemble and generalize to the (...) ‘real-world.’ However, researchers seldom explain what they mean with this term, nor how more ecological validity should be achieved. In our opinion, the popular concept of ecological validity is ill-formed, lacks specificity, and falls short of addressing the problem of generalizability. To move beyond the ‘real-world or the lab’-dilemma, we believe that researchers in psychological science should always specify the particular context of cognitive and behavioral functioning in which they are interested, instead of advocating that experiments should be more ‘ecologically valid’ in order to generalize to the ‘real-world.’ We believe this will be a more constructive way to uncover the context-specific and context-generic principles of cognition and behavior. (shrink)

On the horizon between metaphysics and philosophy of religion stands the question of God’s relation to various abstracta. Like other contemporary philosophical debates, this one has resulted in a broadly dichotomous stalemate between Platonic realists on the one hand and varieties of nominalism/antirealism on the other. In this paper, I offer Aquinas’s moderaterealism as a true middle ground between realist or nominalist solutions. What Platonists take to be abstracta are actually the result of intellect’s abstractive work on sensible objects. Further, (...) the Christian philosopher should be concerned as much, if not more so, by nominalism than by Platonism. Given the problems associated with either Platonist or nominalist solutions, one should be open to a Thomistic moderate-realist solution to the problem of God and abstracta. (shrink)

A weak constructive sequential compactness property of metric spaces is introduced. It is proved that for complete, totally bounded metric spaces this property is equivalent to Brouwer's fan theorem for detachable bars. Our results form a part of constructive reverse mathematics.

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)

Contemporary biomedical ethics and environmental ethics share a common ancestry in Aldo Leopold's and Van Rensselaer Potter's initial broad visions of a connected biosphere. Over the past five decades, the two fields have become strangers. Public health ethics, a new subfield of bioethics, emerged from the belly of contemporary biomedical ethics and has evolved over the past 25 years. It has moved from its traditional concern with the tension between individual autonomy and community health to a wider focus on social (...) justice and solidarity. Public health has a broad focus that includes individual, community, and environmental health. Public health ethics attends to these broad commitments reflected in the increasing concern with the connectedness of health of individuals to the health of populations, to the health of animals, to the health of the environment; it is well situated to reconnect all three “fields” of ethics to promote a healthier planet. (shrink)

This paper develops a bridge from AL issues about the symbol–matter relation to AI issues about symbol-grounding by focusing on the concepts of formality and syntactic interpretability. Using the DNA triplet-amino acid specification relation as a paradigm, it is argued that syntactic properties can be grounded as high-level features of the non-syntactic interactions in a physical dynamical system. This argu- ment provides the basis for a rebuttal of John Searle’s recent assertion that syntax is observer-relative (1990, 1992). But the argument (...) as developed also challenges the classic symbol-processing theory of mind against which Searle is arguing, as well as the strong AL thesis that life is realizable in a purely computational medium. Finally, it provides a new line of support for the autonomous systems approach in AL and AI (Varela & Bourgine 1992a, 1992b). © 1997 Academic Press. (shrink)

I argue that once one holds (as Kant does) that the mind is equipped with innate, pre-existing, i.e. a priori structures, one can ask (as materialists or empiricists would), Is there an identifiable source of such structures and what does it imply? Already Schopenhauer, Moses Mendelssohn and others have taken that route of argument, without fully drawing the implications. In this paper I attempt to do so, posing the query: Is Kant's very explicit separation of the transcendent from the transcendental (...) necessary in his critical system? I try to answer from various perspectives. (shrink)

In “Mathematical Truth,” Paul Benacerraf raises an epistemic challenge for mathematical platonists. In this paper, I examine the assumptions that motivate Benacerraf’s original challenge, and use them to construct a new causal challenge for the epistemology of mathematics. This new challenge, which I call ‘Gödel’s Gap’, appeals to intuitive insights into mathematical knowledge. Though it is a causal challenge, it does not rely on any obviously objectionable constraints on knowledge. As a result, it is more compelling than the original challenge. (...) It is also more general; the challenge applies equally to platonistic and non-platonistic accounts of mathematical truth. And it can be generalized beyond the case of mathematical knowledge to pose a challenge for, e.g., moral knowledge. (shrink)

A sympathetic exegesis of themes in Barry Stroud's later writings, with a particular emphasis on the role of a certain conception of "perceptual experience" in generating the skeptical challenge to our knowledge of the external world. The resultant morals are brought to bear on John McDowell's evolving account of the role of contentful "experiences" in providing for empirical thought. For Stroud's response to this essay (and others) see: http://philosophicalskepticism.org/skepsis/numero-14/.