We give an overview of the role of equicontinuity of sequences of real-valued functions on [0,1] and related notions in classical mathematics, intuitionistic mathematics, Bishop’s constructive mathematics, and Russian recursive mathematics. We then study the logical strength of theorems concerning these notions within the programme of Constructive Reverse Mathematics. It appears that many of these theorems, like a version of Ascoli’s Lemma, are equivalent to fan-theoretic principles.

Working within the framework of Bishop's constructive mathematics, we will show that it is possible to define compactness in a more general setting than that of uniform spaces. It is also shown that it is not possible to do this in a topological space.

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.

Bishop's Lemma is a centrepiece in the development of constructive analysis. We show that its proof requires some form of the axiom of choice; and that the completeness requirement in Bishop's Lemma can be weakened and that there is a vast class of non‐complete spaces that Bishop's Lemma applies to.

The so-called paradoxes of material implication have motivated the development of many non-classical logics over the years, such as relevance logics, paraconsistent logics, fuzzy logics and so on. In this note, we investigate some of these paradoxes and classify them, over minimal logic. We provide proofs of equivalence and semantic models separating the paradoxes where appropriate. A number of equivalent groups arise, all of which collapse with unrestricted use of double negation elimination. Interestingly, the principle ex falso quodlibet, and several (...) weaker principles, turn out to be distinguishable, giving perhaps supporting motivation for adopting minimal logic as the ambient logic for reasoning in the possible presence of inconsistency. (shrink)

It is shown that a principle, which can be seen as a constructivised version of sequential compactness, is equivalent to a form of Brouwer’s fan theorem. The complexity of the latter depends on the geometry of the spaces involved in the former.

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.

Varieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational hierarchy. Some of the implications have been shown to be strict, others strict in a weak context, and yet others not at all, using disparate techniques. Here we present a family of related Kripke models which separates all of the as yet identified fan theorems.

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)

The notions of permutable and weak-permutable convergence of a series|$\sum _{n=1}^{\infty }a_{n}$|of real numbers are introduced. Classically, these two notions are equivalent, and, by Riemann’s two main theorems on the convergence of series, a convergent series is permutably convergent if and only if it is absolutely convergent. Working within Bishop-style constructive mathematics, we prove that Ishihara’s principle BD-|$\mathbb {N}$|implies that every permutably convergent series is absolutely convergent. Since there are models of constructive mathematics in which the Riemann permutation theorem for (...) series holds but BD-|$\mathbb{N}$|does not, the best we can hope for as a partial converse to our first theorem is that the absolute convergence of series with a permutability property classically equivalent to that of Riemann implies BD-|$\mathbb {N}$|. We show that this is the case when the property is weak-permutable convergence. (shrink)

Published in honor of Victor L. Selivanov, the 17 articles collected in this volume inform on the latest developments in computability theory and its applications in computable analysis; descriptive set theory and topology; and the theory of omega-languages; as well as non-classical logics, such as temporal logic and paraconsistent logic. This volume will be of interest to mathematicians and logicians, as well as theoretical computer scientists.

Many discussions between realists and non-realists have centered on the issue of reference, especially whether there is referential stability during theory change. In this paper, I shall summarize the debate, sketching the problems that remain within the two opposing positions, and show that both have ended on their own slippery slope, sliding away from their original position toward that of their opponents. In the search for a viable intermediate position, I shall then suggest an account of reference which, to a (...) degree, follows the causal theory in explaining reference as carving the world at its joints. Contrary to the causal theory, however, I submit that this world is a phenomenal world whose variable joints exist only in a historical process in which they are transmitted gradually from one generation to the next. According to this account, the joints of the phenomenal world are constituted by family resemblance, where bundles of features that span bounded areas in perceptual space underlie the joints. Furthermore, the integrity of the cognitive process by which these joints are recognized depends on a transmission process by which new generations are presented with given joints and bundles by the preceding generation. Contrary to a traditional realist account, this heritage from the preceding generation may be transformed into new joints and bundles before transmission to new generations. This permits a continuous process of referential change in which the joints and bundles at different stages in the development of a theory can be connected by chains-of-reasoning. (shrink)

Recently, several scholars have argued that scientists can accept scientific claims in a collective process, and that the capacity of scientific groups to form joint acceptances is linked to a functional division of labor between the group members. However, these accounts reveal little about how the cognitive content of the jointly accepted claim is formed, and how group members depend on each other in this process. In this paper, I shall therefore argue that we need to link analyses of joint (...) acceptance with analyses of distributed cognition. To sketch how this can be done, I shall present a detailed case study, and on the basis of the case, analyze the process through which a group of scientists jointly accept a new scientific claim and at a later stage jointly accept to revise previously accepted claims. I shall argue that joint acceptance in science can be established in situations where an overall conceptual structure is jointly accepted by a group of scientists while detailed parts of it are distributed among group members with different areas of expertise, a condition that I shall call a heterogeneous conceptual consensus. Finally, I shall show how a heterogeneous conceptual consensus can work as a constraint against scientific change and address the question how changes may nevertheless occur. (shrink)

It is a commonly raised argument against the family resemblance account of concepts that there is no limit to a concept's extension. An account of family resemblance which attempts to provide a solution to this problem by including both similarity among instances and dissimilarity to non-instances has been developed by the philosopher of science Thomas Kuhn. Similar solutions have been hinted at in the literature on family resemblance concepts, but the solution has never received a detailed investigation. I shall provide (...) a reconstruction of Kuhn's theory and argue that his solution necessitates a developmental perspective wchich builds on both the transmission of taxonomies between generations and a progressive development through history. (shrink)

One of the fundamental problems of epistemology is to say when the evidence in an agent’s possession justifies the beliefs she holds. In this paper and its prequel, we defend the Bayesian solution to this problem by appealing to the following fundamental norm: Accuracy An epistemic agent ought to minimize the inaccuracy of her partial beliefs. In the prequel, we made this norm mathematically precise; in this paper, we derive its consequences. We show that the two core tenets of Bayesianism (...) follow from the norm, while the characteristic claim of the Objectivist Bayesian follows from the norm along with an extra assumption. Finally, we consider Richard Jeffrey’s proposed generalization of conditionalization. We show not only that his rule cannot be derived from the norm, unless the requirement of Rigidity is imposed from the start, but further that the norm reveals it to be illegitimate. We end by deriving an alternative updating rule for those cases in which Jeffrey’s is usually supposed to apply. (shrink)

Business scholars have recently proposed that the virtue of personal wisdom may predict leadership behaviors and the quality of leader–follower relationships. This study investigated relationships among leaders’ personal wisdom—defined as the integration of advanced cognitive, reflective, and affective personality characteristics (Ardelt, Hum Dev 47:257–285, 2004)—transformational leadership behaviors, and leader–member exchange (LMX) quality. It was hypothesized that leaders’ personal wisdom positively predicts LMX quality and that intellectual stimulation and individualized consideration, two dimensions of transformational leadership, mediate this relationship. Data came from (...) 75 religious leaders and 1–3 employees of each leader (N = 158). Results showed that leaders’ personal wisdom had a positive indirect effect on follower ratings of LMX quality through individualized consideration, even after controlling for Big Five personality traits, emotional intelligence, and narcissism. In contrast, intellectual stimulation and the other two dimensions of transformational leadership (idealized influence and inspirational motivation) did not mediate the positive relationship between leaders’ personal wisdom and LMX quality. Implications for future research on personal wisdom and leadership are discussed, and some tentative suggestions for leadership development are outlined. (shrink)

In everyday life we either express our beliefs in all-or-nothing terms or we resort to numerical probabilities: I believe it's going to rain or my chance of winning is one in a million. The Stability of Belief develops a theory of rational belief that allows us to reason with all-or-nothing belief and numerical belief simultaneously.

This essay develops a joint theory of rational (all-or-nothing) belief and degrees of belief. The theory is based on three assumptions: the logical closure of rational belief; the axioms of probability for rational degrees of belief; and the so-called Lockean thesis, in which the concepts of rational belief and rational degree of belief figure simultaneously. In spite of what is commonly believed, this essay will show that this combination of principles is satisfiable (and indeed nontrivially so) and that the principles (...) are jointly satisfied if and only if rational belief is equivalent to the assignment of a stably high rational degree of belief. Although the logical closure of belief and the Lockean thesis are attractive postulates in themselves, initially this may seem like a formal “curiosity”; however, as will be argued in the rest of the essay, a very reasonable theory of rational belief can be built around these principles that is not ad hoc and that has various philosophical features that are plausible independently. In particular, this essay shows that the theory allows for a solution to the Lottery Paradox, and it has nice applications to formal epistemology. The price that is to be paid for this theory is a strong dependency of belief on the context, where a context involves both the agent's degree of belief function and the partitioning or individuation of the underlying possibilities. But as this essay argues, that price seems to be affordable. (shrink)

Thomas Kuhn's Structure of Scientific Revolutions became the most widely read book about science in the twentieth century. His terms 'paradigm' and 'scientific revolution' entered everyday speech, but they remain controversial. In the second half of the twentieth century, the new field of cognitive science combined empirical psychology, computer science, and neuroscience. In this book, the theories of concepts developed by cognitive scientists are used to evaluate and extend Kuhn's most influential ideas. Based on case studies of the Copernican revolution, (...) the discovery of nuclear fission, and an elaboration of Kuhn's famous 'ducks and geese' example of concept learning, this volume, first published in 2006, offers accounts of the nature of normal and revolutionary science, the function of anomalies, and the nature of incommensurability. (shrink)

This chapter provides a historical reconstruction of how Alfred Schutz’s American writings were critically engaged by the feminist sociologists Dorothy E. Smith and Patricia Hill Collins. Schutz’s articulation of a phenomenological sociology in relation to, among others, the sociology of Talcott Parsons and the philosophies of science of Ernest Nagel and Carl G. Hempel proved fruitful to Smith in the development of her feminist standpoint theory in her 1987 The Everyday World as Problematic: A Feminist Sociology. Collins likewise draws on (...) Schutz’s writing in the development of her own standpoint theory in her 1986 paper “Learning from the Outsider Within: The Sociological Significance of Black Feminist Thought,” but in a way that addresses some of her own concerns with Smith’s feminist sociology. As I hope to show with the recovery of this underappreciated history, the critical insights of Smith and Collins with regard to the possible uses and limits of phenomenology for feminist theorizing, are still valuable today. (shrink)

Transfers of critically ill neonates are frequent phenomena. Even though parents’ participation is regarded as crucial in neonatal care, a transfer often means that parents and neonates are separated. A systematic review of the parents’ experiences of neonatal transfer is lacking. This paper describes a meta‐study addressing qualitative research about parents’ experiences of neonatal transfer. Through deconstruction and reflections of theories, methods, and empirical data, the aim was to achieve a deeper understanding of theoretical, empirical, contextual, historical, and methodological issues (...) of qualitative studies concerning parents’ experiences of neonatal transfer over the course of this meta‐study (2000–2017). Meta‐theory and meta‐method analyses showed that caring, transition, and family‐centered care were main theoretical frames applied and that interviewing with a small number of participants was the preferred data collection method. The meta‐data‐analysis showed that transfer was a scary, unfamiliar, and threatening experience for the parents; they were losing familiar context, were separated from their neonate, and could feel their parenthood disrupted. We identified ‘wavering and wandering’ as a metaphoric representation of the parents’ experiences. The findings add knowledge about meta‐study as an approach for comprehensive qualitative research and point at the value of meta‐theory and meta‐method analyses. (shrink)

Based on fieldwork in northern Senegal, this paper shows how some pastoralists in Ferlo have managed to use market opportunities as a means to maintain their “pastoral way of life” Increased market involvement has enlarged the field of opportunities for pastoral activities as well as the vulnerability of these activities. This has given rise to a dialectic process of diversification and specialization. The paper is concerned with the portfolio of livelihood activities pastoralists use in order to respond to adverse socio-economic (...) and environmental conditions. Depending on the possibilities and values of a household, a certain combination of activities is chosen and this may change from one year to another. Hence, the activities are used in a dynamic way within households. On the basis of pastoral livelihood activities, four ideal types of pastoral livelihood strategies can be constructed: “agro-pastoralism,” “Tabaski pastoralism,” “commercial pastoralism,” and “non-herding pastoralism.” These four types illustrate how pastoralists re-invent their livelihoods in order to continue a pastoral way of life. (shrink)

Obtaining a valid informed consent from an elderly person, especially when frail or with possible dementia, will initially involve the practical problem of assessing the ability to communicate. Only then can the assessment of decisionmaking capacities and the obtaining of informed consent for participation in research be progressed. Normal ageing does not impair communication or decision-making, but pathological status does, this may, or may not, be associated with the ageing process. Perceptual impairment may, in particular, interfere with the communication. Once (...) the subject appreciates and understands that he/she has the right to make a choice then it is important to ensure that he/she fully understands the decision he/she is being asked to make and can communicate and explain in his/her own words why a particular decision was made. In this paper suggestions, based upon existing guidelines or texts, will be made as to how to improve communication with the elderly and the capabilities that the subject must demonstrate to show his capacity to make a decision will be discussed. (shrink)

One of the fundamental problems of epistemology is to say when the evidence in an agent’s possession justifies the beliefs she holds. In this paper and its sequel, we defend the Bayesian solution to this problem by appealing to the following fundamental norm: Accuracy An epistemic agent ought to minimize the inaccuracy of her partial beliefs. In this paper, we make this norm mathematically precise in various ways. We describe three epistemic dilemmas that an agent might face if she attempts (...) to follow Accuracy, and we show that the only inaccuracy measures that do not give rise to such dilemmas are the quadratic inaccuracy measures. In the sequel, we derive the main tenets of Bayesianism from the relevant mathematical versions of Accuracy to which this characterization of the legitimate inaccuracy measures gives rise, but we also show that Jeffrey conditionalization has to be replaced by a different method of update in order for Accuracy to be satisfied. (shrink)

This is the second part of a paper dealing with truth and translation. In Part A a revised version of Tarski's Convention T has been presented, which explicitly refers to a translation mapping from the object language to the metalanguage; the vague notion of a translation has been replaced by a precise definition. At the end of Part A it has been shown that interpreted languages exist, which allow for vicious self-reference but which nevertheless contain their own truth predicate - (...) this is possible if truth is based on a nonstandard translation mapping. However, this result has only been proved for languages without quantifiers. In Part B we now extend the result to first-order languages, and we show that this can be done in three different ways. In each case, the addition of a truth predicate to an interpreted language with a high degree of expressiveness leads to changes in the ontology of the language. (shrink)

In this book, Hannes Charen presents an alternative examination of kinship structures in political theory. Employing a radically transdisciplinary approach, On the Politics of Kinship is structured in a series of six theoretical vignettes or frames. Each chapter frames a figure, aspect, or relational context of the family or kinship. Some chapters are focused on a critique of the family as a state-sanctioned institution, while others cautiously attempt to recast kinship in a way to reimagine mutual obligation through the (...) generation of kinship practices understood as a perpetually evolving set of relational responses to finitude. In doing so, Charen considers the ways in which kinship is a plastic social response to embodied exposure, both concealed and made more evident in the bloated, feeble, and broken individualities and nationalities that seem to dominate our social and political landscape today. On the Politics of Kinship will be of interest to political theorists, feminists, anthropologists, and social scientists in general. (shrink)

Scientific Change How do scientific theories, concepts and methods change over time? Answers to this question have historical parts and philosophical parts. There can be descriptive accounts of the recorded differences over time of particular theories, concepts, and methods—what might be called the shape of scientific change. Many stories of scientific change attempt to give […].

The nature of well-being is one of the most enduring and elusive subjects of human inquiry. Well-Being draws upon the latest scientific research to transform our understanding of this ancient question. With contributions from leading authorities in psychology, social psychology, and neuroscience, this volume presents the definitive account of current scientific efforts to understand human pleasure and pain, contentment and despair. The distinguished contributors to this volume combine a rigorous analysis of human sensations, emotions, and moods with a broad assessment (...) of the many factors, from heredity to nationality, that bear on our well-being. Using the tools of experimental science, the contributors confront the puzzles of human likes and dislikes. Why do we grow accustomed and desensitized to changes in our lives, both good and bad? Does our happiness reflect the circumstances of our lives or is it determined by our temperament and personality? Why do humans acquire tastes for sensations that are initially painful or unpleasant? By examining the roots of our everyday likes and dislikes, the book also sheds light on some of the more extreme examples of attraction and aversion, such as addiction and depression. Among its wide ranging inquiries, Well-Being examines systematic differences in moods and behaviors between genders, explaining why women suffer higher rates of depression and anxiety than men, but are also more inclined to express positive emotions. The book also makes international comparisons, finding that some countries' populations report higher levels of happiness than others. The contributors deploy an array of methods, from the surveys and questionnaires of social science to psychological and physiological experiments, to develop a comprehensive new approach to the study of well-being. They show how the sensory pleasures of the body can tells us something about the higher pleasures of the mind and even how the effectiveness of our immune system can depend upon the health of our social relationships. (shrink)

In “On what matters: Personal identity as a phenomenological problem” (2020), Steven Crowell engages a number of contemporary interpretations of Husserl’s account of the person and personal identity by noting that they lack a phenomenological elucidation of the self as commitment. In this article, in response to Crowell, I aim to show that such an account of the self as commitment can be drawn from Husserl’s work by looking more closely at his descriptions from the time of Ideas and after (...) of the self as ego or I and egoic experience as attentive experience. I specifically aim to sketch the beginning of a response to three questions I take Crowell to be posing to a Husserlian account of the person and personal identity: (1) What more than pre-reflective self-awareness can be attributed to the self on phenomenological grounds so that we can understand, phenomenologically speaking, how selves become persons? (2) How can what characterizes the self in addition to pre-reflective self-awareness be discerned in both our commitment to truth and our feeling bound by love and other emotive commitments that cannot be fully rationally justified, which Husserl acknowledges are both sources of personal self-constitution? And (3), do all selves become persons? In the paper I elaborate how my answers to the first two questions turn on the self not just being self-aware but active in a particular sense. And to begin to address the third question, I suggest that while any form of wakeful conscious experience is both self-aware and active, this activity of the self makes a difference for those who are socio-historically embedded in the way we are. Specifically, on the proposed Husserlian account, selves that are socio-historically embedded become persons in and through their active relating to what they attentively experience. In concluding, I indicate how this Husserlian account might compare to Crowell’s claim that “self-identity (ipseity) is not mere logical identity (A=A) but a normative achievement […] which makes a ‘personal’ kind of identity possible” (2020). (shrink)

In Glas Derrida asserts that Hegel’s Phenomenology of Spirit, in its reading of Antigone, favors consciousness (over the unconscious) by first acknowledging the achievement of ethical plenitude by Antigone, as she comes to full recognition of two contradictory laws, that of the divine and that of the communal spheres, and consequently repressing this speculative accomplishment by her fateful disappearance from both texts. This article complicates the argument by looking at the role that literature takes not only in philosophy, but in (...) the expression of speculative dialectics as such. What for Hegel can be included in a system? How does the impossible figure (Antigone), its expression and then exclusion enter and abandon the system? This text looks at war, burial and incest expressed by the role of Antigone in the Phenomenology of Spirit. (HC) © 2011 by The Board of Regents of the University of Wisconsin System . (shrink)

This is the second part of a paper dealing with truth and translation. In Part A a revised version of Tarski's Convention T has been presented, which explicitly refers to a translation mapping from the object language to the metalanguage; the vague notion of a translation has been replaced by a precise definition. At the end of Part A it has been shown that interpreted languages exist, which allow for vicious self-reference but which nevertheless contain their own truth predicate - (...) this is possible if truth is based on a nonstandard translation mapping. However, this result has only been proved for languages without quantifiers. In Part B we now extend the result to first-order languages, and we show that this can be done in three different ways. In each case, the addition of a truth predicate to an interpreted language with a high degree of expressiveness leads to changes in the ontology of the language. (shrink)

This article introduces, studies, and applies a new system of logic which is called ‘HYPE’. In HYPE, formulas are evaluated at states that may exhibit truth value gaps and truth value gluts. Simple and natural semantic rules for negation and the conditional operator are formulated based on an incompatibility relation and a partial fusion operation on states. The semantics is worked out in formal and philosophical detail, and a sound and complete axiomatization is provided both for the propositional and the (...) predicate logic of the system. The propositional logic of HYPE is shown to contain first-degree entailment, to have the Finite Model Property, to be decidable, to have the Disjunction Property, and to extend intuitionistic propositional logic conservatively when intuitionistic negation is defined appropriately by HYPE’s logical connectives. Furthermore, HYPE’s first-order logic is a conservative extension of intuitionistic logic with the Constant Domain Axiom, when intuitionistic negation is again defined appropriately. The system allows for simple model constructions and intuitive Euler-Venn-like diagrams, and its logical structure matches structures well-known from ordinary mathematics, such as from optimization theory, combinatorics, and graph theory. HYPE may also be used as a general logical framework in which different systems of logic can be studied, compared, and combined. In particular, HYPE is found to relate in interesting ways to classical logic and various systems of relevance and paraconsistent logic, many-valued logic, and truthmaker semantics. On the philosophical side, if used as a logic for theories of type-free truth, HYPE is shown to address semantic paradoxes such as the Liar Paradox by extending non-classical fixed-point interpretations of truth by a conditional as well-behaved as that of intuitionistic logic. Finally, HYPE may be used as a background system for modal operators that create hyperintensional contexts, though the details of this application need to be left to follow-up work. (shrink)

When do children acquire a propositional attitude folk psychology or theory of mind? The orthodox answer to this central question of developmental ToM research had long been that around age 4 children begin to apply “belief” and other propositional attitude concepts. This orthodoxy has recently come under serious attack, though, from two sides: Scoffers complain that it over-estimates children’s early competence and claim that a proper understanding of propositional attitudes emerges only much later. Boosters criticize the orthodoxy for underestimating early (...) competence and claim that even infants ascribe beliefs. In this paper, the orthodoxy is defended on empirical grounds against these two kinds of attacks. On the basis of new evidence, not only can the two attacks safely be countered, but the orthodox claim can actually be strengthened, corroborated and refined: what emerges around age 4 is an explicit, unified, flexibly conceptual capacity to ascribe propositional attitudes. This unified conceptual capacity contrasts with the less sophisticated, less unified implicit forms of tracking simpler mental states present in ontogeny long before. This refined version of the orthodoxy can thus most plausibly be spelled out in some form of 2-systems-account of theory of mind. (shrink)