Classically, weak König's lemma and Brouwer's fan theorem for detachable bars are equivalent. We give a direct constructive proof that the former implies the latter.

The confusion/non-consequential thinking explanation proposed by Newstead, Girotto, and Legrenzi (1995) for poor performance on Wason's THOG problem (a hypothetico-deductive reasoning task) was examined in three experiments with 300 participants. In general, as the cognitive complexity of the problem and the possibility of non-consequential thinking were reduced, correct performance increased. Significant but weak facilitation (33-40% correct) was found in Experiment 1 for THOG classification instructions that did not include the indeterminate response option. Substantial facilitation (up to 75% correct) was (...) obtained in Experiment 2 with O'Brien et al.'s (1990) one-other-THOG classification instruction. In Experiment 3, a revised version of O'Brien et al.'s pre-test problem format also led to substantial facilitation, even with the use of the standard three-choice THOG classification instruction. These findings are discussed in terms of Newstead et al.'s theoretical proposal and possible attentional factors. (shrink)

We develop measure theory in the context of subsystems of second order arithmetic with restricted induction. We introduce a combinatorial principleWWKL (weak-weak König's lemma) and prove that it is strictly weaker thanWKL (weak König's lemma). We show thatWWKL is equivalent to a formal version of the statement that Lebesgue measure is countably additive on open sets. We also show thatWWKL is equivalent to a formal version of the statement that any Borel measure on a compact (...) metric space is countably additive on open sets. (shrink)

We provide a fine‐grained analysis on the relation between König's lemma, weak König's lemma, and the decidable fan theorem in the context of constructive reverse mathematics. In particular, we show that double negated variants of König's lemma and weak König's lemma are equivalent to double negated variants of the general decidable fan theorem and the binary decidable fan theorem, respectively, over a nearly intuitionistic system containing a weak countable choice only. This implies that (...) the general decidable fan theorem is not equivalent to the binary decidable fan theorem in the absence of a strong countable choice. In addition, we introduce a principle which fills the gap between König's lemma and weak König's lemma, and show that König's lemma is equivalent to weak König's lemma plus this principle. We also solve several problems arising from the investigation. (shrink)

The so-called weak König's lemma WKL asserts the existence of an infinite path b in any infinite binary tree . Based on this principle one can formulate subsystems of higher-order arithmetic which allow to carry out very substantial parts of classical mathematics but are Π 2 0 -conservative over primitive recursive arithmetic PRA . In Kohlenbach 1239–1273) we established such conservation results relative to finite type extensions PRA ω of PRA . In this setting one can consider also (...) a uniform version UWKL of WKL which asserts the existence of a functional Φ which selects uniformly in a given infinite binary tree f an infinite path Φf of that tree. This uniform version of WKL is of interest in the context of explicit mathematics as developed by S. Feferman. The elimination process in Kohlenbach [10] actually can be used to eliminate even this uniform weak König's lemma provided that PRA ω only has a quantifier-free rule of extensionality QF-ER instead of the full axioms of extensionality for all finite types. In this paper we show that in the presence of , UWKL is much stronger than WKL: whereas WKL remains to be Π 2 0 -conservative over PRA, PRA ω ++ UWKL contains full Peano arithmetic PA. We also investigate the proof–theoretic as well as the computational strength of UWKL relative to the intuitionistic variant of PRA ω both with and without the Markov principle. (shrink)

We show how to interpret weak Kőnig's lemma in some recently defined theories of nonstandard arithmetic in all finite types. Two types of interpretations are described, with very different verifications. The celebrated conservation result of Friedman's about weak Kőnig's lemma can be proved using these interpretations. We also address some issues concerning the collecting of witnesses in herbrandized functional interpretations.

We continue the work of [14, 3, 1, 19, 16, 4, 12, 11, 20] investigating the strength of set existence axioms needed for separable Banach space theory. We show that the separation theorem for open convex sets is equivalent to WKL 0 over RCA 0 . We show that the separation theorem for separably closed convex sets is equivalent to ACA 0 over RCA 0 . Our strategy for proving these geometrical Hahn-Banach theorems is to reduce to the finite-dimensional case (...) by means of a compactness argument. (shrink)

We continue the work of [14, 3, 1, 19, 16, 4, 12, 11, 20] investigating the strength of set existence axioms needed for separable Banach space theory. We show that the separation theorem for open convex sets is equivalent to WKL$_0$ over RCA$_0$. We show that the separation theorem for separably closed convex sets is equivalent to ACA$_0$ over RCA$_0$. Our strategy for proving these geometrical Hahn-Banach theorems is to reduce to the finite-dimensional case by means of a compactness argument.

By , we denote the system of second-order arithmetic based on recursive comprehension axioms and Σ10 induction. is defined to be plus weak König's lemma: every infinite tree of sequences of 0's and 1's has an infinite path. In this paper, we first show that for any countable model M of , there exists a countable model M′ of whose first-order part is the same as that of M, and whose second-order part consists of the M-recursive sets and (...) sets not in the second-order part of M. By combining this fact with a certain forcing argument over universal trees, we obtain the following result : if proves X!Y with arithmetical, so does . We also discuss several improvements of this results. (shrink)

We introduce a herbrandized functional interpretation of a first-order semi-intuitionistic extension of Heyting Arithmetic and study its main properties. We then extend the interpretation to a certain system of second-order arithmetic which includes a (classically false) formulation of the FAN principle and weak König's lemma. It is shown that any first-order formula provable in this system is classically true. It is perhaps worthy of note that, in our interpretation, second-order variables are interpreted by finite sets of natural numbers.

In this paper, we show within RCA 0 that weak Konig's lemma is necessary and sufficient to prove that any (separable) compact group has a Haar measure. Within WKL 0 , a Haar measure is constructed by a non-standard method based on a fact that every countable non-standard model of WKL 0 has a proper initial part isomorphic to itself [10].

We explore the connections between Dickson’s lemma and weak Ramsey theory. We show that a weak version of the Paris–Harrington principle for pairs in c colors and miniaturized Dickson’s lemma for c-tuples are equivalent over \. Furthermore, we look at a cascade of consequences for several variants of weak Ramsey’s theorem.

An infinite binary sequence X is Kolmogorov–Loveland random if there is no computable non-monotonic betting strategy that succeeds on X in the sense of having an unbounded gain in the limit while betting successively on bits of X. A sequence X is KL-stochastic if there is no computable non-monotonic selection rule that selects from X an infinite, biased sequence.One of the major open problems in the field of effective randomness is whether Martin-Löf randomness is the same as KL-randomness. Our first (...) main result states that KL-random sequences are close to Martin-Löf random sequences in so far as every KL-random sequence has arbitrarily dense subsequences that are Martin-Löf random. A key lemma in the proof of this result is that for every effective split of a KL-random sequence at least one of the halves is Martin-Löf random. However, this splitting property does not characterize KL-randomness; we construct a sequence that is not even computably random such that every effective split yields two subsequences that are 2-random. Furthermore, we show for any KL-random sequence A that is computable in the halting problem that, first, for any effective split of A both halves are Martin-Löf random and, second, for any computable, nondecreasing, and unbounded function g and almost all n, the prefix of A of length n has prefix-free Kolmogorov complexity at least n−g. Again, the latter property does not characterize KL-randomness, even when restricted to left-r.e. sequences; we construct a left-r.e. sequence that has this property but is not KL-stochastic and, in fact, is not even Mises–Wald–Church stochastic.Turning our attention to KL-stochasticity, we construct a non-empty class of KL-stochastic sequences that are not weakly 1-random; by the usual basis theorems we obtain such sequences that in addition are left-r.e., are low, or are of hyperimmune-free degree.Our second main result asserts that every KL-stochastic sequence has effective dimension 1, or equivalently, a sequence cannot be KL-stochastic if it has infinitely many prefixes that can be compressed by a factor of α<1. This improves on a result by Muchnik, who has shown that were they to exist, such compressible prefixes could not be found effectively. (shrink)

We study the computational content of the Brouwer Fixed Point Theorem in the Weihrauch lattice. Connected choice is the operation that finds a point in a non-empty connected closed set given by negative information. One of our main results is that for any fixed dimension the Brouwer Fixed Point Theorem of that dimension is computably equivalent to connected choice of the Euclidean unit cube of the same dimension. Another main result is that connected choice is complete for dimension greater than (...) or equal to two in the sense that it is computably equivalent to Weak Kőnig’s Lemma. While we can present two independent proofs for dimension three and upward that are either based on a simple geometric construction or a combinatorial argument, the proof for dimension two is based on a more involved inverse limit construction. The connected choice operation in dimension one is known to be equivalent to the Intermediate Value Theorem; we prove that this problem is not idempotent in contrast to the case of dimension two and upward. We also prove that Lipschitz continuity with Lipschitz constants strictly larger than one does not simplify finding fixed points. Finally, we prove that finding a connectedness component of a closed subset of the Euclidean unit cube of any dimension greater than or equal to one is equivalent to Weak Kőnig’s Lemma. In order to describe these results, we introduce a representation of closed subsets of the unit cube by trees of rational complexes. (shrink)

In this paper, we propose a weak regularity principle which is similar to both weak König's lemma and Ramsey's theorem. We begin by studying the computational strength of this principle in the context of reverse mathematics. We then analyze different ways of generalizing this principle.

Drawing on a landscape analysis of existing data-sharing initiatives, in-depth interviews with expert stakeholders, and public deliberations with community advisory panels across the U.S., we describe features of the evolving medical information commons. We identify participant-centricity and trustworthiness as the most important features of an MIC and discuss the implications for those seeking to create a sustainable, useful, and widely available collection of linked resources for research and other purposes.

"Et toutes ces belles idées sur la liberté, elles sont appliquées quelque part? - Ensemble, non. Mais par petits bouts, oui. Enfin, je crois. - Hé bien, tu n'as qu'à aller voir." C'est ainsi que je fus arraché à la torpeur de ma bibliothèque. Depuis lors, je voyage à travers le monde avec une ambition simple : étudier les thèmes de philosophie politique qui me sont chers là où ils sont mis en oeuvre. Faire apparaître derrière les concepts des histoires, (...) des visages. Pour comprendre la tolérance religieuse, j'ai parcouru le Kerala, en Inde, où les grands monothéismes coexistent depuis la nuit des temps. Pour me faire une opinion sur le libre-échange, j'ai suivi dans son quotidien le directeur de l'Organisation mondiale du commerce. Pour tester la libéralisation des drogues, j'ai côtoyé les entrepreneurs de la marijuana au Colorado. Pour mieux saisir les enjeux du revenu universel, j'ai enquêté dans les villages brésiliens où il est expérimenté. Pour apprécier la réalité du micro-crédit, j'ai sillonné les bidonvilles de Lima. Et pour m'assurer des vertus de la liberté, j'ai rencontré ceux qui en sont privés, dans les "prisons ouvertes" finlandaises. Chemin faisant, j'ai perdu certains préjugés, découvert de nouvelles idées, croisé des auteurs insoupçonnés. Et j'ai acquis une conviction : les problèmes posés par la liberté se résolvent par... davantage de liberté. G.K. (shrink)

No consensus yet exists on how to handle incidental fnd-ings in human subjects research. Yet empirical studies document IFs in a wide range of research studies, where IFs are fndings beyond the aims of the study that are of potential health or reproductive importance to the individual research participant. This paper reports recommendations of a two-year project group funded by NIH to study how to manage IFs in genetic and genomic research, as well as imaging research. We conclude that researchers (...) have an obligation to address the possibility of discovering IFs in their protocol and communications with the IRB, and in their consent forms and communications with research participants. Researchers should establish a pathway for handling IFs and communicate that to the IRB and research participants. We recommend a pathway and categorize IFs into those that must be disclosed to research participants, those that may be disclosed, and those that should not be disclosed. (shrink)

Genomic research results and incidental findings with health implications for a research participant are of potential interest not only to the participant, but also to the participant's family. Yet investigators lack guidance on return of results to relatives, including after the participant's death. In this paper, a national working group offers consensus analysis and recommendations, including an ethical framework to guide investigators in managing this challenging issue, before and after the participant's death.

The exponential rise in transgender self-identification invites consideration of what constitutes an ethical response to transgender individuals’ claims about how best to promote their well-being. In this paper, we argue that ‘accepting’ a claim to medical transitioning in order to promote well-being would be in the person’s best interests iff at the point of request the individual is correct in their self-diagnosis as transgender (i.e., the distress felt to reside in the body does not result from another psychological and/or societal (...) problem) such that the medical interventions they are seeking will help them to realise their preferences. If we cannot assume this—and we suggest that we have reasonable grounds to question an unqualified acceptance in some cases—then ‘acceptance’ potentially works against best interests. We propose a distinction between ‘acceptance’ and respectful, in-depth exploration of an individual’s claims about what promotes their well-being. We discuss the ethical relevance of the unconscious mind to considerations of autonomy and consent in working with transgender individuals. An inquisitive stance, we suggest, supports autonomous choice about how to realise an embodied form that sustains well-being by allowing the individual to consider both conscious and unconscious factors shaping wishes and values, hence choices. (shrink)

Background: Genomic analysis may reveal both primary and secondary findings with direct relevance to the health of probands’ biological relatives. Researchers question their obligations to return findings not only to participants but also to family members. Given the social value of privacy protection, should researchers offer a proband’s results to family members, including after the proband’s death? Methods: Preferences were elicited using interviews and a survey. Respondents included probands from two pancreatic cancer research resources, plus biological and nonbiological family members. (...) Hypothetical scenarios based on actual research findings from the two cancer research resources were presented; participants were asked return of results preferences and justifications. Interview transcripts were coded and analyzed; survey data were analyzed descriptively. Results: Fifty-one individuals (17 probands, 21 biological relatives, 13 spouses/partners) were interviewed. Subsequently, a mailed survey was returned by 464 probands, 1,040 biological family members, and 399 spouses/partners. This analysis highlights the interviews, augmented by survey findings. Probands and family members attribute great predictive power and lifesaving potential to genomic information. A majority hold that a proband’s genomic results relevant to family members’ health ought to be offered. While informants endorse each individual’s choice whether to learn results, most express a strong moral responsibility to know and to share, particularly with the younger generation. Most have few concerns about sharing genetic information within the family; rather, their concerns focus on the health consequences of not sharing. Conclusions: Although additional studies in diverse populations are needed, policies governing return of genomic results should consider how families understand genomic data, how they value confidentiality within the family, and whether they endorse an ethics of sharing. A focus on respect for individual privacy—without attention to how the broad social and cultural context shapes preferences within families—cannot be the sole foundation of policy. (shrink)

Psychologists have emphasized children's acquisition of information through firsthand observation. However, many beliefs are acquired from others' testimony. In two experiments, most 4yearolds displayed sceptical trust in testimony. Having heard informants' accurate or inaccurate testimony, they anticipated that informants would continue to display such differential accuracy and they trusted the hitherto reliable informant. Yet they ignored the testimony of the reliable informant if it conflicted with what they themselves had seen. By contrast, threeyearolds were less selective in trusting a reliable (...) informant. Thus, young children check testimony against their own experience and increasingly recognise that some informants are more trustworthy than others. (shrink)

The psychological and neurobiological processes underlying moral judgement have been the focus of many recent empirical studies1–11. Of central interest is whether emotions play a causal role in moral judgement, and, in parallel, how emotion-related areas of the brain contribute to moral judgement. Here we show that six patients with focal bilateral damage to the ventromedial prefrontal cortex (VMPC), a brain region necessary for the normal generation of emotions and, in particular, social emotions12–14, produce an abnor- mally ‘utilitarian’ pattern of (...) judgements on moral dilemmas that pit compelling considerations of aggregate welfare against highly emotionally aversive behaviours (for example, having to sacrifice one person’s life to save a number of other lives)7,8. In contrast, the VMPC patients’ judgements were normal in other classes of moral dilemmas. These findings indicate that, for a selective set of moral dilemmas, the VMPC is critical for normal judgements of right and wrong. The findings support a necessary role for emotion in the generation of those judgements. (shrink)

Notini et al 1 offer a timely addition in the wake of a significant increase in young people identifying as transgender and gender diverse. The authors focus specifically on the case of 18-year-old Phoenix’s request for ongoing puberty suppression to affirm a non-binary gender identity. A central issue raised by Phoenix’s predicament, and that I suggest we can extend to ethical consideration of requests for other types of medical intervention by binary and non-binary TGD individuals, is whether we should ‘affirm’ (...) the claims made by TGD young people about what promotes their well-being. As a clinician working with TGD young people who have undergone a range of medical interventions to align their bodies with their gender identity, my starting presumption is that it is important to respect what people think will help them: there are some TGD young people for whom, all things considered, medical interventions to affirm gender identity promote their well-being. Well-being has become an important conceptual currency in ethical debates and lies at the core of the authors’ analysis of Phoenix’s case. While the authors do not ground their argument in favour of OPS in a specific theory of well-being, welfarist considerations 2 appear to underpin …. (shrink)

Notini _et al_ 1 offer a timely addition in the wake of a significant increase in young people identifying as transgender and gender diverse. The authors focus specifically on the case of 18-year-old Phoenix’s request for ongoing puberty suppression to affirm a non-binary gender identity. A central issue raised by Phoenix’s predicament, and that I suggest we can extend to ethical consideration of requests for other types of medical intervention by binary and non-binary TGD individuals, is whether we should ‘affirm’ (...) the claims made by TGD young people about what promotes their well-being. As a clinician working with TGD young people who have undergone a range of medical interventions to align their bodies with their gender identity, my starting presumption is that it is important to respect what people think will help them: there are some TGD... (shrink)

Biological kin share up to half of their genetic material, including predisposition to disease. Thus, variants of clinical significance identified in each individual’s genome can implicate an exponential number of relatives at potential risk. This has renewed the dilemma over family access to research participant’s genetic results, since prevailing US practices treat these as private, controlled by the individual. These individual-based ethics contrast with the family-based ethics – in which genetic information, privacy, and autonomy are considered to be familial – (...) endorsed in UK genomic medicine and by participants in a multi-method study of US research participants presented here. The dilemma reflects a conflict between US legal and ethical frameworks that privilege “the individual” and exclude “the family” versus actual human genetics that are simultaneously individual and familial. Can human genetics succeed in challenging bioethics’ hegemonic individualism to recognize and place the family at the center of the room where bioethics happens? (shrink)

What is the nature of children's trust in testimony? Is it based primarily on evidential correlations between statements and facts, as stated by Hume, or does it derive from an interest in the trustworthiness of particular speakers? In this essay, we explore these questions in an effort to understand the developmental course and cognitive bases of children's extensive reliance on testimony. Recent work shows that, from an early age, children monitor the reliability of particular informants, differentiate between those who make (...) true and false claims and keep that differential accuracy in mind when evaluating new information from these people. We argue that this selective trust is likely to involve the mentalistic appraisal of speakers rather than surface generalizations of their behavior. Finally, we review the significance of children's deference to adult authority on issues of naming and categorization. In addition to challenging a purely inductive account of trust, these and other findings reflect a potentially rich set of tools brought by children to the task of learning from people's testimony. (shrink)

Cultural difference has been largely ignored within bioethics, particularly within the end-of-life discourses and practices that have developed over the past two decades in the U.S. healthcare system. Yet how should culturebe taken into account?

Within the growing developmental literature on children's testimonial learning, the emphasis placed on children's evaluations of testimonial evidence has shielded from view some of the more collaborative dimensions of testimonial learning. Drawing on recent philosophical work on testimony and interpersonal trust, we argue for an alternative way of conceptualizing the social nature of testimonial learning. On this alternative, some testimonial learning is the result of a jointly collaborative epistemic activity, an activity that aims at the epistemic goal of true belief, (...) but that does so by means of an irreducibly social process. (shrink)

Returning genomic research results to family members raises complex questions. Genomic research on life-limiting conditions such as cancer, and research involving storage and reanalysis of data and specimens long into the future, makes these questions pressing. This author group, funded by an NIH grant, published consensus recommendations presenting a framework. This follow-up paper offers concrete guidance and tools for implementation. The group collected and analyzed relevant documents and guidance, including tools from the Clinical Sequencing Exploratory Research Consortium. The authors then (...) negotiated a consensus toolkit of processes and documents. That toolkit offers sample consent and notification documents plus decision flow-charts to address return of results to family of living and deceased participants, in adult and pediatric research. Core concerns are eliciting participant preferences on sharing results with family and on choice of a representative to make decisions about sharing after participant death. (shrink)

We support Jaswal & Akhtar's interrogation of social motivational accounts of autism and discuss two sources of bias that contribute to how others construe autistic people's communications: an experience-based bias that limits our ability to discern the speaker's action as communicative and a prejudice against the credibility of certain speakers that limits a listener's willingness to believe their testimony.

ABSTRACTWhat is the nature of children's trust in testimony? Is it based primarily on evidential correlations between statements and facts, as stated by Hume, or does it derive from an interest in the trustworthiness of particular speakers? In this essay, we explore these questions in an effort to understand the developmental course and cognitive bases of children's extensive reliance on testimony. Recent work shows that, from an early age, children monitor the reliability of particular informants, differentiate between those who make (...) true and false claims and keep that differential accuracy in mind when evaluating new information from these people. We argue that this selective trust is likely to involve the mentalistic appraisal of speakers rather than surface generalizations of their behavior. Finally, we review the significance of children's deference to adult authority on issues of naming and categorization. In addition to challenging a purely inductive account of trust, these and other findings reflect a potentially rich set of tools brought by children to the task of learning from people's testimony. (shrink)

This paper argues for a largely unnoted distinction between relational and modal components in the lexical semantics of verbs. Wehypothesize that many verbs encode two kinds of semantic information:a relationship among participants in a situation and a subset ofcircumstances or time indices at which this relationship isevaluated. The latter we term sublexical modality.We show that linking regularities between semantic arguments andsyntactic functions provide corroborating evidence in favor of thissemantic distinction, noting cases in which the semantic groundingof linking through participant-role properties (...) apparently fails. Thissemantic grounding can be preserved, however, once we abstractaway from sublexical modality in lexical semantic representations.Semantically-based linking constraints are insensitive to the sublexicalmodality component of lexical entries and depend only on informationin a predicator's situational core. (shrink)

Data are lacking with regard to participants' perspectives on return of genetic research results to relatives, including after the participant's death. This paper reports descriptive results from 3,630 survey respondents: 464 participants in a pancreatic cancer biobank, 1,439 family registry participants, and 1,727 healthy individuals. Our findings indicate that most participants would feel obligated to share their results with blood relatives while alive and would want results to be shared with relatives after their death.

Les œuvres musicales et les sons semblent devoir résister aux tentatives faites pour leur attribuer un sens stable et clairement défini. Historiquement, le flou sémantique qui les caractérise a toujours compliqué la tâche de ceux qui se sont efforcés de leur attribuer une « valeur » esthétique, par exemple au sein d’une hiérarchie des genres. Il s’agit toujours d’endiguer leur dangereux excès asymbolique en les déchiffrant, en leur imposant symboles et prédicats. Le présent essai propose une analyse d’ Un re (...) in ascolto [ Un roi à l’écoute ] d’Italo Calvino (1976), redéfinissant à nouveaux frais la notion de souveraineté afin de mieux comprendre la nature d’une telle stratégie herméneutique, et les raisons de son échec. Le souverain tel que nous le décrit Calvino est-il en mesure de conférer un sens à la musique et au chant en les intégrant au sein d’un système sémantique clos? Ou l’expérience musicale doit-elle au contraire être décrite comme fondamentalement incompatible avec une telle herméneutique totalisante, appelant une analyse fondée sur une vision pluraliste, horizontale, et non-hiérarchique des relations entre les différents modes d’expression artistique? (shrink)