We prove a ‘Whitney’ presentation, and a ‘Coulomb branch’ presentation, for the torus equivariant quantum K theory of the Grassmann manifold $\mathrm {Gr}(k;n)$, inspired from physics, and stated in an earlier paper. The first presentation is obtained by quantum deforming the product of the Hirzebruch $\lambda _y$ classes of the tautological bundles. In physics, the $\lambda _y$ classes arise as certain Wilson line operators. The second presentation is obtained from the Coulomb branch equations involving the partial derivatives of a twisted superpotential from supersymmetric gauge theory. This is closest to a presentation obtained by Gorbounov and Korff, utilizing integrable systems techniques. Algebraically, we relate the Coulomb and Whitney presentations utilizing transition matrices from the (equivariant) Grothendieck polynomials to the (equivariant) complete homogeneous symmetric polynomials. Along the way, we calculate K-theoretic Gromov-Witten invariants of wedge powers of the tautological bundles on $\mathrm {Gr}(k;n)$, using the ‘quantum=classical’ statement.

The internet has been increasingly employed in the treatment of binge eating, including to facilitate guided self-help (GSH). However, few studies have investigated provision of GSH over email and there are questions regarding the viability of this approach, and how facilitators might best deliver this treatment. We describe a case study of a woman in her early 50s with a diagnosis of binge-eating disorder (BED) who received email-supported GSH over 12 weeks within a larger randomised controlled trial. At assessment, she presented with regular binge eating episodes (approximately twice a week) in addition to co-morbid medical and psychiatric issues, for which she was prescribed several medications. Treatment, provided within the UK National Health Service, involved provision of a self-help manual (Overcoming Binge Eating; Fairburn, 2013) in addition to email support over 12 weeks. A summary of the intervention is provided, along with email excerpts to demonstrate practice, illustrate how treatment might be delivered, and outline the type of interaction that may occur during email support. Consistent with larger studies, improvement on several self-report symptom measures was seen, including eating disorder symptoms, psychosocial impairment, psychological distress, self-esteem, and therapeutic alliance, all of which met criteria for reliable improvement at post-treatment. This case study, which provides data from one individual, demonstrates delivery of GSH with email support for regular binge eating, which could be considered as an alternative to face-to-face treatment. Future work might look to enhance outcomes following GSH, including reducing drop-out, and increase dissemination and uptake of GSH.

Key learning aims

1. (1) Consider the potential role of email-assisted self-help in the treatment of recurrent binge eating.

2. (2) Provide guidance to support the delivery of guided self-help, particularly in an online format.

3. (3) Review an example of using a CBT-based self-help intervention to overcome binge eating in the presence of medical and psychiatric co-morbidity.

4. (4) Understand how to implement guided self-help for binge eating and use this approach to facilitate a strong therapeutic alliance and symptom change.

Eugenic arguments are not a thing of the past. In 2016, geneticist Michael Lynch published an article in Genetics arguing that human mental and physical performance are declining at a rate of 1% per generation. This estimate is not based on measurements of performance but on an argument from mutational load: Medical interventions are relaxing selection on the human population, which will lead to a buildup of deleterious mutations. This simple argument from mutational load is invalid. When the argument is made valid, it is not obvious that there are any significant consequences for human population health.

P. Kyle Stanford’s Exceeding our Grasp (2006) shows how the problem of unconceived alternatives presents a significant challenge to realism. Stanford argues that the history of science offers repeated instances of scientists failing to conceptualize rational alternatives to ruling scientific doctrines, implying that our present scientific theories are likely to be similarly underdetermined. This article extends Stanford’s argument and provides it with a longer history. It shows how the principle of unconceived alternatives was explicitly deployed during the medieval and early modern periods to undermine scientific realism in particular cases. These arguments typically made reference to divine omnipotence and the principle that God could have produced phenomena in numerous ways inconceivable to finite human minds. In this theological register, unconceived alternatives offered a way of minimizing potential tensions between theological doctrines and prevailing scientific theories. The article concludes with some brief reflections on the applicability of the principle of unconceived alternatives to conceptions of God.

How do digital platforms affect coordination in the restaurant market? In particular, how do they reshape firms’ positions in the quality space and their dependence on both consumers’ valuations and competitors’ choices? Focusing on the case of a widely used platform for restaurant booking and reviewing, we analyze the dine-in services market in the city of Lille, France. In line with economic sociology’s definition of markets as concrete social spaces, we frame these restaurants as a producer market in which multiple quality conventions coexist. We use sequential mixed methods and data (observations and interviews, web-scraping and business data) to show that platforms rationalize firms’ practice of observing one another as a basis for making decisions on volume and quality. The rise of digital platforms provides producers with devices that amplify their view of competitors, standardize their offerings and support the stability of their business choices over time, conditional on spatial constraints and quality choices.

Philosophers of science have overlooked the role of theory in neuroscience, resulting in a somewhat surprising naïveté regarding the nature and function of neuroscientific theories. Here I provide a framework that identifies and begins to characterize what we need to know about neuroscientific theories so as to improve our epistemic standing. I argue that we need an account of the structural, interpretive, and functional aspects of neuroscientific theories, using the neuron doctrine as an illustrative case study. I introduce the novel metaphor of theoretical infrastructure as a guide for making sense of neuroscientific theories and their place within neuroscientific practice.

The realisation that climate tipping points may be triggered in the upcoming decades underscores the urgent need for transformative educational responses to the climate crisis that integrate scientific knowledge with socio-political dimensions. However, the consolidation of Education for Sustainable Development has gradually displaced Environmental Education (EE) from institutional and academic spaces, shifting the focus away from systemic critiques of the socio-economic drivers of the environmental crisis. Through a historical perspective on the consolidation of the paradigm of sustainable development, this article calls for an EE capable of addressing the root causes rather than the symptoms of anthropogenic climate change, contending that the survival of EE as an independent, counter-hegemonic field is essential for fostering transformative educational practices that confront climate emergency.

Christine Korsgaard avers that the value we place on specific personal choices — understood as goals or ends — involves committing to them, or forming a care, which is itself conditioned by the value-conferring ability of the valuer. In other words, personal autonomy implies the objective value of the agent’s autonomous choosing and their coeval cares projects. Commentators like Andrea Sangiovanni, Paul Guyer, and Rae Langton criticize Korsgaard’s commitment-based conception of autonomous choosing. This article reviews these objections and then proposes a modified Korsgaardian framework concerning the objective value of autonomous choosing, which, I propose, avoids these critical objections.

The complex relation between a person and their mental disorder is a recurring theme in (reflections on) psychiatric practice. As there is no uncontested concept of ‘self’, nor of ‘mental disorder’, the ‘self-illness’ relation is riddled with ambiguity. In this feature article, we summarise recent philosophical work on the phenomenon of ‘self-illness ambiguity’, to provide conceptual tools for psychiatric reflections on the self-illness relation. Specifically, we argue that the concept of self-illness ambiguity may contribute to patients’ self-understanding and shed light on how paradigms of care and research should be revised in order to help clinicians support that self-understanding. We also suggest that the concept of self-illness ambiguity may improve the understanding of particular mental disorders, and may offer conceptual tools to address various ethical matters (including stigma and responsibility).

Within a single month in 2024, media in three provinces wrote about government spending by special warrant. This is unusual public attention to an obscure financial instrument. Governor’s special warrants are a practical solution to the problem of government urgently needing to spend money in the public interest when the legislature cannot readily be convened to grant approval. We describe how special warrants are being used less in exigent circumstances and more as a convenience. This practice is evident across jurisdictions and the parties in power and is persistent over decades. This research note shows how legal grey holes and the accelerated pace of decision making can result in changes in the practice of government that go unrecognized in our understanding of law and constitutional convention. Using an original compendium of statutory provisions combined with historical analysis, we raise research questions about public finance and parliamentary constitutionalism in Canada.

Recent epistemological debates have increasingly focused on the contentious counter-closure principle, which holds that, necessarily, if an agent S believes q solely on the basis of a competent inference from p, and S knows q, then S also knows p. This principle has drawn attention due to various challenges, particularly the issue of inferential knowledge derived from false premises. In this article, we pursue two objectives. First, we argue that the counter-closure principle is untenable but for reasons that depart from traditional critiques. Specifically, we will present a novel argument against the internalist approach that supports the cases of knowledge from falsehoods. Second, we show that the counter-closure principle’s failure can be better addressed within an externalist framework by exploring novel theories of defeaters and the relationship between doxastic and propositional warrant.

There has been significant interest in addressing the underrepresentation of various demographic groups in philosophy. Indeed, many have proposed remedies at the disciplinary level. However, underrepresentation is an issue that varies by subfield in philosophy. Women, for example, are especially underrepresented in subfields considered formal (e.g., logic). As has already been argued in the existing literature, addressing underrepresentation, even within subfields, is not as simple as recruiting more students from underserved populations. Instead, we advocate for a student-centered approach, promoting inclusive pedagogy. In this paper, we share a case study in which we implemented feminist and trauma-informed interventions in two undergraduate formal logic courses and investigated their impact with respect to elements of structural injustice. We found that our interventions successfully eliminated existing gender-based differences in perceptions of self-efficacy and largely diminished students’ perceptions of the objectivity of logic, but were unsuccessful at changing students’ impressions of the broader applicability of logic. By sharing our interventions, we hope to provide educators with practical tools and ideas for implementing similar approaches in their classrooms. By sharing our results, we invite educators to reflect on the potential impact of similar approaches in formal philosophy courses and on tools for measuring that impact.

We show how finiteness properties of a group and a subgroup transfer to finiteness properties of the Schlichting completion relative to this subgroup.n Further, we provide a criterion when the dense embedding of a discrete group into the Schlichting completion relative to one of its subgroups induces an isomorphism in (continuous) cohomology. As an application, we show that the continuous cohomology of the Neretin group vanishes in all positive degrees.