Saunders Mac Lane has drawn attention many times, particularly in his book Mathematics: Form and Function, to the system of set theory of which the axioms are Extensionality, Null Set, Pairing, Union, Infinity, Power Set, Restricted Separation, Foundation, and Choice, to which system, afforced by the principle, , of Transitive Containment, we shall refer as . His system is naturally related to systems derived from topos-theoretic notions concerning the category of sets, and is, as Mac Lane emphasises, one that is (...) adequate for much of mathematics. In this paper we show that the consistency strength of Mac Lane's system is not increased by adding the axioms of Kripke–Platek set theory and even the Axiom of Constructibility to Mac Lane's axioms; our method requires a close study of Axiom H, which was proposed by Mitchell; we digress to apply these methods to subsystems of Zermelo set theory , and obtain an apparently new proof that is not finitely axiomatisable; we study Friedman's strengthening of , and the Forster–Kaye subsystem of , and use forcing over ill-founded models and forcing to establish independence results concerning and ; we show, again using ill-founded models, that proves the consistency of ; turning to systems that are type-theoretic in spirit or in fact, we show by arguments of Coret and Boffa that proves a weak form of Stratified Collection, and that is a conservative extension of for stratified sentences, from which we deduce that proves a strong stratified version of ; we analyse the known equiconsistency of with the simple theory of types and give Lake's proof that an instance of Mathematical Induction is unprovable in Mac Lane's system; we study a simple set theoretic assertion—namely that there exists an infinite set of infinite sets, no two of which have the same cardinal—and use it to establish the failure of the full schema of Stratified Collection in ; and we determine the point of failure of various other schemata in . The paper closes with some philosophical remarks. (shrink)

We investigate in this work the meaning of weak values through the prism of property ascription in quantum systems. Indeed, the weak measurements framework contains only ingredients of the standard quantum formalism, and as such weak measurements are from a technical point of view uncontroversial. However attempting to describe properties of quantum systems through weak values—the output of weak measurements—goes beyond the usual interpretation of quantum mechanics, that relies on eigenvalues. We first recall the usual form of property ascription, based (...) on the eigenstate-eigenvalue link and the existence of “elements of reality”. We then describe against this backdrop the different meanings that have been given to weak values. We finally argue that weak values can be related to a specific form of property ascription, weaker than the eigenvalues case but still relevant to a partial description of a quantum system. (shrink)

Working in Z + KP, we give a new proof that the class of hereditarily finite sets cannot be proved to be a set in Zermelo set theory, extend the method to establish other failures of replacement, and exhibit a formula Φ(λ, a) such that for any sequence $\langle A_{\lambda} \mid \lambda \text{a limit ordinal} \rangle$ where for each $\lambda, A_{\lambda} \subseteq ^{\lambda}2$ , there is a supertransitive inner model of Zermelo containing all ordinals in which for every λ A (...) λ = {α ∣Φ(λ, a)}. (shrink)

This paper, a contribution to “micro set theory”, is the study promised by the first author in [M4], as improved and extended by work of the second. We use the rudimentarily recursive functions and the slightly larger collection of gentle functions to initiate the study of provident sets, which are transitive models of $\mathsf{PROVI}$, a subsystem of $\mathsf{KP}$ whose minimal model is Jensen’s $J_{\omega}$. $\mathsf{PROVI}$ supports familiar definitions, such as rank, transitive closure and ordinal addition—though not ordinal multiplication—and Shoenfield’s unramified (...) forcing. Providence is preserved under directed unions. An arbitrary set has a provident closure, and the extension of a provident $M$ by a set-generic $\mathcal{G}$ is the provident closure of $M\cup\{\mathcal{G}\}$. The improvidence of many models of $\mathsf{Z}$ is shown. The final section uses similar but simpler recursions to show, in the weak system $\mathsf{MW}$, that the truth predicate for $\dot{\varDelta}_{0}$ formulæ is $\Delta_{1}$. (shrink)

Explores intellectual and philosophical evolution of German philosopher Martin Heidegger, focusing on period after World War II. Analyzes how Heidegger s ideas, particularly his notion of being, influenced and were influenced by postwar context, including confrontation with Nazism and emergence of new philosophical currents. Argues that Heidegger s work offers relevant insights for contemporary philosophical debates and calls for a critical dialogue with his legacy. Discusses Heidegger s philosophy in the context of French and German philosophical schools, highlighting relevance of (...) his ideas and impact they had on contemporary philosophy. (shrink)

Social suffering commands increasing public attention in the wake of several historical processes that have changed the ways victims are perceived. In making suffering eloquent by rendering it in conceptual form, philosophy runs the risk of muting suffering, thereby neutralizing its ability to mobilize responses. In the experience of suffering philosophy finds a limit it must recognize as its own. Yet only by fulfilling its duty towards suffering - only by having the abolition of suffering as its ultimate goal - (...) can philosophical thinking withstand a tacit complicity with injustice. (shrink)

Working in Z + KP, we give a new proof that the class of hereditarily finite sets cannot be proved to be a set in Zermelo set theory, extend the method to establish other failures of replacement, and exhibit a formula $\Phi$ such that for any sequence $\langle A_{\lambda} \mid \lambda \text{a limit ordinal} \rangle$ where for each $\lambda, A_{\lambda} \subseteq ^{\lambda}2$, there is a supertransitive inner model of Zermelo containing all ordinals in which for every $\lambda A_{\lambda} = \{\alpha (...) \mid\Phi\}$. (shrink)

En una época de éxodo masivo global, se explora el documental De Nadie (2005) de Tin Dirdamal, el cual, a través de una variedad de instancias narrativas, presenta la experiencia y condición migrante, aún actual, de centroamericanos en su tránsito por México en su camino hacia EE.UU. Frente a la exclusión en el pasado de personajes migrantes femeninos, el cine y la narrativa literaria contemporánea despliegan significados culturales y sociales que avivan la presencia de mujeres como protagonistas en el vertiginoso (...) cruce entre fronteras, bajo los regímenes de movilidad. Estas narrativas ponen en evidencia la trascendencia identitaria de las mujeres migrantes a partir del desplazamiento. En específico, en este trabajo se examina el documental De Nadie (2005) bajo la lupa de la performatividad de género de la hondureña María, antes y durante su recorrido migratorio. (shrink)

Feyerabend and others have been defending for some time the thesis that even observation sentences depend for their meanings on the thegries in which they play a role. According to the most radical version of this thesis, if two theories contain incompatible theoretical statements, then even if the observation terms and sentences associated with the two theories are the same, these terms and sentencesmeansomething different, according as they are associated with one theory or the other. This claim has made it (...) hard to see how, on this view, any two theories could be said to compete, or be incompatible, or be comparable on the basis of observation.The whole dispute over this claim seems highly suspect to begin with. For look at the philosophical terms in which it is couched. On the one hand there is the notion of the “meaning” of a term or sentence, whose status as a useful tool of philosophical analysis has been in serious question for the past two or three decades. (shrink)

The purpose of the article is to analyze the meaning of examples in C. Hempel’s works. Hempel uses many examples referring to readings of magnetic hand, burning of white phosphorus, predictions of properties of some elements of the table of Mendeleev, to astrophysical hypotheses, terms of total solar eclipse, throwing of dice, as well as on unmarried men, on white and black swans, green mermaids, black crows and white shoes, blue roses, predictions of Jones’ recovery, the eruption of Vesuvius, the (...) assassination of Julius Caesar, and other “special cases” and “concrete facts”. The question is raised as to whether the case studies are mere illustrative material, a form of argumentation; a way of verifying Hempel’s ideas, their “demonstrable confirmation”, and in this sense a definite empirical basis for the study. The necessity of analyzing concrete examples in the context of Hempel’s theoretical research is shown, for which the examples turn out to be an occasion for investigating the logic of confirmation and the logic of explanation, for analyzing the structures of explanans and explanandum, for understanding the differences in inductive and deductive logical constructions, and for analyzing “quasi-induction”. The paper discusses Hempel’s famous example, the crow paradox, which is named in his honor and is a kind of logical provocation. (shrink)

In a challenge to Basic Emotion theories, Ortony suggested in a recent article that the existence of affect-free surprise means that surprise is not necessarily valenced and therefore arguably not an emotion. In an article in response, Neta and Kim argued that surprise is always valenced and therefore is an emotion, with apparent cases of affect-free surprise actually being cases of the cognitive state of unexpectedness rather than surprise. We view Neta and Kim's position as resting on an idiosyncratic stipulation (...) of word usage. We further suggest that rejecting affect-free surprise by appealing to examples of affect-laden surprise has no bearing on whether surprise is always valenced, and propose that when surprise appears to be affect-laden the locus of the experienced valence is a co-occurring emotion. (shrink)

Remhof contends that Nietzsche is a metaphysician. According to his Meta-Metaphysical Argument, Nietzsche’s texts satisfy the criteria for an adequate conception of metaphysics. According to his Constructivist Argument, Nietzsche adopts a metaphysical position on which concepts’ application conditions constitute the identity conditions of their objects. This article critically appraises these arguments. I maintain that the criteria advanced in the Meta-Metaphysical Argument are collectively insufficient for delineating metaphysics as a distinct field of inquiry and that the Constructivist Argument attributes a position (...) to Nietzsche that remains vulnerable to his evaluative and psychological indictments of two-world metaphysics. I conclude by discussing how these objections might help non-metaphysical readers of Nietzsche resist Remhof’s interpretation. (shrink)

Warne's original study provides an insightful analysis of the role of contemplation and creation in the thought of Josef Pieper, illustrating the importance of this practice to earthly happiness and human flourishing. What is the relationship between creation, contemplation, human flourishing, and moral development? Nathaniel Warne's Josef Pieper on the Spiritual Life offers a sophisticated answer to this question through a systematic analysis of philosopher Josef Pieper's (1904-1997) thought. Warne's examination centers on the role of contemplation and creation in Pieper's (...) thinking, arguing that contemplation of the created order is a key feature of earthly happiness. By emphasizing the importance of contemplation, Pieper illustrates the deep interconnections between ethics, creation, and spirituality. For Warne, to posit a binary between the contemplative life and active life creates a false dichotomy. Following Pieper, Warne claims that theology and spirituality cannot be bracketed from ethics and social action--indeed, our lived experience in the world blurs the lines between these practices. Contemplation and action are closer together than are typically assumed, and both have important implications for both our spiritual development and our engagement with the world around us. Ultimately, Warne's emphasis on creation and contemplation represents an attempt to resist a view of ethics and the spiritual life that is divorced from our environment. In response to this view, Warne argues that we need a renewed sense that creation and place are important for self-understanding. Contemplation of creation is, at bottom, a form of communion with God--we thus need a more robust sense of how ethics and politics are rooted in God's creative action. Taking Pieper as a guide, Warne's study helps to deepen our thinking about these connections. (shrink)

Background Machine learning (ML) is utilized increasingly in health care, and can pose harms to patients, clinicians, health systems, and the public. In response, regulators have proposed an approach that would shift more responsibility to ML developers for mitigating potential harms. To be effective, this approach requires ML developers to recognize, accept, and act on responsibility for mitigating harms. However, little is known regarding the perspectives of developers themselves regarding their obligations to mitigate harms.Methods We conducted 40 semi-structured interviews with (...) developers of ML predictive analytics applications for health care in the United States.Results Participants varied widely in their perspectives on personal responsibility and included examples of both moral engagement and disengagement, albeit in a variety of forms. While most (70%) of participants made a statement indicative of moral engagement, most of these statements reflected an awareness of moral issues, while only a subset of these included additional elements of engagement such as recognizing responsibility, alignment with personal values, addressing conflicts of interests, and opportunities for action. Further, we identified eight distinct categories of moral disengagement reflecting efforts to minimize potential harms or deflect personal responsibility for preventing or mitigating harms.Conclusions These findings suggest possible facilitators and barriers to the development of ethical ML that could act by encouraging moral engagement or discouraging moral disengagement. Regulatory approaches that depend on the ability of ML developers to recognize, accept, and act on responsibility for mitigating harms might have limited success without education and guidance for ML developers about the extent of their responsibilities and how to implement them. (shrink)

In this article, I explore Namita Goswami’s Subjects That Matter. Goswami has laid out an extensive excavation of the variety, depth, and breadth of antagonistic encounters between the Western world and subaltern subjects. I am interested in Goswami’s take on the production of the unknowable women of color who are constructed either as good wives, animate objects without wills of their own, or transgressors of the genre of producing women of color as oppressed. I argue that the question of heterogeneity (...) already assumes the very thing that is under question: to presuppose heterogeneity is already to presuppose its limit conditions—to already understand what difference looks like, which could preempt the possibility of infinite, or indefinite iterations. The irony is that we run the risk of assuming the very thing that we are trying not to presuppose, anticipate, or cordon off. Moreover, I question whether it is possible to encounter deep radical differences in any way other than antagonistically, since the unknown, from experience, is assumed to threaten. (shrink)

The implementation of the thoracoabdominal normothermic regional perfusion in organ donation after circulatory determination of death (TANRP-DCDD) protocol is garnering increasing attention and pre...

There is much in the responses by Dolores Morris, Doug Geivett, and Jim Beilby with which I fully agree. But here I try to clarify a few issues and to identify points where we might simply disagree. I focus on the issue of those who experience the world as godless (Dolores); broadening the definition of religious experience (Dolores and Doug); suggested revisions of the argument from fulfilled expectations (Dolores); and especially the vexing questions associated with epistemic peer disagreement (Jim and (...) Doug). (shrink)

Arguments concerning divine conservation and concurrence often assume that actions of certain descriptions would be superfluous if God were to perform them, and it is then concluded that God does not perform such actions. In particular, it often seems that atomic actions cannot be the result of cooperative activity between God and creatures since there is no apparent way to divide the labor between the two. However, the actions that are atomic in one model of divine action may not be (...) atomic on another. On fine-grained models there may be unexpected prospects for nonredundant divine action. (shrink)

This paper examines the perceived ethical values of Malaysian managers. It is based on the opinions of 15 hypothetical ethical/unethical business situations from the 81 managers who agreed to participate in the survey. The findings of this study showed that these Malaysian managers have high ethical values. However 53% of the respondents believed that the ethical standards of today are lower than that of 15 years ago. Apparently, this is related to the existence of many unethical business practices prevalent in (...) the modern business world. The behavior of one's immediate superior is the most important factor in influencing managers to commit unethical practices. The results also indicate only a slight variation among the managers in terms of perceived ethical values by virtue of job position, job specialization, type of business activity or the size of the business organization. (shrink)

The target article covers a large amount of ground and offers a provocative perspective. This commentary focuses on (a) assumptions, namely that there are discrete stages in the creative process and that novelty and usefulness are inextricable, (b) hidden variables in the creativity–curiosity relationship, and (c) the difference between an explanation of creativity versus a description of influence on it.

Improvements in the health capital of citizens are central to the development of countries. By exploiting steep decreases in antiretroviral drug prices and the subsequent increases in antiretroviral therapy (ART) coverage, we test whether the resulting improvements in the health of the population are associated with the prevalence of entrepreneurial activity and whether entrepreneurial activity strengthens the relationship between ART coverage and a country’s development. Drawing on a sample of 87 low- and middle-income countries (2006–2019), we find that a 1% (...) increase in ART coverage is associated with a 1.5% increase in the number of newly registered limited liability firms; however, there is no significant relationship with (male or female) self-employment. Higher ART coverage is particularly associated with development—as proxied by gross domestic product (GDP) per capita and the Human Development Index—in countries with low levels of new business formation and high proportions of self-employment. (shrink)