Gillian Russell has recently proposed counterexamples to such elementary argument forms as Conjunction Introduction and Identity. These purported counterexamples involve expressions that are sensitive to linguistic context—for example, a sentence which is true when it appears alone but false when embedded in a larger sentence. If they are genuine counterexamples, it looks as though logical nihilism—the view that there are no valid argument forms—might be true. In this paper, I argue that the purported counterexamples are not genuine, on the grounds (...) that they equivocate. Having defused the threat of logical nihilism, I argue that the kind of linguistic context sensitivity at work in Russell’s purported counterexamples, if taken seriously, far from leading to logical nihilism, reveals new, previously undreamt-of valid forms. By way of proof of concept I present a simple logic, Solo-Only Propositional Logic, designed to capture some of them. Along the way, some interesting subtleties about the fallacy of equivocation are revealed. (shrink)

The question of man -- Time and the will -- Receptivity and spatiality -- Distance and concealment -- Art and difference -- The 'speaking' of language -- Human nature and sensus communis -- Inspiration and genius -- Thought and expression -- A history of truth and truthfulness -- Being and the hidden God.

What is a thing? What is an object? Tristan Garcia decisively overturns 100 years of Heideggerian orthodoxy about the supposedly derivative nature of objects to put forward a new theory of ontology that gives us deep insights into the world and our place in it."e.

Viewing emotion from an evolutionary perspective, researchers have argued that simple responses to affective stimuli can be triggered without mediation of cognitive processes. Indeed, findings suggest that positively and negatively valenced stimuli trigger approach and avoidance movements automatically. However, affective stimulus–response compatibility phenomena share so many central characteristics with nonaffective stimulus–response compatibility phenomena that one may doubt whether the underlying mechanisms differ. We suggest an “affectively enriched” version of the theory of event coding (TEC) that is able to account for (...) both affective and nonaffective compatibility, and that can account for the observation that both types of compatibility seem to be modulated by goals and intentions. Predictions from the model are tested in an experiment where participants carried out approach and avoidance responses to either the valence or the orientation of emotionally charged pictures. Under affective instruction the positive-approach/negative-avoid mapping yielded faster responses than the positive-avoid/negative-approach mapping, but no such effect was observed under spatial instruction. Conversely, spatial compatibility effects were obtained under spatial, but not under affective instruction. We conclude that affective and nonaffective compatibility effects reflect the same mechanism. (shrink)

I defend Haze’s argument against the Breckenridge-Magidor theory of instantial reasoning from an objection by Meléndez Gutiérrez. According to Breckenridge and Magidor, in reasoning like ‘Some x is mortal. Let n be such an x…’, the ‘n’ refers to a particular object but we cannot know which. This surprisingly defensible view poses an obvious threat to widespread notions in the philosophy of language. Haze argues that the theory leads to absurdity in cases like ‘Some x is unreferred-to by any expression. (...) Let n be such an x…’ and should therefore be rejected. Meléndez Gutiérrez counters that Haze’s argument is just a case of Berry-like paradox and thus fails to refute the Breckenridge-Magidor theory. I argue that the analogy breaks down: unlike the intuitively compelling and widely believed well-ordering principle about positive integers, the principle drawn from Breckenridge and Magidor that plays a supposedly analogous role enjoys no such status, and is instead simply shown to be false by Haze’s reductio. The possibility of such a response is obscured when Meléndez Gutiérrez portrays Haze’s argument as involving a stipulation that ‘n’ is to refer to an unreferred-to object. On the contrary, Haze’s argument does not assume that expressions like ‘n’ work by means of referring at all, and simply lets stipulations like ‘Let n be such an x’ be themselves, without imposing a theory on them. Once this is clarified, we can see that Haze’s argument is unaffected by Meléndez Gutiérrez’s objection. (shrink)

A great need for systematic evaluation of ethics training programs exists. Those tasked with developing an ethics training program may be quick to dismiss the value of training evaluation in continuous process improvement. In the present effort, we use a case study approach to delineate how to leverage formative and summative evaluation measures to create a high-quality ethics education program. With regard to formative evaluation, information bearing on trainee reactions, qualitative data from the comments of trainees, in addition to empirical (...) findings, can ensure that the training program operates smoothly. Regarding summative evaluation, measures examining trainee cognition, behavior, and organization-level results provide information about how much trainees have changed as a result of taking the ethics training. The implications of effective training program evaluation are discussed. (shrink)

Heidegger’s ‘serious idealism’ aims at capturing the realist impulses of our natural consciousness whilst avoiding a collapse into metaphysical realism. This idealism is best conceived as a form of transcendental empiricism. But we need to distinguish two varieties of transcendental empiricism, corresponding to Heidegger’s early and later work. The latter, transcendental empiricism2, is superior. Here, Heidegger’s ontology of gift gives full, conceptual shape to the two-way dependency between man and world characteristic of transcendental empiricism as a whole. In exemplary forms (...) of inspired experience, marked by the 'animation' of our conceptually-structured natural powers, things call on us in a speech that is their very own. This moves us decisively beyond not only early Heidegger’s transcendental empiricism1 but also the picture of experience presented in McDowell’s Mind and World. (shrink)

The object of this paper is to sketch an approach to propositions, meaning and names. The key ingredients are a Twin-Earth-inspired distinction between internal and external meaning, and a middle-Wittgenstein-inspired conception of internal meaning as role in language system. I show how the approach offers a promising solution to the problem of the meaning of proper names. This is a plea for a neglected way of thinking about these topics.

The seven articles included in the AJOB Neuroscience special issue map important ethical issues that have and will continue to emerge with advances in neuroscience and neurotechnology. A critical c...

Political philosophy was once dominated by discussion of the virtues of character and their importance to the good life and the good society. Contemporary political philosophers, however, following the towering influence of John Rawls, have primarily focused on a single virtue of institutions: justice, while largely avoiding controversial claims about the good life. As a result, political philosophy lacks a unified account of the virtues of institutions and the virtues of character. More importantly, we lack an understanding of the connection (...) between the just society and the good life. This book begins to mend this broken seam, which, on reflection, lies at the heart of our deepest political problems. The book’s central argument is that the virtues of character require institutions, while good institutions enable persons to live together virtuously. Political institutions are a necessary precondition for the moral agency exhibited by the virtues. But good institutions enable virtue to grow, while helping to constrain the excesses of vice. On this view, justice emerges primarily as a virtue of character, not institutions. The just person balances conformity to existing institutional norms with practically wise reforms. Ultimately, this book concludes that the just society and the good life are linked through the common good of virtuous activity within the shared institutions of a political community. (shrink)

Hydraulic fracturing (‘fracking') has enabled the recovery of previously inaccessible resources and rendered new areas of the underground ‘productive’. While a number of studies in the US and UK have examined public attitudes toward fracking and its various impacts, how people conceptualise the deep underground itself has received less attention. We argue that views on resources, risk and the deep underground raise important questions about how people perceive the desirability and viability of subterranean interventions. We conducted day-long deliberation workshops (two (...) in each country), facilitating discussions among diverse groups of people on prospective shale extraction in the US and UK. Themes that emerged in these conversations include seeing the Earth as a foundation; natural limits (a greater burden than the subsurface can withstand versus simply overuse of natural resources); and ideas about the fragility, instability and opacity of the deep underground. We find that concerns in both countries were not limited to specific, localised impacts but also addressed ecosystem links between surface and subsurface environments and broader questions about the use, identification and value of natural resources. (shrink)

What is the relationship between justice as an individual virtue and justice as an institutional virtue? The latter has been exhaustively explored by political philosophers, whereas the former remains underexplored in the literature on virtue ethics. This article defends the view that individual justice is logically prior to institutional justice, and argues that this view requires a conception of individual justice I call ‘justice as lawfulness’. The resulting view consists of three claims. First, just institutions are composed of the relations (...) between just persons. Second, the just person has a disposition to act in accordance with the legal and social norms (collectively, thenomoi) of the existing political tradition. Third, departures from thenomoirequire that the just person act with practical wisdom to reform thenomoiaccording to an implicit standard of justice in the political tradition. (shrink)

Here I present a new objection to the material or "hook" analysis of indicative conditionals - the thesis that an indicative conditional 'If A then C' has the truth-conditions of the so-called material conditional - based on Liar-like reasoning. This objection seems invulnerable to any Grice-Lewis-Jackson-inspired pragmatic rejoinder.

In Conservatism Past and Present: A Philosophical Introduction, Tristan J. Rogers argues that philosophical conservatism is a coherent and compelling set of historically rooted ideas about conserving and promoting the human good. Part I, "Conservatism Past," presents a history of conservative ideas, exploring themes, such as the search for wisdom, the limits of philosophy, reform in preference to revolution, the relationship between authority and freedom, and liberty as a living tradition. Major figures include Aristotle, Saint Aquinas, Edmund Burke, G.W.F. Hegel, (...) and Roger Scruton. Part II, "Conservatism Present," applies philosophical conservatism to contemporary conservative politics, focusing on issues such as nationalism, populism, the family, education, and responsibility. Rogers shows that conservatism has been defined differently at different times: as a loose set of connected ideas reacting against the French Revolution; as a kind of disposition or instinct in favor of the status quo; and more recently as any ideas opposed to the political left. But he also allows a set of questions to guide his argument for conservatism's merits: What is conservatism? Is it a coherent and attractive philosophy? What are conservatives for? And how is today's conservatism related to its past? In his answers, Rogers paints a compelling and coherent picture of an aligned and attractive set of ideas. (shrink)

Tristan J. Rogers ABSTRACT: What might a Stoic approach to politics look like? David Goodhart aptly describes the political divide pervading Western societies in terms of the ‘somewheres,’ who are communitarian, rooted in particular places, and resistant to social and political change, versus the ‘anywheres,’ who are cosmopolitan, mobile, and enthusiastic embracers of change. Stoicism ….

Heidegger argues that for being x to count as ‘alive’ it must satisfy three metaphysical conditions. It must be capable of engaging in active behaviour with a form of intentional directedness that offers to us a “sphere of transposition” into which we can intelligibly “transpose ourselves.” Heidegger’s discussion of these conditions, as they apply to the being of animals, is well-known. But, if his argument is sound, they ought also to apply to the being of plants. Heidegger, unfortunately, does not (...) supply this part of his ontology of life in any systematic detail. However, my thesis is that it is possible to interpret the nature and activities of plants, along the lines of –, and thus to make good on Heidegger’s omission. The key to this reconstruction is a reconceptualization of plant movements as constituted by a form of representationally blind, motor-intentionality. (shrink)

Criteria of historical assessment are applied to the Turin Shroud to determine which hypothesis relating to the image formation process is the most likely. To implement this, a ‘Minimal Facts’ approach is followed that takes into account only physicochemical and historical data receiving the widest consensus among contemporary scientists. The result indicates that the probability of the Shroud of Turin being the real shroud of Jesus of Nazareth is very high; historians and natural theologians should therefore pay it increased attention.

In this paper, we prove a definable version of Kirszbraun's theorem in a non‐Archimedean setting for definable families of functions in one variable. More precisely, we prove that every definable function, where and, that is λ‐Lipschitz in the first variable, extends to a definable function that is λ‐Lipschitz in the first variable.

Journal of Social Philosophy, EarlyView.

Sound-producing movements in percussion performance require a high degree of fine motor control. However, there remains a relatively limited empirical understanding of how performance level abilities develop in percussion performance in general, and marimba performance specifically. To address this issue, nine percussionists performed individualised excerpts on marimba within three testing sessions spaced 29 days apart to assess early, intermediate, and late stages of motor learning. Motor learning was quantified via analyses of both the temporal control of mallet movements, and the (...) spatial variability of upper-limb movements. The results showed that temporal control of mallet movements was greater in the intermediate compared to the early learning session, with no significant additional improvements revealed in the late learning session. In addition, spatial variability in the left and right elbows decreased within the intermediate compared to the early learning session. The results suggest that temporal control of mallet movements may be driven by reductions in spatial variability of elbow movements specifically. As a result, this study provides novel evidence for kinematic mechanisms underlying motor learning in percussion which can be applied towards enhancing musical training. (shrink)

Georges Palante, figure oubliée de la sociologie naissante, fut le théoricien d'une révolte intransigeante de l'individu face aux mécanismes oppressifs déployés par la société. Lecteur de Nietzsche et de Schopenhauer, ennemi déclaré des durkheimiens, socialiste non marxiste, farouche défenseur de l'individu, Georges Palante est un penseur iconoclaste qui n'a eu de cesse de développer une éthique individualiste et libertaire en vue du plein épanouissement des facultés et des potentialités individuelles. Cependant, par un étrange paradoxe, l'éthique palantienne prend sa source dans (...) une philosophie pessimiste qui offre à la révolte un caractère tragique et indompté : elle doit avoir lieu et ce, malgré la certitude de sa défaite. C'est précisément ce paradoxe que cet ouvrage entend questionner tout en offrant une introduction à l'oeuvre de Georges Palante. Interroger la possibilité d'une révolte pessimiste, c'est interroger ce moment de l'insoumission et de la désobéissance propre à la condition humaine. Palante ouvre la voie qui inscrit la révolte et le mouvement du refus dans la constitution même de l'homme. Avec Albert Camus, Palante pourrait affirmer : "Qu'est-ce qu'un homme révolté? Un homme qui dit non. Mais s'il refuse, il ne renonce pas : c'est aussi un homme qui dit oui dès son premier mouvement.". (shrink)

Résumé Ni le présentisme, ni l’éternalisme ne peuvent rendre compte de l’ensemble des modalités du temps. La théorie dite du « Growing Block Universe », qui nie la réalité du futur mais concède le même degré de réalité au passé qu’au présent, n’est pas non plus entièrement satisfaisante. Nous proposons donc de distinguer des intensités de présence : l’avenir a une absence maximale et le présent une présence maximale. Il en résulte que, à mesure que le temps passe, nous nous (...) éloignons de l’avenir. (shrink)

This paper is a conceptual study in the philosophy of logic. The question considered is 'How may formulae of the propositional calculus be brought into a representational relation to the world?'. Four approaches are distinguished: (1) the denotational approach, (2) the abbreviational approach, (3) the truth-conditional approach, and (4) the modelling approach. (2) and (3) are very familiar, so I do not discuss them. (1), which is now largely obsolete, led to some interesting twists and turns in early analytic philosophy (...) which will come as news to many contemporary readers, so I discuss it in some detail. The modelling approach is, to the best of my knowledge, newly introduced here. I am not presenting it as a rival to the other approaches, but as a philosophically interesting possibility. (shrink)

I argue that the unthought philosophical bias in favor of seriousness and sense rather than nonsense and joking blocks the path to reality. Because of this bias we obsess over significant signs and forget to consider what signs are signs of; we lose sight of the forest because there are so many interesting trees. Through a thoroughgoing interrogation of signs or appearances, we can reveal what it is that all signs present or represent: the underlying real joke. Once the “sensible (...) bias” of philosophy is overcome and the sense of nonsense restored, we can reveal the object of ontology—the Kantian noumenon—and, therefore, understand the necessary order of signification or representation. In this way, I argue, we can come to be equally amused by all appearances, recognizing that their deceptive character is necessitated by the playful nature of the real thing which, qua joke, provokes amusement. (shrink)

Edmund Burke was an Irish-born British statesman and political philosopher who is best known as the father of modern conservatism. Developed in response to the French Revolution, Burke's conservatism aims to preserve and promote the existing (or traditional) institutions of society, including the rule of law, property, the family, and religion. Burke himself sought to defend these things, as embodied in the British Constitution, against the revolutionary spirit sparked in France. In his Reflections on the Revolution in France, Burke develops (...) the idea of society as an inheritance that must be conserved before it can be improved upon. In this piece, we examine Burke’s arguments, which draw on tradition, observable cause and effect, and a mix of moral and religious sentiments. Contrary to expectations, Burke insists that the principles of conservation and change are not opposed. (shrink)

A oposição às taxas universitárias e a outras barreiras de acesso é, muitas vezes, encarada como uma defesa do ensino superior como um “direito”, ao invés de um “privilégio”. No entanto, a base e a natureza desse direito não são claras. Este artigo apresenta uma exploração conceitual da questão a partir de uma análise inicial do direito internacional. Apresenta um argumento a favor do direito à educação superior, visto como uma das várias formas possíveis de educação pós-escolar, restrito apenas por (...) uma exigência de um nível mínimo de preparação acadêmica. Palavras-chave: Acesso à educação superior. Ação afirmativa. Política de educação superior. Direitos humanos. Direito à educação. (shrink)

This paper suggests a new emendation to the text of the final passage of Pliny's Panegyric, where a small lacuna has long been suspected after substiti.

Justice under Law Law and justice are near synonyms in common speech. We expect the law to deliver justice, and we cannot imagine justice absent some system of law. In his recent book, Justice before the Law, Michael Huemer challenges this traditional view of law and justice. Given the prevalence of unjust laws and legal practices in the United States, and the deference shown to law by agents of the American legal system, Huemer argues that we ought to affirm the (...) primacy of justice over the law. This article argues that Huemer is right about the primacy of justice, but he errs in his understanding of what justice is, and the means through which it is best achieved. Law operates as a form of enquiry that seeks to discover what justice is. Law is a necessary means to justice. True justice must be justice under law. (shrink)

Although research in ecopsychology commonly identifies the value of spiritual experiences in nature for psychological well-being and environmental behaviour, previous research has not compared the outcomes of these experiences in natural and human-built settings. In the present study, the relationship between self-reported mystical experiences in natural and human-built environments for psychological well-being and environmental behaviour was investigated. A sample of 305 participants completed an amended version of Hood's Mysticism Scale, a measure of psychological well-being, and brief environmental behaviour scale. Correlations (...) indicated that mystical experiences in natural and in human-built environments both significantly predicted psychological well-being, but only mystical experiences in natural settings predicted environmental behaviour. This study suggests that mystical experiences in natural and human-built environments may be related to different outcomes. (shrink)

Résumé Depuis la publication en français du Léviathan de Carl Schmitt, l’antisémitisme du juriste a constitué, en France, le cœur des débats autour de la pensée du théoricien du politique. Dans cet article, l’auteur tente d’approcher l’aversion du penseur catholique à l’égard du judaïsme en privilégiant un angle bien particulier. Partant des phénomènes bibliques et des thèmes religieux présents dans les écrits du penseur allemand, cet article cherche à évaluer l’intuition d’après laquelle il existerait une affinité intellectuelle entre Schmitt et (...) Marcion ; intuition entendue çà et là, qui réclame un approfondissement spécifique. Pour ce faire, l’auteur formule l’hypothèse d’un « marcionisme théologico-politique » qu’il tente d’appliquer et de tester à travers l’entière trajectoire de l’œuvre de Schmitt. L’enjeu étant de savoir si, pour le juriste catholique, les implications théologiquement politiques du judaïsme seraient, oui ou non, radicalement incompatibles avec celles du christianisme. (shrink)

Cultural capital and hegemonic masculinity are two concepts that have received intense attention. While both have received serious consideration, critique and analysis, the context or field-specificity of each is sometimes ignored. They have been used in a diversity of ways. Using ethnographic and interview data from a US male bodybuilding community, this study highlights one useful employment. Hegemonic masculinity takes different shapes in different fields of interaction, acting as a form of cultural capital: gender capital. Inherent in this discussion are (...) the cultural contradictions apparent among individuals striving for either physical or ideological embodiments of gender capital. Individuals can attempt to embody hegemonic idealizations, but bodies are not only inscribed with gender, inscriptions are read, and read differently by different social actors and in different settings. The capacity of gender capital to remain elusive is precisely what enables gender practices and projects like bodybuilding to retain passionate participation. (shrink)

State Medical Boards (SMBs) can take severe disciplinary actions (e.g., license revocation or suspension) against physicians who commit egregious wrongdoing in order to protect the public. However, there is noteworthy variability in the extent to which SMBs impose severe disciplinary action. In this manuscript, we present and synthesize a subset of 11 recommendations based on findings from our team’s larger consensus-building project that identified a list of 56 policies and legal provisions SMBs can use to better protect patients from egregious (...) wrongdoing by physicians. (shrink)

Over the years, phenomenology has provided illuminating descriptions of discrimination, with its mechanisms and effects being thematised at the most basic levels of embodiment, (dis)orientation, selfhood, and belonging. What remains somewhat understudied is the lived experience of the discriminator. In this paper I draw on Husserl's phenomenological account of normality to reflect on the ways in which we discriminate at the prereflective levels of perceptual experience and bodily being. By critically reflecting on the intentional structures undergirding discriminatory practices, I argue (...) that discrimination is characteristic of a naïve normalising attitude which is habitually interested in securing a familiar experience of a static normality. I first demonstrate how this attitude problematically tends to reproduce, enforce, and further sediment discriminatory and exclusionary norms. Further, I provide an internal critique which problematises discrimination—without recourse to external normative standards—on three fronts: as epistemically unproductive, experientially obscuring, and normatively non-instantiating. In discriminatory acts we see an abnormal refusal to enrich, revise, and genetically establish new normative commitments, new ways of seeing, and a new normality. (shrink)

This article addresses a paradoxical stance taken by young straight men in three groups who identify aspects of themselves as “gay” to construct heterosexual masculine identities. By subjectively recognizing aspects of their identities as “gay,” these men discursively distance themselves from stereotypes of masculinity and privilege and/or frame themselves as politically progressive. Yet, both of these practices obscure the ways they benefit from and participate in gender and sexual inequality. I develop a theory of “sexual aesthetics” to account for their (...) behavior and its consequences, contributing to a growing body of theory regarding the hybridization of contemporary masculinities and complicating theories of sexual practice. (shrink)

Les logiciels d’aide à la décision basés sur des techniques d’intelligence artificielle sont de plus en plus utilisés dans le domaine de la justice. Or ces techniques nécessitent souvent d’accéder à de grandes quantités d’informations personnelles afin de réaliser un apprentissage de qualité. En France, le cadre légal semble aujourd’hui favorable à l’ouverture des jugements, pourvu que la vie privée des personnes concernées soit respectée. Cependant, la protection des données personnelles destinées à être publiées reste difficile techniquement. Cet article a (...) pour objectif de décrire une attaque minimaliste qui a été réalisée en 2014 sur un jeu de données protégé par l’application d’un algorithme de pseudonymisation. L’originalité de cette attaque réside dans sa simplicité de fonctionnement – elle ne nécessite pas d’accès à un jeu de données auxiliaire – et dans sa cible – l’algorithme de pseudonymisation. Nous présentons la famille des algorithmes de pseudonymisation, décrivons et analysons l’attaque, et concluons sur la place de la pseudonymisation dans le Règlement Général sur la Protection des Données personnelles. (shrink)

The notion of rigidity looms large in philosophy of language, but is beset by difficulties. This paper proposes a simple theory of rigidity, according to which an expression has a world-relative semantic property rigidly when it has that property at, or with respect to, all worlds. Just as names, and certain descriptions like The square root of 4, rigidly designate their referents, so too are necessary truths rigidly true, and so too does cat rigidly have only animals in its extension. (...) After spelling out the theory, I argue that it enables us to avoid the headaches that attend the misbegotten desire to have a simple rigid/non-rigid distinction that applies to expressions, giving us a simple solution to the problem of generalizing the notion of rigidity beyond singular terms. (shrink)

Educational undertakings are subject to disjunctures at three separate stages: in the creation of curricular programmes, in the implementation of these curricula in practice and in their effects on students. These disjunctures are the result of complex ‘leaps’ between ends and means, and between ideal and real. This article proposes a response in the form of ‘seamless enactment’, applied here to citizenship education. Seamless enactment involves, first, the harmonisation of the principles underlying the different stages in the passage of the (...) curriculum, avoiding problematic tensions between, for example, democratic aims and undemocratic teaching practices. Second, it requires the involvement of teachers and students in the design and development of the educational initiative, as well as in its implementation. Taken to its fullest extent, seamless enactment involves a unification of the separate stages, leading to the collapsing of the curricular transposition framework onto a single point. Finally, some possible justifications for and potential objections to the notion are considered. (shrink)

Two sets are said to be almost disjoint if their intersection is finite. Almost disjoint subsets of [ω]ω and ωω have been studied for quite some time. In particular, the cardinal invariants \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{a}}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{a}_e}$$\end{document}, defined to be the minimum cardinality of a maximal infinite almost disjoint family of [ω]ω and ωω respectively, are known to be consistently less than \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} (...) \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{c}}$$\end{document}. Here we examine analogs for functions in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}^\omega}$$\end{document} and projections on l2, showing that they too can be consistently less than \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{c}}$$\end{document}. (shrink)