This paper is intended to give for a general mathematical audience a survey of intriguing connections between analytic combinatorics and logic. We define the ordinals below ε0 in non-logical terms and we survey a selection of recent results about the analytic combinatorics of these ordinals. Using a versatile and flexible compression technique we give applications to phase transitions for independence results, Hilbert’s basis theorem, local number theory, Ramsey theory, Hydra games, and Goodstein sequences. We discuss briefly universality and renormalization issues (...) in this context. Finally, we indicate how regularity properties of ordinal count functions can be used to prove logical limit laws. (shrink)

We give a self-contained and streamlined version of the classification of the provably computable functions of PA. The emphasis is put on illuminating as well as seems possible the intrinsic computational character of the standard cut elimination process. The article is intended to be suitable for teaching purposes and just requires basic familiarity with PA and the ordinals below ε0. (Familiarity with a cut elimination theorem for a Gentzen or Tait calculus is helpful but not presupposed).

In this article I will discuss some systematic issues of Arthur Danto's philosophy of art and art history from a Hegelian perspective. Belonging to "Absolute Spirit," art can be called a "spiritual kind." Since spiritual kinds are reflective and self-determining, they are not susceptible to philosophical definition. Nevertheless, elements of essentialism can be maintained when describing art's historicity and conceptual structure. To this end, "art" can be interpreted as a two-tier concept: in inherently reflecting its concept, it projects its own (...) conditions into the past, co-opting "prehistorical" artworks as predecessors and classical examples. Hegel's view of art as conceptually structured in itself can have disenfranchising or reenfranchising consequences: either reducing art to minor philosophy, or acknowledging its privileged access to its own essence. After Danto's detachment of the philosophy of art from aesthetics, Hegel would himself be deprived of the possibility to "define" art by intuition . Even if the spirit consists of essential kinds, philosophy is not in a privileged position to establish the essence of art and thus the difference between art and philosophy. Rather, philosophy must acknowledge art as a neighbor and as partner in a dialogue. (shrink)

Reflexivity does not presuppose linguistic articulation or even propositional content. If it did, art could not be called reflexive. Reflexivity can be found in the self-contact of the living, in mental reflection or in symbolic self-reference. Art is a medium which claims these different modes of reflexivity and intertwines them. Aesthetic reflexivity as such has been established by Kant and his epigones, following the model of transcendetal reflection. Thus it could be specified as the reflexive structure of aesthetic judgement, or (...) as an emphasis on a work’s being created, or as a reference to perception itself in the process of perceiving, or as a way of reflecting concepts. Aesthetic reflexivity can only be detached from the model of transcendental reflection, if it is seen as oriented towards the interaction among the three modes of reflection mentioned above, leaving aside the difference, interplay or competition between perception and conceptual capacities. (shrink)

Spinal muscular atrophy (SMA) type 1 is a genetic neuromuscular disease in children that leads to degeneration of spinal cord motor neurons. This sometimes results in severe muscular paralysis requiring mechanical ventilation to sustain the child’s life. The onset of SMA type 1, the most severe form of the disease, is during the first year of life. These children become severely paralysed, but retain their intellectual capacity. Ethical concerns arise when mechanical ventilation becomes necessary for survival. When professionals assess the (...) resulting life for the child and family, they sometimes fear it will result in unreasonably excessive care. The aim of this article is to present an analysis of ethical arguments that could support or oppose the provision of invasive ventilation in this population. This examination is particularly relevant as France is one of the few countries performing tracheotomies and mechanical ventilation for this condition. (shrink)

This paper deals with some structural properties of the sequent calculus and describes strong symmetries between cut-free derivations and derivations, which do not make use of identity axioms. Both of them are discussed from a semantic and syntactic point of view. Identity axioms and cuts are closely related to the treatment of negation in the sequent calculus, so the results of this article explain some nice symmetries of negation.

This is the first day of our confinement here in Paris, which soon will feel a bit like house arrest. So, to help cheer you up, in these times of doom and gloom, I have decided to bring the museum to you in the form of a virtual exhibition thrice weekly. I have picked 25 photos from a work in progress I started years ago. The photos are portraits of visitors or guards in museums. It's candid photography, capturing life on (...) the run, a moment in time. I hope you will find many other ways to - Résidence numérique - Brigitte Cavanagh. (shrink)

It is shown that the so called slow growing hierarchy depends non trivially on the choice of its underlying structure of ordinals. To this end we investigate the growth rate behaviour of the slow growing hierarchy along natural subsets of notations for $\Gamma_0$. Let T be the set-theoretic ordinal notation system for $\Gamma_0$ and $T^{tree}$ the tree ordinal representation for $\Gamma$. It is shown in this paper that $_{\alpha \in T}$ matches up with the class of functions which are elementary (...) recursive in the Ackermann function as does $_{\alpha \in T^{tree}}$. By thinning out terms in which the addition function symbol occurs we single out subsystems $T* \subseteq T$ and $T^{tree*} \subseteq T^{tree}$ and prove that $_{\alpha \in T^{tree*}}$ still matches up with $_{\alpha \in T^{tree}}$ but $_{\alpha \in T*}$ now consists of elementary recursive functions only. We discuss the relationship between these results and the $\Gamma_0$-based termination proof for the standard rewrite system for the Ackermann function. (shrink)

This paper aims to determine whether we can locate temporal passage in a non-dynamical (block universe) world. In particular, we seek to determine both whether temporal passage can be located somewhere in our world if it is non-dynamical, and also to home in on where in such a world temporal passage can be located, if it can be located anywhere. We investigate this question by seeking to determine, across three experiments, whether the folk concept of temporal passage can be satisfied (...) in our world if it is non-dynamical, and, if it can, what sort of thing in our world satisfies that concept. In particular, we focus on the question of whether that concept (if satisfied) is satisfied by something mind-dependent or something mind-independent. In other words, we ask, is temporal passage something that is at least partially in the mind, or is it entirely external to the mind? We find, contrary to what is often assumed by dynamists and non-dynamists alike, that the folk concept of temporal passage is satisfied in our world conditional on it being non-dynamical, and that the concept is satisfied by something mind-independent. This provides further ammunition for recent deflationary accounts of temporal passage that attempt to locate passage somewhere in our non-dynamical world. (shrink)

We introduce strong Goodstein principles which are true but unprovable in strong impredicative theories like IDn.

Grace de Laguna was a philosopher working in the first part of the twentieth century on analytic and speculative philosophy, as well as on the psychology and philosophy of language, especially the social function of language. Joel Katzav’s lead essay focuses mainly on the former part of her work, while my commentary focuses mostly on the latter. Katzav shows how her work played a role in the development of analytic philosophy, I try to show how her work played a role (...) in the development of pragmatic linguistics, whose development overlapped with some aspects of analytic philosophy. I situate it in the context of an emerging ‘pragmatic Weltanschauung’ that was embraced by many working in linguistics, philology, philosophy, psychology, anthropology and what would later be called linguistic pragmatics. (shrink)

Gödel’s first incompleteness result from 1931 states that there are true assertions about the natural numbers which do not follow from the Peano axioms. Since 1931 many researchers have been looking for natural examples of such assertions and breakthroughs were obtained in the seventies by Jeff Paris [Some independence results for Peano arithmetic. J. Symbolic Logic 43 725–731] , Handbook of Mathematical Logic, North-Holland, Amsterdam, 1977] and Laurie Kirby [L. Kirby, Jeff Paris, Accessible independence results for Peano Arithmetic, Bull. of (...) the LMS 14 285–293]) and Harvey Friedman [S.G. Simpson, Non-provability of certain combinatorial properties of finite trees, in: Harvey Friedman’s Research on the Foundations of Mathematics, North-Holland, Amsterdam, 1985, pp. 87–117; R. Smith, The consistency strength of some finite forms of the Higman and Kruskal theorems, in: Harvey Friedman’s Research on the Foundations of Mathematics, North-Holland, Amsterdam, 1985, pp. 119–136] who produced the first mathematically interesting independence results in Ramsey theory and well-order and well-quasi-order theory .In this article we investigate Friedman-style principles of combinatorial well-foundedness for the ordinals below ε0. These principles state that there is a uniform bound on the length of decreasing sequences of ordinals which satisfy an elementary recursive growth rate condition with respect to their Gödel numbers.For these independence principles we classify their phase transitions, i.e. we classify exactly the bounding conditions which lead from provability to unprovability in the induced combinatorial well-foundedness principles.As Gödel numbering for ordinals we choose the one which is induced naturally from Gödel’s coding of finite sequences from his classical 1931 paper on his incompleteness results.This choice makes the investigation highly non-trivial but rewarding and we succeed in our objectives by using an intricate and surprising interplay between analytic combinatorics and the theory of descent recursive functions. For obtaining the required bounds on count functions for ordinals we use a classical 1961 Tauberian theorem of Parameswaran which apparently is far remote from Gödel’s theorem. (shrink)

On 14 July 2021, the western states of Germany, Rheinland Palatinate and North-Rhein-Westphalia experienced major flash floods and about two hundred people died. This article explores how those affected and journalists they spoke to created meaning from the mayhem of an unprecedented disaster and how social representations of flooding emerged in which language, politics and values were intimately intertwined. Combining thematic analysis with elements of social representations theory, and analysing a sample of articles from a national news magazine, we show (...) how social representations of the floods were shaped by the objectification of the floods through metonymy (mud and debris) and the anchoring of the floods through personification and metaphors (natural and mechanical forces), thus adding a new dimension to the existing body of work on flood and metaphors. We claim that the immediate focus on the extreme force of the 2021 floods, on the one hand, and the weakness of political response, on the other, may entrench feelings of helplessness and divert attention away from more systematic and long-term engagement with flood dangers in the context of climate change, including extreme weather events. (shrink)

This article provides a detailed comparison between two systems of collapsing functions. These functions play a crucial role in proof theory, in the analysis of patterns of resemblance, and the analysis of maximal order types of well partial orders. The exact correspondence given here serves as a starting point for far reaching extensions of current results on patterns and well partial orders. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Inspired by Pohlers' proof-theoretic analysis of KPω we give a straightforward non-metamathematical proof of the (well-known) classification of the provably total functions of $PA, PA + TI(\prec\lceil)$ (where it is assumed that the well-ordering $\prec$ has some reasonable closure properties) and KPω. Our method relies on a new approach to subrecursion due to Buchholz, Cichon and the author.

Does incommensurability threaten the realist’s claim that physical magnitudes express properties of natural kinds? Some clarification comes from measurement theory and scientific practice. The standard (empiricist) theory of measurement is metaphysically neutral. But its representational operational and axiomatic aspects give rise to several kinds of a one-sided metaphysics. In scientific practice. the scales of physical quantities (e.g. the mass or length scale) are indeed constructed from measuring methods which have incompatible axiomatic foundations. They cover concepts which belong to incomensurable theories. (...) I argue, however, that the construction of such scales conmmits us to a modest version of scientific realism. (shrink)

This article discusses how Merleau-Ponty’s existential phenomenology may serve as the lens and theoretical frame in a qualitative research study of the lived experience of patients, their families, and nurses during critical illness in the intensive care unit. Merleau-Ponty's unique existential concepts of corporeality, spatiality, temporality, and relationality provide a useful foundation and serve as a unifying philosophy of science in understanding this nursing phenomenon that is grounded in philosophical beliefs about humans, and the holistic nature of professional nursing that (...) is not amenable to experimental investigative research methods. The research sheds light on the patients, families, and nurses’ embodied temporal, spatial, and relational horizons, and reveals a new conception of critical illness that will provide caregivers with knowledge about effective humanistic, and more holistic care, that opens new ways for coping amongst patients and their families, as well as caregiving possibilities for the nurses. Findings from this qualitative inquiry can help contribute knowledge about family engagement that would impact the provision of care in the intensive care unit, thus improving patient, family, and organizational outcomes. (shrink)

The slow growing hierarchy is commonly defined as follows: G0 = 0, Gx−1 := Gx + 1 and Gλ := Gλ[x] where λ<0 is a limit and ·[·]:0∩ Lim × ω → 0 is a given assignment of fundamental sequences for the limits below 0. The first obvious question which is encountered when one looks at this definition is: How does this hierarchy depend on the choice of the underlying system of fundamental sequences? Of course, it is well known and (...) easy to prove that for the standard assignment of fundamental sequence the hierarchy x<0 is slow growing, i.e. each Gx is majorized by a Kalmar elementary recursive function.It is shown in this paper that the slow growing hierarchy x<0 — when it is defined with respect to the norm-based assignment of fundamental sequences which is defined in the article by Cichon — is actually fast growing, i.e. each PA-provably recursive function is eventually dominated by Gx for some α<0. The exact classification of this hierarchy, i.e. the problem whether it is slow or fast growing, has been unsolved since 1992. The somewhat unexpected result of this paper shows that the slow growing hierarchy is extremely sensitive with respect to the choice of the underlying system of fundamental sequences.The paper is essentially self-contained. Only little knowledge about ordinals less than 0 — like the existence of Cantor normal forms, etc. and the beginnings of subrecursive hierarchy theory as presented, for example, in the 1984 textbook of Rose — is assumed. (shrink)

After the UN Guiding Principles on Business and Human Rights were adopted in 2011, an international treaty has been being negotiated since 2014. The two instruments reveal similarities and also conflicts regarding the adequate organization of the global economy based on human rights. The focus in this article will be on the processes leading to these instruments, because they themselves mirror different understandings of governance in the field of business and human rights as well as the struggle over the power (...) of definition and legitimacy. The UNGPs were developed on the basis of global multi-stakeholder consultations, underlining legitimacy through broad inclusion. There are varying judgements as to the success of this approach. The process towards the treaty follows the traditional path of negotiations at UN level. These negotiations reveal a struggle for recognition of the legitimacy of the process itself. Both procedures have shortcomings with regard to legitimacy and show the need for a revision concerning the inclusion of stakeholders. The complementarity of a soft and hard law instrument may enhance the creation of a level playing field in the global economy, thereby strengthening human rights. (shrink)

Astroparticle physics is a recent sub-discipline of physics that emerged from early cosmic ray studies, astrophysics, and particle physics. Its theoretical foundations range from quantum field theory to general relativity, but the underlying “standard models” of cosmology and particle physics are far from being unified. The paper explores the pragmatic strategies employed in astroparticle physics in order to unify a disunified research field, the concept of observation involved in these strategies, and their relations to scientific realism.

In this paper we calibrate the exact proof-theoretic strength of Kruskal's theorem, thereby giving, in some sense, the most elementary proof of Kruskal's theorem. Furthermore, these investigations give rise to ordinal analyses of restricted bar induction.

Par son rôle déterminant dans la réussite scolaire et professionnelle, ainsi que dans l’insertion sociale, l’apprentissage de l’orthographe lexicale représente un défi majeur pour les élèves du primaire. Dans ce contexte, nombreux sont les enseignants, orthophonistes et chercheurs à s’intéresser à la question des outils utiles à son enseignement et à son apprentissage, et à avoir recours notamment à des bases de données lexicales. Bien qu’elles constituent un apport considérable pour le domaine, les ressources existantes souffrent de plusieurs insuffisances. D’une (...) part, elles s’appuient sur des corpus de référence peu représentatifs du lexique scolaire auquel les élèves sont exposés au primaire, et d’autre part, elles ne permettent pas aux utilisateurs de déterminer la façon dont se développe l’acquisition de l’orthographe lexicale. À la lumière de ces constats, nous avons élaboré une ressource lexicale hybride, rendant compte à la fois de la fréquence et des caractéristiques linguistiques du lexique scolaire présent dans les manuels du primaire au Québec et, pour une partie des mots de ce lexique, de la capacité des élèves à les orthographier à chaque niveau du primaire. Dans cet article, nous revenons dans un premier temps sur la méthodologie d’élaboration de cette nouvelle base de données - nommée ÉQOL - dotée d’une Échelle Québécoise d’acquisition de l’Orthographe Lexicale, à l’origine de la création de la base de données. Dans un deuxième temps, nous évaluons l’apport de cet outil. La comparaison de notre base de données (Stanké, Royle, Rezzonico, Moreau, Dumais & Le Mené 2018) à des outils existants (trois bases de données et une échelle d’acquisition lexicale) témoigne de la pertinence de la création d’un outil propre au lexique scolaire adressé aux élèves du primaire et de la nécessité d’utiliser une nouvelle échelle d’acquisition de l’orthographe lexicale, spécifique aux compétences orthographiques des élèves québécois. (shrink)

Welche Erkenntnisse bietet Michel Foucaults Ansatz der Gouvernementalität für eine politische Theorie, die Geschlecht als zentrale Kategorie setzt? In diesem Band werden Grundbegriffe aus Foucaults Spätwerk aus feministischer Sicht beleuchtet, z.B. Gouvernementalität, Macht, Staat, Subjekt, Sicherheit, Wissen und Kritik. Diese Re-Lektüre möchte zum einen Foucaults Ansatz geschlechtertheoretisch weiterentwickeln und vertiefen, zum anderen Anstöße für eine politische Theoretisierung von Geschlecht geben.

It is widely believed by historians of linguistics that the 19th-century was largely devoted to historical and comparative studies, with the main emphasis on the discovery of soundlaws. Syntax is typically portrayed as a mere sideline of these studies, while semantics is seldom even mentioned. If it comes into view at all, it is usually assumed to have been confined to diachronic lexical semantics and the construction of some (mostly ill-conceived) typologies of semantic change. This book aims to destroy some (...) of these prejudices and to show that in Europe semantics was an important, although controversial, area at that time. Synchronic mechanisms of semantic change were discovered and increasing attention was paid to the context of the sentence, to the speech situation and the users of the language. From being a semantics of transformations', a child of the biological-geological paradigm of historical linguistics with its close links to etymology and lexicography, the field matured into a semantics of comprehension and communication, set within a general linguistics and closely related to the emerging fields of psychology and sociology. (shrink)

This article explores a German philosophy of metaphor, which proposed a close link between the body and the mind as the basis for metaphor, debunked the view that metaphor is just a decorative rhetorical device and questioned the distinction between the literal and the figurative. This philosophy of metaphor developed at the intersection between a reflection on language and thought and a reflection on the nature of beauty in aesthetics. Thinkers such as Giambattista Vico, Johann Wolfgang von Goethe, Jean Paul (...) and others laid the foundations for this philosophy and it was successively refined by Gustav Gerber, Alfred Biese and Friedrich Nietzsche. It influenced in its turn in various ways the linguistic study of metaphor and the psychology of metaphor as elaborated, for instance, by a lesser-known American scholar, Gertrude Buck. All these thinkers contributed to a philosophy and psychology of the metaphoric according to which metaphors are not only nice, but necessary for the structure and growth of human thought and language. Obvious parallels between this 19th-century philosophy of metaphor and the 20th-century theory of metaphor developed by Lakoff and his followers are examined throughout. (shrink)

For f: On → On let supp: = ξ: 0, and let S := {f : On → On : supp finite}. For f,g ϵ S definef ≤ g : ↔ [h one-to-one ⁁ f ≤ g)].A function ψ : S → On is called monotonic increasing, if f≤ψ and if f ≤ g implies ψ ≤ ψ. For a mapping ψ : S → On let Clψ be the least set T of ordinals which contains 0 as an element (...) and which is closed under the following rule: If f ϵ S, range ⊆ T and supp ⊆ T, then ψ ϵ T. Let φ be the enumeration function of the class {ξ: [ξ = ωn]}. Let φ be the induced Schütte-Klammerterm-function which generates the Schütte-Veblen-hierarchy of ordinals. Then φ is monotonic increasing. We show: If ψ: S → On is monotonic increasing, then otyp) ≤ min {ξ : ξ = Φ, where 1ξ = 1 if α = ξ and 1ξ = 0 if α ↔ = 0 if α ≠ ξ. For τ an ordinal let Sτ := {f ϵ S : supp ⊆ τ}. A function ψ : Sτ → On is called τ-monotonic increasing if fξ and if f ≤ g implies ψ ≤ . For a function ψ Sτ → On let Clψ ↔ τ be the least set T of ordinals, which contains 0 as an element, such that if f ϵ Sτ and range ϵ T, then ψ ϵ T. We show: if ≥2 and if ψ Sτ → On is τ-monotonic increasing, then otyp ↔ τ) ≤. We also prove a generalization of this theorem in terms of well-partial orderings. MSC: 03F15, 03E10, 06A06. (shrink)

One of the first Swiss performance artists, Manon has fashioned a career for herself out of the identities of others. Whether exploring the limits of gender or the beauty of decay, Manon—through her personas, installations, and performance pieces—continually foregrounds the instability of place and self. Her most recent project, She Was Once MISS RIMINI, is one of her most brutal and touching. Here, she literally depicts imagined futures for an aging beauty queen. Each exquisite image in this pictorial essay teases (...) out the possible paths Miss Rimini—an alter-ego for Manon who “happened” upon a beauty pageant in the early 1970s and walked away with the crown—could have taken. A small-town diva? A hypersensitive viola player? Perhaps even a psychiatric patient? She Was Once MISS RIMINI is a trenchant meditation on the art, or artifice, of growing older. Costume, lipstick, lighting, attitude—all aspects of self-presentation are in concert here with quiet critiques of social and economic systems that limit the options of older women. Accompanied by an enlightening introduction by art theorist Brigitte Ulmer, She Was Once MISS RIMINI is the first and only documentation of Miss Rimini and one of the first books in English on Manon. (shrink)

Communicating Biological Sciences discusses the 'ethics' of science communication in light of recent developments in biotechnology and biomedicine. It focuses on the role of metaphors in the creation of visions and the framing of scientific advances, as well as their impact on patterns of public acceptance and rejection, trust and scepticism. Its rigorous investigation will appeal not only to science writers and scientists, but also to scholars of sociology, science and technology studies, media and journalism.

Im Dezember 2014 fand das erste zweitatige Symposium von der SWIP (Society of Women In Philosophy) Austria statt, unter dem Titel: Neuere Aspekte in der Philosophie - aktuelle Projekte von Philosophinnen am Forschungsstandort Osterreich." Als Resultat dieser Tagung soll der vorliegende Band die Breite und Pluralitat der Themen und die Themenoffenheit widerspiegeln. Er enthalt 22 Beitrage aus den verschiedensten Teildisziplinen der Philosophie, wie feministische Sprachphilosophie, Performance/Philosophie, Erkenntnis- und Wissenschaftstheorie, Wissenschaftsgeschichte, philosophische Bezugnahme auf Literatur, feministisch-philosophische Literaturbetrachtung, praktische Philosophie, Religion und Ethik, (...) interkulturelle Philosophie, feministisch-politische Theorie, feministische Sozialphilosophie und queere Perspektiven.". (shrink)

Contrairement à ce que l’on entend généralement par mécénat - la commande d’images, peintes ou sculptées, passée entre deux individus vivants – on propose ici d’en élargir les termes pour y englober une autre modalité de la circulation des biens culturels : l’héritage, particulièrement significatif pour les femmes, qui disposaient souvent d’un important patrimoine artistique sans en avoir été les commanditaires. En examinant la manière dont Blanche de Navarre († 1398), épouse de Philippe VI de Valois et reine douairière pendant (...) près d’un demi-siècle, disposa de ses objets les plus précieux, joyaux et livres, dans un testament exceptionnel par son détail, l’accent est mis sur l’acte de tester comme un moment créateur, sinon d’objets, du moins de faits sociaux. Car, par la distribution savante de ses objets, Blanche construisit, pour ses successeurs, une mémoire, solidifiée dans des choses, des liens unissant les membres épars, vivants ou morts, de sa parenté. (shrink)