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 book, first published in 2000, offers translations of the initial critical reactions to Kant's philosophy. Also included is a selection of writings by Kant's contemporaries who took on the task of defending the critical philosophy against early attacks. The first aim of this collection is to show in detail how Kant was understood and misunderstood by his contemporaries. The second aim is to reveal the sorts of arguments that Kant and his first disciples mounted in their defense of the (...) theoretical philosophy. The third aim of the book is to contribute to an understanding of the development of Kant's critical philosophy after its initial formulation in the Critique of Pure Reason, and in particular why Kant made the changes he did in the second edition of the work in 1787. This collection, which includes a glossary of key terms and biographical sketches of the critics on both sides of the debate, is a major addition to Kant scholarship and should be seen as a companion volume to the Cambridge Edition of the Works of Immanuel Kant. (shrink)

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)

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).

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)

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.

The aim of this dissertation is twofold: first, to provide an account of the notion of creativity, and second, to consider some aspects of the scope of the concept of creativity, in particular whether it makes sense to speak of creativity in science. ;With regard to the first issue, I argue that creativity consists in the production of a radically new intelligibility and that for this production special, creative processes are required. The latter point is established through an analysis of (...) non-creative processes, which in turn is provided in terms of Kant's notion of schemata, interpreted as patterns of cognition. My claim is that these processes are not sufficient to bring about the radically new intelligibility that characterizes creative outcomes. The creative process is properly to be analysed through a consideration of Kant's conception of artistic genius and reference to some recent work in psychology. ;The final chapter treats the second issue, the topic of creativity in the sciences. I question whether it makes sense to speak of creativity in science. I argue that since the sciences provide radically novel, yet intelligible, ways of understanding the world, creativity is required here as well. (shrink)

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)

La Renaissance commence vraiment avec Pléthon, contemporain de Nicolas de Cues et qui se voulait comme lui romain, mais du point de vue de Constantinople. Pléthon a conçu le modèle d'une constitution qui permettrait à tous les peuples de coexister en paix. Au temps où l'Occident latin est largement aristotélicien, il plaide pour le retour à Platon, l'idéalisme, la théologie affirmative.

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)

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.

Selbstgerechtes Wohlwollen in der Psychoanalyse - J. Körner: Mitleid. Das Ende der Empathie - II. Moral und das Böse - P. Stoellger: Lesarten des Bösen - R. Bittner: Verwüstung durch Moral? - III. Moral als Gewalt?

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)

The roots of pragmatics reach back to Antiquity, especially to rhetoric as one of the three liberal arts. However, until the end of the 18th century proto-pragmatic insights tended to be consigned to the pragmatic, that is rhetoric, wastepaper basket and thus excluded from serious philosophical consideration. It can be said that pragmatics was conceived between 1780 and 1830 in Britain, but also in Germany and in France in post-Lockian and post-Kantian philosophies of language. These early ‘conceptions’ of pragmatics are (...) described in the first part of the book. The second part of the book looks at pragmatic insights made between 1830 and 1880, when they were once more relegated to the philosophical and linguistic underground. The main stage was then occupied by a fact-hunting historical comparative linguistics on the one hand and a newly spiritualised philosophy on the other. In the last part the period between 1880 and 1930 is presented, when pragmatic insights flourished and were sought after systematically. This was due in part to a new upsurge in empiricism, positivism and later behaviourism in philosophy, linguistics and psychology. Between 1780 and 1930 philosophers, psychologists, sociologists and linguists came to see that language could only be studied in the context of dialogue, in the context of human life and finally as being a kind of human action itself. (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)

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)

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)

Hauptbeschreibung Oftmals wird der Beschäftigung mit Platon ein selektives Philosophieverständnis zugrunde gelegt, das der Komplexität des Begriffs im platonischen Werk nicht gerecht wird. Die Arbeit zeigt darum durch das gesamte Ouvre, wie Platons Interesse an dem Philosophiebegriff in Auseinandersetzung mit traditionellen Auffassungen wächst und sich ausdifferenziert. Das philosophische Gespräch, das philosophische Leben, der philosophische Eros, der philosophische Tod und die philosophische Erkenntnis bilden systematische Aspekte, unter denen das Philosophieverständnis einzelner.

A travers les différents thèmes abordés le réel, la poésie, la pulsion de mort, l'interprétation, la télépathie, le rêve, l'inconscient ou le rire est ici interrogée la relation entre ces deux penseurs strictement contemporains du XXe siècle. L'exégèse textuelle recrée un dialogue qui n'a pas réellement existé entre eux. Elle l'inscrit dans un contexte épistémique très riche où se livre une bataille spéculative à l'origine d'une rupture majeure dans les sciences humaines, dont les retombées sont encore palpables aujourd'hui, se nouant (...) autour de nombreux points théoriques liés à la naissance de la psychologie. La finalité revendiquée par celle-ci est ambivalente : à la fois se distinguer de la philosophie et de la médecine, et s'y rattacher. Dans cette optique, autant Bergson que Freud vont se trouver au centre d'un débat sur la "scientificité" de la science du psychique, revendiquant, à l'instar de T Ribot ou P Janet par exemple, le recours à l'expérimentation et aux thèses psychophysiologistes et psychophysiques. La métaphysique de Bergson, comme la métapsychologie de Freud, ainsi désignée en 1896, seront redevables de ces théories, tout en s'en détachant pour aller vers l'idée d'inconscient, concept fondateur de la psychoanalysefreudienne. (shrink)

Goodstein’s principle is arguably the first purely number-theoretic statement known to be independent of Peano arithmetic. It involves sequences of natural numbers which at first appear to diverge, but eventually decrease to zero. These sequences are defined relative to a notation system based on exponentiation for the natural numbers. In this article, we provide a self-contained and modern analysis of Goodstein’s principle, obtaining some variations and improvements. We explore notions of optimality for notation systems and apply them to the classical (...) Goodstein process and to a weaker variant based on multiplication rather than exponentiation. In particular, we introduce the notion of base-change maximality, and show how it leads to far-reaching extensions of Goodstein’s result. We moreover show that by varying the initial base of the Goodstein process, one readily obtains independence results for each of the fragments $\mathsf {I}\Sigma _n$ of Peano arithmetic. (shrink)