,Etwa zwei Monate vor dem Tode sagte Husserl:,Man solle seine Vergangenheit nicht trivialisieren. ' "1 Die Herausforderung dieser Worte lieB sich nur schwer abschatzen, als ich dem Stifter des Husserl-Archivs, meinem Freund Pater Van Breda, im Januar I974- zwei Monate vor seinem unzeitigen Hingang- den von ihm so sehr begruBten und geforderten EntschluB, eine Husserl-Bio­ graphie zu schreiben, naher erlauterte. Mancherlei ware darin ein­ zubringen gewesen: Ubersicht uber die Geschicke des Bismarck­ Staates und das aufkommende Hitler-Reich, Vertrautheit mit Stifter (...) und Hofmannsthal, Kenntnis der Theorie mathematischer Funktionen wie der Psychologie der Wurzburger Schule, Einsicht in die Einfuhlungslehre von Lipps wie auch Heideggers Seins­ frage. Aber solche Absicht erwies sich hauptsachlich deswegen als undurchfiihrbar, weil es derzeit noch am Notigsten fehlt: an einer verlaBlichen Durcharbeitung von Husserls Denken und seiner Entwicklung, wie sie sich in den veroffentlichten Werken, vor al­ lem aber im Meer bewahrter Manuskripte niederschlug. Hier galt es, da viel bisher im Dunkeln liegt, die Materialien zu einer Bio­ graphie erst einmal bereitzustellen und, wenn auch oft nur um­ riBhaft, fur die Zukunft sicherzustellen. Ergebnis dieser Beschei­ dung ist die vorliegende Chronik. GewiB, Husserl ware selbst der befugteste interpres sui gewe­ sen. Doch was er unterm 20. Juni rg2r an den Meiner Verlag schrieb - der,Stand seiner Lebensarbeit" erlaube es ihm zur Zeit nicht, zu der in diesem Verlag erscheinenden Reihe von Selbstdarstellungen einen Beitrag zu liefern (F I r8/r + 25) -, galt, wie gerade unsere Chronik deutlich macht, fur ihn zeitlebens. (shrink)

Als Fritz Linder, Schtiler und Nachfolger von K. H. Bauer auf dem Heidelberger Lehrstuhl rur Chirurgie, am 12. Juli 1978 am Grabe seines Lehrers im Namen aller Freunde und Schuler sprach, erfuh­ ren wir, daB der Entschlafene "auf dem todlichen Krankenlager" noch seinen Briefwechsel mit Karl Jaspers las und ordnete. Diese letztwillige Vergegenwartigung einer freundschaftlichen Ver­ bindung aus den Jahren nach 1945 schien uns groBe menschliche Bedeutung zu haben, und wir waren erfreut, spater von Frau Bauer und Heinz Gotze, (...) Mitinhaber des Springer-Verlages, den Auftrag zur Herausgabe der Briefe zu erhalten, zumal sich mit beiden Kor­ respondenzpartnern eigene, dankbare Erinnerungen seit 1940 ver­ banden. Der Briefwechsel begann unmittelbar nach der ersten Begegnung yom 5.4. 1945 im Hause von Jaspers, als der Krieg rur Heidelberg vorbei war und politisch unbelastete Professoren vor der Aufgabe standen, die inzwischen geschlossene Universitat im Einvernehmen mit der Besatzungsbehorde wieder zu eroffnen und die Vorausset­ zungen rur die Wiederaufnahme freier Forschung und Lehre zu schaff en. Fur diesen Neubeginn, der natiirlich ein Neubeginn im Geiste des unveranderlich Gultigen sein sollte, war die daran anknupfende Freundschaft zwischen Bauer und Jaspers entscheidend. Die Person­ lichkeiten erganzten sich, und was beide damals suchten, war jeweils beim Partner zu finden: bei Jaspers die lebendige Idee in ihrem kla­ ren, wenn auch geschichtlich wandelbaren Wahrsein, bei Bauer die anpassungsfahige Vitalitat und die Gabe, Denken und Handeln zu verbinden. (shrink)

Wie vielleicht kein anderes seiner Werke reprasentieren Reinholds Verhandlungen sein lebenslanges Bemuhen, die Aufklarung in Kooperation und Auseinandersetzung mit anderen Selbstdenkern voranzutreiben. Sie umfassen drei Beitrage. Der zweite, der Entwurf zu einem Einverstandnisse unter Wohlgesinnten, resultiert aus Diskussionen, die Reinhold mit freimaurerischen Freunden fuhrte. Hier geht es im Kern um die Frage, wie sich dem aufgeklarten Denken kantischer Pragung die notige soziale Wirkung und organisatorische Kraft verschaffen liesse. Dieser Entwurf wurde weithin an Freunde und Bekannte verschickt, mit der Bitte, dem (...) Einverstandnis beizutreten. Aber auch konstruktive Kritik erbat Reinhold. Von den Antworten, die er erhielt, druckte er neun Briefe mit seinen eigenen Repliken ab - der dritte Beitrag. Der erste Beitrag enthalt Reinholds ausfuhrliche, im Umfang stark erweiterte Umarbeitung des Entwurfs. (shrink)

Die Soncino-Gesellschaft war ein bibliophiler Verein, der sich 1924 in Berlin gründete und bis zu seiner Auflösung 1937 über hundert Publikationen aus vielen Gebieten der jüdischen Geschichte und Kultur herausgegeben hat. Sie versammelte Mitglieder aus allen Strömungen des Judentums unter ihrem Dach und entwickelte sich mit ihrem Anspruch, ästhetische Vorbilder für das jüdische Buch zu geben, zu einem jüdischen Integrationsprojekt. Der Beitrag geht den kulturzionistischen Bruchlinien nach, die sich in der zionistischen Rezeption, dem Streit um die hebräische Bibelausgabe und der (...) Positionierung einiger prominenter Protagonisten der Soncino-Gesellschaft zeigen. Diese Bruchlinien blieben jedoch so marginal, dass sie den bibliophilen Konsens nicht gefährdeten. Im historischen Rückblick kann das Programm der Soncino-Gesellschaft vielmehr als Kanon der deutsch-jüdischen Integration in der Diaspora gelesen werden. (shrink)

Der Kunsthistoriker Ernst Hans Josef Gombrich hat einen „wissenschaftlichen“ oder kognitiven Ansatz zur Erforschung der Geschichte und Psychologie der Künste entwickelt, der sehr maßgeblich von der Wissenschaftstheorie seines engen Freundes Karl Popper beeinflusst worden ist. Die geistige Nähe zwischen beiden wird in Gombrichs zentraler Arbeit zur Wiederentdeckung der Repräsentation in der Renaissance und zur Historiografie der Kunst deutlich. Ihre Differenzen verdienen allerdings ebenfalls Beachtung. Gombrichs Ansicht zufolge verändern sich Geschmack und Stil entsprechend der von ihm so genannten „Logik der (...) Mode“. Gombrich hat dargelegt, auf welch vielfältige Weise Veränderungen in der Kunst sich vollziehen. Während sich die Moden in der Kunst auf unvorhersehbare, launenhafte Weise wandeln, tauchen technische Veränderungen als Lösungen für technische Probleme auf und werden im Modus von Versuch und Irrtum ermittelt. Auf diese Weise stieß Gombrich auf eine Antinomie in der Kunsttheorie: Handwerkliche Fähigkeiten und Können wandeln sich durch rationalen Fortschritt, während sich Stile durch den irrationalen Mitläufereffekt verändern. In der Kunst ist der relativistische Pluralismus zur Mode geworden, und diese Mode hat seine Antinomie ignoriert – und zwar, sofern er richtig liegt, recht willkürlich. (shrink)

Friedrich Schiller ist bei seiner Kant-Rezeption nicht nur von seinem Dresdener Freund Christian Gottfried Körner unterstützt worden. Auch auf kompetente Belehrungen und Anregungen seitens des Jenaer Philosophieprofessors Karl Leonhard Reinhold konnte er stets zählen. Reinhold führt ihn ab 1787 an kantische Schriften heran und konfrontiert ihn mit illuminatischen Geschichts- und Aufklärungsideen. Nach dem Antritt seiner Professur steht Schiller unter dem Einfluss des praktischen Teils von Reinholds System der Elementarphilosophie. So verdanken Schillers kantisch-ästhetische Reflexionen der frühen 1790er-Jahre ihr thematisches (...) Grundprofil maßgeblich einer dialogischen Auseinandersetzung mit Lehrstücken des Philosophenkollegen zum ästhetischen Vergnügen, zu den menschlichen Grundtrieben, zur Freiheit des Willens sowie zur Idee moralischer Gemeinschaft. (shrink)

Der vorliegende Aufsatz stellt den Versuch dar, die normative Seite von Wittgensteins Frühwerk herauszuarbeiten und dabei an seinem Ansatz insofern Kritik zu üben, als gezeigt wird, wie sehr dessen Implikationen mit unseren üblichen ethischen Vorstellungen in Konflikt stehen. Die Arbeit hat aber auch einen etwas wohlwollenderen Aspekt: Sie versucht zu zeigen, wie Wittgensteins scheinbar widersinnige Ansichten so formuliert werden können, daß sie zumindest begreifbar erscheinen. Zu diesem Zweck beginnen wir mit der Untersuchung des demjenigen Wittgensteins erstaunlich ähnlichen ethischen Ansatzes, wie (...) er von einem seiner frühen väterlichen Freunde vertreten wurde, nämlich von Karl Kraus. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:196 HISTORY OF PHILOSOPHY in 1943, was to write an Epilogue to Julian Marias' History o] Philosophy. In early 1944, the Epilogue was conceived as a volume of 400 pages, and later of 700. In 1945 a part of the Epilogue was to be detached and given the title The Origin ol Philosophy. Then one completed part of that was published in 1953 as an essay in a Festschrift (...) for Karl Jaspers. That, and other sections, have been put together here. The first part of the book treats philosophy as a cumulative enterprise in which each man rethinks and thinks further what other men have thought. Even when past thought has reached an end, or taken a direction we will not follow, it is only for the reason that it has already happened that we do not have to do it ourselves. This is not because history is rational but because thought is historical, rooted in ideas we did not ourselves create and based on methods we have acquired and sometimes altered. The second part of the book deals with the origin of philosophy--and the origin of "philosophy" for Ortega is concerned throughout with language and etymology. The word "philosophy" is not one Ortega likes; he prefers the word "aletheia," which was used by Parmenides and his contemporaries. In popular language, aletheia meant discovery, exposure, denudation, revelation. For the thinker, "aletheia" is "truth" as a verb, the activity of uncovering reality, which is concealed under the robes of appearance or falsehood. Philosophy, for Ortega, begins with Parmenides and Heraclitus; "proto-philosophers" he calls them. The Ionians had been scientists; their attempts at natural explanation upset religion and tradition, and prepared the way for philosophy. In a remarkably subtle and complex analysis for so short a space, Ortega argues that skepticism, atheism, wealth, and knowledge of nature created a freedom based on a need to create or choose one's own beliefs in a world in which relative abundance demands choice, since in poverty "an individual is never in the position of being able to choose; for choice assumes that the circle of one's possibilities is notably greater than that of one's needs" (p. 98). The social need to define the thinker and so grant him professional status that might minimize the hostility of the tradition-ridden and reactionary populace, especially in Athens, led to the name "sophist," which became disreputable to a hostile citizenry, and then to "philosopher." Socrates was, unfortunately, the only philosopher, the man who liked, had a taste for, or loved wisdom, but made no pretense that he had any, saying only he sought it. But the name persisted, and helped institutionalize the new profession. I haven't even intimated the delight of Ortega's incidental insights. He was probably justified in believing that his stature as a thinker was much greater than his reputation. A first-rate, full-scale study of Ortega in English would help, but what we need most is a collection and translation of his complete works. RSLPH ROSS ~cripps College Discourse on Thinking. By Martin Heidegger. Translated by John M. Anderson and E. Hans Freund. (New York: Harper and Row, 1966. Pp. 93. $3.50.) This is a translation of a speech and conversation originally published under the thematic title Gelassenheit (Pfullingen: Giinther Neske, 1959). Heidegger uses this unusual German word to remind us that there is another way of thinking than the calculative and dialectical modes made prominent by the mathematical sciences and modem cultural philosophy respectively. We have forgotten a less busy mode of thinking, a thinking released from all desire to control reality. Gelassenheit is rendered throughout as "releasement" in this translation. But Gelassenheit does not just mean letting go, or freedom from, as "releasement" may suggest. It also has the more positive sense of composure and a patient letting things be. In the context of Heidegger's attempts to define a mode of thinking not concerned with dominating reality, Gelassenheit comes to mean the freedom to be open to reality. BOOK REVIEWS 197 Heidegger stresses the ability to wait for insight, which is not, however, a mere passive waiting for something fixed. It would be... (shrink)

Mit Hilfe von Leo Strauss, seinem Freund und philosophischen Kollegen, verließ Hans Jonas Israel und siedelte 1949 nach Kanada. Nachdem Jonas einige Jahre in Kanada an der Carleton University gelehrt hatte, erhielt er 1955 einen Ruf als Professor an die New School for Social Research. Leo Strauss und Karl Löwith, die beide dort lehrten, hatten sich für ihn eingesetzt.

In his preface to the English edition, Apel (identified with critical theory) explains that the title of his two-volume German collection connotes both a reconstruction of the process of hermeneutic transformation in recent philosophy and the author's semiotical transformation of transcendental logic. The emphasis here is on the latter with discussions of the a priori nature of language per Wittgenstein, Peirce, and Chomsky, and its implications for a rational foundation for ethics in modern science. Includes a new foreword. Name index (...) only. Annotation copyrighted by Book News, Inc., Portland, OR. (shrink)

Bd. 1. Sprachanalytik, Semiotik, Hermeneutik. Bd. 2. Das Apriori der Kommunikationsgemeinschaft.

Reflecting a revival of Peirce studies and the rediscovery of the pragmatist tradition in American philosophical thinking, this study articulates a contemporary and relevant interpretation that may offer a challenge to neo-pragmatists.

In the following I discuss the debate between epistemological internalists and externalists from an unfamiliar meta-epistemological perspective. In doing so, I focus on the question of whether rationality is best captured in externalist or internalist terms. Using a conception of epistemic judgments as “doxastic plans,” I characterize one important subspecies of judgments about epistemic rationality—focusing on the distinctive rational/functional role these judgments play in regulating how we form beliefs. Then I show why any judgment that plays this role should be (...) expected to behave the manner internalists predict. In this way, I argue, we can explain why our basic toolbox for epistemic evaluation includes an internalist conception of rationality. (shrink)

Marxism and philosophy [1923].--The present state of the problem of 'Marxism and philosophy' [1930].--Introduction to the Critique of the Gotha Programme [1922].--The Marxism of the First International [1924].

This paper explores the perversion of reality in the context of advanced technologies, such as AI, VR, and AR, through the lens of Jean Baudrillard’s theory of hyperreality and the precession of simulacra. By examining the transformative effects of these technologies on our perception of reality, with a particular focus on the usage of digital avatars, the paper highlights the blurred distinction between the real and the simulated, where the copy becomes more ‘real’ than the original. Drawing on Baudrillard’s concept (...) of hyperreality, the paper delves into the perversion of reality as individuals seek refuge in virtual pleasure paradises and embrace artificial pleasures through their digital avatars, disconnecting from genuine human experiences. The convergence of AI, VR, and AR technologies amplifies this hyperreal condition, where digital avatars mimic or surpass the depth of human relationships, challenging our understanding of what is real. In line with Baudrillard’s theory, the paper explores the objectification and commodification of reality within digital spaces, specifically examining the digital avatars’ role in the erosion of genuine human connections. It explores the implications of these avatars in terms of consent, exploitation, and loss of authenticity, echoing Baudrillard’s concerns about the distortion of reality in contemporary society. Recognizing the implications of these technologies, the paper calls for a critical reflection on their transformative power. It emphasizes the need for a nuanced understanding of the hyperreal condition and ethical responsibility in engaging with AI, VR, and AR, particularly in relation to the usage of digital avatars. By resisting the seductive allure of digital escapism and preserving genuine human connections, we can navigate the perversion of reality and cultivate empathy, compassion, and meaningful interactions that transcend the simulated experiences offered by technology. (shrink)

This paper explores the intersection of René Girard's mimetic theory and the algorithmic society, particularly in the context of the potential advent of Artificial General Intelligence (AGI). Girard's theory, which elucidates the dynamics of desire, rivalry, scapegoating, and the sacrificial crisis, provides a unique lens through which to examine the complexities of our relationship with AI and its role in the creation of the sacred. As individuals increasingly rely on AI recommendations, the distinction between personal choice and algorithmic manipulation becomes (...) less clear, raising concerns about the authenticity of cultural expressions and the role of algorithms in shaping cultural narratives. The triangular structure of desire, with AI as the model and individuals as the imitators, underscores the power of algorithms in this process. The sacrificial crisis, a key concept in Girard's theory, becomes a critical point of reflection in the algorithmic society. The exposure of the scapegoating mechanism reveals the destructive potential of algorithmic manipulation and calls for new forms of understanding, empathy, and non-violent solutions. This paper argues that recognizing the sacrificial crisis can prompt individuals and society to critically examine the impact of AI's influence, challenge the narratives it perpetuates, and reclaim agency in the face of algorithmic dominance. This paper further discusses the potential implications of the emergence of AGI, which could intensify the influence of algorithms on the creation of the sacred due to its advanced cognitive capabilities and deep understanding of human desires and behaviors. This could fuel a rapid evolution of the mimetic ecosystem, with profound implications for personal freedom, independent decision-making, and the formation and preservation of individual identity. This paper concludes by emphasizing the need for responsible algorithmic practices and ethical considerations to ensure that the creation of the sacred serves the common good in the algorithmic society. (shrink)

Four experiments demonstrate category congruency priming by subliminal prime words that were never seen as targets in a valence-classification task and a gender-classification task . In Experiment 1, overlap in terms of word fragments of one or more letters between primes and targets of different valences was larger than between primes and targets of the same valence. In Experiments 2 and 3, the sets of prime words and target words were completely disjoint in terms of used letters. In Experiment 4, (...) pictures served as targets. The observed subliminal priming effects for novel primes cannot be driven by partial analysis of primes at the word-fragment level; they suggest instead that primes were processed semantically as whole words contingent upon prime duration. (shrink)

In this essay, I discuss two familiar objections to Hume's account of cognition, focusing on his ability to give a satisfactory account of the more normative dimensions of thought and language use. In doing so, I argue that Hume’s implicit account of these issues is far richer than is normally assumed. In particular, I show that Hume’s account of convention-driven artificial virtues like justice also applies to the proper use of conventional public languages. I then use this connection between Hume’s (...) conception of language and his moral theory to show how he can respond to a number of basic objections to his views. In doing so, I explore the sense in which human cognition is essentially linguistic, and so social, for Hume, as well as many other issues concerning the relationship between Hume’s philosophy of mind and language, his epistemology, and his ethics. (shrink)

We have previously established that [Formula: see text]-comprehension is equivalent to the statement that every dilator has a well-founded Bachmann–Howard fixed point, over [Formula: see text]. In this paper, we show that the base theory can be lowered to [Formula: see text]. We also show that the minimal Bachmann–Howard fixed point of a dilator [Formula: see text] can be represented by a notation system [Formula: see text], which is computable relative to [Formula: see text]. The statement that [Formula: see text] (...) is well founded for any dilator [Formula: see text] will still be equivalent to [Formula: see text]-comprehension. Thus, the latter is split into the computable transformation [Formula: see text] and a statement about the preservation of well-foundedness, over a system of computable mathematics. (shrink)

Sortal concepts are at the center of certain logical discussions and have played a significant role in solutions to particular problems in philosophy. Apart from logic and philosophy, the study of sortal concepts has found its place in specific fields of psychology, such as the theory of infant cognitive development and the theory of human perception. In this monograph, different formal logics for sortal concepts and sortal-related logical notions are characterized. Most of these logics are intensional in nature and possess, (...) in addition, a bidimensional character. That is, they simultaneously represent two different logical dimensions. In most cases, the dimensions are those of time and natural necessity, and, in other cases, those of time and epistemic necessity. Another feature of the logics in question concerns second-order quantification over sortal concepts, a logical notion that is also represented in the logics. Some of the logics adopt a constant domain interpretation, others a varying domain interpretation of such quantification. Two of the above bidimensional logics are philosophically grounded on predication sortalism, that is, on the philosophical view that predication necessarily requires sortal concepts. Another bidimensional logic constitutes a logic for complex sortal predicates. These three sorts of logics are among the important novelties of this work since logics with similar features have not been developed up to now, and they might be instrumental for the solution of philosophically significant problems regarding sortal predicates. The book assumes a modern variant of conceptualism as a philosophical background. For this reason, the approach to sortal predicates is in terms of sortal concepts. Concepts, in general, are here understood as intersubjective realizable cognitive capacities. The proper features of sortal concepts are determined by an analysis of the main features of sortal predicates. Posterior to this analysis, the sortal-related logical notions represented in the above logics are discussed. There is also a discussion on the extent to which the set-theoretic formal semantic systems of the book capture different aspects of the conceptualist approach to sortals. These different semantic frameworks are also related to realist and nominalist approaches to sortal predicates, and possible modifications to them are considered that might represent those alternative approaches. (shrink)

On its face, Hume's account of mental representation involves at least two elements. On the one hand, Hume often seems to write as though the representational properties of an idea are fixed solely by what it is a copy or image of. But, on the other, Hume's treatment of abstract ideas makes it clear that the representational properties of a Humean idea sometimes depend, not just on what it is copied from, but also on the manner in which the mind (...) associates it with other ideas. Past interpretations of Hume have tended to focus on one of these elements of his account to the neglect of the other. But no interpretation of this sort is likely to capture the role that both copying and association play within Hume's discussion. In what follows, I argue that the most plausible way of understanding Hume's discussion involves attributing to him a unified account of mental representation in which both of these elements play a central role. I close by discussing the manner in which reading Hume in this way would alter our understanding of the relationship between Hume's thought and contemporary philosophy of mind. (shrink)

With respect to the topic of “powers and abilities,” most readers will associate David Hume with his multi-pronged critique of traditional attempts to make robust explanatory use of those notions in a philosophical or scientific context. But Hume’s own philosophy is also structured around the attribution to human beings of a variety of basic faculties or mental powers – such as the reason and the imagination, or the various powers involved in Hume’s account of im- pressions of reflection and the (...) passions. Indeed, there is a clear case to be made that, despite his deflationary account of our concept of power, Hume continues to treat certain basic powers or faculties as forming the explanatory bedrock for his new “science of man”. In this essay, I will discuss how this apparent conflict between the “critical” (if not outright skeptical) and “constructive” aspects of Hume’s discussion of powers and abilities is best resolved – with special attention to the question of how this illuminates Hume’s place in the development of early modern conceptions of the proper method for philosophy. (shrink)

Professors Hildt (2023), Shepherd (2023), and Zilio and Lavazza (2023) jointly considered the ethical and philosophical implications of acknowledging non-human (e.g., machine) consciousness. Althou...

In previous work, the author has shown that $\Pi ^1_1$ -induction along $\mathbb N$ is equivalent to a suitable formalization of the statement that every normal function on the ordinals has a fixed point. More precisely, this was proved for a representation of normal functions in terms of Girard’s dilators, which are particularly uniform transformations of well orders. The present paper works on the next type level and considers uniform transformations of dilators, which are called 2-ptykes. We show that $\Pi (...) ^1_2$ -induction along $\mathbb N$ is equivalent to the existence of fixed points for all 2-ptykes that satisfy a certain normality condition. Beyond this specific result, the paper paves the way for the analysis of further $\Pi ^1_4$ -statements in terms of well ordering principles. (shrink)

Accused of the murder of two men and the rape and murder of a Tombstone businessman's fiancâee, Matt Donohue must find the girl in the middle of Apache territory in order to clear his name.

We shall distinguish between sortal predication and standard predication. The former kind of predication necessarily involves sortal concepts but the latter, as it is customarily viewed, does not. It is generally thought that the only essential occurrence of a concept in a standard predication is the concept being predicated. In this paper, we shall put forward an alternative view. We shall propose to understand standard predication as a cognitive act essentially requiring sortal concepts. We shall call this view conceptual predication (...) sortalism and ground it on the basis of epistemic-semantic reasons. Concepts are understood as intersubjectively realizable capacities or abilities that fulfill particular cognitive roles, such as those of classification, categorization, individuation, and referring. (shrink)

The present book tries to show that the transcentendal-pragmatic approach to discourse ethics can reconstruct the genesis of this situation and provide a ...

Michael Rathjen and the present author have shown that ‐bar induction is equivalent to (a suitable formalization of) the statement that every normal function has a derivative, provably in. In this note we show that the base theory can be weakened to. Our argument makes crucial use of a normal function f with and. We shall also exhibit a normal function g with and.

Let Con↾x denote the finite consistency statement “there are no proofs of contradiction in T with ≤x symbols.” For a large class of natural theories T, Pudlák has shown that the lengths of the shortest proofs of Con↾n in the theory T itself are bounded by a polynomial in n. At the same time he conjectures that T does not have polynomial proofs of the finite consistency statements Con)↾n. In contrast, we show that Peano arithmetic has polynomial proofs of Con)↾n, (...) where Con∗ is the slow consistency statement for Peano arithmetic, introduced by S.-D. Friedman, Rathjen, and Weiermann. We also obtain a new proof of the result that the usual consistency statement Con is equivalent to ε0 iterations of slow consistency. Our argument is proof-theoretic, whereas previous investigations of slow consistency relied on nonstandard models of arithmetic. (shrink)

In the context of reverse mathematics, effective transfinite recursion refers to a principle that allows us to construct sequences of sets by recursion along arbitrary well orders, provided that each set is ‐definable relative to the previous stages of the recursion. It is known that this principle is provable in. In the present note, we argue that a common formulation of effective transfinite recursion is too restrictive. We then propose a more liberal formulation, which appears very natural and is still (...) provable in. (shrink)