In this analysis of one of the most difficult and neglected topics in Hegelian studies, Songsuk Susan Hahn tackles the status of contradiction in Hegel's ...

In this chapter, we outline the range of argument forms involving causation that can be found in everyday discourse. We also survey empirical work concerned with the generation and evaluation of such arguments. This survey makes clear that there is presently no unified body of research concerned with causal argument. We highlight the benefits of a unified treatment both for those interested in causal cognition and those interested in argumentation, and identify the key challenges that must be met for a (...) full understanding of causal argumentation. (shrink)

The present study examines how online instruction during the COVID pandemic impacted learning and performs a partial replication of a study by Hahn et al. (2012), which compared students’ testing outcomes of the Major Field Test in Business (MFTB) and the Comprehensive Business Exam (CBE). Our results find that online instruction during the 2020-2021 pandemic isolation period had no significant impact on pre- and post-COVID testing outcomes for either exam. It was further found that the question set employed by (...) the CBE exam appears to have changed from the pre- to the post-COVID testing timeframes, making this exam questionable for assurance of learning purposes when compared to prior year results. (shrink)

O presente trabalho tem por objetivo fornecer uma resposta à crítica direcionada pelo jurista Fábio Konder Comparato ao formalismo jurídico de Kant. Explicarei porque essa crítica se equivoca quando identifica, na Doutrina do Direito de Kant, uma Teoria do Direito incompleta e insatisfatória. Para tanto, pretendo mostrar que o propósito do filósofo alemão não era apresentar uma teoria do direito, mas sim uma Metafísica do Direito. O que explica, por conseguinte, a razão para o direito ter sido concebido como um (...) conceito puro. Além disso, a fim de determinar o significado do formalismo jurídico, ocupar-me-ei da crítica hegeliana ao suposto formalismo ético de Kant, bem como da resposta a essa crítica. (shrink)

Este artigo pretende mostrar que e como ocorrem, na Doutrina da virtude de Kant, problemas relativos aosentido e referência dos juízos e conceitos fundamentais dessa obra, isto é, problemas semânticos. Tendo em vistaesse fim, explicitaremos de forma breve o desenvolvimento dessa problemática na filosofia prática de Kant e, em seguida, realizaremos a análise da Doutrina da virtude a partir do ponto de vistasemântico, a fim de identificar os mencionados problemas e as soluções fornecidas por Kant para estes problemas. -/- This (...) paper intends to show what and how problems related to the sense and reference of the fundamental judgments and concepts in Kant's Doctrine of virtue happen, that is, semantic problems. In order to perform this end, I shortly make explicit the development of this problematic in Kant's practical philosophy and, soon after, we will accomplish the analysis of the Doctrine of virtue from the semantic point of view, in order to identify the mentioned problems and the solutions supplied by Kant for these problems. (shrink)

Hegel's most interesting and controversial claims about nonconceptual knowledge arise in contexts of value. This paper examines the relation between nonconceptual and conceptual knowledge in Hegel's Phenomenology, specifically in connection with early Greek aesthetics. I take up Hegel's claim that the ancient Greeks expressed in their myths, religious narratives, sculpture, and artistic materials certain high powered philosophical truths which they shouldn't express in words. I raise a paradox about his claims and show how his claims about ineffable knowledge clash with (...) his general propositional criterion of knowledge, namely, that for something to count as knowledge it must be expressible in words. However I argue that Hegel's thoughts about the matter were coherent and I solve the paradox. (shrink)

The Impossibility of Poetry Adorno's aesthetic theory bears the profound scars of his personal experience of fascism. Even after Auschwitz, he feared that modern bourgeois society is a breeding ground for new forms of fascist terror. It was said that, after Auschwitz, one could no longer write poems. But Adorno insisted that postwar art is an indispensable means for telling the truth about how the social order was fundamentally changed by that catastrophe.1 Not to tell the truth is to be (...) guilty of complicitous silence; yet, the unbearable truth is that society is pervasively and radically evil. As long as…. (shrink)

A large body of work has demonstrated the utility of the Bayesian framework for capturing inference in both specialist and everyday contexts. However, the central tool of the framework, conditionalization via Bayes’ rule, does not apply directly to a common type of learning: the acquisition of conditional information. How should an agent change her beliefs on learning that “If A, then C”? This issue, which is central to both reasoning and argumentation, has recently prompted considerable research interest. In this paper, (...) we critique a prominent proposal and provide a new, alternative, answer. -/- . (shrink)

The present text provides a logical theory which originated in the unification of a number of well-known philosophical logics as well as the introduction and study of new operators. Further M-logic contains an object theory. With both the logical part and the object part we achieve a formal calculus that is able to express many metaphysical dogmas.

In this article, we explore some of the roles of cameras in policing in the United States. We outline the trajectory of key new media technologies, arguing that cameras and social media together generate the ambient surveillance through which graphic violence is now routinely captured and circulated. Drawing on Michel Foucault, we suggest that there are important intersections between this video footage and police subjectivity, and propose to look at two: recruit training at the Washington state Basic Law Enforcement Academy (...) and the Seattle Police Department’s body-worn camera project. We analyze these cases in relation to the major arguments for and against initiatives to increase police use of cameras, outlining what we see as techno-optimistic and techno-pessimistic positions. Drawing on the pragmatism of John Dewey, we argue for a third position that calls for field-based inquiry into the specific co-production of socio-techno subjectivities. (shrink)

As we enter the 2020s, global poverty is still a grave and persistent problem. Alleviating and eradicating poverty within and across the world’s societies requires a thorough understanding of its nature and extent. Although economists still standardly measure absolute and relative poverty in monetary terms, a consensus is emerging that poverty is a socially relational problem involving deprivations in multiple dimensions, including health, standard of living, education and political participation. The anthology Dimensions of Poverty advances the interdisciplinary debate on multidimensional (...) poverty, and features contributions from leading international experts and early career researchers (including from the Global South). This introductory chapter gives an overview of formative debates, central concepts and key findings. While monetary poverty measures are still dominant in public and academic debate, their explanatory power has been drawn into question. We discuss relevant criticisms before outlining the normative concepts that can inform both multidimensional poverty and monetary measures, including basic capabilities, basic needs and social primary goods. Next, we introduce several influential multidimensional poverty indices, including the Human Development Index and the Multidimensional Poverty Index. The anthology shows in detail how such measures can be improved, from a variety of disciplinary perspectives. It shows that there are different methods of poverty research that require further investigation, including participatory studies, (value) surveys, public consensus building, the constitutional approach, and financial diaries. Finally, we show that there is an ongoing problem of epistemic asymmetries in global poverty research, and discuss responsibility for addressing poverty, including the responsibilities of academics. The remainder of the chapter is dedicated to a more detailed preview of the volume’s 20 contributions, which are assembled along the following five themes: (I) poverty as a social relation; (II) epistemic injustices in poverty research; (III) the social context of poverty; (IV) measuring multidimensional poverty; and (V) country cases. (shrink)

Digitalisierung ist nicht nur ein technisches Geschehen, sondern erfasst als machtvoller kultureller Prozess alle Lebensbereiche. Die Einsicht, dass soziotechnische Vorgänge gestaltbar sind, erlaubt eine grundsätzliche Reflexion über die neuen Handlungsmöglichkeiten und Zumutungen sowohl in individueller wie auch in kollektiver Perspektive. Welche Herausforderungen stellen sich für unsere bewährten Überzeugungen und sozialen Praktiken in den Prozessen von Verantwortung, Verständigung, Vernunft und Macht? Die Beiträger*innen analysieren aktuelle Entwicklungen der Digitalisierung und tragen im Lichte provisorischer Maßstäbe praktischer Vernunft zu einer aufgeklärten öffentlichen Diskussion über (...) (nicht) wünschenswerte technokulturelle Zukünfte bei. (shrink)

Suppose that two competing norms, N1 and N2, can be identified such that a given person’s response can be interpreted as correct according to N1 but incorrect according to N2. Which of these two norms, if any, should one use to interpret such a response? In this paper we seek to address this fundamental problem by studying individual variation in the interpretation of conditionals by establishing individual profiles of the participants based on their case judgments and reflective attitudes. To investigate (...) the participants’ reflective attitudes we introduce a new experimental paradigm called the Scorekeeping Task. As a case study, we identify the participants who follow the Suppositional Theory of conditionals (N1) versus Inferentialism (N2) and investigate to what extent internally consistent competence models can be reconstructed for the participants on this basis. After extensive empirical investigations, an apparent reasoning error with and-to-if inferences was found in one of these two groups. The implications of this case study for debates on the proper role of normative considerations in psychology are discussed. (shrink)

In the last two decades, WORDNET has evolved as the most comprehensive computational lexicon of general English. In this article, we discuss its potential for supporting the creation of an entirely new kind of information resource for public health, viz. MEDICAL WORDNET. This resource is not to be conceived merely as a lexical extension of the original WORDNET to medical terminology; indeed, there is already a considerable degree of overlap between WORDNET and the vocabulary of medicine. Instead, we propose a (...) new type of repository, consisting of three large collections of (1) medically relevant word forms, structured along the lines of the existing Princeton WORDNET; (2) medically validated propositions, referred to here as medical facts, which will constitute what we shall call MEDICAL FACTNET; and (3) propositions reflecting laypersons’ medical beliefs, which will constitute what we shall call the MEDICAL BELIEFNET. We introduce a methodology for setting up the MEDICAL WORDNET. We then turn to the discussion of research challenges that have to be met in order to build this new type of information resource. (shrink)

In this paper, new evidence is presented for the assumption that the reason-relation reading of indicative conditionals ('if A, then C') reflects a conventional implicature. In four experiments, it is investigated whether relevance effects found for the probability assessment of indicative conditionals (Skovgaard-Olsen, Singmann, and Klauer, 2016a) can be classified as being produced by a) a conversational implicature, b) a (probabilistic) presupposition failure, or c) a conventional implicature. After considering several alternative hypotheses and the accumulating evidence from other studies as (...) well, we conclude that the evidence is most consistent with the Relevance Effect being the outcome of a conventional implicature. This finding indicates that the reason-relation reading is part of the semantic content of indicative conditionals, albeit not part of their primary truth-conditional content. (shrink)

Culture and socialization influence how individuals perceive and express emotional distress. Research therefore, must consider the context to capture individual experiences. However, the majority of studies on factors associated with emotional distress among migrants use quantitative approaches, limiting an in-depth understanding. This study investigates emic themes of emotional distress among Vietnamese migrants by integrating anthropological and psychiatric approaches. The mixed methods study first quantified differences in reported themes of distress between Vietnamese (n = 104) and German (n = 104) patients, (...) who utilized two psychiatric outpatient clinics in Berlin, Germany. Based on these differences, ethnographic interviews were conducted with 20 Vietnamese patients. In the quantitative part, differences in frequency of reported distress between Vietnamese and German patients indicate cultural and migration-related issues among Vietnamese migrants, such as the upbringing of children in a transcultural context. In the qualitative part, interviews with Vietnamese patients elicited contextualizing information and additional themes of distress. Besides commonly expressed socioeconomic themes, such as work and finances, we identified affectively charged themes concerning roles toward partnership and children. A central emic theme is expressed as “moments of speechlessness,” which go beyond a lack of language proficiency and challenge patients in different spheres of life. Migration entails complex affective dynamics, determined by a specific migratory and post-migratory context. Within this context, norms and values determine which themes of distress patients articulate openly. Therefore, an interdisciplinary, mixed-methods approach can yield a contextualized understanding of emotional distress and the complex nature of migration. (shrink)

In this manuscript we study individual variation in the interpretation of conditionals by establishing individual profiles of the participants based on their behavioral responses and reflective attitudes. To investigate the participants’ reflective attitudes we introduce a new experimental paradigm called the Scorekeeping Task, and a Bayesian mixture model tailored to analyze the data. The goal is thereby to identify the participants who follow the Suppositional Theory of conditionals and Inferentialism and to investigate their performance on the uncertain and-to-if inference task.

The pivotal role of the relation part-of in the description of living organisms is widely acknowledged. Organisms are open systems, which means that in contradistinction to mechanical artifacts they are characterized by a continuous flow and exchange of matter. A closer analysis of the spatial relations in biological organisms reveals that the decision as to whether a given particular is part-of a second particular or whether it is only contained-in the second particular is often controversial. We here propose a rule-based (...) approach which allows us to decide on the basis of well-defined criteria which of the two relations holds between two anatomical objects, given that one spatially includes the other. We discuss the advantages and limitations of this approach, using concrete examples from human anatomy. (shrink)

The 2013 Rostock Symposium on Systems Biology and Bioinformatics in Aging Research was again dedicated to dissecting the aging process using in silico means. A particular focus was on ontologies, as these are a key technology to systematically integrate heterogeneous information about the aging process. Related topics were databases and data integration. Other talks tackled modeling issues and applications, the latter including talks focussed on marker development and cellular stress as well as on diseases, in particular on diseases of kidney (...) and skin. (shrink)

Článek se zabývá demystifikací dodnes panující legendy o ikoně světové vědy, nositeli Nobelovy ceny za objev štěpení těžkých jader, chemiku Otto Hahnovi. Desítky let byl považován za vzor německé slušnosti, zodpovědnosti a příklad antinacistického vědce, který nekolaboroval se zločinným režimem na jeho válečné mašinérii. Teprve od devadesátých let 20. století se dostávají k rukám historiků archivní materiály, jež umožňují získat ucelenou představu o Hahnově působení v době nacistického Německa a o jeho aktivním zapojení ve válečném uranovém výzkumu, jehož výsledkem mělo (...) být sestrojení jaderných reaktorů a bomb. (shrink)

We examine some of Connes’ criticisms of Robinson’s infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes’ own earlier work in functional analysis. Connes described the hyperreals as both a “virtual theory” and a “chimera”, yet acknowledged that his argument relies on the transfer principle. We analyze Connes’ “dart-throwing” thought experiment, but reach an opposite conclusion. In S , all definable sets of reals are (...) Lebesgue measurable, suggesting that Connes views a theory as being “virtual” if it is not definable in a suitable model of ZFC. If so, Connes’ claim that a theory of the hyperreals is “virtual” is refuted by the existence of a definable model of the hyperreal field due to Kanovei and Shelah. Free ultrafilters aren’t definable, yet Connes exploited such ultrafilters both in his own earlier work on the classification of factors in the 1970s and 80s, and in Noncommutative Geometry, raising the question whether the latter may not be vulnerable to Connes’ criticism of virtuality. We analyze the philosophical underpinnings of Connes’ argument based on Gödel’s incompleteness theorem, and detect an apparent circularity in Connes’ logic. We document the reliance on non-constructive foundational material, and specifically on the Dixmier trace −∫ (featured on the front cover of Connes’ magnum opus) and the Hahn–Banach theorem, in Connes’ own framework. We also note an inaccuracy in Machover’s critique of infinitesimal-based pedagogy. (shrink)

Kein Hahn kräht mehr nach dem Verifikationsprinzip, das Moritz Schlick zusammen mit seinen Mitstreitern des Wiener Kreises verfochten hat. Seit einem halben Jahrhundert gilt das Prinzip als philosophisch erledigt; doch Totgesagte leben länger. Ich versuche, eine Fassung des Prinzips zu formulieren, die auch unter den Bedingungen der Nachkriegs-Philosophie verteidigt werden kann: Grob gesagt, muss jeder sinnvolle Satz im Prinzip empirisch (oder doch aposteriori) überprüft werden können, einerlei ob verifiziert oder falsifiziert, ob fallibel oder infallibel, ob direkt oder indirekt, ob (...) deduktiv, abduktiv oder induktiv, ob durch Sinneswahrnehmung oder durch Selbstwahrnehmung. Je nach Situation verlangt das Prinzip die unterschiedlichsten Formulierungen; es wäre verfehlt, es ein für allemal zu fixieren. Vermutlich können wir es sogar auf Sätze ausdehnen, die sich apriori rechtfertigen lassen. Anhand einer Serie von Beispielen (die z.T. aus Schlicks Schriften stammen) demonstriere ich, welche guten Dienste das Prinzip leistet. Erstens dient es dazu, intellektuelle Hochstapelei aus dem Spiel zu werfen und von sinnvollen Aussagen zu unterscheiden. Nun gibt es Sätze, an deren Sinn wir nicht gern rütteln lassen wollen, selbst wenn zunächst nicht klar ist, wie sie sich überprüfen lassen sollen. Das legt einen zweiten Einsatz des Prinzips nahe: Wir sind in diesem Fall aufgerufen, mehr Mühe in den scheinbar unüberprüfbaren Satz zu investieren, ihn besser zu explizieren und dabei doch noch einen Weg zu seiner Überprüfung freizuschaufeln. Bei dieser Übung kann sich sogar unser Überprüfungsbegriff verändern (und damit auch der Gehalt des Verifikationsprinzips selbst). Insgesamt sollten wir den Überprüfungsbegriff so fassen, dass laut Prinzip nicht zuviele wichtige Sätze sinnlos erscheinen. In einer aufklärerischen Ethik des klaren Redens, Meinens und Fragens kommt es darauf an, die gegenläufigen Denkbewegungen auszutarieren, in die wir beim verifikationalistischen Philosophieren gezogen werden. Was das heißt, führe ich anhand vermeintlich sinnloser Sätze aus der Raum/Zeit-Philosophie vor. Am Ende des Aufsatzes bringe ich einige Beispiele ausgemachten Unsinns. (shrink)

This paper discusses the connection between epistemic virtues and chemistry in the eighteenth century Dutch Republic. It does so in two ways. First, it presents the virtue epistemology of three Dutch university professors and natural philosophers: Herman Boerhaave, Petrus van Musschenbroek, and Johannes David Hahn. It shows how their criticism of a priori philosophy and their defence of experimental natural philosophy is connected to a specific virtue epistemology. Four epistemic virtues are central for these authors: intellectual patience, diligence and (...) humility, and impartiality. This virtue epistemology informs their presentation of chemistry as an exemplary discipline. The practice of chemistry instils these key epistemic virtues in its practitioners. Second, the article shows how these epistemic virtues also play a role in later debates regarding the reception of Lavoisier’s work in the Dutch Republic. This article hopes to provide an example of what Ian Kidd has called a ‘deep conception of epistemic vice [and virtue]’. It also argues for the fruitfulness of applying a virtue epistemic framework to the study of the Chemical Revolution. (shrink)

ACTION-THEORETICALLY EXPLANATORY INTERPRETATIONS AS A MEANS OF SEMANTIC MEANING ANALYSIS The article first develops a general procedure for semantic meaning analysis in difficult cases where the meaning is very uncertain. The procedure consists of searching for one or more possible hypothetical causal explanations of the text, these explanations containing, among other things, the semantic intention of the author, his subjective reasons for this meaning and for the writing down of the text, but also the path of transmission of the text (...) from the writing down to the respective present text version. These hypothetical explanations (interpretations) are deductive-nomological or probabilistic, therefore presuppose corresponding general law hypotheses. If there is only one possible (hypothetical) explanation of the text at hand, this hypothetical explanation is also true. Very often, however, there are several possible explanations. In this case, the probabilities of these possible explanations must be determined; these probabilities then carry over to the individual hypotheses in the explanation (according to Bayes' law). This general procedure of meaning analysis is used in the second part of the article to reconstruct two famous interpretations (by Wapnewski and Hahn) of a poem by Walther von der Vogelweide ("Nemt, frowe, disen kranz"). -/- GERMAN ABSTRACT In dem Artikel wird zunächst ein allgemeines Verfahren zur semantischen Bedeutungsanalyse in schwierigen Fällen entwickelt, in denen die Bedeutung sehr unsicher ist. Das Verfahren besteht darin, daß eine oder mehrere mögliche hypothetische kausale Erklärungen des Textes gesucht werden, wobei diese Erklärungen u.a. die semantische Intention des Autors enthalten, seine subjektiven Gründe für diese Bedeutung und für die Niederschrift des Textes, aber auch den Weg der Tradierung des Textes von der Niederschrift bis zur jeweils vorliegenden Textversion. Diese hypothetischen Erklärungen (Deutungen) sind deduktiv-nomologisch oder probabilistisch, setzen deshalb entsprechende allgemeine Gesetzeshypothesen voraus. Wenn es nur eine mögliche (hypothetische) Erklärung des vorliegenden Textes gibt, ist diese hypothetische Erklärung auch wahr. Sehr häufig gibt es aber mehrere mögliche Erklärungen. In diesem Fall müssen die Wahrscheinlichkeiten dieser möglichen Erklärungen bestimmt werden; diese Wahrscheinlichkeiten übertragen sich dann auch auf die einzelnen Hypothesen in der Erklärung (nach dem Bayesschen Gesetz). Dieses allgemeine Verfahren der Bedeutungsanalyse wird im zweiten Teil des Artikels zur Rekonstruktion zweier berühmter Interpretationen (von Wapnewski und Hahn) eines Gedichts von Walther von der Vogelweide („Nemt, frowe, disen kranz“) verwendet. (shrink)

This paper responds to the generous comments by Alexander Klein and Cheryl Misak on my “American Pragmatism and the Vienna Circle: The Early Years”. First, besides offering some clarification of my original thesis, I argue that Jerusalem was not liable to the anti-Spencerian criticisms by James that Klein adduces in the course of defending James against the charge of psychologism. Then I investigate the impact of Wittgenstein’s Ramsey-derived pragmatism, importantly foregrounded by Misak, on the Vienna Circle and argue that it (...) was mainly limited to Schlick but not recognized as pragmatist, also leaving unaffected the impact of James’s pragmatism on Frank, Hahn and Neurath specified in my original paper. That said, Klein’s and Misak’s comments add significantly to our understanding of long-neglected transatlantic philosophical connections in the early twentieth century. (shrink)

This study examines the place of the Philosophical Society of the University of Vienna (1888-1938) in the evolution of the history of philosophy in Austria up to the establishment of the Vienna Circle in 1929. I will examine three aspects of the relationship between the Austrian members of the Vienna Circle and the Philosophical Society which has been emphasized by several historians of the Vienna Circle: the first aspect concerns the theory of a first Vienna Circle formed mainly by H. (...) Hahn, P. Frank and O. Neurath; the second aspect is the contention that the missing link between the Vienna Circle and the Bolzano tradition in Austria is Alois Höfler, a student of Brentano and Meinong; I will finally examine the link they established between the annexation of the Philosophical Society to the Kant-Gesellschaft in 1927 and the founding of the Vienna Circle in 1929. I will argue that this institution played a key role in the history of philosophy in Austria and is partly responsible for the formation of the Vienna Circle. (shrink)

In this introduction, I first present the general problematic of the special section. Our world faces several existential challenges war, and global injustice) and some would argue that the only adequate answer to these challenges is setting up a world government. I then introduce the contributions that comprise the scholarly body of the special section: Andrić on global democracy; Hahn on global political reconciliation; Pinheiro Walla on Kant and world government; Miklós & Tanyi on institutional consequentialism and world governance. (...) Lastly, I briefly describe the practical context in which the idea of the special section has arisen and in which the present contributions have taken shape. (shrink)

Kolloquiumsbeiträge des XV. Deutschen Kongresses für Philosophie 1990 in Hamburg. Mit Beiträgen von Herbert Schnädelbach, Hilary Putnam, Karl-Otto Apel, Walter Ch. Zimmerli, Rudolf A. Makkreel, Wolfgang Bartuschat, Elke Hahn und Klaus Vieweg, Roland Simon-Schaefer, Ruedi Imbach, Georg Wieland, Jan Peter Beckmann, Pierre Aubenque, Annemarie Gethmann-Siefert, Gernot Böhme, Dietrich Böhler, Jürgen Habermas, Friedrich Kambartel, Oswald Schwemmer, Dieter Birnbacher, Karl-Friedrich Wessel, Friedrich Rapp, Otfried Höffe, Henning Ottmann und Terry Pinkard.

The purpose of this paper is to provide insights into how the proliferation of globalization has impacted labor markets both in a advanced industrialized nations and well as developing nations. Insightful analysis will be drawn from Oatley (2011) on division of labor, Jaumotte & Tytell (2007) on labor compensation, Hahn & Narjoko (2013) on the impact on South Asian Countries, Basu (2016) on wage as a share of GDP and Wallace, Gauchat & Fullerton (2011) on the impact of globalization (...) and labor markets on inequality. (shrink)

Our visual experience seems to suggest that no continuous curve can cover every point of the unit square, yet in the late nineteenth century Giuseppe Peano proved that such a curve exists. Examples like this, particularly in analysis (in the sense of the infinitesimal calculus) received much attention in the nineteenth century. They helped instigate what Hans Hahn called a “crisis of intuition”, wherein visual reasoning in mathematics came to be thought to be epistemically problematic. Hahn described this (...) “crisis” as follows: Mathematicians had for a long time made use of supposedly geometric evidence as a means of proof in much too naive and much too uncritical a way, till the unclarities and mistakes that arose as a result forced a turnabout. Geometrical intuition was now declared to be inadmissible as a means of proof... (p. 67) Avoiding geometrical evidence, Hahn continued, mathematicians aware of this crisis pursued what he called “logicization”, “when the discipline requires nothing but purely logical fundamental concepts and propositions for its development.” On this view, an epistemically ideal mathematics would minimize, or avoid altogether, appeals to visual representations. This would be a radical reformation of past practice, necessary, according to its advocates, for avoiding “unclarities and mistakes” like the one exposed by Peano. (shrink)