Why did Bernhard Riemann, arguably the most original mathematician of his generation, spend the last year of life investigating the mechanism of hearing? Fighting tuberculosis and the hostility of eminent scientists such as Hermann Helmholtz, he appeared to forsake mathematics to prosecute a case close to his heart. Only sketchy pages from his last paper remain, but here we assemble some significant clues and triangulate from them to build a broad picture of what he might have been driving (...) at. Our interpretation is that Riemann was a committed idealist and from this philosophical standpoint saw that the scientific enterprise was lame without the “poetry of hypothesis”. He believed that human thought was fundamentally the dynamics of “mind-masses” and that the human mind interpenetrated, and became part of, the microscopic physical domain of the cochlea. Therefore, a full description of hearing must necessarily include the perceptual dimensions of what he saw as a single manifold. The manifold contains all the psychophysical aspects of hearing, including the logarithmic transformations that arise from Fechner’s law, faithfully preserving all the subtle perceptual qualities of sound. For Riemann, hearing was a unitary physical and mental event, and parallels with modern ideas about consciousness and quantum biology are made. A unifying quantum mechanical model for an atom of consciousness—drawing on Riemann’s mind-masses and the similar “psychons” proposed by Eccles—is put forward. (shrink)

A book-length study of Riemann's multi-dimensional work (in Spanish), which considers his contributions to physics, philosophy and mathematics. Plus a bi-lingual edition (German-Spanish) of some of his landmark papers: the lecture on geometry, with Weyl's comments; the paper introducing the Riemann Conjecture, part of his 1857 paper on function theory; all of the philosophical fragments, etc. These different contributions, and their interconnections, are carefully studied in the introductory essay of 150 pages.

info:eu-repo/semantics/publishedVersion.

Cet article étudie l’édition des œuvres de mathématiciens au xixe siècle Je me concentre sur une étude de cas : l’édition des œuvres du mathématicien allemand B. Riemann, par R. Dedekind et H. Weber, publiées pour la première fois en 1876, puis republiées en 1892 et en 1902, par Teubner, et partiellement traduites en français en 1898 chez Gauthier-Villars. Pour l’édition des textes de mathématiciens au xixe siècle, les éditeurs ne sont plus historiens ou philologues, mais eux-mêmes des mathématiciens (...) de premier plan. Le mathématicien éditeur devient celui qui à la fois lit et fabrique le texte à publier. Le cas des œuvres de Riemann est particulièrement intéressant, car une large majorité du travail éditorial s’est effectué par lettres. Ces lettres, ainsi que les Nachlässe de Riemann et Dedekind fournissent une documentation exceptionnellement riche. Il est possible d’obtenir une vision détaillée du processus d’édition. Après avoir replacé l’édition des œuvres de Riemann et ses rééditions dans leur contexte, j’étudierai certains choix faits par les éditeurs dans la sélection des textes à publier. Enfin, je considérerai la question des modifications et adaptations des textes de Riemann par les éditeurs. (shrink)

Cet article étudie l’édition des œuvres de mathématiciens au xixe siècle Je me concentre sur une étude de cas : l’édition des œuvres du mathématicien allemand B. Riemann, par R. Dedekind et H. Weber, publiées pour la première fois en 1876, puis republiées en 1892 et en 1902, par Teubner, et partiellement traduites en français en 1898 chez Gauthier-Villars. Pour l’édition des textes de mathématiciens au xixe siècle, les éditeurs ne sont plus historiens ou philologues, mais eux-mêmes des mathématiciens (...) de premier plan. Le mathématicien éditeur devient celui qui à la fois lit et fabrique le texte à publier. Le cas des œuvres de Riemann est particulièrement intéressant, car une large majorité du travail éditorial s’est effectué par lettres. Ces lettres, ainsi que les Nachlässe de Riemann et Dedekind fournissent une documentation exceptionnellement riche. Il est possible d’obtenir une vision détaillée du processus d’édition. Après avoir replacé l’édition des œuvres de Riemann et ses rééditions dans leur contexte, j’étudierai certains choix faits par les éditeurs dans la sélection des textes à publier. Enfin, je considérerai la question des modifications et adaptations des textes de Riemann par les éditeurs. (shrink)

In recent years, the ideas of the mathematician Bernhard Riemann have come to the fore as one of Deleuze's principal sources of inspiration in regard to his engagements with mathematics, and the history of mathematics. Nevertheless, some relevant aspects and implications of Deleuze's philosophical reception and appropriation of Riemann's thought remain unexplored. In the first part of the paper I will begin by reconsidering the first explicit mention of Riemann in Deleuze's work, namely, in the second (...) chapter of Bergsonism. In this context, as I intend to show first, Deleuze's synthesis of some key features of the Riemannian theory of multiplicities is entirely dependent, both textually and conceptually, on his reading of another prominent figure in the history of mathematics: Hermann Weyl. This aspect has been largely underestimated, if not entirely neglected. However, as I attempt to bring out in the second part of the paper, reframing the understanding of Deleuze's philosophical engagement with Riemann's mathematics through the Riemann–Weyl conjunction can allow us to disclose some unexplored aspects of Deleuze's further elaboration of his theory of multiplicities and profound confrontation with contemporary science. This finally permits delineation of a correlation between Deleuze's plane of immanence and the contemporary physico-mathematical space of fundamental interactions. (shrink)

A look at the dynamical concept of space and space-generating processes to be found in Kant, J.F. Herbart and the mathematician Bernhard Riemann's philosophical writings.

A central claim of Deleuze's reading of Bergson is that Bergson's distinction between space as an extensive multiplicity and duration as an intensive multiplicity is inspired by the distinction between discrete and continuous manifolds found in Bernhard Riemann's 1854 thesis on the foundations of geometry. Yet there is no evidence from Bergson that Riemann influences his division, and the distinction between the discrete and continuous is hardly a Riemannian invention. Claiming Riemann's influence, however, allows Deleuze to (...) argue that quantity, in the form of ‘virtual number’, still pertains to continuous multiplicities. This not only supports Deleuze's attempt to redeem Bergson's argument against Einstein in Duration and Simultaneity, but also allows Deleuze to position Bergson against Hegelian dialectics. The use of Riemann is thereby an important element of the incorporation of Bergson into Deleuze's larger early project of developing an anti-Hegelian philosophy of difference. This article first reviews the role of discrete and continuous multiplicities or manifolds in Riemann's Habilitationsschrift, and how Riemann uses them to establish the foundations of an intrinsic geometry. It then outlines how Deleuze reinterprets Riemann's thesis to make it a credible resource for Deleuze's Bergsonism. Finally, it explores the limits of this move, and how Deleuze's later move away from Bergson turns on the rejection of an assumption of Riemann's thesis, that of ‘flatness in smallest parts’, which Deleuze challenges with the idea, taken from Riemann's contemporary, Richard Dedekind, of the irrational cut. (shrink)

With Fermat’s Last Theorem finally disposed of by Andrew Wiles in 1994, it’s only natural that popular attention should turn to arguably the most outstanding unsolved problem in mathematics: the Riemann Hypothesis. Unlike Fermat’s Last Theorem, however, the Riemann Hypothesis requires quite a bit of mathematical background to even understand what it says. And of course both require a great deal of background in order to understand their significance. The Riemann Hypothesis was first articulated by Bernhard (...) Riemann in an address to the Berlin Academy in 1859. The address was called “On the Number of Prime Numbers Less Than a Given Quantity” and among the many interesting results and methods contained in that paper was Riemann’s famous hypothesis: all non-trivial zeros of the zeta function, ζ(s) = ∞ n=1 n−s, have real part 1/2. Although the zeta function as stated and considered as a real-valued function is defined only for s > 1, it can be suitably extended. It can, as a matter of fact, be extended to have as its domain all the complex numbers (numbers of the form x + yi, where x and y √ −1) with the exception of 1 + 0i (at which point are real numbers and i =. (shrink)

The concept of a Mannigfaltigkeit in Husserl has been given various interpretations, due to its shifting role in his works. Many authors have been misled by this term, placing it in the context of Husserl’s early period in Halle, while writing the Philosophy of Arithmetic, as a friend and colleague of Georg Cantor.Yet at the time, Husserl distanced himself explicitly from Cantor’s definition and rather took Bernhard Riemann as example, having studied and lectured extensively on Riemann’s theories (...) of space. Husserl’s Mannigfaltigkeitslehre would then not be a Cantorian set-theory, but come rather closer to topology. Then, in the Prolegomena, Husserl introduces the idea of a pure Mannigfaltigkeitslehre as a meta-theoretical enterprise which studies the relations among theories, e.g. how to derive or found one upon another. When Husserl announces that in fact the best example of such a pure theory of manifolds is what is actually practiced in mathematics, this sounds slightly misleading. The pure theory of theories cannot simply be the mathematics underlying topology, but should rather be considered as a mathesis universalis. Indeed, while this might not have been fully clear yet in 1900/1901, Husserl will explicitly tie together the notions of pure theory of manifolds and mathesis universalis. The mathesis universalis in this sense is formal, a priori and analytic, as theory of theory in general. It is an analysis of the highest categories of meaning and their correlative categories of objects. In my paper I try to understand the development of the notion of Mannigfaltigkeit in Husserl’s thought from its mathematical beginnings to its later central philosophical role, taking into account the mathematical background and context of Husserl’s own development. (shrink)

The concept of a Mannigfaltigkeit in Husserl has been given various interpretations, due to its shifting role in his works. Many authors have been misled by this term, placing it in the context of Husserl’s early period in Halle, while writing the Philosophy of Arithmetic, as a friend and colleague of Georg Cantor.Yet at the time, Husserl distanced himself explicitly from Cantor’s definition and rather took Bernhard Riemann as example, having studied and lectured extensively on Riemann’s theories (...) of space. Husserl’s Mannigfaltigkeitslehre would then not be a Cantorian set-theory, but come rather closer to topology. Then, in the Prolegomena, Husserl introduces the idea of a pure Mannigfaltigkeitslehre as a meta-theoretical enterprise which studies the relations among theories, e.g. how to derive or found one upon another. When Husserl announces that in fact the best example of such a pure theory of manifolds is what is actually practiced in mathematics, this sounds slightly misleading. The pure theory of theories cannot simply be the mathematics underlying topology, but should rather be considered as a mathesis universalis. Indeed, while this might not have been fully clear yet in 1900/1901, Husserl will explicitly tie together the notions of pure theory of manifolds and mathesis universalis. The mathesis universalis in this sense is formal, a priori and analytic, as theory of theory in general. It is an analysis of the highest categories of meaning and their correlative categories of objects. In my paper I try to understand the development of the notion of Mannigfaltigkeit in Husserl’s thought from its mathematical beginnings to its later central philosophical role, taking into account the mathematical background and context of Husserl’s own development. (shrink)

Pseudo‐mechanistic explanations in psychology and cognitive neuroscienceThis paper focuses on the level of systems/cognitive neuroscience. It argues that the great majority of explanations in psychology and cognitive neuroscience is “pseudo‐mechanistic.” On the basis of various case studies, Hommel argues that cognitive neuroscience should move beyond what he calls an “Aristotelian phase” to become a mature “Galilean” science seeking to discover actual mechanisms of cognitive phenomena.

Is there a language of transcendence which does not fall under the well-worn categories of monism, theism, pantheism, biblical or pagan monotheism, personal or tripersonal God, or an impersonal absolute, conceived as immanent and/or transcendent? The present set of studies from different fields of research centers on the question whether it is possible to speak at all of transcendence or a divinity, and if it is, under what limitations does such speech proceed. In current discussion in theology and in philosophy (...) of religion, there is a pervasive awareness that the inherited terms and alternatives, developed in the western tradition, no longer facilitate an adequate understanding of the divine. Increasing familiarity with the languages of 'immanence' and 'transcendence' (under erasure) in Hindu and Buddhist thought has further jumbled our coordinates, while holding out the promise of a more subtle and vital engagement with the matter itself of religious inquiry. A further long-established distinction, between 'personal' and 'impersonal, ' also takes on rich new hues in Asian contexts, where the very notion of 'person' may undergo unsettling critiques. Transgressing the categories of 'personal' and 'impersonal' points to the mystical depth of religious traditions, emphasizes their openness and reintegrates essential elements of both perspectives. Advancing with curiosity and caution, all the contributors take seriously the diversity of historical religious traditions, while nevertheless searching for a fresh language that may connect these traditions and provide a common ground of understanding. (shrink)

In den 1860er Jahren entwarf der Zoologe Ernst Haeckel die wissenschaftliche Weltanschauung des Monismus, die er in einer Vielzahl popularwissenschaftlicher Schriften mit grossem Erfolg verbreitete. Auf der Grundlage der Darwinschen Theorie rief er die Biologie zur neuen Leitwissenschaft aus und postulierte die Einheit von Natur und Kultur. Seither galt Haeckel vielen als der deutsche Darwin, der die Gottesebenbildlichkeit des Menschen sowie die Schopfungstheologie zu Grabe getragen und so dem modernen Weltbild zum Durchbruch verholfen habe. Infolgedessen wurden die naturtheologischen und pantheistischen (...) Zuge des Monismus lange Zeit vernachlassigt. Demgegenuber formuliert Bernhard Kleeberg die These, dass gerade diese nicht-darwinistischen Elemente das monistische Denken nachdrucklich bestimmt haben. Anhand der wesentlichen Schriften Haeckels sowie an Auszugen aus seiner Korrespondenz rekonstruiert der Autor Genese und Kernaussagen des Monismus. Es wird deutlich, dass auch Haeckels Naturphilosophie letztlich im Banne romantischer und naturtheologischer Deutungsmuster steht. (shrink)

Good’s theorem is the apparent platitude that it is always rational to ‘look before you leap’: to gather information before making a decision when doing so is free. We argue that Good’s theorem is not platitudinous and may be false. And we argue that the correct advice is rather to ‘make your act depend on the answer to a question’. Looking before you leap is rational when, but only when, it is a way to do this.

This chapter covers the traditional role of responsibility, and the possible connections between response and responsibility. These connections are explored through the advance of trust and the surplus of the extraordinary in relation to the Third Party. The idea of responsibility comes from the sphere of juridical law, and has a theological touch. The classical conception presented suffers from a permanent erosion that is reinforced by systemic constraints. Trust is a natural element of every community that is together applied by (...) common aims in life. The phenomenon of trust refers to the bond, the nexus, which holds together the members of a community, creating the requisite solidarity. The term ‘trust’ or ‘confidence’ should not primarily read as a substantive, but as a verb or as the derivative of a verb. Furthermore, it is noted that the responsive ethics proposed could function as a permanent corrective. (shrink)

This chapter challenges the assumption of attention functioning as a means of preventing consciousness from getting overloaded, and also challenges the assumption of any relationships between management of scarce resources and the original biological function of attention. It emphasizes that attention is directly derived from mechanisms governing the control of basic movements. The author establishes the theoretical stage through discussions on the implications of the brain’s preference to stimulus events and action plans in a feature-based manner and processing information through (...) different mechanisms. The chapter also discusses many empirical findings supporting the conception of action planning and action control having the potential to determine perception and attention. (shrink)

Wiederkehr des Raumes?. Topologisches Paradigmen ; Rückkehr zum gelebten Raum ; Raumkonzepte und Raumpraktiken ; Regionale oder fundamentale Räumlichkeit ; Zweideutigkeiten und Paradoxien der Lebenswelt -- Polarität von Ort und Raum. Phänomenologische Topik ; Wo-Frage im Schatten der Was-Frage ; Ortsbestimmung als Antwort auf eine Wo-Frage ; Fremde und eigene Wo-Frage ; Hier als Standort : Grund und Boden ; Woher und Wohin : Wegstrecken ; Worin : offene und geschlossene Räume ; Ringsum : Umgebung, Umwelt und Welt ; Wie (...) weit : Vermessene Räume -- Leibliches Wohnen im Raum. Vielfalt des Raumes ; Verankerung im Hier ; Raumachsen ; Durchmessung, Dehnung und Schrumpfung des Raumes ; Nähe und Ferne ; Drinnen und Draußen ; Interieur und Exterieur im Blickfield der Malerei ; Raumanlage und Raumbühne ; Raumtechniken und Ortskarten ; Lokale Räume und globaler Raum -- Ortsverschiebungen. Hier und Anderswo ; Aktualität, Habitualität und Virtualität der räumlichen Bewegung ; Spuren der Zeit im Raum ; Zersprengter Raum ; Telepräsenz ; Fremdorte und andere Räume ; Gemeinorte und globaler Raum ; Gastlichkeit ; Coda : Topos : Atopie : Heterotopien -- Zeitverdoppelung und Zeitverschiebung. Zwischen Mythos und Logos ; Frage nach der Zeit ; Zeitverdoppelung in der Rede und Zeitverkörperung ; Zeitverschiebung zwischen Pathos und Respons ; Zeitverschiebung und Reaktionszeit ; Der entrückte Anfang im Roman und auf der Bühne ; Zeit der Sinne ; Jenseits von Erinnerung und Erwartung ; Rhythmen und Tempi ; Zwischen Leere und Erfüllung ; Coda : Anderswo enden -- Die verändernde Kraft der Wiederholung. Wiederholungsexperiment ; Sich wiederholdende Erfahrung ; Widerholung als Rettung aus der Zeit ; Altes und Neues im Widerstreit ; Unwiederholbares in der Zeit -- Die Wahrscheinlichkeit von Zukünftigem im Anschluß an Aristoteles. Handlungsperspektive ; Die drohende Seeschlacht ; Wahrscheinlichkeit und Häufigkeit ; Zwischen Gewißheit und Ungewißheit ; Rückzug auf pratische Gewißheit ; Zwischen Entwurf und Erwartung ; Unwahrscheinliche Zukunft -- Kommen und Gehen in der Zeit im Anschluß an Merleau-Ponty. Frühe dialektik der Zeit ; Zeit als bloßes Nacheinander ; Totalität der Zeit : Präsenzfeld ; Riß der Zeit : Selbstaffektion ; Bewegung der Zeit : Vor- und Rückläufigkeit ; Wahrnehmung zwischen Vor- und Rückblick ; Handeln zwischen Vorsatz und Vorschlag ; Kommen und Gehen ; Chiasmus der Zeit -- Epilog : Verquickung von Ort, Raum und Zeit. (shrink)

Epistemologists have recently noted a tension between (i) denying access internalism, and (ii) maintaining that rational agents cannot be epistemically akratic, believing claims akin to ‘p, but I shouldn’t believe p’. I bring out the tension, and develop a new way to resolve it. The basic strategy is to say that access internalism is false, but that counterexamples to it are ‘elusive’ in a way that prevents rational agents from suspecting that they themselves are counterexamples to the internalist principles. I (...) argue that this allows us to do justice to the motivations behind both (i) and (ii). And I explain in some detail what a view of evidence that implements this strategy, and makes it independently plausible, might look like. (shrink)

Keine ausführliche Beschreibung für "Die Rationalität der Metapher" verfügbar.

Bernhard Nickel presents a theory of generic sentences and the kind-directed modes of thought they express. The theory closely integrates compositional semantics with metaphysics to solve the problem that generics pose: what do generics mean? Generic sentences are extremely simple, yet if there are patterns to be discerned in terms of which are true and which are false, these patterns are subtle and complex. Ravens are black, and lions have manes: statistical measures cannot do justice to the facts, but (...) what else is there that has a hope of giving us insight into what we are capturing across so many domains? Nickel argues that generics are the top of a fundamentally explanatory iceberg, and that this explanatory framework is deeply intertwined with the semantics of the language we use to express them. In providing an integrated semantic and metaphysical theory of generics, he aims to solve old puzzles and draw attention to new phenomena. (shrink)

Religions commonly are taken to provide general orientation in leading one's life. We develop here the idea that religions also may have a much more concrete guidance function in providing systematic decision biases in the face of cognitive-control dilemmas. In particular, we assume that the selective reward that religious belief systems provide for rule-conforming behavior induces systematic biases in cognitive-control parameters that are functional in producing the wanted behavior. These biases serve as default values under uncertainty and affect performance in (...) any task that shares cognitive-control operations with the religiously motivated rule-conforming behavior the biases were originally developed for. Such biases therefore can be unraveled and objectified by means of rather simple tasks that are relatively well understood with regard to the cognitive mechanisms they draw on. (shrink)

In this paper, I distinguish three claims, which I label individual intentional autonomy, individual intentional autarky, and intentional individualism. The autonomy claim is that under normal circumstances, each individual's behavior has to be interpreted as his or her own action. The autarky claim is that the intentional interpretation of an individual's behavior has to bottom out in that individual's own volitions, or pro-attitudes. The individualism claim is weaker, arguing that any interpretation of an individual's behavior has to be given in (...) terms of individual intentional states. I argue that individual intentional autonomy implies neither individual intentional autarky, nor intentional individualism, with which it is usually lumped together. I further argue that this insight is the key to an adequate view of an important class of actions, i.e., plural actions. Key Words: joint action • shared intentions • methodological individualism • intentional interpretation • collective agents • influence • autonomy. (shrink)

Traditional approaches to human information processing tend to deal with perception and action planning in isolation, so that an adequate account of the perception-action interface is still missing. On the perceptual side, the dominant cognitive view largely underestimates, and thus fails to account for, the impact of action-related processes on both the processing of perceptual information and on perceptual learning. On the action side, most approaches conceive of action planning as a mere continuation of stimulus processing, thus failing to account (...) for the goal-directedness of even the simplest reaction in an experimental task. We propose a new framework for a more adequate theoretical treatment of perception and action planning, in which perceptual contents and action plans are coded in a common representational medium by feature codes with distal reference. Perceived events (perceptions) and to-be-produced events (actions) are equally represented by integrated, task-tuned networks of feature codes – cognitive structures we call event codes. We give an overview of evidence from a wide variety of empirical domains, such as spatial stimulus-response compatibility, sensorimotor synchronization, and ideomotor action, showing that our main assumptions are well supported by the data. Key Words: action planning; binding; common coding; event coding; feature integration; perception; perception-action interface. (shrink)

Living corporeity is the intermediate element between nature and culture, which must be thought of as a reciprocal interconnection, since as corporeal beings we always move on a threshold. In the reflection of the bodily self, a doubling between the living body as a functioning subject and as a material object is revealed; after all, even one's own body sometimes takes on the features of a foreign body, as is the case in the experience of illness. In the technical instrument, (...) the body is prolonged and this highlights the connection between the technique of the thing and the technique of the self; however, despite the gradual autonomisation of the technical element from the living corporeity, there remains what escapes calculation and looms large in the subtraction of the alien. (shrink)