This book began with my edition of the anonymous treatise. A translation and notes seemed essential if the material of the treatise was to be understood. It then seemed that Chapter 5 of Heytesbury's Rules for Solving Sophismata, on which the treatise was based, should also be included. My translation of the Heytesbury treatise is based on a fifteenth-century edition, supplemented by readings from a few of the better manuscripts. (A critical edition from all the manuscripts, of which Chapter 5 (...) will be mine, is now in progress under the supervision of Paul Spade, but only a few insignificant changes in the translation should be necessitated by the completed edition. ) An examination of related materials seemed reasonable, and these included Heytesbury's commentator Gaetano, as well as a chapter from a treatise by Johannes Venator (in an edition in progress provided by Francesco del Punta). It seemed unnecessary to publish Gaetano's and Venator's related works in this volume, but all their departures from Heytesbury and the anonymous treatise are noted here. I have not examined other works in the tradition in any detail. I owe a great deal to my teacher, Norman Kretzmann, not only as regards the edition and translations, but also as regards the notes, study and introduction. The referees of the typescript (to me unknown) made unusually thorough criticisms and suggestions to which I have paid close attention. The book is far better for my having done so. (shrink)

This paper inquires into how the new techniques of 14th-century physics, especially the doctrines of the maxima and minima of powers and the latitudes of forms, were applied to the issue of propagation of light. The focus is on several Prague disputed questions, originating between 1377 and 1409, dealing with whether illumination has infinite or finite reach and whether illumination’s intensity remains constant (uniformis) or is rather uniformly decreasing (uniformiter difformis). These questions are contextualised through examination of Oxford, (...) Paris, and Prague sources of the era (John Dumbleton, John Buridan, Nicole Oresme, Albert of Saxony, Henry of Langenstein, John of Holland) to construct a fresh survey of late medieval theories of light. Along the way, the discovery of a hitherto unknown Prague disputation from the 1370s is announced, and new evidence for the dating and Central European dissemination of Jacobus de Sancto Martino’s De latitudinibus formarum and Nicole Oresme’s Questiones super Geometriam is uncovered. (shrink)

Where are we to look for the unique hues? Out in the world? In the eye? In more central processing? 1. There are difficulties looking for the structure of the unique hues in simple combinations of cone-response functions like ( L − M ) and ( S − ( L + M )): such functions may fit pretty well the early physiological processing, but they don’t correspond to the structure of unique hues. It may seem more promising to look to, (...) e.g., Hurvich & Jameson’s ‘chromatic response functions’; but these report on psychophysical behaviour, not on underlying physiology. So ‘opponent processing’ isn’t any particular help on the unique hues—and even physiology in general seems not to have come up with any good correlate or explanation. 2. Wright ( Review of Philosophy and Psychology 2: 1–17, 2011 ) looks in a different place: to (a) magnitude of total visual response that a stimulus light provokes, the maxima and minima of which, he thinks, give us the boundaries of the main hue categories (Wright connects these with Thornton’s ‘prime’ and ‘antiprime’ colours in an illuminant: Journal of the Optical Society of America 61 ( 1971 ): 1155–1163); and (b) the ratio of chromatic to achromatic response, the maxima and minima of which, he suggests, give us the focal points of the unique hues. The suggestions are extremely interesting; but the desired correspondences have some counterexamples; and where they hold, one could wonder how much they depend upon the particular choice of functions to measure (a) and (b); and one could hope for more of an explanatory linkage between the sets of items in question. 3. Could the unique hues come from, so to speak, the external world? White and black can easily be defined as particular kinds of reflectance. What of the standard four unique hues? Variation in kinds of sunlight and skylight coincides well with variation along a line from unique yellow to unique blue (cf. Shepard 1992 , Mollon 2006 ). If we wanted something to calibrate our standards for unique yellow and blue as the lens of the eye changes with age, and despite interpersonal cone differences, this would be a good basis—and there are several ways this can be extended to surface colours. But is there any essential connection between these things: is there any rationale why the light of the sun and the sky should be counted as unique hued ? An answer may be: because in our environment, these illuminants are as close to white (or the natural illuminant colour) as you can get—to see things tinged with sunlight or skylight should be to see them minimally tinged with any alien colour. Whereas other hues in an illuminant would be treated as tinging with a more alien colour the thing seen. (shrink)

We continue the program of looking for increased complexity within aesthetic field theory. We study a solution with five planar maxima and minima. Another solution in which we counted 19 planar maxima and minima is also studied. This latter solution was obtained by modifying our previous principles by allowing for an arbitrariness associated with the integration path in conjunction with the equation Γ jk:1 i =0.

Adequality, or παρισóτης (parisotēs) in the original Greek of Diophantus 1 , is a crucial step in Fermat’s method of finding maxima, minima, tangents, and solving other problems that a modern mathematician would solve using infinitesimal calculus. The method is presented in a series of short articles in Fermat’s collected works (1891, pp. 133–172). The first article, Methodus ad Disquirendam Maximam et Minimam 2 , opens with a summary of an algorithm for finding the maximum or minimum value (...) of an algebraic expression in a variable A. For convenience, we will write such an expression in modern functional notation as f (a). 3 The algorithm can be broken up into six steps in the following way:Introduce an auxiliary .. (shrink)

La contemporaneidad es facticidad sin sentido, un “espacio de crisis” donde al “ocultamiento de Dios” (teología) le corresponde “la imposibilidad del Absoluto” (filosofía), y a ambos les son correlativas la imposición de un “universo infinito e inestable” (ciencia) y la consecuente pérdida de significancia (semiótica) que implican el vacío y las ausencias. Esa contemporaneidad es asimismo preludio que inaugura la emergencia hegemónica de la efectividad (tecnología), al costo de una debacle espiritual que tiene consecuencias trágicas para la vida y la (...) convivencia humanas. El agotamiento de las dimensiones imaginarias o no de ese universo, determinadas por las repeticiones inexorables de su geografía máxima y mínima, o la imposibilidad de progresar “más allá de la inmanencia” que reitera los recorridos reales y virtuales por la materia, proyecta nefastos efectos desexistenciarios sobre una humanidad que se hunde en la facticidad sin sentido y pervierte cualquier posibilidad de conocimiento, valor y virtud. La emergencia de novedosas modalidades de subjetividad, que atentan contra la existencia colectiva de comunidades, culturas y modos de vida, tienen directa relación con originales formas de reproducción del capital (economía) y modos traumáticos para realizar el prometeico sueño de producción de poder privado (política). También influye de manera decisiva la vigencia de un sistema de poder tecnocrático que sustituye “lo real” por virtualidades e impone una “convivencia” determinada por flujos digitales efímeros e inconsistentes. Esta obra demuestra que tales cuestiones económicas o políticas, científicas o técnicas, lejos de ser contradictorias con un tratamiento teológico o filosófico de la realidad, dependen de la previa respuesta de éste a los problemas elementales que la ciencia y la tecnología deben tener por resueltos antes de aplicar sus progresos por más elocuentes que estos pudieran parecer. Y tal demostración, en el presente texto, no gira en el vacío sino que perdura fundamentada en un recorrido ejemplificador a través de las diversas culturas “occidentales” que han predominado, primero en la misión de “ordenar a la Humanidad” en el tiempo y el espacio, para luego desatar la tragedia que signa un porvenir de convulsiones y pérdidas. Un “mundo” llega a su fin y las formas y elementos que lo sostenían se degradan fungiendo una transición hacia nuevas dimensiones de un “futuro” donde el hombre será un mendigo de lo inexorable. Sólo la conciencia plena del colapso y las causas que lo generan puede abrir una herida en ese futuro a favor del ser humano, evitando la pérdida de su condición de persona y de las virtudes propias que pueden salvarlo. (shrink)

This article is a brief overview of major ontological arguments. The most noteworthy feature of this article is the statement of a new parody of the Anselmian and Cartesian arguments that is obviously immune to objections adverting to intrinsic minima and maxima.

We present a general theory of series-parallel mental architectures with selectively influenced stochastically non-independent components. A mental architecture is a hypothetical network of processes aimed at performing a task, of which we only observe the overall time it takes under variable parameters of the task. It is usually assumed that the network contains several processes selectively influenced by different experimental factors, and then the question is asked as to how these processes are arranged within the network, e.g., whether they are (...) concurrent or sequential. One way of doing this is to consider the distribution functions for the overall processing time and compute certain linear combinations thereof (interaction contrasts). The theory of selective influences in psychology can be viewed as a special application of the interdisciplinary theory of (non)contextuality having its origins and main applications in quantum theory. In particular, lack of contextuality is equivalent to the existence of a “hidden” random entity of which all the random variables in play are functions. Consequently, for any given value of this common random entity, the processing times and their compositions (minima, maxima, or sums) become deterministic quantities. These quantities, in turn, can be treated as random variables with (shifted) Heaviside distribution functions, for which one can easily compute various linear combinations across different treatments, including interaction contrasts. This mathematical fact leads to a simple method, more general than the previously used ones, to investigate and characterize the interaction contrast for different types of series-parallel architectures. (shrink)

Analyzing geometric properties of high-dimensional loss functions, such as local curvature and the existence of other optima around a certain point in loss space, can help provide a better understanding of the interplay between neural network structure, implementation attributes, and learning performance. In this work, we combine concepts from high-dimensional probability and differential geometry to study how curvature properties in lower-dimensional loss representations depend on those in the original loss space. We show that saddle points in the original space are (...) rarely correctly identified as such in expected lower-dimensional representations if random projections are used. The principal curvature in the expected lower-dimensional representation is proportional to the mean curvature in the original loss space. Hence, the mean curvature in the original loss space determines if saddle points appear, on average, as either minima, maxima, or almost flat regions. We use the connection between expected curvature in random projections and mean curvature in the original space (i.e., the normalized Hessian trace) to compute Hutchinson-type trace estimates without calculating Hessian-vector products as in the original Hutchinson method. Because random projections are not suitable to correctly identify saddle information, we propose to study projections along dominant Hessian directions that are associated with the largest and smallest principal curvatures. We connect our findings to the ongoing debate on loss landscape flatness and generalizability. Finally, for different common image classifiers and a function approximator, we show and compare random and Hessian projections of loss landscapes with up to about 7×10^6 parameters. (shrink)

L’illégitimité de la bande dessinée a une histoire. Elle est le fruit de processus historiques mêlantcritiques de la bande dessinée et efforts de réhabilitation. L’après-guerre a été une période-clé dans ladisqualification de la bande dessinée, alors principalement publiée dans les journaux pour enfants,d’importantes mobilisations en affirmant le caractère criminogène et démoralisateur. Ces discours onttrouvé une validation et une consécration institutionnelles à travers l’adoption de la loi du 16 juillet 1949,qui a organisé, jusqu’à nos jours, un contrôle des publications de bande (...) dessinée. A maxima,ce contrôle a opéré une disqualification en pratique de cette forme d’expression. A minima, il a en tout casentretenu l’image de la bande dessinée comme une forme potentiellement dangereuse, certainement peuéducative, de toute façon faiblement légitime. C’est en ce sens que la loi de 1949 a contribué àl’institutionnalisation, et donc à la relative pérennité, de l’illégitimité de la bande dessinée.The illegitimacy of the comic strip has its own history. It is the result of historical processes that havecombined criticism of comic strips with efforts to rehabilitate them. The post-war years were a pivotal timein the process of disqualifying comic strips as considerableefforts were made to assert their criminalising and demoralising nature. This type of discourse was institutionalisedand enshrined in France by the Act of 16 July 1949, which – until today – has organised controls over the publication of comic strips. At the very least, these controls have sustainedthe view of comic strips as a potentially dangerous, definitely non-educational and scarcely legitimate form,and have even gone so far as to disqualify them entirely in practice. Thus did the Act of 1949 help toinstitutionalise, on a relatively enduring basis, the illegitimate nature of the comic strip. (shrink)

We respond to criticism of our paper “Paradox in Wave-Particle Duality for Non-Perturbative Measurements”. We disagree with Steuernagel’s derivation of the visibility of the Afshar experiment. To calculate the fringe visibility, Steuernagel utilizes two different experimental situations, i.e. the wire grid in the pattern minima and in the pattern maxima. In our assessment, this procedure cannot lead to the correct result for the complementarity properties of a wave-particle in one particular experimental set-up.

Es gibt Eigenschaften, die in ihren empirischen Vorkommnissen gradativ sind, wie z.B. die Eigenschaften, etwas zu wissen und mächtig zu sein] d.h. man kann mehr oder weniger wissen, jemand ist mächtiger oder weniger mächtig als sein Gegenüber usw. usf. Dieser Aufsatz versucht Eigenschaftsexemplifikationen im Bereich von empirischen (Minima und) Maxima an Beispielen von Macht und Wissen dahingehend zu analysieren, ob sie tatsächlich dieselben Eigenschaften wie die durch Standardbeispiele aus dem "mittleren Bereich" definierten (Begriffe von) Eigenschaften betreffen. Es werden (...) Argumente für die Auffassung vorgelegt, im (Grenz-)Bereich der Minima und Maxima (wenigstens der Beispieleigenschaften) gebe es Fälle, wo es sich nicht (mehr) um dieselbe Eigenschaft handeln kann. Paradox formuliert: Es gibt Eigenschaften, deren Maxima (oder Minima) nicht mehr dieselbe Eigenschaft sind. (shrink)

Philosophers no longer argue whether Hume ever read Berkeley, yet some remain puzzled as to why so little of Berkeley appears in Hume's works. Professor Popkin has remarked that even “where Hume and Berkeley come closest to discussing the same subject or holding the same view, Hume neither uses Berkeley's terms nor refers to him.” An apparent exception to this generalization is Berkeley's doctrine ofminima sensibilia, for both philosophers use this term to denote indivisible sensible points, and both invoke such (...) points in order to show that sensible extension is not infinitely divisible. Yet it has been suggested that, although Berkeley and Hume employ the same terms, they nevertheless maintain different doctrines: Hume'sminimaare unextended, whereas Berkeley's are extended. (shrink)

One of the conundrums of Wittgenstein’s so-called ‘1914–1916 Notebooks’ concerns the role played by the visual instances of logical analysis. As a matter of fact, in discussing in that work the requirement that the logical analysis of meaningful sentences be complete, Wittgenstein often takes as examples statements about the colored parts of the subject's visual image (Gesichtsbild). In view of this, it might be thought that the requirement is not laid down in the Notebooks on logical grounds, but somehow on (...) psychological or psychophysical ones. In this paper I argue this is not so and that the requirement is exemplified rather than justified by the analysis of statements about the products of the subject’s visual imagination. I also argue that, on Wittgenstein’s syntactic notion of a complete logical analysis, our unanalyzed statements embody as they are the requirement that their sense be fully determinate; which is just what is meant by the idea that the analysis must be complete. (shrink)

Es gibt Eigenschaften, die in ihren empirischen Vorkommnissen gradativ sind, wie z.B. die Eigenschaften, etwas zu wissen und mächtig zu sein] d.h. man kann mehr oder weniger wissen, jemand ist mächtiger oder weniger mächtig als sein Gegenüber usw. usf. Dieser Aufsatz versucht Eigenschaftsexemplifikationen im Bereich von empirischen (Minima und) Maxima an Beispielen von Macht und Wissen dahingehend zu analysieren, ob sie tatsächlich dieselben Eigenschaften wie die durch Standardbeispiele aus dem "mittleren Bereich" definierten (Begriffe von) Eigenschaften betreffen. Es werden (...) Argumente für die Auffassung vorgelegt, im (Grenz-)Bereich der Minima und Maxima (wenigstens der Beispieleigenschaften) gebe es Fälle, wo es sich nicht (mehr) um dieselbe Eigenschaft handeln kann. Paradox formuliert: Es gibt Eigenschaften, deren Maxima (oder Minima) nicht mehr dieselbe Eigenschaft sind. (shrink)

In a letter from June 3, 1945, Adorno candidly relates to Thomas Mann his innermost feelings about meeting the novelist in the United States: “When I was able to meet you here in person, upon this remote western coast, I had the feeling that I was only now, for the first time, actually encountering that German tradition from which I have received everything—including the strength to resist the tradition.”1 At first glance, there is nothing too remarkable about this note from (...) an admirer of one of the masters of European letters. Under closer scrutiny, however, this seemingly innocuous letter accentuates…. (shrink)

This article attempts to think of thinking as the essence of critical education. While contemporary education tends to stress the conveying of knowledge and skills needed to succeed in present-day information society, the present article turns to the work of Theodor W. Adorno to develop alternative thinking about education, thinking, and the political significance of education for thinking. Adorno touched upon educational questions throughout his writings, with growing interest in the last ten years of his life. Education, he argues following (...) Kant, must enable students to think for themselves and to break free of the authority of teachers, parents and other adults. Nevertheless, in his discussions of education Adorno says little about the nature of thinking, and the secondary literature on his educational theory addresses this question only cursorily. Important claims on the nature of thinking do appear elsewhere in Adorno's work. From his early writings up to Negative Dialectics, Adorno is preoccupied with thinking, sketching the outlines of critical-dialectical thought. Still, these reflections rarely touch upon educational questions, and the Adorno scholarship has yet to establish this link. Unlike studies which read Adorno's educational thought against the backdrop of the history of education and the German Bildung tradition, or in relation to art and aesthetics, the present article brings together Adorno's ideas on education and thinking in an attempt to contribute both to the Adorno scholarship and to the growing field of education for thinking. (shrink)

This interdisciplinary volume revisits Adorno's lesser-known work, Minima Moralia, and makes the case for its application to the most urgent concerns of the 21st century. Contributing authors situate Adorno at the heart of contemporary debates on the ecological crisis, the changing nature of work, the idea of utopia, and the rise of fascism. Exploring the role of critical pedagogy in shaping responses to fascistic regimes, alongside discussions of extractive economies and the need for leisure under increasingly precarious working conditions, (...) this volume makes new connections between Minima Moralia and critical theory today. Another line of focus is the aphoristic style of Minima Moralia and its connection to Adorno's wider commitment to small and minor literary forms, which enable capitalist critique to be both subversive and poetic. This critique is further located in Adorno's discussion of a utopia that is reliant on complete rejection of the totalising system of capitalism. The distinctive feature of such a utopia for Adorno is dependent upon individual suffering and subsequent survival, an argument this book connects to the mutually constitutive relationship between ecological destruction and right-wing authoritarianism. These timely readings of Adorno's Minima Moralia teach us to adapt through our survival, and to pursue a utopia based on his central ideas. In the process, opening up theoretical spaces and collapsing the physical borders between us in the spirit of Adorno's lifelong project. (shrink)

En este artículo, me propongo exponer algunas dificultades relacionadas con la posibilidad de que la Teoría de Modelos pueda constituirse en una Teoría General de la Interpretación. Específicamente la idea que sostengo es que lo que nos muestra la Paradoja de Orayen es que las interpretaciones no pueden ser ni conjuntos ni objetos. Por eso, una elucidación del concepto intuitivo de interpretación, que apele a este tipo de entidades, está condenada al fracaso. De manera secundaria, muestro que no hay algún (...) supuesto conjuntista que sea imprescindible para que surja la mencionada paradoja: sólo se necesita que las interpretaciones sean objetos. Voy a argumentar que si las interpretaciones son objetos, tal como lo supone la posibilidad de cuantificar sobre las mismas para poder dar una caracterización satisfactoria de consecuencia lógica, la au-toaplicación (como un caso de aplicación de los recursos semánticos de la teoría de modelos para encontrar una interpretación con máxima generalidad) es imposible. Finalmente, discuto cada una de las dos soluciones que el propio Orayen imaginó frente a su paradoja, y muestro que cada una posee diferentes dificultades.In this paper, I intend to present some problems to construe the Model Theory as a Theory of Interpretation. Specifically, I am going to defend that, according to the Paradox of Orayen, interpretations can not be neither set nor object. Thus, an explication of the intuitive concept of interpretation that appeals to these types of entities will be condemned to failure. Secondary, I will show that there is not any like-set assumption indispensable to get rise to that paradox: only all is needed is the assumption that interpretations are objects. I am going to argue that if interpretations are objects, as it is assumed by the possibility of quantifying over interpretations in order to offer an satisfactory characterization of logical consequence, self-application (as a case of application of semantics resources of the Model Theory for finding a interpretation with absolute generality) is not possible. Eventually, I will discuss both of the solutions provided by Orayen to his paradox and I will support that both have different difficulties. (shrink)

A reflection on everyday existence in the 'sphere of consumption of late Capitalism', this work is Adorno's literary and philosophical masterpiece.

En este artículo, me propongo exponer algunas dificultades relacionadas con la posibilidad de que la Teoría de Modelos pueda constituirse en una Teoría General de la Interpretación. Específicamente la idea que sostengo es que lo que nos muestra la Paradoja de Orayen es que las interpretaciones no pueden ser ni conjuntos ni objetos. Por eso, una elucidación del concepto intuitivo de interpretación, que apele a este tipo de entidades, está condenada al fracaso. De manera secundaria, muestro que no hay algún (...) supuesto conjuntista que sea imprescindible para que surja la mencionada paradoja: sólo se necesita que las interpretaciones sean objetos. Voy a argumentar que si las interpretaciones son objetos, tal como lo supone la posibilidad de cuantificar sobre las mismas para poder dar una caracterización satisfactoria de consecuencia lógica, la au-toaplicación (como un caso de aplicación de los recursos semánticos de la teoría de modelos para encontrar una interpretación con máxima generalidad) es imposible. Finalmente, discuto cada una de las dos soluciones que el propio Orayen imaginó frente a su paradoja, y muestro que cada una posee diferentes dificultades.In this paper, I intend to present some problems to construe the Model Theory as a Theory of Interpretation. Specifically, I am going to defend that, according to the Paradox of Orayen, interpretations can not be neither set nor object. Thus, an explication of the intuitive concept of interpretation that appeals to these types of entities will be condemned to failure. Secondary, I will show that there is not any like-set assumption indispensable to get rise to that paradox: only all is needed is the assumption that interpretations are objects. I am going to argue that if interpretations are objects, as it is assumed by the possibility of quantifying over interpretations in order to offer an satisfactory characterization of logical consequence, self-application (as a case of application of semantics resources of the Model Theory for finding a interpretation with absolute generality) is not possible. Eventually, I will discuss both of the solutions provided by Orayen to his paradox and I will support that both have different difficulties. (shrink)

_Minima Memoria_ attests to the impact of the works of Jean-François Lyotard, one of the most influential French philosophers of the twentieth century, and the continuing effects of these works across a wide array of fields: philosophy, literature, political theory, gender theory, aesthetics, and psychoanalysis. Particular attention is paid to Lyotard's repeated warnings regarding the way in which the complexity of events can be occluded in the very attempt to represent them. Indeed, through the contributors' careful and critical analysis, Lyotard's (...) complex intellectual trajectory—all the way up to the posthumously published works _The Confession of Augustine_ and _The Misery of Philosophy_—is traced in different and often conflicting manners, which bring out the different currents that traverse his writings and the sites of tension that such terms as "different," "affect," and "infancy" mark. What emerges is not a grand narrative that would organize Lyotard's life and work around one unifying idea, but multifaceted approaches that extend in new and unforeseen directions. (shrink)

Transparency has come to enact a fantasy of renewal and immediacy that Theodor W. Adorno himself criticized decades before its widespread deployment in the embassies, ministries, and other government and commercial buildings dotting the landscape of the “New Berlin”. His work criticizes transparency in asserting that the potential promise of insight is only to be realized, if ever, through a recognition of reason's own limitations and the coercive influence of social relations upon critical perception. This chapter traces this critique in (...) the thought-images of Minima Moralia in Adorno's essay “Functionalism Today”, in which he brings much of his critique of aesthetics and politics to bear on architecture. It has set off an intense local debate about the appropriateness of the transparency metaphor, as well as the practical considerations of the use of glass in a public space. (shrink)

The existence and uniqueness of a maximum point for a continuous real—valued function on a metric space are investigated constructively. In particular, it is shown, in the spirit of reverse mathematics, that a natural unique existence theorem is equivalent to the fan theorem.

In our wakeful conscious lives, the experience of time and dynamic temporal phenomena—such as continuous motion and change—appears to be ubiquitous. How is it that temporality is woven into our conscious experience? Is it through perceptual experience presenting a series of instantaneous states of the world, which combine together—in a sense which would need to be specified—to give us experience of dynamic temporal phenomena? In this paper, I argue that this is not the case. -/- Several authors have recently proposed (...) dynamic snapshot models of temporal experience— such as Prosser and Arstila, building upon Le Poidevin— according to which perceptual experience has no temporal content of a non‐zero extent. I argue that there is an absence of motivation for such a view; I develop and defend the claim that perceptual experience minimally presents something of some non‐zero temporal extent as such. (shrink)

Suppose that 〈xk〉k∈ℕ is a countable sequence of real numbers. Working in the usual subsystems for reverse mathematics, RCA0 suffices to prove the existence of a sequence of reals 〈uk〉k∈ℕ such that for each k, uk is the minimum of {x0, x1, …, xk}. However, if we wish to prove the existence of a sequence of integer indices of minima of initial segments of 〈xk〉k∈ℕ, the stronger subsystem WKL0 is required. Following the presentation of these reverse mathematics results, we (...) will derive computability theoretic corollaries and use them to illustrate a distinction between computable analysis and constructive analysis. (shrink)

As a rational discourse philosophy can not be reduced to any cultural concern. Culture we call that civilization which became aware of its own mortality and henceforth cultivates the aesthetic pleasure of representing its ruined ideals. It is the responsibility of philosophy to think through to the end the project of modern philosophical aesthetics, thus accomplishing it. The description of the aesthetic condition shows that aisthesis does not have to provide the fake peace of consentment with the sensible but on (...) the contrary should question and discredit the aistheton that confronts us with a double bind experience. This experience stirs to life the 'minimal soul' in its pure affectibility, and at the same time threatens it with slavery and death. Therefore art has to consist in the achievement of a work, not in disguising nihilism but in carrying it out. Should philosophy accomplish a work of art? The activity of reflexivity in writing which caracterizes philosophy persists in interrogating its own singularity, thereby incessantly dispossessing itself. (shrink)

Este trabajo fue pensado a modo de homenaje a Antoni Domènech, quien nos legó un Programa de Investigación sobre “las raíces históricas y conceptuales del republicanismo democrático clásico”, también valedero para el momento actual del modo de producir capitalista en el que nos encontramos al inicio de la tercera década del siglo XXI. Nos ocuparemos i) de fundamentar y mostrar la viabilidad de una Renta Básica, entendida como resguardo de un mínimum de existencia social para todos, que permitiría garantizar una (...) universalización de la libertad republicana; y también ii) abordaremos el tema de la justificación de una Renta Máxima, entendiendo que la acumulación de riqueza y, por ello mismo, de poder económico y político de los muy ricos, atenta contra el deber fiduciario de las repúblicas democráticas de garantizar una “vida normal” para todos sus habitantes. This article is envisaged as a homage to Antoni Domènech who bequeathed us a Research Programme on “the historical and conceptual origins of classical democratic republicanism”, which is also valid for the phase of the capitalist mode of production we are presently facing at the beginning of the third decade of the twenty-first century. Our aims are 1) to establish and demonstrate the viability of a basic income, which is understood as safeguarding a minimum of social existence for everyone, and that would guarantee the universalisation of republican freedom; and 2) to tackle the question of justifying a Maximum Income, in the understanding that the accumulation of wealth, and hence of the political and economic power of the very rich, is an assault against the fiduciary duty of democratic republics to guarantee a “normal” life for all citizens. (shrink)