We characterize the collapse of Buss' bounded arithmetic in terms of the provable collapse of the polynomial time hierarchy. We include also some general model-theoretical investigations on fragments of bounded arithmetic.

Summary This article opens with a brief introduction to Giuseppe Mazzini, with particular reference to his commitment to republicanism, an ideal that would be fulfilled in Italy only after considerable time and with great difficulty. It then focuses on Mazzini's critical reception of Byron. Although Giuseppe Mazzini and Percy Bysshe Shelley would have allowed a more obvious comparison, it was Byron who really attracted Mazzini's attention and criticism. Mazzini uses Byron, on the one hand, as a means to demonstrate that (...) Italians could discuss European poetry without putting at risk their national identity, or, as the classicists maintained, that fragile and fragmented profile of a nation that contemporary Italy offered to the minds and hearts of thousands of young people. On the other hand, however, Mazzini questions Byron's authority by subverting and converting his value, in a very personal way: he gradually substitutes Byron's with a different authority and credits him with new values. Mazzini could not accept Byron as the emblem of elitism and isolation: Byron's solipsism needed to be purified, and his renowned cynical attitude tempered; eventually Byron's myth needed to be connected to the destiny of peoples and nations. (shrink)

We show that every model of IΔ0 has an end extension to a model of a theory where log-space computable function are formalizable. We also show the existence of an isomorphism between models of IΔ0 and models of linear arithmetic LA.

Despite the burgeoning literature on the governance and impact of cross-sector partnerships in the past two decades, the debate on how and when these collaborative arrangements address globally relevant problems and contribute to systemic change remains open. Building upon the notion of wicked problems and the literature on governing such wicked problems, this paper defines harnessing problems in multi-stakeholder partnerships as the approach of taking into account the nature of the problem and of organizing governance processes accordingly. The paper develops (...) an innovative analytical framework that conceptualizes MSPs in terms of three governance processes harnessing three key dimensions of wicked problems. The Roundtable on Sustainable Palm Oil provides an illustrative case study on how this analytical framework describes and explains organizational change in partnerships from a problem-based perspective. The framework can be used to better understand and predict the complex relationships between MSP governance processes, systemic change and societal problems, but also as a guiding tool in organizing governance processes to continuously re-assess the problems over time and address them accordingly. (shrink)

At nearly forty, Science and the Enlightenment (Cambridge, 1985) by Thomas L. Hankins is seriously dated but still widely used, broadly reliable for what it covers and frustrating for its omissions, richly informative in its contents and somewhat opaque in its intellectual coordinates. For better or for worse, with its compact two hundred pages of text and remarkably well-chosen images, it remains the best textbook on the period, even though recent research has greatly enriched, problematized, and subverted older assumptions. This (...) essay situates Hankins’s textbook within our changing understanding of the sciences in the Enlightenment, providing a critical evaluation of its achievements, problems, and intellectual agenda. I focus on periodization and the role Isaac Newton’s main works, Philosophiae naturalis principia mathematica (1687) and Opticks (1704)—both with much expanded later editions—play in Hankins’s narrative with respect to their intellectual and methodological agenda. While offering some thoughts on what mid-1980s readers may have reasonably expected from a textbook on the Enlightenment, I also include brief reflections on how the field has changed in recent times and some comments on what a new textbook may look like, forty years later. (shrink)

The present contribution develops some key issues of the work of Luigi Stefanini, starting from his work on cinema dating back to 1954. The relationships between philosophical esthetics and film criticism have not been particularly fruitful in Italy (or elsewhere). However it can be surmised, following Formaggio 1961, that “cinema is a testbed for contemporary esthetics, insofar as the latter tries to provide a universal theorization of art”.

Starting from the works by Aselli on the milky veins and Harvey on the motion of the heart and the circulation of the blood, the practice of vivisection witnessed a resurgence in the early modern period. I discuss some of the most notable cases in the century spanning from Aselli’s work to the investigations of fluid pressure in plants and animals by Stephen Hales. Key figures in my study include Johannes Walaeus, Jean Pecquet, Marcello Malpighi, Reinier de Graaf, Richard Lower, (...) Anton Nuck, and Anton de Heide. Although vivisection dates from antiquity, early modern experimenters expanded the range of practices and epistemic motivations associated with it, displaying considerable technical skills and methodological awareness about the problems associated with the animals being alive and the issue of generalizing results to humans. Many practitioners expressed great discomfort at the suffering of the animals; however, many remained convinced that their investigations were not only indispensable from an epistemic standpoint but also had potential medical applications. Early modern vivisection experiments were both extensive and sophisticated and cannot be ignored in the literature of early modern experimentation or of experimentation on living organisms across time. (shrink)

Numerical tables are important objects of study in a range of fields, yet they have been largely ignored by historians of science. This paper contrasts and compares ways in which numerical tables were used by Galileo and Mersenne, especially in the Dialogo and Harmonie Universelle. I argue that Galileo and Mersenne used tables in radically different ways, though rarely to present experimental data. Galileo relied on tables in his work on error theory in day three of the Dialogo and also (...) used them in a very different setting in the last day of the Discorsi. In Mersenne's case they represent an important but so far unrecognized feature of his notion of universal harmony. I conclude by presenting a classification of different ways in which tables were used within the well-defined disciplinary and temporal boundaries of my research. In doing so, however, I provide a useful tool for extending similar investigations to broader domains. (shrink)

Cassirer’s concept of symbolic forms represents a cultural-philosophical approach in which specific modes of objectification, the symbolic forms themselves, establish an independent truth. This truth does not consist in a purely analytical truth, but in the fact that we live along these symbolic forms in a specific stubbornness. When we use language, we live and experience language in its specific autonomy. The same applies to the other symbolic forms developed by Cassirer. Both before the cultural-philosophical phase of creation and within (...) the philosophy of symbolic forms, Cassirer refers to mathematics several times. An interesting tension arises as to whether Cassirer could have understood mathematics as a symbolic form in its own right. On the one hand, cultural-historical considerations in Cassirer’s work speak in favour of this; on the other hand, Cassirer embeds mathematics as a mere formal science in physics and thus in the philosophical form of science as a whole. The article explores this tension—mathematics as a symbolic form—and shows that only indications within the framework of the historical-hermeneutical treatment would speak in favour of such an interpretation. Furthermore, the article argues that a specific, cultural-historical semiotics can be considered for mathematics in Cassirer’s work. (shrink)

As a reply to the commentary (Lenhard in Found Sci, 2012), we stress here that structural understanding of data analysis techniques is the natural counterpart to the lack of understanding of phenomena in agnostic science. We suggest moreover that the dynamics of computational processes, and their parallels with the dynamics of natural processes, will increasingly be, possibly, the driving force of the development of data analysis.

A collection of articles originally presented at two conferences, the first at Ventura Hall, Stanford, in April 1998; and the second at the University of Bologna in September 1999.

Diesen Ausführungen liegt eine Auswahl von Leibniz' Briefen und Aufsätzen zugrunde‚ die sein Interesse an der Aufhebung der Zensur des kopernikanischen Systems bekunden. Die hier gesammelten Dokumente stammen aus den Jahren 1684 bis 1705 und enthalten Auszüge aus der Korrespondenz mit dem Landgrafen Ernst von Hessen-Rheinfels sowie Briefe und Memoranda von der italienischen Reise und Passagen aus dem Specimen Dynamicum und den Nouveaux Esseais. Im besonderen wird gezeigt, daß der von Louis Couturat als Vorrede zum Phoranomus herausgegebene Aufsatz als ein (...) vom Phoranomus unabhängiges Werk betrachtet werden muß.Ferner wird ein neuer Korrespondent von Leibniz als der italienische Jesuit Antonio Baldigiani identifiziert. Sodann wird die sogenannte „Zweite Bearbeitung“ vom Tentamen de Motuum Coelestium Causis datiert und es wird dargelegt‚ daß dieser Aufsatz im Rahmen der Auseinandersetzung Leibnizens mit der Zensur zu verstehen ist. (shrink)

Multiple authorship is so common and pervasive in our world that it is tempting to take it for granted. Prior to the twentieth century, however, multiple authorship was exceedingly rare.

Summary The investigation and representation of insects in the seventeenth century posed huge problems: on the one hand, their size and texture required optical tools and fixation techniques to disentangle and identify their tiny parts; on the other, the esoteric nature of those parts required readers to make sense of images alien to their daily experiences. Naturalists and anatomists developed sophisticated techniques of investigation and representation, involving tacit and unusual conventions that even twentieth-century readers found at times baffling. This essay (...) develops a comparative approach based on seven pairs of investigations involving Francesco Stelluti, Francesco Redi, Giovanni Battista Hodierna, Robert Hooke, Marcello Malpighi, and Jan Swammerdam. Seen together, they document an extraordinary time in the study of insects and reconstruct a number of iconographic dialogues shedding light on the conventions and styles adopted. (shrink)

We present some algebraic tools useful to the study of the expressive power of bounded formulas in second-order arithmetic (alternatively, second-order formulas in finite models). The techniques presented here come from Boolean circuit complexity and are adapted to the context of arithmetic. The purpose of this article is to expose them to a public with interests ranging from arithmetic to finite model theory. Our exposition is self-contained.

Le projet de Pierre THévenaz d�une �philosophie sans absolu� est le fruit de la rencontre entre la raison philosophique et l�expérience-choc de l�annonce chrétienne, qui restitue à l�humain sa dimension uniquement et radicalement humaine. Le monde d�ici-bas devient ainsi le lieu de l�homme dans son historicité. La méthode de cette conversion à l�en deça est celle d�une radicalisation de la philosophie réflexive. Si désormais �la raison c�est l�homme�, la tâche d�une �philosophie sans absolu� devient l�herméneutique de la condition humaine.