Marcus Giaquinto presents an investigation into the different kinds of visual thinking involved in mathematical thought, drawing on work in cognitive psychology, philosophy, and mathematics. He argues that mental images and physical diagrams are rarely just superfluous aids: they are often a means of discovery, understanding, and even proof.

Marcus Giaquinto traces the story of the search for firm foundations for mathematics. The nineteenth century saw a movement to make higher mathematics rigorous; this seemed to be on the brink of success when it was thrown into confusion by the discovery of the class paradoxes. That initiated a period of intense research into the foundations of mathematics, and with it the birth of mathematical logic and a new, sharper debate in the philosophy of mathematics. The Search for Certainty (...) focuses mainly on two major twentieth-century programmes: Russell's logicism and Hilbert's finitism. Giaquinto examines their philosophical underpinnings and their outcomes, asking how successful they were, and how successful they could be, in placing mathematics on a sound footing. He sets these questions in the context of a clear, non-technical exposition and assessment of the most important discoveries in mathematical logic, above all Gödel's underivability theorems.More than six decades after those discoveries Giaquinto asks what our present perspective should be on the question of certainty in mathematics. Taking recent developments into account, he gives reasons for a surprisingly positive response. (shrink)

In this article I explore ways to argue about punishment of personal representations in virtual reality. I will defend the idea that such punishing might sometimes be morally required. I offer four different lines of argument: one consequentialistic, one appealing to an idea of appropriateness, one using the notion of organic wholes, and one starting from a supposed inability to determine the limits of the extension of the moral agent. I conclude that all four approaches could, in some cases, justify (...) punishing a virtual reality representation; an avatar. As a consequence of my conclusion, I suggest that our institutionalized criminal justice system must be broadened in scope and punitive measures, in order to cover the new and difficult cases arising in virtual reality. (shrink)

Starting from the problem of tolerance in a multicultural society, the author undermines the limits of a classical‐liberal foundation (negative tolerance) and suggests the need for a new meaning: a positive concern of tolerance implying appreciation of a variety of social cultures and value traditions. On an ethical level, positive tolerance can be grounded in the Discourse Theory, developing the classical Kantian deontological ethics in a transcendental‐pragmatic and in a transcendental‐hermeneutic sense. In this way, discourse ethics can answer two questions (...) posed by tolerance in a multicultural society: the duty to support all in the pursuit of their ideals and realize positive tolerance as well as its restrictions. (shrink)

This essay analyzes the use of military robots in terms of the jus in bello concepts of discrimination and proportionality. It argues that while robots may make mistakes, they do not suffer from most of the impairments that interfere with human judgment on the battlefield. Although robots are imperfect weapons, they can exercise as much restraint as human soldiers, if not more. Robots can be used in a way that is consistent with just war theory when they are programmed to (...) avoid using force against all but the most clearly hostile targets. However, the essay also cautions against using robots for counterinsurgency because they may alienate people in the contested area and lead to an escalation of hostilities. (shrink)

This paper shows that non-normal modal logics can be simulated by certain polymodal normal logics and that polymodal normal logics can be simulated by monomodal (normal) logics. Many properties of logics are shown to be reflected and preserved by such simulations. As a consequence many old and new results in modal logic can be derived in a straightforward way, sheding new light on the power of normal monomodal logic.

In 1885, Georg Cantor published his review of Gottlob Frege's Grundlagen der Arithmetik . In this essay, we provide its first English translation together with an introductory note. We also provide a translation of a note by Ernst Zermelo on Cantor's review, and a new translation of Frege's brief response to Cantor. In recent years, it has become philosophical folklore that Cantor's 1885 review of Frege's Grundlagen already contained a warning to Frege. This warning is said to concern the defectiveness (...) of Frege's notion of extension. The exact scope of such speculations varies and sometimes extends as far as crediting Cantor with an early hunch of the paradoxical nature of Frege's notion of extension. William Tait goes even further and deems Frege 'reckless' for having missed Cantor's explicit warning regarding the notion of extension. As such, Cantor's purported inkling would have predated the discovery of the Russell-Zermelo paradox by almost two decades. In our introductory essay, we discuss this alleged implicit (or even explicit) warning, separating two issues: first, whether the most natural reading of Cantor's criticism provides an indication that the notion of extension is defective; second, whether there are other ways of understanding Cantor that support such an interpretation and can serve as a precisification of Cantor's presumed warning. (shrink)

Paraconsistent and dialetheist approaches to a theory of truth are faced with a problem: the expressive resources of the logic do not suffice to express that a sentence is just true—i.e., true and not also false—or to express that a sentence is consistent. In his recent book, Spandrels of Truth, Jc Beall proposes a ‘just true’-operator to identify sentences that are true and not also false. Beall suggests seven principles that a ‘just true’-operator must fulfill, and proves that his operator (...) indeed fulfills all of them. He concludes that just true has been expressed in the language. I argue that, while the seven conditions may be necessary for an operator to express just true, they are not jointly sufficient. Specifically, first, I prove that a further plausible desideratum for necessary conditions on ‘just true’ is not fulfilled by Beall's proposal, namely that ‘just true’ ascriptions should themselves be just true, and not also false (or equivalently, that the ‘just true’-operator iterates). Second, I show that Beall's operator does not adequately express just true, but that it merely captures an arbitrary proper subset of the just true sentences. Further, there is no prospect of extending the proposal in order to encompass a more reasonable subset of the just true sentences without presupposing that we have antecedent means to characterize the class of just true sentences. (shrink)

Researchers have long suspected that grapheme-color synaesthesia is useful, but research on its utility has so far focused primarily on episodic memory and perceptual discrimination. Here we ask whether it can be harnessed during rule-based Category learning. Participants learned through trial and error to classify grapheme pairs that were organized into categories on the basis of their associated synaesthetic colors. The performance of synaesthetes was similar to non-synaesthetes viewing graphemes that were physically colored in the same way. Specifically, synaesthetes learned (...) to categorize stimuli effectively, they were able to transfer this learning to novel stimuli, and they falsely recognized grapheme-pair foils, all like non-synaesthetes viewing colored graphemes. These findings demonstrate that synaesthesia can be exploited when learning the kind of material taught in many classroom settings. (shrink)

In this article, I reconstruct and evaluate Merleau-Ponty’s main responses to philosophical skepticism in the relevant parts of his work. To begin with, I introduce the skeptical argument that Merleau-Ponty most often tried to refute, namely, the dream argument. Secondly, I show how Merleau-Ponty, in his initial works, excludes the skeptical problem by appealing to a general contact with the world guaranteed by perception. Finally, I analyze how in his last texts Merleau-Ponty considers at least some uses of the skeptical (...) arguments as tools to make our opaque contact with being explicit. (shrink)

Given a normal (multi-)modal logic a characterization is given of the finitely presentable algebras A whose logics L A split the lattice of normal extensions of . This is a substantial generalization of Rautenberg [10] and [11] in which is assumed to be weakly transitive and A to be finite. We also obtain as a direct consequence a result by Blok [2] that for all cycle-free and finite A L A splits the lattice of normal extensions of K. Although we (...) firmly believe it to be true, we have not been able to prove that if a logic splits the lattice of extensions of then is the logic of an algebra finitely presentable over ; in this respect our result remains partial. (shrink)

Can visual thinking be a means of discovery in elementary analysis, as well as a means of illustration and a stimulus to discovery? The answer to the corresponding question for geometry and arithmetic seems to be ‘yes’ (Giaquinto [1992], [1993]), and so a positive answer might be expected for elementary analysis too. But I argue here that only in a severely restricted range of cases can visual thinking be a means of discovery in analysis. Examination of persuasive visual routes to (...) two simple theorems (Rolle, Bolzano) shows that they are not ways of discovering the theorems; the type of visual thinking involved can never be used to discover analytic theorems of a certain generality. The hypothesis that visual thinking is never a means of discovering the existence or nature of the limit of some infinite process is considered, and a likely counter-example is set out. It is still possible that restricted theorems can be discovered visually: an example from Littlewood is examined in detail and not found wanting. Even when visual thinking is not a means of discovery it can provide the idea for a proof in a direct way; an example is presented (Intermediate Value Theorem). In conclusion: it may be possible to discover theorems in elementary real analysis by visual means, but only theorems of a restricted kind; however, visual thinking in analysis can be very useful in other ways. (shrink)

In this thesis I provide a survey over different approaches to second-order logic and its interpretation, and introduce a novel approach. Of special interest are the questions whether second-order logic can count as logic in some proper sense of logic, and what epistemic status it occupies. More specifically, second-order logic is sometimes taken to be mathematical, a mere notational variant of some fragment of set theory. If this is the case, it might be argued that it does not have the (...) "epistemic innocence" which would be needed for, e.g., foundational programmes in mathematics for which second-order logic is sometimes used. I suggest a Deductivist conception of logic, that characterises logical consequence by means of inference rules, and argue that on this conception second-order logic should count as logic in the proper sense. (shrink)

Este artigo explora alguns aspectos da noção de "mundo da vida" apresentada por Edmund Husserl, de modo a contribuir com o desenvolvimento do modelo da interação entre ciência e valores proposto por Hugh Lacey. Em particular, almeja-se mostrar a fundação das estratégias descontextualizadoras de pesquisa científica nas experiências concretas, compostas de diversos níveis de operações intencionais.

Contextualist accounts of free will recently proposed by Hawthorne and Rieber imply that the same action can be both free and unfree (depending on the attributor's context). This paradoxical consequence can be avoided by thinking of contexts not as constituted by arbitrary moves in a conversation, but rather by (relatively stable) social practices (such as the practices of attributing responsibility or of giving scientific explanations). The following two conditions are suggested as each necessary and jointly sufficient for free will: (i) (...) the agent is able to form considered practical judgements and to act accordingly, and (ii) the agent (or some agent‐involving event) is the original cause of her actions. A contextualist reformulation of the second condition is developed according to which only contexts in which responsibility is attributed are relevant for the kind of original causation required for free will, which allows for a non‐relativist contextualism about free will. (shrink)

Mathematicians sometimes judge a mathematical proof to be beautiful and in doing so seem to be making a judgement of the same kind as aesthetic judgements of works of visual art, music or literature. Mathematical proofs are also appraised for explanatoriness: some proofs merely establish their conclusions as true, while others also show why their conclusions are true. This paper will focus on the prima facie plausible assumption that, for mathematical proofs, beauty and explanatoriness tend to go together. To make (...) headway we need to have some grip on what it is for a proof to be beautiful, and for that we need some account of judgements of beauty in general. That is the concern of the first section. The second section faces the problem that it is far from obvious how abstract entities, such as mathematical proofs, can be beautiful, strictly and literally speaking. Reasons are given for the view that they can be. The third section introduces the distinction between proofs which explain their conclusions and proofs which do not. Finally, the question whether, for mathematical proofs, the beautiful and the explanatory tend to coincide is addressed. It is argued that we have reason to doubt that explanatory proofs tend to be beautiful, and insufficient reason to believe or disbelieve that beautiful proofs tend to be explanatory. (shrink)

Medical practitioners of all specialisms are identified by their professional titles. Their function is determined by their regulators, and subject to voluntary employment contracts....

In this paper I offer an appraisal of James Bogen and James Woodward’s distinction between data and phenomena which pursues two objectives. First, I aim to clarify the notion of a scientific phenomenon. Such a clarification is required because despite its intuitive plausibility it is not exactly clear how Bogen and Woodward’s distinction has to be understood. I reject one common interpretation of the distinction, endorsed for example by James McAllister and Bruce Glymour, which identifies phenomena with patterns in data (...) sets. Furthermore, I point out that other interpretations of Bogen and Woodward’s distinction do not specify the relationship between phenomena and theories in a satisfying manner. In order to avoid this problem I propose a contextual understanding of scientific phenomena according to which phenomena are states of affairs which play specific roles in scientific practice and to which we adopt a special epistemic attitude. Second, I evaluate the epistemological significance of Bogen and Woodward’s distinction with respect to the debate between scientific realists and constructive empiricists. Contrary to what Bogen and Woodward claim, I argue that the distinction does not provide a convincing argument against constructive empiricism. (shrink)

Im Ersten Weltkrieg wurde eine Debatte um Bedeutung und Stellenwert des Demokratiegedankens ausgetragen, die die wilhelminische Ära des politischen Denkens abschloß und die Demokratiediskussion in der Weimarer Republik einleitete. Autoren wie Hugo Preuß, Max Weber Hans Delbrück und Hugo Sinzheimer im bürgerlichen Lager und Eduard Bernstein, Karl Kautsky und Wolfgang Heine im sozialistischen Lager beförderten durch ihre leidenschaftliche Parteinahme für den Volksstaat und gegen den Obrigkeitsstaat, für die politische Selbstregierung und gegen den Untertanengeist den Durchbruch der Demokratie in Deutschland. Aber (...) sie hatten dabei gegen zahlreiche Widerstände anzukämpfen. Der heute selbstverständliche Vorrang der Demokratie als politischer Idee war bei Kriegsausbruch noch keineswegs vorhanden. Die Demokratien des Westens wurden nicht als Vorbild angesehen, zumal deren eigene politische Theorie vor dem Krieg von der Demokratie abgerückt war. Das Erlebnis des Krieges verhalf zunächst einer ganz neuartigen Idee von Demokratie zur Vorherrschaft, die zwischen dem Kriegssozialismus in der Heimat und der Gleichheit vor dem Tod an der Front die Demokratie als Volksgemeinschaft propagierte und normative und institutionelle Aspekte der Politik ausblendete. Die politische Argumentation gegen diese "deutsche Idee der Demokratie" mußte sich gegen eine demagogisch aufgehetzte öffentlichen Meinung stemmen. Die demokratische Argumentation im Krieg fand als geistiger Kampf um die Demokratie statt. (shrink)

Sustainability reports are a crucial instrument to inform outside stakeholders not only about a company's sustainability performance but also to manage impressions. However, they are often prone to greenwashing and the reporting of negative topics can jeopardize corporate legitimacy. Therefore, this paper aims to analyze reporting quality and how grocery retailing companies deal with this challenge of reporting the true picture. The empirical material is taken from the latest sustainability reports and information available on the Internet for two major German (...) supermarkets, six grocery discount retailers, and two organic supermarkets. The Global Reporting Initiative standards are used to assess and compare the extent of information disclosure. A qualitative content analysis is applied to identify negative disclosure aspects and their legitimation. While the main focus areas (supply chain, employees, environment/climate, and society) are similar for the companies, different levels of reporting quality appeared. Negative information is rarely reported and “abstraction” and “indicating facts” are the dominant legitimation strategies. (shrink)

According to most accounts of just war theory, jus ad bellum is concerned with the morality of initiating war. This gives jus ad bellum a temporal dimension, making it a set of principles that are applied to judge belligerents’ actions at the outset of a war, but that cannot be revisited after a war begins. I challenge this synchronic conception of jus ad bellum by arguing that the considerations the principles of jus ad bellum are meant to judge can, and (...) often do, change substantially over the course of wars. It is inappropriate to determine the ad bellum justice of a war solely based on how the principles of jus ad bellum are satisfied at a war’s outset. Because of the mercurial nature of war, jus ad bellum principles should be applied diachronically, as moral norms that can be used to guide or to judge belligerents even after a war has been initiated. (shrink)

The seduction-theory defines film in a broader sense as a medium of seduction, based on the French concept of séduction. It is a theoretical approach influenced by continental philosophy and classical film theory, linked to a three-stage analytical model. The book introduces the theoretical foundations and, using various classical and contemporary examples from film history, presents a genuine method of film analysis.

m primeiro lugar, este artigo esclarece que o sentido de fundação das ciências proposto por Husserl não deve ser confundido com algum tipo de fundacionismo epistêmico (seção 1). Em seguida, expõe o primeiro modelo de fundação do conhecimento defendido por Husserl, em Filosofia da aritmética, e as principais críticas recebidas (seções 2-3). Por fim, acompanha a elaboração de um segundo modelo, apresentado em Prolegômenos à lógica pura (seções 4-7).

Over the past decade, New Atheists have campaigned against the influence of religion in public life and favored a more enlightened understanding of the world ? one based on the methods and theories of the natural sciences. Although the leaders of this movement refuse to give religion, even moderate religion, any place in determining moral conduct, they offer few alternatives. Most define moral responsibility by referring to facts about human biology or natural moral intuitions, yet without adequately defending this or (...) exploring the possibilities of non-naturalistic secular moralities. This essay argues that New Atheists' moral theories tend to be weak because of their naturalist assumptions. Its leading proponents seem to be unwilling to acknowledge that moral philosophy can play a role in developing secular moral precepts because philosophy fails to meet their strong criteria of scientific validity. This position is misguided not only because it has led New Atheists to defend weak moral theories but also because the methods of inquiry used in moral philosophy make it distinct from faith for many of the same reasons that the New Atheists think that science is distinct from faith. (shrink)

The primary purpose of this randomized controlled trial (RCT) was to evaluate the efficacy of an unguided, two-week internet-based training program to overcome procrastination, called ON.TOP. Because adherence is a typical problem among individuals who tend to procrastinate, especially with internet-based interventions, the secondary purpose of the present study was to investigate whether adding SMS support increases subjects’ frequency of engagement in training. In a three-armed RCT (N = 161), the effects of the intervention alone and intervention with daily SMS-support (...) were compared to a waiting list control condition in a sample of students. The primary outcome of interest was procrastination. The secondary outcome of interest was the extent of training behavior. Baseline (T0), immediate post-treatment (T1) and 8-week post-treatment (T2) assessments were conducted. Results indicated that procrastination decreased significantly only with intervention group with daily SMS support, relative to control. Moreover, incorporating SMS support also may enhance extent of training behavior. (shrink)

There are many kinds of number. This chapter concentrates on finite cardinal numbers, as they have a basic role in our thinking. Numbers cannot be seen, heard, touched, tasted, or smelled; they do not emit or reflect signals; they leave no traces. So what kind of thing are they? How can we have knowledge of them? The aim of this chapter is to present and assess the main answers to these questions – classical and neo-classical, nominalism, mentalism, fictionalism, logicism, and (...) the set-size view. All views are disputed, including the view I will argue for, the set-size view. The final section relates the finite cardinal numbers to the natural numbers. (shrink)

Laura Marcus is one of the leading literary critics of modernist literature and culture. Dreams of Modernity: Psychoanalysis, Literature, Cinema covers the period from around 1880 to 1930, when modernity as a form of social and cultural life fed into the beginnings of modernism as a cultural form. Railways, cinema, psychoanalysis and the literature of detection - and their impact on modern sensibility - are four of the chief subjects explored. Marcus also stresses the creativity of modernist women (...) writers, including H. D., Dorothy Richardson and Virginia Woolf. The overriding themes of this work bear on the understanding of the early twentieth century as a transitional age, thus raising the question of how 'the moderns' understood the conditions of their own modernity. (shrink)