Luitzen Egburtus Jan Brouwer founded a school of thought whose aim was to include mathematics within the framework of intuitionistic philosophy; mathematics was to be regarded as an essentially free development of the human mind. What emerged diverged considerably at some points from tradition, but intuitionism has survived well the struggle between contending schools in the foundations of mathematics and exact philosophy. Originally published in 1981, this monograph contains a series of lectures dealing with most of the fundamental (...) topics such as choice sequences, the continuum, the fan theorem, order and well-order. Brouwer's own powerful style is evident throughout the work. (shrink)

Dutch Mathematician Luitzen Egbertus Jan Brouwer (1881-1966) was a rebel. His doctoral thesis... was the manifesto of an angry young man taking on the mathematical establishment on all fronts. In a short time he established a world-wide reputation for himself; his genius and originality were acknowledged by the great mathematicians of his time... The Intuitionist-Formalist debate became a personal feud between the mathematical giants Brouwer and Hilbert, and ended in 1928 with the expulsion of Brouwer from (...) the editorial board of the Mathematische Annalen by dictat of Hilbert. Forsaken, humiliated and disillusioned Brouwer abandoned his Intuitionist Programme and withdrew into silence just about the time when the Formalist Programme appeared to be fundamentally flawed and major opposition collapsed... This book attempts to follow the `genetic' development of Brouwer's ideas, linking the man Brouwer, his Weltanschauung, his philosophy of mathematics and his reconstruction of mathematics. Brouwer's own writings, his publications as well as his unpublished papers, are its immediate and main source of reference. It is the second volume in the new series Studies in the History and Philosophy of Mathematics, and is written for the specialist as well as for the general reader interested in mathematics and the interpretation of its status and function. (shrink)

Luitzen Egburtus Jan Brouwer founded a school of thought whose aim was to include mathematics within the framework of intuitionistic philosophy; mathematics was to be regarded as an essentially free development of the human mind. What emerged diverged considerably at some points from tradition, but intuitionism has survived well the struggle between contending schools in the foundations of mathematics and exact philosophy. Originally published in 1981, this monograph contains a series of lectures dealing with most of the fundamental (...) topics such as choice sequences, the continuum, the fan theorem, order and well-order. Brouwer's own powerful style is evident throughout the work. (shrink)

Friedrich Nietzsche and Luitzen Egbertus Jan Brouwer had strong personalities and freely expressed unconventional opinions. In particular, they dared to challenge the traditional view that considered Aristotelian logic as being absolute and intrinsic to man. Although they formed this opinion in different ways and in different contexts, they both based it on a view of life that considered it as a struggle for power in which logic was a weapon. Therefore, it is interesting to carry out an in-depth (...) analysis on the origins, the core of their opinions concerning logic and the consequences. As a matter of fact, a detailed analysis and a comparison of their contributions to the philosophy of logic have not yet been carried out. In this paper, I intend to present the results of my research.. (shrink)

Summary Franz Brentano, 1838–1917, introduced the intriguing concept of “plerosis” in order to account for aspects of the continuum that were “explained” by formal mathematics in ways that he considered absurd from the perspective of intuition, especially visual awareness and imagery. In doing this, he pointed in directions later developed by the Dutch mathematician Luitzen Brouwer. Brentano’s notion of plerosis involves distinct though coincident points, which one might call “atomic entities with parts”. This notion fits the modern concepts (...) of “receptive field” in neurophysiology, “perceptive field” in psychology and “differential operator” in the formal theory of scale space. We identify Brentano’s boundary points as the primordial atomic Gestalts of visual imagery. The concept deserves to play a key role in Gestalt theory. (shrink)

Dirk van Dalen’s biography studies the fascinating life of the famous Dutch mathematician and philosopher Luitzen Egbertus Jan Brouwer. Brouwer belonged to a special class of genius; complex and often controversial and gifted with a deep intuition, he had an unparalleled access to the secrets and intricacies of mathematics. Most mathematicians remember L.E.J. Brouwer from his scientific breakthroughs in the young subject of topology and for the famous Brouwer fixed point theorem. Brouwer’s main interest, (...) however, was in the foundation of mathematics which led him to introduce, and then consolidate, constructive methods under the name ‘intuitionism’. This made him one of the main protagonists in the ‘foundation crisis’ of mathematics. As a confirmed internationalist, he also got entangled in the interbellum struggle for the ending of the boycott of German and Austrian scientists. This time during the twentieth century was turbulent; nationalist resentment and friction between formalism and intuitionism led to the Mathematische Annalen conflict. It was here that Brouwer played a pivotal role. The present biography is an updated revision of the earlier two volume biography in one single book. It appeals to mathematicians and anybody interested in the history of mathematics in the first half of the twentieth century. (shrink)

When talking about decisionmaking for children with a life-threatening condition, the death of children with brain tumors deserves special attention. The last days of the lives of these children can be particularly harsh for bystanders, and raise questions about the suffering of these children themselves. In the Netherlands, these children are part of the group for whom a wide range of end-of-life decisions are discussed, and questions raised. What does the end-of-life for these children look like, and what motivates physicians (...) and parents to make decisions that may affect the life and death of these children? This article highlights the story of the parents of the sisters Roos and Noor. When both their daughters were diagnosed with a hereditary brain tumor, they had to make similar decisions twice. Their story sheds light on the suffering of children in the terminal phase, and how this suffering may motivate parents and physicians to make decisions that influence the end of life of these children’s lives.We argue that complete knowledge about suffering in the terminal phase of children with brain tumors is impossible. However, by collecting experiences like those of Roos and Noor, we can move toward an experienced-based understanding and better guide parents and physicians through these hardest of decisions. (shrink)

Introduction Life, art and mysticism Luitzen Egbertus Jan Brouwer Logic and ethics as the limits of the world Anthony Rudd To what extent is solipsism a truth? Michael Kremer Frege at therapy Kelly Dean Jolley 'Making sense' of nonsense Conant and Diamond read Wittgenstein's Tractatus Diarmuid Costello More making sense of nonsense: from logical form to forms of life Daniel D. Hutto Saying and showing: an example from Anscombe Cora Diamond Why worry about the Tractatus? James Conant Transcendence (...) and contradiction in the Tractatus Barry Stocker Wittgenstein's onto-logic Barry Allen Bibliography Index. (shrink)

Besides sensory characteristics of food, food-evoked emotion is a crucial factor in predicting consumer’s food preference and therefore in developing new products. Many measures have been developed to assess food-evoked emotions. The aim of this literature review is (i) to give an exhaustive overview of measures used in current research and (ii) to categorize these methods along measurement level (physiological, behavioral, and cognitive) and emotional processing level (unconscious sensory, perceptual / early cognitive, and conscious / decision making) level. This 3x3 (...) categorization may help researchers to compile a set of complementary measures (‘toolbox’) for their studies. We included 101 peer-reviewed articles that evaluate consumer’s emotions and were published between 1997 to 2016, providing us with 59 different measures. More than 60% of these measures are based on self-reported, subjective ratings and questionnaires (cognitive measurement level) and assess the conscious / decision-making level of emotional processing. This multitude of measures and their overrepresentation in a single category hinders the comparison of results across studies and building a complete multi-faceted picture of food-evoked emotions. We recommend (1) to use widely applied, validated measures only, (2) to refrain from using (highly correlated) measures from the same category but use measures from different categories instead, preferably covering all three emotional processing levels, and (3) to acquire and share simultaneously collected physiological, behavioral, and cognitive datasets to improve the predictive power of food choice and other models. (shrink)

In the nineteenth and twentieth centuries many mathematicians referred to intuition as the indispensable research tool for obtaining new results. In this essay we will analyse a group of mathematicians who interacted with Luitzen Egbertus Jan Brouwer in order to compare their conceptions of intuition. We will see how to the same word “intuition” very different meanings corresponded: they varied from geometrical vision, to a unitary view of a demonstration, to the perception of time, to the faculty of (...) considering concepts that habitually occur in our thinking separately. Furthermore, we will discover that these different meanings had a philosophical, very relevant counterside: they passed from a racial characterization of mathematics to a pluralistic view of it. (shrink)

The paper examines Andrei A. Markov’s critical attitude towards L.E.J. Brouwer’s intuitionism, as is expressed in his endnotes to the Russian translation of Heyting’s Intuitionism, published in Moscow in 1965. It is argued that Markov’s algorithmic approach was shaped under the impact of the mathematical style and values prevailing in the Petersburg mathematical school, which is characterized by the proclaimed primacy of applications and the search for rigor and effective solutions.

ArgumentIt would have been easy for a less imaginative historian of mathematics than Herbert Mehrtens to have portrayed the work of Hilbert, Hausdorff, and other modernists as pioneers, and those who did not subscribe to their program as people who failed, were not good enough to make the turn, and were eventually and convincingly left behind. That he did not do so is not only because this would have been a shallow, selective view of the facts: it is incompatible with (...) his Foucauldian approach to the relations between knowledge and power. Instead, he defined what I see as the most intriguing category of actor in his Moderne—Sprache—Mathematik (1990), the Gegenmoderner, or counter-moderns. The three men who characterize this position are Felix Klein, Henri Poincaré, and Luitzen Brouwer, and each merits a section in the book.Of the three, Poincaré is the hardest to contain within that category. The range of his work, the nature of his influence, and the shifting standards by which mathematical significance has been evaluated by mathematicians, historians of mathematics, and society at large, all contribute to the problem. After thirty years, the methodological presumptions and aspirations of historians of mathematics have also changed, and I shall suggest that one way to appreciate the richness of Mehrtens’ book, to gain insight into what is meant by mathematical modernism, and to acknowledge a generation of work by other historians since 1990, is to re-examine aspects of Poincaré’s life and work and scholarship about him. Prodded by remarks by Leo Corry, Moritz Epple, and David Rowe, I shall suggest that the simple but useful dichotomy modern/counter-modern must be seen as a way into a more complicated situation, one in which different aspects of mathematics, specifically applied mathematics and the relationship of mathematics to contemporary physics, require fresh accounts of the role of modern mathematics in society. (shrink)

Essays on Husserl’s Logic and Philosophy of Mathematics sets out to fill up a lacuna in the present research on Husserl by presenting a precise account of Husserl’s work in the field of logic, of the philosophy of logic and of the philosophy of mathematics. The aim is to provide an in-depth reconstruction and analysis of the discussion between Husserl and his most important interlocutors, and to clarify pivotal ideas of Husserl’s by considering their reception and elaboration by some of (...) his disciples and followers, such as Oskar Becker and Jacob Klein, as well as their influence on some of the most significant logicians and mathematicians of the past century, such as Luitzen E. J. Brouwer, Rudolf Carnap, Kurt Gödel and Hermann Weyl. Most of the papers consider Husserl and another scholar – e.g. Leibniz, Kant, Bolzano, Brentano, Cantor, Frege – and trace out and contextualize lines of influence, points of contact, and points of disagreement. Each essay is written by an expert of the field, and the volume includes contributions both from the analytical tradition and from the phenomenological one. (shrink)

Wellbeing describes how good life is for the person living it. Wellbeing comes in degrees. Subjective theories of wellbeing maintain that for objects or states of affairs to benefit us, we need to have a positive attitude towards these objects or states of affairs: the Resonance Constraint. In this article, we investigate to what extent subjectivism can plausibly account for degrees of wellbeing. There is a vast literature on whether preference-satisfaction theory – one particular subjective theory – can account for (...) degrees of wellbeing. This is generally taken to be problematic. However, other subjective theories – namely, desire-satisfaction, judgment- and value-fulfillment theories – do not suffer from the same difficulties. We introduce two models of degrees of wellbeing a subjectivist can employ: the Relative and the Absolute Model, and defend the claim that both models face difficulties. In particular, we argue that a subjectivist theory should describe instances of depression as instances of low degrees of wellbeing. We also argue that a reduction of desires may sometimes improve one’s degree of wellbeing, an idea we call the Epicurean Intuition. We then argue that the Relative Model fails to account for the disbenefit of certain types of depression, while the Absolute Model fails to meet a central commitment of subjectivism – the Resonance Constraint – and is unable to accommodate the Epicurean Intuition. The upshot of the paper is that subjectivist theories cannot account for degrees of well-being in a plausible way. (shrink)

Evaluating clinical ethics support services has been hailed as important research task. At the same time, there is considerable debate about how to evaluate CESS appropriately. The criticism, which has been aired, refers to normative as well as empirical aspects of evaluating CESS. In this paper, we argue that a first necessary step for progress is to better understand the intervention in CESS. Tools of complex intervention research methodology may provide relevant means in this respect. In a first step, we (...) introduce principles of “complex intervention research” and show how CESS fulfil the criteria of “complex interventions”. In a second step, we develop a generic “conceptual framework” for “ethics consultation on request” as standard for many forms of ethics consultation in clinical ethics practice. We apply this conceptual framework to the model of “bioethics mediation” to make explicit the specific structural and procedural elements of this form of ethics consultation on request. In a final step we conduct a comparative analysis of two different types of CESS, which have been subject to evaluation research: “proactive ethics consultation” and “moral case deliberation” and discuss implications for evaluating both types of CESS. To make explicit different premises of implemented CESS interventions by means of conceptual frameworks can inform the search for sound empirical evaluation of CESS. In addition, such work provides a starting point for further reflection about what it means to offer “good” CESS. (shrink)

What's wrong with joining corona parties? In this article, I defend the idea that reasons to avoid such parties come in degrees. I approach this issue from a participation-based perspective. Specifically, I argue that the more people are already joining the party, and the more likely it is that the virus will spread among everyone, the stronger the participation-based reason not to join. In defense of these degrees, I argue that they covary with the expression of certain attitudes.

Of all the attitudes and theories associated with or identified as "pacifism," only the doctrine that everyone ought not to resist violence with force is of philosophical interest, And it is logically incoherent. Pacifism's popularity rests on confusions about what the doctrine really is. If we have rights, We have the right to prevent infringements upon them. We have the right to use force to protect our rights, And in the degree necessary to accomplish that end. (staff).

This paper explores the fact that linear opinion pooling can be represented as a Bayesian update on the opinions of others. It uses this fact to propose a new interpretation of the pooling weights. Relative to certain modelling assumptions the weights can be equated with the so-called truth-conduciveness known from the context of Condorcet's jury theorem. This suggests a novel way to elicit the weights.

Hilbert's axiomatization program of physical theories met an interesting challenge when it confronted the rise of quantum mechanics in the mid-twenties. The novelty of the mathematical apparatus of the then newly born theory was to be matched only by its substantial lack of any definite physical interpretation. The early attempts at axiomatization, which are described here, reflect all the difficulty of the task faced by Jordan, Hilbert, von Neumann and others. The role of von Neumann is examined in considerable detail (...) as he can be viewed here as the most outstanding of Hilbert's heirs. Von Neumann, especially in his work devoted to the proof of the impossibility of hidden variables, not only continued Hilbert's program but pushed it to its very limits, blending axiomatic rigor and interpretative commitment. (shrink)

Bastiat's great contribution to economics, in his own view, was his identification of service as the source of economic value. What is anything worth to anybody? In the cases where we are not dealing with what our fellow men do for us, the answer is to be found in its utility - how much the thing contributes to our satisfaction. In the case where we deal with our fellows, we are interested specifically in what they can do for us, that (...) is, how much service they can render us - how much they can or could, by their actions, contribute to the purchaser's satisfactions. If the providers are free beings, then the recipient will obtain those satisfactions only by agreement with that provider. It is to be assumed that the purchaser will get the best outcome he can: he will pay the lowest price feasible, for the option that is better than any known alternative. (shrink)

This paper discusses ἐπιβολαὶ τῆς διανοίας, which later Epicureans are supposed to have elevated to a fourth criterion of truth to complement perceptions, preconceptions and feelings. By examining Epicurus’ extant writings, the paper distinguishes three different senses of the term: ‘thought in general’, ‘act of attention’ and ‘mental perception’. It is argued that only the sense ‘mental perception’ yields a plausible reading of ἐπιβολαί as a criterion of truth. The paper then turns to the textual evidence on ἐπιβολαί in later (...) authors. While the term ἐπιβολή is not used by Cicero, Lucretius and Philodemus in the sense of mental perception, it is argued that this still is the most plausible way of understanding ἐπιβολή as a criterion of truth. (shrink)

Die leitende These der Untersuchung lautet, dass der von Berkeley inaugurierte und uneingeschränkt verteidigte Idealismus bei Kant und Schopenhauer eine spannungsreiche Bewegung der Problematisierung und Kritik freisetzt. In der bisherigen Forschung wurden die Positionen George Berkeleys, Immanuel Kants und Arthur Schopenhauers noch nicht systematisch miteinander verglichen. Die Entwicklungsgeschichte des Idealismus erstmals anhand dieser drei Referenzautoren zu dokumentieren, bildet das zentrale Thema der Untersuchung, das die detaillierten Einzeluntersuchungen organisch verbindet. Darüber hinaus ist es ein eminentes Beweisziel der vorliegenden Monographie, Berkeley als (...) einen beeindruckend konsequenten Denker zu erschließen, dessen Immaterialismus sowohl argumentationstheoretisch wie historisch rekonstruiert wird. Insgesamt möchte die Monographie dazu beitragen, die gängige Oppositionsbildung zwischen dem britischen Empirismus auf der einen Seite und der deutschsprachigen Transzendentalphilosophie auf der anderen Seite zu hinterfragen. Die Relevanz und Originalität des Buches beruht dabei nicht nur in der Zusammenführung dieser bislang separat behandelten Traditionslinien, sondern zugleich in der Profilierung einer idealistischen Metaphysik. (shrink)

The focus of this article is a question that has been neglected in debates about digitalization: Could machines replace human scientists? To provide an intelligible answer to it, we need to answer a further question: What is it that makes (or constitutes) a scientist? I offer an answer to this question by proposing a new demarcation criterion for science which I call “the discoverability criterion”. I proceed as follows: (1) I explain why the target question of this article is important, (...) and (2) show that it leads to a variant of the demarcation problem of science. (3) By arguing that it is probably an essential feature of science that we can make scientific discoveries, I suggest a novel way of dealing with this problem by proposing a new demarcation criterion. Before introducing it, (4) I analyze an exemplary case of a real scientific discovery, and (5) argue that scientific discovery processes have a general underlying structure. (6) I introduce my discoverability criterion for science and present my master argument that helps us understand which criteria have to be fulfilled in order to decide whether machines can replace human scientists or not. (7) I conclude by answering the article’s target question and bringing forward a take-home message. (shrink)

Notes on the life of Adolf Lindenbaum, a complete bibliography of his published works, and selected references to his unpublished results.

There is a wide spectrum in reading Michael Ondaatje’s novel Anil’s Ghost, ranging from thinkers who explore literary, historical, to ethico-ontological and political aspects. I confine the study by strictly retrieving the subjectivity of the human rights victim as not rested in its being a subject and victim, hence as a specter that haunts or ‘retaliates’ into exposing its victimization. This article attempts to read the spectral nature of this victim using Derrida and Žižek. The Derridean reading grounds the central (...) spectrality on his hauntology and what it says about the victim’s ghostly character. Later, I expound on the act of haunting from a Žižekean standpoint by hinging on the notion of ‘drive’ that exposes the nature of victimization as depoliticizing the subject. (shrink)