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)

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)

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)

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)

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)

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)

Dans la seconde moitié des années 1900, Bertrand Russell et Hugh MacColl échangèrent sans s’entendre sur les questions de l’implication et de l’existence, dans le cadre d’un débat plus général sur la nature de la logique. Il est tentant de voir dans cet échange une opposition entre le moniste logique Russell et le pluraliste MacColl. Dans cet article, j’affirme que cette interprétation est inexacte, et que les deux hommes étaient tous deux monistes, bien qu’ayant des allégeances différentes. La transition du (...) monisme au pluralisme ne s’effectue en réalité qu’à partir du début des années 1910, peu après la mort de MacColl en 1909. Les premiers signes de cette transition sont à trouver particulièrement chez le philosophe américain C. I. Lewis, le mathématicien néerlandais L. E. J. Brouwer, et le logicien polonais Jan Łukasiewicz. Ces auteurs sont des exemples de l’avènement graduel de la métalogique. (shrink)

In view of the philosophical problems that vex the debate on situated affectivity, it can seem wise to focus on simple cases. Accordingly, theorists often single out scenarios in which an individual employs a device in order to enhance their emotional experience, or to achieve new kinds of experience altogether, such as playing an instrument, going to the movies or sporting a fancy handbag. I argue that this narrow focus on cases that fit a ‘user/resource model’ tends to channel attention (...) away from more complex and also more problematic instances of situated affectivity. Among these are scenarios in which a social domain draws individuals into certain modes of affective interaction, often by way of attunement and habituation to affective styles and interaction patterns that are normative in the domain in question. This can lead to a phenomenon that is not so much ‘mind extension’ than ‘mind invasion’: affectivity is dynamically framed and modulated from without, often contrary to the prior orientations of the individuals in question. As an example, I discuss affective patterns prevalent in today’s corporate workplace. I claim that workplace affect sometimes contributes to what is effectively a ‘hack’ of employees’ subjectivity. (shrink)

Marx’s vision of unalienated production is often thought to be subject to decisive objections. This article argues that these objections rely on a misinterpretation of Marx’s position. It provides a new interpretation of Marx’s vision of unalienated production. Unlike another well-known account, it suggests that unalienated production involves realizing oneself through providing others with the goods and services they need for their self-realization. It argues that this view is appealing and that it offers a more successful response to objections than (...) previous interpretations. In doing so, it hopes to put Marx’s concern with alienation and nonalienation back on the table. (shrink)

The recent progress in the development of autonomous cars has seen ethical questions come to the forefront. In particular, life and death decisions regarding the behavior of self-driving cars in trolley dilemma situations are attracting widespread interest in the recent debate. In this essay we want to ask whether we should implement a mandatory ethics setting for the whole of society or, whether every driver should have the choice to select his own personal ethics setting. While the consensus view seems (...) to be that people would not be willing to use an automated car that might sacrifice themselves in a dilemma situation, we will defend the somewhat contra-intuitive claim that this would be nevertheless in their best interest. The reason is, simply put, that a PES regime would most likely result in a prisoner’s dilemma. (shrink)

This paper analyses recent calls for so called “neurorights”, suggested novel human rights whose adoption is allegedly required because of advances in neuroscience, exemplified by a proposal of the Neurorights Initiative. Advances in neuroscience and technology are indeed impressive and pose a range of challenges for the law, and some novel applications give grounds for human rights concerns. But whether addressing these concerns requires adopting novel human rights, and whether the proposed neurorights are suitable candidates, are a different matter. This (...) paper argues that the proposed rights, as individuals and a class, should not be adopted and lobbying on their behalf should stop. The proposal tends to promote rights inflationism, is tainted by neuroexceptionalism and neuroessentialism, and lacks grounding in relevant scholarship. None of the proposed individual rights passes quality criteria debated in the field. While understandable from a moral perspective, the proposal is fundamentally flawed from a legal perspective. Rather than conjuring up novel human rights, existing rights should be further developed in face of changing societal circumstances and technological possibilities. (shrink)

This paper presents a critique of left republican writings from a non-republican socialist standpoint. It examines three claims that have been advanced by left republican authors: that workers are dominated 1) by their lack of access to the means of production; 2) by the market; and 3) by their employer. With regard to 1) and 2), it argues that alternative conceptions of freedom can identify the unfreedom in question, and that there are good reasons for pressing these complaints on the (...) basis of these alternative conceptions. With regard to 3), it argues that, while alternative conceptions of freedom may be able to identify the unfreedom in question, republican freedom provides a more suitable basis for pressing this claim. It concludes that while left republicans have shown that socialists have reason to care about republican freedom, they have not shown that socialists should adopt republican freedom at the expense of other conceptions of freedom. (shrink)

I defend the proposal that certain forms of work—specifically forms that are socially necessary but involve the imposition of considerable burdens—be shared between citizens. I argue that sharing burdensome work would achieve several goals, including a more equal distribution of the benefits and burdens of work, a greater appreciation of each other's labour contributions, and an amelioration of problematic inequalities of status. I conclude by considering three objections: that sharing burdensome work would (1) involve morally unacceptable constraints on freedom, (2) (...) be prohibitively inefficient, and (3) forbid mutually advantageous trades. I argue that none of these objections succeed. (shrink)

The impact of smaller firm size on corporate social responsibility (CSR) is ambiguous. Some contend that small businesses are socially responsible by nature, while others argue that a smaller firm size imposes barriers on small firms that constrain their ability to take responsible action. This paper critically analyses recent theoretical and empirical contributions on the size–social responsibility relationship among small businesses. More specifically, it reviews the impact of firm size on four antecedents of business behaviour: issue characteristics, personal characteristics, organizational (...) characteristics and context characteristics. It concludes that the small business context does impose barriers on social responsibility taking, but that the impact of the smaller firm size on social responsibility should be nuanced depending on a number of conditions. From a critical analysis of these conditions, opportunities for small businesses and their constituents to overcome the constraining barriers are suggested. (shrink)

The focus of this article is the question whether the notion of being in a position to know is closed under modus ponens. The question is answered negatively.

Why are conditional degrees of belief in an observation E, given a statistical hypothesis H, aligned with the objective probabilities expressed by H? After showing that standard replies are not satisfactory, I develop a suppositional analysis of conditional degree of belief, transferring Ramsey’s classical proposal to statistical inference. The analysis saves the alignment, explains the role of chance-credence coordination, and rebuts the charge of arbitrary assessment of evidence in Bayesian inference. Finally, I explore the implications of this analysis for Bayesian (...) reasoning with idealized models in science. (shrink)

This paper develops axiomatic foundations for a probabilistic-interventionist theory of causal strength. Transferring methods from Bayesian confirmation theory, I proceed in three steps: I develop a framework for defining and comparing measures of causal strength; I argue that no single measure can satisfy all natural constraints; I prove two representation theorems for popular measures of causal strength: Pearl's causal effect measure and Eells' difference measure. In other words, I demonstrate these two measures can be derived from a set of plausible (...) adequacy conditions. The paper concludes by sketching future research avenues. (shrink)

According to an influential view by Elizabeth Harman, moral ignorance, as opposed to factual ignorance, never excuses one from blame. In defense of this view, Harman appeals to the following considerations: that moral ignorance always implies a lack of good will, and that moral truth is always accessible. In this paper, I clearly distinguish these considerations, and present challenges to both. If my arguments are successful, sometimes moral ignorance excuses.

Strategic ignorance is a widespread phenomenon. In a laboratory setting, many participants avoid learning information about the consequences of their behaviour in order to act egoistically. In real life, many consumers avoid information about their purchases or the working conditions in which they were produced in order to retain their lifestyle. The question is whether agents are blameworthy for such strategically ignorant behaviour. In this paper, I explore quality of will resources, according to which agents are blameworthy, roughly, depending on (...) their moral concern. The account I will propose—the Maximal Account—has three innovative features: it utilizes a suitable concept of maximal moral concern, it offers an accountability version of the account which significantly differs from the more familiar attributability variant, and it maintains that agents without maximal concern are blameworthy. (shrink)

The last decade has seen an increasing number of references to quantum mechanics in the humanities and social sciences. This development has in particular been driven by Karen Barad’s agential realism: a theoretical framework that, based on Niels Bohr’s interpretation of quantum mechanics, aims to inform social theorizing. In dealing with notions such as agency, power, and embodiment as well as the relation between the material and the discursive level, the influence of agential realism in fields such as feminist science (...) studies and posthumanism has been profound. However, no one has hitherto paused to assess agential realism’s proclaimed quantum mechanical origin including its relation to the writings of Niels Bohr. This is the task taken up here. We find that many of the implications that agential realism allegedly derives from a Bohrian interpretation of quantum mechanics dissent from Bohr’s own views and are in conflict with those of other interpretations of quantum mechanics. Agential realism is at best consistent with quantum mechanics and consequently, it does not capture what quantum mechanics in any strict sense implies for social science or any other domain of inquiry. Agential realism may be interesting and thought provoking from the perspective of social theorizing, but it is neither sanctioned by quantum mechanics nor by Bohr’s authority. This conclusion not only holds for agential realism in particular, it also serves as a general warning against the other attempts to use quantum mechanics in social theorizing. (shrink)

Should Marxists support universal basic income (UBI), i.e., a regular cash income paid to all without a means test or work requirement? This paper considers one important argument that they should, namely that UBI would be instrumentally effective in helping to bring about communism. It argues that previous answers to this question have paid insufficient attention to a logically prior question: what is Marx’s account of communism? In reply, it distinguishes two different accounts: a left-libertarian version that associates communism with (...) the freedom to live and work how one wants, and a perfectionist version that associates communism with the overcoming of alienated labour and self-realisation in work. It argues that UBI would make steps towards the left-libertarian account but not the perfectionist account. Ultimately, then, the question “should Marxists support basic income?” is shown to partly depend on which account of communism Marxists want to bring about. (shrink)

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and (...) made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

This book investigates the idea of inequality. According to the author, it does not address the question whether one should care about inequality nor which version is more plausible. Instead, its purpose is “to understand egalitarianism”, to “elucidate the notion of inequality”. The general thesis is that inequality is a “complex notion,” as shown by the fact that there are many different ways of measuring it. This is relentlessly detailed in a series of chapters that many will find rather hard (...) on the brain, with their panoplies of diagrams and technical distinctions, complete with acronyms. Still, the diagrams are clear enough, and the terminology to the point. (shrink)

From Leibniz to Krauss philosophers and scientists have raised the question as to why there is something rather than nothing. Why-questions request a type of explanation and this is often thought to include a deductive component. With classical logic in the background only trivial answers are forthcoming. With free logics in the background, be they of the negative, positive or neutral variety, only question-begging answers are to be expected. The same conclusion is reached for the modal version of the Question, (...) namely ‘Why is there something contingent rather than nothing contingent?’. The categorial version of the Question, namely ‘Why is there something concrete rather than nothing concrete?’, is also discussed. The conclusion is reached that deductive explanations are question-begging, whether one works with classical logic or positive or negative free logic. I also look skeptically at the prospects of giving causal-counterfactual or probabilistic answers to the Question, although the discussion of the options is less comprehensive and the conclusions are more tentative. The meta-question, viz. ‘Should we not stop asking the Question’, is accordingly tentatively answered affirmatively. (shrink)

According to Vallicella's 'Relations, Monism, and the Vindication of Bradley's Regress' (2002), if relations are to relate their relata, some special operator must do the relating. No other options will do. In this paper we reject Vallicella's conclusion by considering an important option that becomes visible only if we hold onto a precise distinction between the following three feature-pairs of relations: internality/externality, universality/particularity, relata-specificity/relata-unspecificity. The conclusion we reach is that if external relations are to relate their relata, they must be (...) relata-specific (and no special operator is needed). As it eschews unmereological complexes, this outcome is of relevance to defenders of the extensionality of composition. (shrink)

This paper presents an account of what it is for a property or relation (or ‘attribute’ for short) to be logically simple. Based on this account, it is shown, among other things, that the logically simple attributes are in at least one important way sparse. This in turn lends support to the view that the concept of a logically simple attribute can be regarded as a promising substitute for Lewis’s concept of a perfectly natural attribute. At least in part, the (...) advantage of using the former concept lies in the fact that it is amenable to analysis, where that analysis—i.e., the account put forward in this paper—requires the adoption neither of an Armstrongian theory of universals nor of a primitive notion of naturalness, fundamentality, or grounding. (shrink)

The article starts from the questions: what is it to be an inhabitant or citizen of a globalised world, and how are we to think of education in relation to such inhabitants? We examine more specifically the so–called ‘European area of higher education’ that is on the way to being established and that can be regarded as a concrete example of a process of globalisation. In the first part of the paper we try to show that the discursive horizon, and (...) the concrete techniques and strategies that accompany the establishment of this space of higher education, invite the inhabitants of that space to see themselves as entrepreneurial and autonomous entities. In the second part we show how this specific kind of subjectivation (this production of subjects), related as it is to this globalised space, involves what we call an immunisation that also affects our thinking and our ideas in and about education. To refer to this as a kind of immunisation implies that globalisation could in fact be considered a closing or enclosing rather than an opening up. We argue, therefore, that this immunisation needs to be refused in favour of the invention of other kinds of subjectivity, other ways of speaking and writing about the world and about education, such that we relate to ourselves in a different way. (shrink)

Sometimes also called retro causation. A common feature of our world seems to be that in all cases of causation, the cause and the effect are placed in time so that the cause precedes its effect temporally. Our normal understanding of causation assumes this feature to such a degree that we intuitively have great difficulty imagining things differently. The notion of backward causation, however, stands for the idea that the temporal order of cause and effect is a mere contingent feature (...) and that there may be cases where the cause is causally prior to its effect but where the temporal order of the cause and effect is reversed with respect to normal causation, i.e. there may be cases where the effect temporally, but not causally, precedes its cause. (shrink)

LK is a natural modification of Gentzen sequent calculus for propositional logic with connectives ¬ and $\bigwedge, \bigvee$. Then for every d ≥ 0 and n ≥ 2, there is a set Td n of depth d sequents of total size O which are refutable in LK by depth d + 1 proof of size exp) but such that every depth d refutation must have the size at least exp). The sets Td n express a weaker form of the pigeonhole (...) principle. (shrink)