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)

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)

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)

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)

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)

The middle of the second until the middle of the first century BCE is one of the most creative periods in the history of human thought, and an important part of this was the interaction between Roman jurists and Hellenistic philosophers. In this highly original book, René Brouwer shows how jurists transformed the study of law into a science with the help of philosophical methods and concepts, such as division, rules and persons, and also how philosophers came to share (...) the jurists' preoccupations with cases and private property. The relevance of this cross-fertilization for present-day law and philosophy cannot be overestimated: in law, its legacy includes the academic study of law and the Western models of dispute resolution, while in philosophy, the method of casuistry and the concept of just property. (shrink)

This volume, edited by René Brouwer and Emmanuele Vimercati, deals with the debate about fate, providence and free will in the early Imperial age. This debate is rekindled in the 1st century CE during emperor Augustus' rule and ends in the 3rd century CE with Plotinus and Origen, when the different positions in the debate were more or less fully developed. The book aims to show how in this period the notions of fate, providence and freedom were developed and (...) debated, not only within and between the main philosophical schools, that is Stoicism, Aristotelianism, and Platonism, but also in the interaction with other, "religious" movements, here understood in the general sense of groups of people sharing beliefs in and worship of (a) superhuman controlling power(s), such as Gnosticism, Hermetism as well as Judaism and Christianity. (shrink)

It can be tempting to think of affect as a matter of the present moment – a reaction, a feeling, an experience or engagement that unfolds right now. This paper will make the case that affect is better thought of as not only temporally extended but as saturated with temporality, especially with the past. In and through affectivity, concrete, ongoing history continues to weigh on present comportment. In order to spell this out, I sketch a Heidegger-inspired perspective. It revolves around (...) two claims. The first is that we should understand what Heidegger calls 'Befindlichkeit' (findingness) as radical situatedness. Affectivity is a matter of 'finding oneself' constellated – thrown – into the world in ways that outrun what an individual or collective might grasp and process. The second claim is that the temporal dimension, as a relatedness to the past, takes precedence in affect's situatedness. Key to affect is the way in which the past continues to hold sway over present comportment, collectively and individually. In order to articulate this perspective, it is important to overcome the idea that affect must be understood mainly in terms of feeling or experiential states of other kinds. Better suited to grasp the idea of findingness is the concept of 'disclosive posture', as proposed by Katherine Withy. I suggest that this notion should be put at the fore of a phenomenological approach to situated affectivity. (shrink)

The paper examines the interplays between logic and politics in the Polish School of Logic starting from 1914. The Polish School of Logic flourished between 1920 and 1939. Philosophically, it was influenced by Kazimierz Twardowski (1866–1938). For Twardowski logic is fundamental for every kind of human activity, professional and private and this means that every argument should be formulated and proceed by correct inferential rules. These rules involve semiotics, formal logic and methodology of science. The paper shows how this position (...) was shared by Twardowski’s students, including Jan Łukasiewicz, Stanisław Leśniewski, Kazimierz Ajdukiewicz and Tadeusz Kotrabiński, as well as by the next generation of logicians and philosophers and especially by Alfred Tarski. These authors considered logic, philosophy and science as completely neutral with respect to politics and ideology but they also considered logical skills as indispensable in political activities. (shrink)

We introduce a cyclic proof system for the two-way alternation-free modal μ-calculus. The system manipulates one-sided Gentzen sequents and locally deals with the backwards modalities by allowing analytic applications of the cut rule. The global effect of backwards modalities on traces is handled by making the semantics relative to a specific strategy of the opponent in the evaluation game. This allows us to augment sequents by so-called trace atoms, describing traces that the proponent can construct against the opponent’s strategy. The (...) idea for trace atoms comes from Vardi’s reduction of alternating two-way automata to deterministic one-way automata. Using the multi-focus annotations introduced earlier by Marti and Venema, we turn this trace-based system into a path-based system. We prove that our system is sound for all sequents and complete for sequents not containing trace atoms. (shrink)

Higher-order logic, with its type-theoretic apparatus known as the simple theory of types (STT), has increasingly come to be employed in theorizing about properties, relations, and states of affairs—or ‘intensional entities’ for short. This paper argues against this employment of STT and offers an alternative: ordinal type theory (OTT). Very roughly, STT and OTT can be regarded as complementary simplifications of the ‘ramified theory of types’ outlined in the Introduction to Principia Mathematica (on a realist reading). While STT, understood as (...) a theory of intensional entities, retains the Fregean division of properties and relations into a multiplicity of categories according to their adicities and ‘input types’ and discards the division of intensional entities into different ‘orders’, OTT takes the opposite approach: it retains the hierarchy of orders (though with some modifications) and discards the categorisation of properties and relations according to their adicities and input types. In contrast to STT, this latter approach avoids intensional counterparts of the Epimenides and related paradoxes. Fundamental intensional entities lie at the base of the proposed hierarchy and are also given a prominent part to play in the individuation of non-fundamental intensional entities. (shrink)

By and large, the conditional connective in three-valued logic has two different functions. First, by means of a deduction theorem, it can express a specific relation of logical consequence in the logical language itself. Second, it can represent natural language structures such as "if/then'' or "implies''. This chapter surveys both approaches, shows why none of them will typically end up with a three-valued material conditional, and elaborates on connections to probabilistic reasoning.

International institutions such as UNESCO are deliberating on a new standard setting instrument for neurotechnologies. This will likely lead to the adoption of a soft law document which will be the first global document specifically tailored to neurotechnologies, setting the tone for further international or domestic regulations. While some stakeholders have been consulted, these developments have so far evaded the broader attention of the neuroscience, neurotech, and neuroethics communities. To initiate a broader debate, this target article puts to discussion twenty-five (...) considerations and desiderata for recognition by a future instrument. They are formulated at different levels of abstraction, from the big picture to technical details, seek to widen the perspective of preparatory reports and transcend the narrow debate about “neurorights” which overshadows many richer and more relevant aspects. These desiderata are not an exhaustive enumeration but a starting point for discussions about what deserves and what requires protection by an international instrument. (shrink)

Evidence-Based Medicine has little consideration for mechanisms and philosophers of science and medicine have recently made pleas to increase the place of mechanisms in the medical evidence hierarchy. However, in this debate the notions of mechanisms seem to be limited to 'mechanistic processes' and 'complex-systems mechanisms,' understood as 'componential causal systems'. I believe that this will not do full justice to how mechanisms are used in biological, psychological and social sciences and, consequently, in a more biopsychosocial approach to medicine. Here, (...) I propose, following (Kuorikoski, 2009), to pay more attention to 'abstract forms of interaction' mechanisms. The present work scrutinized review articles on depression and medically unexplained pain, which are considered to be of multifactorial pathogenesis, for their use of mechanisms. In review articles on these disorders there seemed to be a range of uses between more 'abstract forms of interaction' and 'componential causal system' mechanisms. I therefore propose to expand the notions of mechanisms considered in medicine to include that of more 'abstract forms of interaction' to better explain and manage biopsychosocial disorders. (shrink)

This book provides for the first time a complete history of the doctrine of the transcendentals and shows its importance for the understanding of philosophy in the Middle Ages.

Niels Bohr and Philosophy of Physics: Twenty-First Century Perspectives examines the work, influences and legacy of the Nobel Prize physicist and philosopher of experiment Niels Bohr. While covering Bohr's groundbreaking contribution to quantum mechanics, this collection reveals the philosophers who influenced his work. Linking him to the pragmatist C.I. Lewis and the Danish philosopher Harald Høffding, it draws strong similarities between Bohr's philosophy and the Kantian way of thinking. Addressing the importance of Bohr's views of classical concepts, it discusses how (...) his interpretation of quantum mechanics now compares with a variety of issues that have arisen only since his lifetime, including decoherence and other non-collapse arguments. Balancing historical themes with contemporary ideas, Niels Bohrs and Philosophy of Physics reveals Bohr's on-going contribution to the philosophy of science and confirms his place in the history of philosophy. (shrink)

Kearns (2021) reconstructs Berkeley’s (1713) Master Argument as a formally valid argument against the Materialist Thesis, with the key premise the Distinct Conceivability Thesis, namely the thesis that truths about sensible objects having or lacking thinkable qualities are (distinctly) conceivable and as its conclusion that all sensible objects are conceived. It will be shown that Distinct Conceivability Thesis entails the Reduction Thesis, which states that de dicto propositional (ordinary or distinct) conceivability reduces to de re propositional (ordinary or distinct) conceivability. (...) While Kearns (2021) set out to avoid the confusion of a de re claim with a de dicto claim, which Prior (1955) accused Berkeley of, Kearns can be accused of making a similar conceptual confusion. (shrink)

A number of well-developed theories shed light on the question, under what circumstances our beliefs enjoy epistemic justification. Yet, comparatively little is known about epistemic defeat--when new information causes the loss of epistemic justification. This book proposes and defends a detailed account of epistemic defeaters. The main kinds of defeaters are analyzed in detail and integrated into a general framework that aims to explain how beliefs lose justification. It is argued that defeaters introduce incompatibilities into a noetic system and thereby (...) prompt a structured re-evaluation process that makes a justified reinstatement of the defeated belief impossible. The account is then applied to the topic of disagreement, where it is used in an argument for conciliationism, as well as a new explanation for higher-order defeat. Throughout the book, the notion of defeat is the center of attention, while a number of new issues are discussed at the intersections of defeat and justification. Specifically, new problems are raised for broadly internalist accounts of defeat, a fully descriptive reliabilist account of defeat is provided, and the case for normative defeat is revisited. (shrink)

This book maps the entire development of Comenius’s considerations on man, from his earliest writings to his philosophical masterwork. Although this book primarily offers an analysis and description of the conception of man in Comenius’s work, it may also serve the reader as a more general introduction to his philosophical conception. The author shows that, in spite of the fact that Comenius has received no small amount of academic attention, funded studies or monographs in English language remain in single figures. (...) Thus, a range of Comenius’s remarkable ideas are still unknown to the wider public. (shrink)

Wprowadzenie -- Roman ingarden -- Antoni kępiński -- Karol wojtyła -- Władysław stróżewski -- Józef tischner.