Context: Strict finitism is usually not taken seriously as a possible view on what mathematics is and how it functions. This is due mainly to unfamiliarity with the topic. Problem: First, it is necessary to present a “decent” history of strict finitism and, secondly, to show that common counterarguments against strict finitism can be properly addressed and refuted. Method: For the historical part, the historical material is situated in a broader context, and for the argumentative part, an evaluation of arguments (...) and counterarguments is presented. Results: The main result is that strict finitism is indeed a viable option, next to other constructive approaches, in mathematics. Implications: Arguing for strict finitism is more complex than is usually thought. For future research, strict finitist mathematics itself needs to be written out in more detail to increase its credibility. In as far as strict finitism is a viable option, it will change our views on such “classics” as the platonist-constructivist discussion, the discovery-construction debate and the mysterious applicability problem . Constructivist content: Strict finitism starts from the idea that counting is an act of labeling, hence the mathematician is an active subject right from the start. It differs from other constructivist views in that the finite limitations of the human subject are taken into account. (shrink)

Context: Strict finitism is usually not taken seriously as a possible view on what mathematics is and how it functions. This is due mainly to unfamiliarity with the topic. Problem: First, it is necessary to present a “decent” history of strict finitism (which is now lacking) and, secondly, to show that common counterarguments against strict finitism can be properly addressed and refuted. Method: For the historical part, the historical material is situated in a broader context, and for the argumentative part, (...) an evaluation of arguments and counterarguments is presented. Results: The main result is that strict finitism is indeed a viable option, next to other constructive approaches, in (the foundations of) mathematics. Implications: Arguing for strict finitism is more complex than is usually thought. For future research, strict finitist mathematics itself needs to be written out in more detail to increase its credibility. In as far as strict finitism is a viable option, it will change our views on such “classics” as the platonist-constructivist discussion, the discovery-construction debate and the mysterious applicability problem (why is mathematics so successful in its applications?). Constructivist content: Strict finitism starts from the idea that counting is an act of labeling, hence the mathematician is an active subject right from the start. It differs from other constructivist views in that the finite limitations of the human subject are taken into account. (shrink)

Context: As one of the major approaches within the philosophy of mathematics, constructivism is to be contrasted with realist approaches such as Platonism in that it takes human mental activity as the basis of mathematical content. Problem: Mathematical constructivism is mostly identified as one of the so-called foundationalist accounts internal to mathematics. Other perspectives are possible, however. Results: The notion of “meaning finitism” is exploited to tie together internal and external directions within mathematical constructivism. The various contributions to this issue (...) support our case in different ways. Constructivist content: Further contributions from a multitude of constructivist directions are needed for the puzzle of an integrative, overarching theory of mathematical practice to be solved. (shrink)

Everyone is familiar with the measure of beauty that has been proposed by Birkhoff, the famous formula M = O/C. Although I show that the formula in its original form cannot be maintained, I present a reinterpretation that adapts the formula for measuring the beauty of mathematical proofs. However, this type of measure is not the only aesthetic element in mathematics. There exists a 'romantic' side as well, to use the term introduced by François Le Lionnais. Thus, a more complex (...) proposal of mathematical beauty is presented. Finally and as a consequence, I argue against the dichotomy that associates science, including mathematics, with the beauty of simplicity and that associates the arts with the beauty of complexity. As an example, the work of Oulipo, Raymond Queneau in particular, is briefly presented. (shrink)

Open peer commentary on the article “Second-Order Science: Logic, Strategies, Methods” by Stuart A. Umpleby. Upshot: The author makes a strong plea for second-order science but somehow mathematics remains out of focus. The major claim of this commentary is that second-order science requires second-order mathematics.

Open peer commentary on the article “Religion: A Radical-Constructivist Perspective” by Andreas Quale. Upshot: An essential feature of Quale’s point of view is the strict distinction between the cognitive and the non-cognitive. I argue that this position is untenable and hence that a radical constructivist can discuss religious matters.

What is philosophy of mathematics and what is it about? The most popular answer, I suppose, to this question would be that philosophers should provide a justification for our presently most cherished mathematical theories and for the most important tool to develop such theories, namely logico-mathematical proof. In fact, it does cover a large part of the activity of philosophers that think about mathematics. Discussions about the merits and faults of classical logic versus one or other ‘deviant’ logics as the (...) logical basis for mathematical theories, ranging from intuitionist over modal logic to paraconsistent logic, typically belong to this area, as do debates about the natural-number concept, its ‘nature’, its properties, especially its uniqueness, and so on. No doubt sociologists of knowledge could explain why philosophers of mathematics came to select these particular problems and deal with them the way they do. What it does imply, however, is that the question is meaningful whether different kinds of philosophies of mathematics are possible, and—why not?—perhaps even desirable. To a certain extent, the answer is trivial: look at what, e.g., phenomenologists have to say about mathematics and you must notice it does not fit into the scheme sketched above.1 Rather, the question should be whether there are forms that, on the one hand, reinterpret the whole enterprise, and, on the other hand, somehow remain related to the work of ‘mainstream’ philosophers of mathematics today.The book under review here does precisely that. Let me be a bit more precise. The general proposal, present throughout all the contributions, is that even at a first, superficial, glance at what mathematicians do when they do mathematics, it is far more complex than ‘just thinking about and …. (shrink)

Doctors’ strikes are legally permissible in the UK, with the situation differing in other countries. But are they morally permissible? Doug McConnell and Darren Mann have systematically attempted to dismiss the arguments for the moral impermissibility of doctors’ strikes and creatively attempted to provide further moral justification for them. Unfortunately for striking doctors, they fail to achieve this. Meanwhile, junior doctors’ strikes have continued in the UK through 2023 and have now extended into 2024. In this response, which focuses on (...) the UK situation and specifically junior doctors’ strikes in the National Health Service (NHS) in England, I will demonstrate a central problem with their arguments—namely that they underplay the harms caused by prolonged doctors’ strikes by ignoring the harms to patients with cancer. This weakens their conclusion that strikes are morally permissible in terms of the conditions and thresholds they set. I then provide a psychological critique of their justification for strikes in terms of the interests of the public. It follows that invoking the controversial concept of supererogatory action is ungrounded but also absurd when you consider time-critical cancer care. If those representing striking doctors wish to maintain a modicum of moral respectability, they should mitigate for patients with cancer and negotiate reasonably and with urgency. (shrink)

The first comprehensive study of Nietzsche's earliest book, The Birth of Tragedy, this important volume by M. S. Silk and J. P. Stern examines the work in detail: its place in Nietzsche's philosophical career; its value as an account of ancient Greek culture; its place in the history of German ideas, and its value as a theory of tragedy and music. Presented in a fresh twenty-first-century series livery, and including a specially commissioned preface written by Lesley Chamberlain, illuminating its enduring (...) importance and relevance to philosophical enquiry, this accessible study has been revived for a new generation of readers. (shrink)

_Naturalism_ provides a rigorous analysis and critique of the major varieties of contemporary philosophical naturalism. The authors advocate the thesis that contemporary naturalism should be abandoned, in light of the serious objections raised against it. Contributors draw on a wide range of topics including: epistemology, the philosophy of science, the philosophy of mind and agency, and natural theology.

Albert and De Ruiter provide an introduction to the Conversation Analytic approach to ‘repair’: the ways in which people detect and deal with troubles in speaking, hearing and understanding in conversation. They explain the basic turn‐taking structures involved, provide examples, explain recent developments in the field and highlight some important points of contact and contrast with work in the Cognitive Sciences.

After describing Heidegger's critique of metaphysics as ontotheology, I unpack the metaphysical assumptions of several transhumanist philosophers. I claim that they deploy an ontology of power and that they also deploy a kind of theology, as Heidegger meant it. I also describe the way in which this metaphysics begets its own politics and ethics. In order to transcend the human condition, they must transgress the human.

Contemporary theories of institutions as clusters of stable solutions to recurrent coordination problems can illuminate and explain some unresolved difficulties and problems adhering to institutional definitions of art initiated by George Dickie and Arthur Danto. Their account of what confers upon objects their institutional character does not fit well with current work on institutions and social ontology. The claim that “the artworld” confers the status of “art” onto objects remains utterly mysterious. The “artworld” is a generic notion that designates a (...) sphere of human activity that involves practices that create goals that have led to the emergence of formal and informal institutions. But those institutions, rather than magically “creating” objects subjected to esthetic appreciation, merely solve familiar and ubiquitous coordination problems created by artistic activity in ways other institutions in other areas solve similar and/or analogous coordination problems. (shrink)

Onderwerp en gezegde, door D. M. Bakker.--Enkele opmerkingen over het Godsbegrip van Justinus Martyr, door J. den Boeft.--Heidegger, Descartes, Luther, door J. van der Hoeven.--"Geschichtlichkeit" bij Carl Friedrich von Weizsäcker, door G. Horsman.--Menselijke ontmaskering en Bijbels démasqué , door R. Huson.--Kleine geschiedenis van het begrip "niets" in de antieke wijsbegeerte (tot e met de Sofisten en Plato), door P. A. Meijer.--De structuur van opvoeden en opvoedkunde, door J. W. Mojet.--Individualiteit in de fysica, door M. D. (...) Stafleu. (shrink)

The research investigates the role of leadership in the transformation of denominational structures towards a missional ecclesiology, and focusses on the Highveld Synod of the Dutch Reformed Church. It describes the missional journey of the denomination, and interprets the transformation. The theory of ‘complex leadership’ in complex systems is applied to the investigation of the impact of leadership on a denominational structure. The theory identifies three mechanisms used by leaders as enablers in emergent, self-organisation systems: Leaders disrupt existing patterns, they (...) encourage novelty, and they act as sensemakers. These insights are applied as a tool to interpret the missional transformation of a denomination. (shrink)

Foundations of Humanism is a primer on secular humanism written by one of the leading figures in the movement. J.P. van Praag writes that the modern world is shaped by a central paradox: the technology that provides us with unprecedented possibilities at the same time imposes an oppressive organization on society. This organization, with its trappings of overspecialization and overcentralization, promotes feelings of impotence and alienation and a spirit of rebellion, especially in the young. In this book, van Praag examines (...) the ways in which the philosophy of humanism can be applied to this paradox of modern life. Humanism holds that the purpose of life is life itself. Van Praag demonstrates how, through the application of this principle, the paradox can be transcended and how personal fulfillment and social creativity can be achieved. Foundations of Humanism is designed to give the reader a comprehensive view of secular humanism, including its historical roots in classical Greece and the Renaissance, its elaboration as a formal philosophy, and its practical aspects as a social philosophy. Finally, it explores the application of humanist principles in counseling and education. (shrink)

Patient centred diagnosis is best practised through shared decision making; an iterative dialogue between doctor and patient, whichrespects a patient’s needs, values, preferences, and circumstances. -/- Shared decision making for diagnostic situations differs fundamentally from that for treatment decisions. This has important implications when considering its practical application. -/- The nature of dialogue should be tailored to the specific diagnostic decision; scenarios with higher stakes or uncertainty usually require more detailed conversations.

This article revisits a reduced model of cardiac electro-physiology which was proposed to understand the genesis of unidirectional block pathology and of ectopic foci. We underline some specificities of the model from the viewpoint of dynamical systems and bifurcation theory. We point out that essentially the same properties are shared by a simpler system more accessible to analysis. With this simpler system, it becomes possible to give a new presentation of the phenomenon in a phase plane with time moving slow (...) manifolds. This presentation can be of interest both for cardiac electro-physiologists and for mathematicians. (shrink)