Einstein's theories of special and general relativity are unanimously praised by scientists for their extraordinary beauty to the extent that some consider the latter to be the most beautiful theory in physics. The grounds for these assertions are assessed here and it is concluded that the beauty of Einstein's theories can be attributed to two of their aspects. The first is that they incorporate all possible ingredients that constitute the beauty of theories: simplicity, symmetry, invariance, unification, etc. The second concerns (...) the perfect logical consistency of Einstein's theories, a crucial factor in the unanimous praise of their beauty. Theories other than Einstein's are also assessed here, namely, electromagnetism and the various quantum theories, and it is concluded that all these suffer from logical flaws. This has resulted in a lack of consensus among scientists with respect to their beauty. Consequently, the unanimous claim that Einstein's theories are of superior beauty as compared to other theories in physics is hereby substantiated. (shrink)

J.D. Trout (2002) presents a challenge to all theorists of scientific explanation who appeal to the notion of understanding. Trout denounces understanding as irrelevant, if not dangerous, from an epistemic perspective and he endorses a radically objectivist view of explanation instead. In this note I accept Trout's challenge. I criticize his argument and defend a non-objectivist, pragmatic conception of understanding that is epistemically relevant.

The collaborative ‹Big Science’ approach prevalent in physics during the mid- and late-20th century is becoming more common in the life sciences. Often computationally mediated, these collaborations challenge researchers’ trust practices. Focusing on the visualisations that are often at the heart of this form of scientific practice, the paper proposes that the aesthetic aspects of these visualisations are themselves a way of securing trust. Kant’s account of aesthetic judgements in the Third Critique is drawn upon in order to show that (...) the image-building capability of imagination, and the sensus communis, both of which are integral parts of aesthetic experience, play an important role in building and sustaining community in these forms of science. Kant’s theory shows that the aesthetic appeal of scientific visualisations is not isolated from two other dimensions of the visualisations: the cognitive-epistemic, aesthetic-stylistic and interpersonal dimensions, and that in virtue of these inter-relationships, visualisations contribute to building up the intersubjectively shared framework of agreement which is basic for trust. (shrink)

It is a common thought that mathematics can be not only true but also beautiful, and many of the greatest mathematicians have attached central importance to the aesthetic merit of their theorems, proofs and theories. But how, exactly, should we conceive of the character of beauty in mathematics? In this paper I suggest that Kant's philosophy provides the resources for a compelling answer to this question. Focusing on §62 of the ‘Critique of Aesthetic Judgment’, I argue against the common view (...) that Kant's aesthetics leaves no room for beauty in mathematics. More specifically, I show that on the Kantian account beauty in mathematics is a non-conceptual response felt in light of our own creative activities involved in the process of mathematical reasoning. The Kantian proposal I thus develop provides a promising alternative to Platonist accounts of beauty widespread among mathematicians. While on the Platonist conception the experience of mathematical beauty consists in an intellectual insight into the fundamental structures of the universe, according to the Kantian proposal the experience of beauty in mathematics is grounded in our felt awareness of the imaginative processes that lead to mathematical knowledge. The Kantian account I develop thus offers to elucidate the connection between aesthetic reflection, creative imagination and mathematical cognition. (shrink)

Should philosophers prefer simpler theories? Huemer (Philos Q 59:216–236, 2009) argues that the reasons to prefer simpler theories in science do not apply in philosophy. I will argue that Huemer is mistaken—the arguments he marshals for preferring simpler theories in science can also be applied in philosophy. Like Huemer, I will focus on the philosophy of mind and the nominalism/Platonism debate. But I want to engage with the broader issue of whether simplicity is relevant to philosophy.

Aesthetic value, often viewed as subjective and even trivial compared to other environmental values, is commonly given low priority in policy debates. In this paper I argue that the seriousness and importance of aesthetic value cannot be denied when we recognise the ways that aesthetic experience is already embedded in a range of human practices. The first area of human practice considered involves the complex relationship between aesthetic experience and the development of an ethical attitude towards the environment. I then (...) discuss how aesthetics has played a role in scientific study and the use of evaluative aesthetic concepts in science, such as variety and diversity. The final section shows the connection between the beneficial effects of aesthetic engagement with nature and the restorative value of nature for human well-being. (shrink)

This paper describes a long-standing, though little-known, debate between Paul Dirac and Werner Heisenberg over the nature of scientific methodology, theory change, and intertheoretic relations. Following Heisenberg’s terminology, their disagreements can be summarized as a debate over whether the classical and quantum theories are “open” or “closed.” A close examination of this debate sheds new light on the philosophical views of two of the great founders of quantum theory.

The practice of attributing aesthetic properties to scientific and philosophical theories is commonplace. Perhaps one of the most famous examples of such an aesthetic judgement about a theory is Quine's in 'On what there is': "Wyman's overpopulated universe is in many ways unlovely. It offends the aesthetic sense of us who have a taste for desert landscapes". Many other philosophers and scientists, before and after Quine, have attributed aesthetic properties to particular theories they are defending or rejecting. One often hears (...) that a view is "elegant", "attractive", "beautiful", or even "sexy". [...] The general claim that aesthetic properties supervene on non-aesthetic properties is a largely debated one. In this paper, I wish to address this issue from an angle which has not been really explored so far: I shall neither concentrate on cases of artefacts nor of natural objects, like the beauty of a painting or the beauty of a sunrise, rather, my main centre of attention will be the somewhat more special, theoretical case of the beauty of philosophical theories (with a focus on metaphysical theories). As we will see, there are some interesting issues concerning claims that attribute aesthetic properties to theories, in part because, even if such claims are commonplace in philosophy and in science, little has been said about the nature of the relevant supervenience basis – that is, about what it is exactly that the beauty of a theory is supposed to supervene on. Moreover, we shall see that aesthetic properties of theories play a crucial role in theory choice and evaluation. Indeed, it seems that the aesthetic properties of a theory can be appealed to in theory evaluation and when it comes to preferring one theory over another. But before we ask ourselves what role the attribution of aesthetic properties to theories can play, I will adress the question how theories come to have their aesthetic properties in the first place. (shrink)

In this article, I defend Lewisian modal realism against objections arising from the possibility of ‘Island Universes’ and other similar cases. The problem comes from Lewis’ claim that possible worlds are spatio-temporally isolated. I suggest a modification of Lewisian modal realism in order to avoid this family of objections. This modification may sound quite radical since it amounts to abandoning the very notion of a possible world, but as radical as it may sound it in fact remains well in the (...) spirit of Lewis’ original view. (shrink)

: Some of the great physicists' belief in the existence of a connection between the aesthetical features of a theory (such as beauty and simplicity) and its truth is still one of the most intriguing issues in the aesthetics of science. In this paper I explore the philosophical credibility of a version of this thesis, focusing on the connection between the mathematical beauty and simplicity of a theory and its truth. I discuss a heuristic interpretation of this thesis, attempting to (...) clarify where the appeal of this Pythagorean view comes from and what are the arguments favoring its acceptance or rejection. Along the way, I sketch the historical context in which this heuristic interpretation gained credibility (the quantum crisis in physics in the 1920s), as well as the more general implications of this thesis for physicists' metaphysical outlook. (shrink)

Continental philosophy of science has developed alongside mainstream analytic philosophy of science. But where continental approaches are inclusive, analytic philosophies of science are not–excluding not merely Nietzsche’s philosophy of science but Gödel’s philosophy of physics. As a radicalization of Kant, Nietzsche’s critical philosophy of science puts science in question and Nietzsche’s critique of the methodological foundations of classical philology bears on science, particularly evolution as well as style (in art and science). In addition to the critical (in Mach, Nietzsche, Heidegger (...) but also Husserl just to the extent that continental philosophy of science tends to depart from a reflection on the crisis of foundations), other continental philosophies of science include phenomenology (Husserl, Bachelard, Merleau‐Ponty, etc.) and hermeneutics (Heidegger, Gadamer, Heelan, etc.), especially incorporating history of science (Nietzsche, Mach, Duhem, Butterfield, Feyerabend, etc.). Examples are drawn from the philosophy of sciences (chemistry, geology, and biology) other than physics. (shrink)

Lakatos held that science proceeds by means of competing research programme, each with its own “hard core” or paradigm. He intended this view to reconcile the competing views of Kuhn and Popper. But what Lakatos overlooked is that science needs to be construed to be one gigantic research programme with, as its “hard core”, a metaphysical thesis that asserts that the universe is such that there is an inherent unity in the laws that govern the way physical phenomena occur. The (...) conception of science that emerges from this insight succeeds in doing what Lakatos’s own view fails to do; it has fruitful implications for science itself, and solves the problem of induction. (shrink)

This paper challenges the appeal to theory virtues in theory choice as well as the appeal to the intellectual and moral virtues of an agent as determining unique choices between empirically equivalent theories. After arguing that theoretical virtues do not determine the choice of one theory at the expense of another theory, I argue that nor does the appeal to intellectual and moral virtues single out one agent, who defends a particular theory, and exclude another agent defending an alternative theory. (...) I analyse Duhem’s concept of good sense and its recent interpretation in terms of virtue epistemology. I argue that the virtue epistemological interpretation does not show how good sense leads to conclusive choices and scientific progress. (shrink)

This book develops a naturalistic aesthetic theory that accounts for aesthetic phenomena in mathematics in the same terms as it accounts for more traditional aesthetic phenomena. Building upon a view advanced by James McAllister, the assertion is that beauty in science does not confine itself to anecdotes or personal idiosyncrasies, but rather that it had played a role in shaping the development of science. Mathematicians often evaluate certain pieces of mathematics using words like beautiful, elegant, or even ugly. Such evaluations (...) are prevalent, however, rigorous investigation of them, of mathematical beauty, is much less common. The volume integrates the basic elements of aesthetics, as it has been developed over the last 200 years, with recent findings in neuropsychology as well as a good knowledge of mathematics. The volume begins with a discussion of the reasons to interpret mathematical beauty in a literal or non-literal fashion, which also serves to survey historical and contemporary approaches to mathematical beauty. The author concludes that literal approaches are much more coherent and fruitful, however, much is yet to be done. In this respect two chapters are devoted to the revision and improvement of McAllister’s theory of the role of beauty in science. These antecedents are used as a foundation to formulate a naturalistic aesthetic theory. The central idea of the theory is that aesthetic phenomena should be seen as constituting a complex dynamical system which the author calls the aesthetic as process theory. The theory comprises explications of three central topics: aesthetic experience, aesthetic value and aesthetic judgment. The theory is applied in the final part of the volume and is used to account for the three most salient and often used aesthetic terms often used in mathematics: beautiful, elegant and ugly. This application of the theory serves to illustrate the theory in action, but also to further discuss and develop some details and to showcase the theory’s explanatory capabilities. (shrink)

В монографии представлены несколько смысловых блоков, связанных с восприятием и интерпретацией человеком исторического бытия. Ранние греческие мыслители пытались получить доступ к исходникам (началам) бытия, и эти интенции легли в основу научного знания, а также привели к появлению метафизики. В классической (и в неклассической) метафизике за основу была принята догма Пифагора и Платона о неизменности подлинной реальности, из чего следовало отрицание бытийного характера времени. Автор монографии отказывается от этой догмы и предлагает стратегию обновления метафизики и перехода ее к новому — постнеклассическому (...) — этапу. Поскольку трансформационный потенциал реальности наиболее явно представлен в историческом становлении, авторская стратегия реализуется в метафизике истории. При этом выявляются начала истории, в каком качестве выступают «дух», «культурно-историческая матрица» и «метафизический проект организации бытия» («онтологический проект»). Исследуются формы и механизмы «работы» человека с прошлым, обсуждаются вопросы, связанные с постижением логики исторического процесса, а также с ролью (творческой) личности в истории. Анализируются причины цивилизационных кризисов и очерчиваются возможные пути их разрешения, предлагается метафизическая интерпретация социальных и военных конфликтов. Завершает исследование рассмотрение трансформации человеческого естества под влиянием информационных, био- и нанотехнологий. (shrink)

'Reason, Causation and Compatibility with the Phenomena' strives to give answers to the philosophical problem of the interplay between realism, explanation and experience. This book is a compilation of essays that recollect significant conceptions of rival terms such as determinism and freedom, reason and appearance, power and knowledge. This title discusses the progress made in epistemology and natural philosophy, especially the steps that led from the ancient theory of atomism to the modern quantum theory, and from mathematization to analytic philosophy. (...) Moreover, it provides possible gateways from modern deadlocks of theory either through approaches to consciousness or through historical critique of intellectual authorities. This work will be of interest to those either researching or studying in colleges and universities, especially in the departments of philosophy, history of science, philosophy of science, philosophy of physics and quantum mechanics, history of ideas and culture. Greek and Latin Literature students and instructors may also find this book to be both a fascinating and valuable point of reference. (shrink)

Karl Popper is famous for having proposed that science advances by a process of conjecture and refutation. He is also famous for defending the open society against what he saw as its arch enemies – Plato and Marx. Popper’s contributions to thought are of profound importance, but they are not the last word on the subject. They need to be improved. My concern in this book is to spell out what is of greatest importance in Popper’s work, what its failings (...) are, how it needs to be improved to overcome these failings, and what implications emerge as a result. The book consists of a collection of essays which dramatically develop Karl Popper’s views about natural and social science, and how we should go about trying to solve social problems. Criticism of Popper’s falsificationist philosophy of natural science leads to a conception of science that I call aim-oriented empiricism. This makes explicit metaphysical theses concerning the comprehensibility and knowability of the universe that are an implicit part of scientific knowledge – implicit in the way science excludes all theories that are not explanatory, even those that are more successful empirically than accepted theories. Aim-oriented empiricism has major implications, not just for the academic discipline of philosophy of science, but for science itself. Popper generalized his philosophy of science of falsificationism to arrive at a new conception of rationality – critical rationalism – the key methodological idea of Popper’s profound critical exploration of political and social issues in his The Open Society and Its Enemies, and The Poverty of Historicism. This path of Popper, from scientific method to rationality and social and political issues is followed here, but the starting point is aim-oriented empiricism rather than falsificationism. Aim-oriented empiricism is generalized to form a conception of rationality I call aim-oriented rationalism. This has far-reaching implications for political and social issues, for the nature of social inquiry and the humanities, and indeed for academic inquiry as a whole. The strategies for tackling social problems that arise from aim-oriented rationalism improve on Popper’s recommended strategies of piecemeal social engineering and critical rationalism, associated with Popper’s conception of the open society. This book thus sets out to develop Popper’s philosophy in new and fruitful directions. The theme of the book, in short, is to discover what can be learned from scientific progress about how to achieve social progress towards a better world. (shrink)

What ought to be the aims of science? How can science best serve humanity? What would an ideal science be like, a science that is sensitively and humanely responsive to the needs, problems and aspirations of people? How ought the institutional enterprise of science to be related to the rest of society? What ought to be the relationship between science and art, thought and feeling, reason and desire, mind and heart? Should the social sciences model themselves on the natural sciences: (...) or ought they to take a different form if they are to serve the interests of humanity objectively, sensitively and rigorously? Might it be possible to get into human life, into art, education, politics, industry, international affairs, and other domains of human activity, the same kind of progressive success that is found so strikingly, on the intellectual level, within science? These are some of the questions tackled by What’s Wrong With Science? But the book is no abstruse treatise on the philosophy of science. Most of it takes the form of a passionate debate between a Scientist and a Philosopher, a debate that is by turns humorous, ironical, bitter, dramatically explosive. Even as the argument explores the relationship between thought and feeling, reason and desire, the two main protagonists find it necessary to examine their own feelings and motivations. (shrink)

The aim of this work is to account for expressions like “Cantor’s diagonal proof is elegant” or “Euler identity is the most beautiful formula of mathematics”. This type of expressions is common among mathematicians; however, they may result in two kinds of puzzled reactions: first, the non mathematician may find the use of the word ‘beautiful’ strange in this context. Second, the mathematician may try to reinterpret mathematical beauty in terms of the principles and precepts of mathematics itself. I present (...) an account of mathematical beauty that offers a way to avoid these puzzled reactions: mathematical beauty is just a type of “normal” beauty and no reinterpretation is necessary. To support this claim, I devise an aesthetic theory -by using insights and findings from experimental psychology, neurology, philosophical and psychological theories of emotion in art, philosophy of music and philosophy of science- that shows that aesthetic judgments in mathematics are genuine aesthetic judgments. (shrink)

In this paper I argue for a priori conjectural scientific knowledge about the world. Physics persistently only accepts unified theories, even though endlessly many empirically more successful disunified rivals are always available. This persistent preference for unified theories, against empirical considerations, means that physics makes a substantial, persistent metaphysical assumption, to the effect that the universe has a (more or less) unified dynamic structure. In order to clarify what this assumption amounts to, I solve the problem of what it means (...) to say of a theory that it is unified. There are, I argue, eight different kinds of unity important in theoretical physics, all varieties of one basic idea. This provides us with a precise way of partially ordering physical theories with respect to their degree of unity. It also leads to a hierarchical view of physics, according to which physics makes a number of increasingly insubstantial metaphysical assumptions concerning the comprehensibility and knowability of the universe. Two of these are identified as constituting a priori conjectures. I conclude by arguing that the view developed in the paper resolves the traditional clash between empiricism and rationalism in the philosophy of science, and has important implications for science, and for academic inquiry more generally. (shrink)

This is a review of Hossenfelder’s book, Lost in Math: How Beauty Leads Physics Astray. The book gives a breezy exposition of the present situation in fundamental physics, and raises important questions: both about the content of the physics, and the way physics research is organized. I first state my main disagreements. Then, I mostly praise the book: I concentrate on Hossenfelder’s discussion of supersymmetry, naturalness and the multiverse.

This paper discusses Theo Kuipers' account of beauty and truth. It challenges Kuipers' psychological account of how scientists come to appreciate beautiful theories, as well as his attempt to justify the use of aesthetic criteria on the basis of a "meta-induction." I propose an alternative psychological/philosophical account based on emotional coherence.

This paper comments on an article by V.S. Ramachandran and William Hirstein (JCS,1999) in which they purport to be identifying the neurological principles of beauty. I draw attention to the way the problem of beauty is construed in the philosophical literature by Mary Mothersill (1984) and Immanuel Kant (Critique of Judgment). I argue that Ramachandran and Hirsteins' principles do not address the problem of beauty because they do not differentiate between the experience of beauty and other closely related phenomena. I (...) then show how one might address the problem of beauty within the framework that they have adopted. (shrink)

Ormerod and Chronicle reported that optimal solutions to traveling salesperson problems were judged to be aesthetically more pleasing than poorer solutions and that solutions with more convex hull nodes were rated as better figures. To test these conclusions, solution regularity and the number of potential intersections were held constant, whereas solution optimality, the number of internal nodes, and the number of nearest neighbors in each solution were varied factorially. The results did not support the view that the convex hull is (...) an important determinant of figural attractiveness. Also, in contrast to the findings of Ormerod and Chronicle, there were consistent individual differences. Participants appeared to be divided as to whether the most attractive figure enclosed a given area within a perimeter of minimum or maximum length. It is concluded that future research in this area cannot afford to focus exclusively on group performance measures. (shrink)