Vladimir Arnold, an eminent mathematician of our time, is known both for his mathematical results, which are many and prominent, and for his strong opinions, often expressed in an uncompromising and provoking manner. His dictum that "Mathematics is a part of physics where experiments are cheap" is well known. This book consists of two parts: selected articles by and an interview with Vladimir Arnold, and a collection of articles about him written by his friends, colleagues, and students. The book is (...) generously illustrated by a large collection of photographs, some never before published. The book presents many a facet of this extraordinary mathematician and man, from his mathematical discoveries to his daredevil outdoor adventures. (shrink)

Neuroscience is a multidisciplinary effort to understand the structures and functions of the brain and brain-mind relations. This effort results in an increasing amount of data, generated by sophisticated technologies. However, these data enhance our descriptive knowledge, rather than improve our understanding of brain functions. This is caused by methodological gaps both within and between subdisciplines constituting neuroscience, and the atomistic approach that limits the study of macro- and mesoscopic issues. Whole-brain measurement technologies do not resolve these issues, but rather (...) aggravate them by the complexity problem. The present article is devoted to methodological and epistemic problems that obstruct the development of human neuroscience. We neither discuss ontological questions nor review data, except when it is necessary to demonstrate a methodological issue. As regards intradisciplinary methodological problems, we concentrate on those within neurobiology and psychology. As regards interdisciplinary problems, we suggest that core disciplines of neuroscience can be integrated using systemic concepts that also entail human-environment relations. We emphasize the necessity of a meta-discussion that should entail a closer cooperation with philosophy as a discipline of systematic reflection. The atomistic reduction should be complemented by the explicit consideration of the embodiedness of the brain and the embeddedness of humans. The discussion is aimed at the development of an explicit methodology of integrative human neuroscience, which will not only link different fields and levels, but also help in understanding clinical phenomena. (shrink)

We question the usefulness of Pylyshyn's dichotomy between cognitively penetrable and cognitively impenetrable mechanisms as the basis for his distinction between cognition and early vision. This dichotomy is comparable to others that have been proposed in psychology prompting disputes that by their very nature could not be resolved. This fate is inevitable for Pylyshyn's thesis because of its reliance on internal representations and their interpretation. What is more fruitful in relation to this issue is not a difficult dichotomy, but a (...) different look at perception such as proposed by Gibson (1979). (shrink)

Despite its computational elegancy, Jackendoff's proposal to reconcile competing approaches by postulating a parallel architecture for phonological, syntactic, and semantic modules is disappointing. We argue that it is a pragmatic version of the leading module which Jackendoff would probably prefer, but which he does not explicitly acknowledge. This internal conflict leads to several shortcomings and even distortions of information presented in the book.

This collective paper on radicalization and violent extremism part of the ‘Philosophy of education in a new key’ initiative by Educational Philosophy and Theory brings together some of the leading contemporary scholars writing on the most pressing epistemological, ethical, political and educational issues facing post-9/11 scholarship on radicalization and violent extremism. Its overall aim is to move beyond the ‘conventional wisdom’ associated with this area of scholarly research best represented by its many slogans, metaphors and other thought-terminating clichés. By providing (...) conceptual lenses on issues previously compartmentalized primarily [or even exclusively] in security and intelligence studies or at the fringes of scholarly interest, radicalization and violent extremism turn out to be much more complex than ‘radicalization studies’ has been eager to acknowledge. (shrink)

Theoria, Volume 87, Issue 4, Page 971-985, August 2021.

I propose a general alethic theory of epistemic risk according to which the riskiness of an agent’s credence function encodes her relative sensitivity to different types of graded error. After motivating and mathematically developing this approach, I show that the epistemic risk function is a scaled reflection of expected inaccuracy. This duality between risk and information enables us to explore the relationship between attitudes to epistemic risk, the choice of scoring rules in epistemic utility theory, and the selection of priors (...) in Bayesian epistemology more generally. (shrink)

Social networks play a significant role in learning and thus in farmers’ adoption of new agricultural technologies. This study examined the effects of social network factors on information acquisition and adoption of new seed varieties among groundnut farmers in Uganda and Kenya. The data were generated through face-to-face interviews from a random sample of 461 farmers, 232 in Uganda and 229 in Kenya. To assess these effects two alternative econometric models were used: a seemingly unrelated bivariate probit model and a (...) recursive bivariate probit model. The statistical evaluation of the SUBP shows that information acquisition and adoption decisions are interrelated while tests for the RBP do not support this latter model. Therefore, the analysis is based on the results obtained from the SUBP. These results reveal that social network factors, particularly weak ties with external support, partially influence information acquisition, but do not influence adoption. In Uganda, external support, gender, farm size, and geographic location have an impact on information acquisition. In Kenya, external support and geographic location also have an impact on information acquisition. With regard to adoption, gender, household size, and geographic location play the most important roles for Ugandan farmers, while in Kenya information from external sources, education, and farm size affect adoption choice. The study provides insight on the importance of external weak ties in groundnut farming, and a need to understand regional differences along gender lines while developing agricultural strategies. This study further illustrates the importance of farmer participation in applied technology research and the impact of social interactions among farmers and external agents. (shrink)

This article informally presents a solution to the paradoxes of truth and shows how the solution solves classical paradoxes (such as the original Liar) as well as the paradoxes that were invented as counterarguments for various proposed solutions (“the revenge of the Liar”). This solution complements the classical procedure of determining the truth values of sentences by its own failure and, when the procedure fails, through an appropriate semantic shift allows us to express the failure in a classical two-valued language. (...) Formally speaking, the solution is a language with one meaning of symbols and two valuations of the truth values of sentences. The primary valuation is a classical valuation that is partial in the presence of the truth predicate. It enables us to determine the classical truth value of a sentence or leads to the failure of that determination. The language with the primary valuation is precisely the largest intrinsic fixed point of the strong Kleene three-valued semantics (LIFPSK3). The semantic shift that allows us to express the failure of the primary valuation is precisely the classical closure of LIFPSK3: it extends LIFPSK3 to a classical language in parts where LIFPSK3 is undetermined. Thus, this article provides an argumentation, which has not been present in contemporary debates so far, for the choice of LIFPSK3 and its classical closure as the right model for the truth predicate. In the end, an erroneous critique of Kripke-Feferman axiomatic theory of truth, which is present in contemporary literature, is pointed out. (shrink)

Boris Kment takes a new approach to the study of modality that emphasises the origin of modal notions in everyday thought. He argues that the concepts of necessity and possibility originate in counterfactual reasoning, which allows us to investigate explanatory connections. Contrary to accepted views, explanation is more fundamental than modality.

According to the aspect theory of instantiation, a particular A instantiates a universal B if and only if an aspect of A is cross-count identical with an aspect of B. This involves the assumption that both particulars and universals have aspects, and that aspects can mediate between different ways of counting things. I will ask what is new about this account of instantiation and, more importantly, whether it is an improvement on its older relatives. It will turn out that the (...) part of it that is new is the notion of cross-count identity among aspects. As I will show, this notion is both dubious and unnecessary. I will end by presenting a simplified aspect theory of instantiation that does not involve cross-count identity. (shrink)

As illiberal and authoritarian trends are on the rise--both in fragile and seemingly robust democracies--there is growing concern about the longevity of liberalism and democracy. The purpose of this volume is to draw on the analytical resources of various disciplines and public policy approaches to reflect on the current standing of liberal democracy. Leading social scientists from different disciplinary backgrounds aim to examine the ideological and structural roots of the current crisis of liberal democracies, in the West and beyond, conceptually (...) and empirically. The volume is divided into two main parts: Part I explores tensions between liberalism and democracy in a longer-term, historical perspective to explain immanent vulnerabilities of liberal democracy. Authors examine the conceptual foundations of Western liberal democracy that have shaped its standing in the contemporary world. What lies at the core of illiberal tendencies? Part II explores case studies from the North Atlantic, Eastern Europe, Turkey, India, Japan, and Brazil, raising questions whether democratic crises, manifested in the rise of populist movements in and beyond the Western context, differ in kind or only in degree. How can we explain the current popular appeal of authoritarian governments and illiberal ideas? The Emergence of Illiberalism will be of great interest to teachers and students of politics, sociology, political theory and comparative government. (shrink)

Instead of the usual asymptotic passage from quantum mechanics to classical mechanics when a parameter tended to infinity, a sharp boundary is obtained for the domain of existence of classical reality. The last is treated as separable empirical reality following d'Espagnat, described by a mathematical superstructure over quantum dynamics for the universal wave function. Being empirical, this reality is constructed in terms of both fundamental notions and characteristics of observers. It is presupposed that considered observers perceive the world as a (...) system of collective degrees of freedom that are inherently dissipative because of interaction with thermal degrees of freedom. Relevant problems of foundation of statistical physics are considered. A feasible example is given of a macroscopic system not admitting such classical reality.The article contains a concise survey of some relevant domains: quantum and classical Bell-type inequalities; universal wave function; approaches to quantum description of macroscopic world, with emphasis on dissipation; spontaneous reduction models; experimental tests of the universal validity of the quantum theory. (shrink)

Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial interpretation of the corresponding language. It follows from the analysis that (i) mathematical objects do not exist in the external world: they are our internally imagined objects, some of which, at least approximately, we can realize or represent; (ii) mathematical truths are not (...) truths about the external world but specifications (formulations) of mathematical conceptions; (iii) mathematics is first and foremost our imagined tool by which, with certain assumptions about its applicability, we explore nature and synthesize our rational cognition of it. (shrink)

While there are satisfactory answers to the question “How should we teach children mathematics?”, there are no satisfactory answers to the question “What mathematics should we teach children?”. This paper provides an answer to the last question for preschool children (early childhood), although the answer is also applicable to older children. This answer, together with an appropriate methodology on how to teach mathematics, gives a clear conception of the place of mathematics in the children’s world and our role in helping (...) children develop their mathematical abilities. Briefly, children’s mathematics consists of the world of children’s internal activities that they eventually purposefully organize in order to understand and control the outside world and organize their overall activities in it. We need to support a child in mathematical activities that she does spontaneously and in which she shows interest, and we need to teach her mathematics that she is interested in developing through these activities. In doing so, we must be fully aware that the child’s mathematics is part of the child’s world of internal activities and is not outside of it. We help the child develop mathematical abilities by developing them in the context of her world and not outside of it. From the point of view of this conception, the standards established today are limiting and too focused on numbers and geometric figures: these topics are too prominent and elaborated, and other mathematical contents are subordinated to them. Adhering to the standards, we drastically limit the mathematics of the child’s world, hamper the correct mathematical development of a child, and we can turn her away from mathematics. (shrink)