Within the last decade, several approaches using quaternion numbers to handle and model multiband images in a holistic manner were introduced. The quaternion Fourier transform can be efficiently used to model texture in multidimensional data such as color images. For practical application, multispectral satellite data appear as a primary source for measuring past trends and monitoring changes in forest carbon stocks. In this work, we propose a texture-color descriptor based on the quaternion Fourier transform to extract relevant information from multiband (...) satellite images. We propose a new multiband image texture model extraction, called FOTO++, in order to address biomass estimation issues. The first stage consists in removing noise from the multispectral data while preserving the edges of canopies. Afterward, color texture descriptors are extracted thanks to a discrete form of the quaternion Fourier transform, and finally the support vector regression method is used to deduce biomass estimation from texture indices. Our texture features are modeled using a vector composed with the radial spectrum coming from the amplitude of the quaternion Fourier transform. We conduct several experiments in order to study the sensitivity of our model to acquisition parameters. We also assess its performance both on synthetic images and on real multispectral images of Cameroonian forest. The results show that our model is more robust to acquisition parameters than the classical Fourier Texture Ordination model. Our scheme is also more accurate for aboveground biomass estimation. We stress that a similar methodology could be implemented using quaternion wavelets. These results highlight the potential of the quaternion-based approach to study multispectral satellite images. (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.

We construct and study structures imitating the field of complex numbers with exponentiation. We give a natural, albeit non first-order, axiomatisation for the corresponding class of structures and prove that the class has a unique model in every uncountable cardinality. This gives grounds to conjecture that the unique model of cardinality continuum is isomorphic to the field of complex numbers with exponentiation.

The volume collects classics of Marxist historiography of science, including a new translation of Boris Hessen's “The Social and Economic Roots of Newton's ...

The aim of Modality and Explanatory Reasoning (MER) is to shed light on metaphysical necessity and the broader class of modal properties to which it belongs. This topic is approached with two goals: to develop a new and reductive analysis of modality, and to understand the purpose and origin of modal thought. I argue that a proper understanding of modality requires us to reconceptualize its relationship to causation and other forms of explanation such as grounding, a relation that connects metaphysically (...) fundamental facts to non-fundamental ones. While many philosophers have tried to give modal analyses of causation and explanation, often in counterfactual terms, I argue that we obtain a more plausible, explanatorily powerful and unified theory if we regard explanation as more fundamental than modality. The function of modal thought is to facilitate a common type of thought experiment – counterfactual reasoning – that allows us to investigate explanatory connections and which is closely related to the controlled experiments of empirical science. Necessity is defined in terms of explanation, and modal facts often reflect underlying facts about explanatory relationships. The study of modal facts is important for philosophy not because these facts are of much metaphysical interest in their own right, but largely because they provide evidence about explanatory connections. (shrink)

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)

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)

On the basis of elementary thinking about language functioning, a solution of truth paradoxes is given and a corresponding semantics of a truth predicate is founded. It is shown that it is precisely the two-valued description of the maximal intrinsic fixed point of the strong Kleene three-valued semantics.

In this paper we develop a general theory of algorithmic fairness. Drawing on Johnson King and Babic’s work on moral encroachment, on Gary Becker’s work on labor market discrimination, and on Strawson’s idea of resentment and indignation as responses to violations of the demand for goodwill toward oneself and others, we locate attitudes to fairness in an agent’s utility function. In particular, we first argue that fairness is a matter of a decision-maker’s relative concern for the plight of people from (...) different groups, rather than of the outcomes produced for different groups. We then show how an agent’s preferences, including in particular their attitudes to error, give rise to their decision thresholds. Tying these points together, we argue that the agent’s relative degrees of concern for different groups manifest in a difference in decision thresholds applied to these groups. (shrink)

In this handbook, I put into practice my philosophical views on children's mathematics. The handbook contains brief instructions and examples of mathematical activities. In the INSTRUCTIONS section, instructions are given on how, and in part why that way, to help preschool children in their mathematical development. In the ACTIVITIES section, there are examples of activities through which the child develops her mathematical abilities.

We further investigate a divisibility relation on the set of BN ultrafilters on the set of natural numbers. We single out prime ultrafilters (divisible only by 1 and themselves) and establish a hierarchy in which a position of every ultrafilter depends on the set of prime ultrafilters it is divisible by. We also construct ultrafilters with many immediate successors in this hierarchy and find positions of products of ultrafilters.

In this paper, I offer a detailed reconstruction and a critical analysis of Abraham Maslow’s neglected psychological reading of Thomas Kuhn’s famous dichotomy between ‘normal’ and ‘revolutionary’ science, which Maslow briefly expounded four years after the first edition of Kuhn’s The Structure of Scientific Revolutions, in his small book The Psychology of Science: A Reconnaissance, and which relies heavily on his extensive earlier general writing in the motivational and personality psychology. Maslow’s Kuhnian ideas, put forward as part of a larger (...) program for the psychology of science, outlined already in his 1954 magnum opus Motivation and Personality, are analyzed not only in the context of Kuhn’s original ‘psychologizing’ attitude toward understanding the nature and development of science, but also in a broader historical, intellectual and social context. (shrink)

The sensorimotor account of perception is akin to Gibsonian direct realism. Both emphasize external properties of the world, challenging views based on the analysis of internal visual processing. To compare the role of distal and retinotopic parameters, distractor effect – an optomotor reaction of midbrain origin – is considered. Even in this case, permanence in the environment, not on the retina, explains the dynamics of habituation.

We continue the research of an extension of the divisibility relation to the Stone‐Čech compactification. First we prove that ultrafilters we call prime actually possess the algebraic property of primality. Several questions concerning the connection between divisibilities in and nonstandard extensions of are answered, providing a few more equivalent conditions for divisibility in. Results on uncountable chains in are proved and used in a construction of a well‐ordered chain of maximal cardinality. Probably the most interesting result is the existence of (...) a chain of type in. Finally, we consider ultrafilters without divisors in and among them find the greatest class. (shrink)

Many philosophers have argued that statistical evidence regarding group characteristics (particularly stereotypical ones) can create normative conflicts between the requirements of epistemic rationality and our moral obligations to each other. In a recent article, Johnson-King and Babic argue that such conflicts can usually be avoided: what ordinary morality requires, they argue, epistemic rationality permits. In this article, we show that as data get large, Johnson-King and Babic’s approach becomes less plausible. More constructively, we build on their project and develop a (...) generalized model of reasoning about stereotypes under which one can indeed avoid normative conflicts, even in a big data world, when data contain some noise. In doing so, we also articulate a general approach to rational belief updating for noisy data. (shrink)

Starting from the idea that functions are formally similar to actions in that they are described and explained in a similar way, so that both admit of an accordion effect, I turn to Anscombe’s insight that the point of practical reasoning is to render explicit the relation between the different descriptions of an action generated by the accordion effect. The upshot is, roughly, that an item has a function if what it does can be accounted for by functional reasoning. Put (...) differently, a part of a system has a function if what it does is a functional part of what the system does. (shrink)

Eye movements play a variety of roles in perception, cognition, and communication. The roles are revealed by the duration of fixations reflecting the quality of processing in the first line. We describe possible roles of eye fixations in different temporal diapasons. These forms of processing may be specific to sensorimotor coordinations. Any generalization to other domains should be cautious.

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.

While sharing the author's interest in the development of an action-based framework for memory research, I think the present version is neither new nor particularly productive. More differentiation is needed to describe memory functioning in a variety of domains and on the many levels of activity regulation. Above all, Glenberg's proposals seem to contradict empirical data.

Im 2009 erschienenen Buch "Philosophie des Leidens" versucht Boris Wandruszka, jene immanente Lebensstruktur und Lebensdynamik aufzudecken, die zu den einfachsten und fundamentalen Strukturmomenten des Leidens vorstosst; diese erste "Wissenschaft vom Leiden" transzendierte daher nicht die Grenzen der Anschaubarkeit, sondern verblieb in der "Immanenz des 'inneren Lebens' bzw. des Erlebens". Im aktuellen Buch "Metaphysik des Leidens" werden die "realen Bedingungen der Moglichkeit von Leiden" ermittelt: Wie muss eine Welt beschaffen sein, damit darin ein leidendes Wesen erscheinen konne? Welche Rolle hat (...) das Leiden in Bezug zum fundamentalen Widerfahrnis-, Resonanz- und Responsivitatscharakter des Lebens? Es wird gezeigt, dass menschliches Leben, das einer plural-agonalen Welt ausgesetzt ist, nicht leidfrei moglich ist, dass aber andererseits das Leid nicht das letzte Wort sein kann, sondern notwendig auf Ganzheit, Reifung, Erlosung und Harmonie bezogen ist. Nur auf dem Hintergrund der Spannung zwischen absoluter Seins-, Sinn- und Lebensfulle und der stets problematischen und fragilen Teilhabe von Menschen am "absoluten und leiduberwindenden Urleben" kann Leiden entstehen, durchlitten, verstanden, aber auch uberwunden werden. Hier erreicht der "Opfergedanke", in dem das unvermeidliche Leid frei angenommen und dadurch transformiert wird, seine reinste und hochste Ausformung. Erst nach Klarung dieser Verhaltnisse wird die "Theodizeefrage" als "das Problem der Probleme" angegangen und am Leitfaden der Hiob-Erzahlung diskutiert. Letztlich erweist sich, dass trotz allem Schmerz, Mangel, Unrecht und Unsinn ein "Potential des Unendlichen" im Leiden verborgen liegt, das auf seine Uberwindung durch Sein-, Sinn- und Werterfullung, durch Tat, Erkenntnis und Liebe verweist und dass diese drei "Machte" der Leidensherausforderung bedurfen, um ihre Weite, Tiefe und Hohe auszuloten. (shrink)

In a wide-ranging 2007 study of Claude Lévi-Strauss's aesthetic thought, Boris Wiseman demonstrates not only its centrality within his oeuvre but also the importance of Levi-Strauss for contemporary aesthetic enquiry. Reconstructing the internal logic of Lévi-Strauss's thinking on aesthetics, and showing how anthropological and aesthetic ideas intertwine at the most elemental levels in the elaboration of his system of thought, Wiseman demonstrates that Lévi-Strauss's aesthetic theory forms an integral part of his approach to Amerindian masks, body decoration and mythology. (...) He reveals the significance of Lévi-Strauss's anthropological analysis of an 'untamed' mode of thinking at work in totemism, classification and myth-making for his conception of art and aesthetic experience. In this way, structural anthropology is shown to lead to ethnoaesthetics. Lévi-Strauss, Anthropology and Aesthetics adopts a broad-ranging approach that combines the different perspectives of anthropology, philosophy, aesthetic theory and literary criticism into an unusual and imaginative whole. (shrink)

This paper analyzes the historical context and systematic importance of Kant's hypothetical use of reason. It does so by investigating the role of hypotheses in Kant's philosophy of science. We first situate Kant’s account of hypotheses in the context of eighteenth-century German philosophy of science, focusing on the works of Wolff, Meier, and Crusius. We contrast different conceptions of hypotheses of these authors and elucidate the different theories of probability informing them. We then adopt a more systematic perspective to discuss (...) Kant's idea that scientific hypotheses must articulate real possibilities. We argue that Kant's views on the intelligibility of scientific hypotheses constitute a valuable perspective on scientific understanding and the constraints it imposes on scientific rationality. (shrink)

Approximate coherentism suggests that imperfectly rational agents should hold approximately coherent credences. This norm is intended as a generalization of ordinary coherence. I argue that it may be unable to play this role by considering its application under learning experiences. While it is unclear how imperfect agents should revise their beliefs, I suggest a plausible route is through Bayesian updating. However, Bayesian updating can take an incoherent agent from relatively more coherent credences to relatively less coherent credences, depending on the (...) data observed. Thus, comparative rationality judgments among incoherent agents are unduly sensitive to luck. (shrink)

Evidential decision theory (EDT) says that the choiceworthiness of an option depends on its evidential connections to possible outcomes. Causal decision theory (CDT) holds that it depends on your beliefs about its causal connections. While Newcomb cases support CDT, Arif Ahmed has described examples that support EDT. A new account is needed to get all cases right. I argue that an option A's choiceworthiness is determined by the probability that a good outcome ensues at possible A‐worlds that match actuality in (...) the facts causally unaffected by your decision (the “unaffected facts”). Moreover, you should evaluate A on the assumption that A is compossible with the unaffected facts. This view entails that you should use EDT when evaluating A on the assumption that the unaffected facts determine your action, but use CDT when assessing A on the opposite assumption. A's choiceworthiness equals a weighted average of these conditional assessments. The weights are determined by your beliefs about whether the unaffected fact determine your action. This account gets both Newcomb and Ahmed cases right. According to an influential view, whether you take the unaffected facts to determine your action can make a difference to whether you can regard yourself as free and the action as being under your control. While my account is neutral on this issue, it entails that whether you take the unaffected facts to determine your action is important in a different way: it matters to whether you should follow EDT or CDT. (shrink)

We continue the exploration of various aspects of divisibility of ultrafilters, adding one more relation to the picture: multiplicative finite embeddability. We show that it lies between divisibility relations \ and \. The set of its minimal elements proves to be very rich, and the \-hierarchy is used to get a better intuition of this richness. We find the place of the set of \-maximal ultrafilters among some known families of ultrafilters. Finally, we introduce new notions of largeness of subsets (...) of \, and compare it to other such notions, important for infinite combinatorics and topological dynamics. (shrink)

Many ethical concerns surrounding human genetics studies remain unresolved. We report here the situation in Cameroon.Objectives: To describe the profile of human genetic studies that used Cameroonian DNA samples, with specific focus on i) the research centres that were involved, ii) authorship, iii) population studied, iv) research topics and v) ethics disclosure, with the aim of raising ethical issues that emerged from these studies.Method: Bibliometric Studies; we conducted a PubMed-based systematic review of all the studies on human genetics that used (...) Cameroonian DNA samples from 1989 to 2009.Results and Discussion: Fifty articles were identified, involving predominantly research centres from Europe (64%) and America (32%). Only 7 (14%) Cameroonian institutions and 14 (28%) Cameroonian authors were associated with these publications.At least 52% of publications were devoted to population genetics (variation/migration patterns) amongst 30 Cameroonian ethnic groups. Very few studies concerned public health related genetic issues and only 5 (10%) references were found for hemoglobinopathies like sickle cell anaemia. Almost all DNA samples are ‘banked’ outside of the African continent.Capacity building, rights to the genetic information and benefits to the individuals, communities and populations who contribute to these studies are addressed.Conclusions: 1) Our data suggests the need for a wider debate towards building capacity and addressing ethical issues related to human genomic research in sub-Saharan Africa and specifically in Cameroon; 2) National ethical guidelines and regulations concerning the collection, use and storage of human DNA are urgently needed in Cameroon. (shrink)

This paper explores the use of new scientific techniques to examine collections of historic scientific apparatus and other technological artefacts. One project under discussion uses interferometry to examine the history of lens development, while another uses X-ray fluorescence to discover the kinds of materials used to make early mathematical and astronomical instruments. These methods lead to surprising findings: instruments turn out to be fake, and lens makers turn out to have been adept at solving the riddle of aperture. Although exciting, (...) in some ways this is neither novel nor particularly unusual. After all, lab techniques have been used in art and archaeological collections for a very long time. In fact, scientific instruments themselves have been examined in this way since at least the 1950s. What, then, is special about the use of new instruments to examine old instruments? We argue that the answer has less to do with measuring historical innovation or establishing priority, and more to do with networks of craft know-how that, typically, have left no other historical traces than those embodied in surviving instruments themselves. We show, in particular, how collections of objects can be mobilised within wider histories of knowledge, placing instruments within a dynamic interplay of craft knowledge, expertise, labour, commerce, and material exchange, over the longue durée. Finally, we suggest that these kinds of lab analyses can be given an extra dimension through the use of computational modelling, and we introduce the “Tools of Knowledge” project, which is designed to bring together XRF with techniques from the digital humanities, in order to tell a new story about the development of scientific instruments from the 16th to the 20th century. (shrink)

In this article, logical concepts are defined using the internal syntactic and semantic structure of language. For a first-order language, it has been shown that its logical constants are connectives and a certain type of quantifiers for which the universal and existential quantifiers form a functionally complete set of quantifiers. Neither equality nor cardinal quantifiers belong to the logical constants of a first-order language.

We continue the research of the relation $\hspace {1mm}\widetilde {\mid }\hspace {1mm}$ on the set $\beta \mathbb {N}$ of ultrafilters on $\mathbb {N}$, defined as an extension of the divisibility relation. It is a quasiorder, so we see it as an order on the set of $=_{\sim }$ -equivalence classes, where $\mathcal {F}=_{\sim }\mathcal {G}$ means that $\mathcal {F}$ and $\mathcal {G}$ are mutually $\hspace {1mm}\widetilde {\mid }$ -divisible. Here we introduce a new tool: a relation of congruence modulo an (...) ultrafilter. We first recall the congruence of ultrafilters modulo an integer and show that $=_{\sim }$ -equivalent ultrafilters do not necessarily have the same residue modulo $m\in \mathbb {N}$. Then we generalize this relation to congruence modulo an ultrafilter in a natural way. After that, using iterated nonstandard extensions, we introduce a stronger relation, which has nicer properties with respect to addition and multiplication of ultrafilters. Finally, we introduce a strengthening of $\hspace {1mm}\widetilde {\mid }\hspace {1mm}$ and show that it also behaves well with respect to the congruence relation. (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)

During the last quarter of a century, a number of philosophers have become attracted to the idea that necessity can be analyzed in terms of a hyperintensional notion of essence. One challenge for proponents of this view is to give a plausible explanation of our modal knowledge. The goal of this paper is to develop a strategy for meeting this challenge. My approach rests on an account of modality that I developed in previous work, and which analyzes modal properties in (...) terms of the notion of a metaphysical law. I discuss what information about the metaphysical laws is required for modal knowledge. Moreover, I describe two ways in which we might be able to acquire this information. The first way employs inference to the best explanation. The metaphysical laws, including the essential truths, play a crucial role in causal and grounding explanations and we can gain knowledge of these laws by abductive inferences from facts of which we have perceptual or a priori knowledge. The second way of gaining information about the metaphysical laws rests on knowledge that is partly constitutive of competence with the concepts that are needed to express the relevant information. Finally, I consider how knowledge of the metaphysical laws can be used to establish modal claims, paying special attention to the much-discussed connection between conceiving and possibility. (shrink)