This book is intended as a historical and critical study on the origin of the equations of motion as established in Newton's Principia. The central question that it aims to answer is whether it is indeed correct to ascribe to Galileo the inertia principle and the law of falling bodies. In order to accomplish this task, the study begins by considering theories on the motion of bodies from classical antiquity, and especially those of Aristotle. The theories developed during the Middle (...) Ages and the Renaissance are then reviewed, with careful analysis of the contributions of, for example, the Merton and Parisian Schools and Galileo's immediate predecessors, Tartaglia and Benedetti. Finally, Galileo's work is examined in detail, starting from the early writings. Excerpts from individual works are presented, to allow the texts to speak for themselves, and then commented upon. The book provides historical evidence both for Galileo's dependence on his forerunners and for the major breakthroughs that he achieved. It will satisfy the curiosity of all who wish to know when and why certain laws have been credited to Galileo. (shrink)

Among others we will prove that the equational theory of ω dimensional representable polyadic equality algebras (RPEA ω 's) is not schema axiomatizable. This result is in interesting contrast with the Daigneault-Monk representation theorem, which states that the class of representable polyadic algebras is finite schema-axiomatizable (and hence the equational theory of this class is finite schema-axiomatizable, as well). We will also show that the complexity of the equational theory of RPEA ω is also extremely high in the recursion theoretic (...) sense. Finally, comparing the present negative results with the positive results of Ildiko Sain and Viktor Gyuris [12], the following methodological conclusions will be drawn: The negative properties of polyadic (equality) algebras can be removed by switching from what we call the "polyadic algebraic paradigm" to the "cylindric algebraic paradigm". (shrink)

It is well-known that, in Peano arithmetic, there exists a formula Theor (x) which numerates the set of theorems and that this formula satisfies Hilbert-Bernays derivability conditions. Recently R. Magari has suggested an algebraization of the properties of Theor, introducing the concept of diagonalizable algebra (see [7]): of course this algebraization can be applied to all these theories in which there exists a predicate with analogous properties. In this paper, by means of methods of universal algebra, we study the equational (...) class of diagonalizable algebras, proving, among other things, that the set of identities satisfied by Theor which are consequences of the known ones is decidable. (shrink)

For a finite von Neumann algebra factor M, the projections form a modular ortholattice L(M). We show that the equational theory of L(M) coincides with that of some resp. all L(ℂ n × n ) and is decidable. In contrast, the uniform word problem for the variety generated by all L(ℂ n × n ) is shown to be undecidable.

We show that the equational theory of representable lower semilattice-ordered residuated semigroups is finitely based. We survey related results.

The article is guided by two main research questions: First, do the Equator Principles (EPs), a voluntary CSR-initiative in the project finance sector, and the recently published working paper of the Thun Group of Banks adequately address the U.N. Guiding Principles on Business and Human Rights or do they fall behind the ‘Ruggie framework’? Second, is the demand for human rights due diligence sufficient to classify the EPs as a positive and leverage-based concept of CSR (à la Wettstein and Wood) (...) or is this requirement still a feature of a negative and impact-based concept of CSR? In case it is a negative and impact-based concept of CSR, the question comes up which further steps should be taken by financial institutions to fulfill their positive and leverage-based responsibilities. The article argues that positive and leverage-based responsibilities for multinational companies exist – due to the moral nature of human rights and due to the political authority of multinational companies – and that the current (Ruggie-like) requirements for human rights due diligence are not adequate for a positive and leverage-based concept of CSR. Further measures should be taken by multinational companies – and especially (Equator) banks which possess a high leverage-influence over their clients – to not only ensure the respect for human rights, but also the on-the-ground protection and realization of human rights. (shrink)

Among others we will prove that the equational theory of $\omega$ dimensional representable polyadic equality algebras is not schema axiomatizable. This result is in interesting contrast with the Daigneault-Monk representation theorem, which states that the class of representable polyadic algebras is finite schema-axiomatizable. We will also show that the complexity of the equational theory of RPEA$_\omega$ is also extremely high in the recursion theoretic sense. Finally, comparing the present negative results with the positive results of Ildiko Sain and Viktor Gyuris (...) [12], the following methodological conclusions will be drawn: The negative properties of polyadic algebras can be removed by switching from what we call the "polyadic algebraic paradigm" to the "cylindric algebraic paradigm". (shrink)

Among others we will see that the equational theory of ω dimensional representable polyadic equality algebras. We will also see that the complexity of the equational theory of RPEAω is also extremely high in the recursion theoretic sense. Finally, comparing the present negative results with the positive results of Ildiko Sain and Viktor Gyuris [10], the following methodological conclusions will be drawn: the negative properties of polyadic algebras can be removed by switching from what we call the `polyadic algebraic paradigm' (...) to the `cylindric algebraic paradigm'. (shrink)

This is an English translation of Waldenfels' German essay: Equality and inequality are basic elements of law, justice and politics. Equality integrates each of us into a common sphere by distributing rights, duties and chances among us. Equality turns into mere indifference as far as we get overintegrated into social orders. When differences are fading away experience loses its relief and individuals lose their face. Our critical reflections start from the inevitable paradox of making equal what is not equal. In (...) various ways they refer to Nietzsche’s concept of order, to Marx’s analysis of money, to Lévinas’s ethics of the Other, and to novelists like Dostoevsky and Musil. Our critique turns against two extremes, on the one hand against any sort of normalism fixed on functioning orders, on the other hand against any sort of anomalism dreaming of mere events and permanent ruptures. Responsive phenomenology shows how we are confronted with extraordinary events. Those deviate from the ordinary and transgress its borders, without leaving the normality of our everyday world behind. The process of equalizing moves between the ordinary and the extraordinary. What makes the difference and resists mere indifference are creative responses which are to be invented again and again. (shrink)

In its original form Dirac's equations have been expressed by use of the γ-matrices γμ, μ=0, 1, 2, 3. They are elements of the matrix algebra M 4 (ℂ). As emphasized by Hestenes several times, the γ-matrices are merely a (faithful) matrix representation of an orthonormal basis of the orthogonal spaceℝ 1,3, generating the real Clifford algebra Cl 1,3 . This orthonormal basis is also denoted by γμ, μ=0, 1, 2, 3. The use of the matrix algebra M 4 (ℂ) (...) to represent Cl 1,3 has some unsatisfactory aspects. The γ-matrices contain imaginary numbers as entries whereas Cl 1,3 is real. Moreover, as a matrix algebra Cl 1,3 is M 2 (ℍ) but only a part of M 4 (ℂ). For that reason we investigate in this paper several forms of Dirac's equations in terms of M 2 (ℍ) instead of M 4 (ℂ). In Section1 we survey Dirac's equations describing the interaction of matter with electromagnetic, electroweak, and strong fields. Section2 deals with electromagnetic/weak interactions employing M 2 (ℍ). Finally, in Section3 we deal with Dirac's equations for strong interactions between quarks. In contrast to su(2) ⊕ u(1), the Lie algebra su(3) is not isomorphic to any subalgebra of Cl 1,3 . Therefore we do not give a description of strong interactions by use of M 2 (ℍ). Instead of such an approach we describe these interactions using the space of quadruples of bivector fields in Cl 1,3 . The thus obtained description has remarkable formal resemblance to the original Dirac equations using wave functions with values in the linear spaceℂ 4. (shrink)

Here is an accurate and readable translation of a seminal article by Henri Poincaré that is a classic in the study of dynamical systems popularly called chaos theory. In an effort to understand the stability of orbits in the solar system, Poincaré applied a Hamiltonian formulation to the equations of planetary motion and studied these differential equations in the limited case of three bodies to arrive at properties of the equations' solutions, such as orbital resonances and horseshoe orbits. Poincaré wrote (...) for professional mathematicians and astronomers interested in celestial mechanics and differential equations. Contemporary historians of math or science and researchers in dynamical systems and planetary motion with an interest in the origin or history of their field will find his work fascinating. (shrink)

The notion of normal proof theory, and yet it has been somewhat neglected by the systems of equational logic. The intention here is then to show the normalization procedure for the equational logic of the Labelled Natural Deduction system . With this we believe we are making a step towards filling a gap in the literature on equational logic. Besides presenting a normalization procedure for the LND equational fragment, we employ a new method to prove the normalization theorems for equational (...) logic: proof transformation by rewriting, based on a algebraic calculus on the 'rewrite reasons'. (shrink)

The manuscripts and writings of the fifteenth-century astronomer and physician Lewis Caerleon (d. c. 1495) have been largely overlooked. To fill this gap, this article focuses on his writings and working methods through a case study of his canons and table for the equation of time. In the first part, an account of his life and writings is given on the basis of new evidence. The context in which his work on the equation of time was produced is (...) explored in detail by reviewing the three key periods of his scientific production. His heavy reliance on Simon Bredon’s Commentum super Almagesti is also analyzed. The article also provides editions of Lewis Caerleon’s canons for calculating his table for the equation of time and a critical edition of Simon Bredon’s Commentum super Almagesti, III, 22–24. In the second part of this article, we analyze the table for the equation of time derived by Lewis around 1485. In addition to the final table, there is a unique table with intermediate results that records every step of his derivation. By following and discussing the details of this derivation, we shed a new light on tabular practices in mathematical astronomy. Following Lewis in his historical mathematical procedure, we argue, offers a novel historiographical approach that allows us to identify different sources and practices used by historical actors. Therefore, beyond the exchange of parameters residing in modern mathematical analysis, this novel approach offers a promising refinement for the analysis of the transmission of knowledge across space, time, and culture. (shrink)

For $\Bbb {F}$ the field of real or complex numbers, let $CG(\Bbb {F})$ be the continuous geometry constructed by von Neumann as a limit of finite dimensional projective geometries over $\Bbb {F}$ . Our purpose here is to show the equational theory of $CG(\Bbb {F})$ is decidable.

We use the Tolman–Oppenheimer–Volkoff equations for a Chaplygin type fluid to study, analytically and numerically, the global behavior of static solutions of spherically symmetric objects. Two possible regimes are especially investigated. The first one is the phantom regime in which the pressure module exceeds the energy density. In this case the equator is absent and all the solutions have the geometry of a truncated spheroid with the same kind of singularity. The second case is the normal regime for which we (...) determine all the solutions, excluding the de Sitter one, corresponding to a tri-dimensional spheroidal geometry. Beyond the equator, three possible cases are considered; the first case has a closed spheroid characterized by a Schwarzschild-kind singularity with an infinite blue-shift at the south pole, the second case configuration has a regular spheroid and the third case has configuration of a truncated spheroid having a scalar curvature singularity to a finite value of the radial distance. We also compare all the geometric configurations with ones obtained in the special case of Chaplygin gas. (shrink)

We show the undecidability of the equational theories of some classes of BAOs with a non-associative, residuated binary extra-Boolean operator. These results solve problems in Jipsen [9], Pratt [21] and Roorda [22], [23]. This paper complements Andréka-Kurucz-Németi-Sain-Simon [3] where the emphasis is on BAOs with an associative binary operator.

ABSTRACTIn political science, there is a profound tension between those who argue that the prediction of human behavior is possible and those who disagree. On the one hand, experimental methods may be able to detect behavioral patterns. On the other hand, events, the evolution of institutions, and individual behavior itself may in many cases be too historically contingent to be reliably predicted. Methodological pluralism, and a greater degree of openness to mere historical understanding, would therefore seem to be called for.

This article focuses on the Russian chemist Dmitri Ivanovich Mendeleev's assessment of certain representations of various aspects of the periodic system that employed more mathematical methodology. The equations of interest were created by E. J. Mills, B. N. Chicherin, and J. H. Vincent. The English chemist Mills tried to find a firmer numerical basis for the periodicity of the elements. The Russian lawyer and political philosopher Chicherin was convinced of the existence of a mathematical law underlying the periodic system. The (...) English physicist Vincent explored the connection between atomic weights and the elements' order in listings based on atomic weights—a project which he associated with the periodic system of elements. Although, for Mendeleev, the equations of Mills, Chicherin, and Vincent promised a more precise expression of the law of periodicity, he continued to invoke his earlier standards. In particular, Mendeleev wanted the equations to respect the individuality of the elements, and called for completeness in conveying the complexities of chemical phenomena. Thus, the very qualities that he had valued while developing his periodic system in 1869–1871 also characterised his evaluation of the new means of representing aspects of that system. (shrink)

We comment on the proposition “that lower temperatures and especially greater seasonal variation in temperature call for individuals and societies to adopt … a greater degree of self-control” (Van Lange et al., sect. 3, para. 4) for which we cannot find empirical support in a large data set with data-driven analyses. After providing greater nuance in our theoretical review, we suggest that Van Lange et al. revisit their model with an eye toward the social determinants of self-control.

The paper presents a renewed Habermasian view on transnational multi-stakeholder initiatives and assesses the institutional characteristics of the Equator Principles Association from a deliberative democracy perspective. Habermas’ work has been widely adopted in the academic literature on the political responsibilities of corporations, and also in assessing the democratic qualities of MSIs. Commentators, however, have noted that Habermas’ approach relies very much on ‘nation-state democracy’ and may not be applicable to democracy in MSIs—in which nation-states are virtually absent. We argue that (...) Habermas’ detailed conceptualization of the institutionalization of deliberative democracy can be applied to transnational MSIs if these initiatives can be said to have their own ‘dèmoi’ that can be represented in associational decision-making. Therefore, we develop a definition of the dèmos of an MSI based on the notion of collective agency. Subsequently, we explain how Habermas’ approach to democracy can be applied to MSIs and show that it has more to offer than hitherto has been uncovered. Our illustrative analysis of the EPA confirms the criticisms regarding this MSI which have recently been articulated by researchers and practitioners, but also yields new findings and possible avenues for the further development of the EPA: That is, although our assessment suggests that the EPA in its current state is still far from being a democratic MSI, the possibility of a sensible analysis of its democratic character indicates that transnational MSIs can, in principle, help to fill governance gaps in a democratic way. (shrink)

Latin American religious political thought includes colonial Spanish and Portuguese ideologies that preceded independence but have survived into the post-independence era, authoritarian ideologies supportive of military governments in the twentieth century, and progressive liberation theologies. In this article, I present a distinct tradition: a version of classical liberal thought. This tradition is skeptical of big government, opposed to caste systems, supportive of a high degree of federalism, uneasy with militarism, and supportive of democratic institutions while affirming religious social norms. This (...) ideology was developed in northeastern Brazil in the early nineteenth century by a Carmelite activist named Frei Caneca (Brother Mug), who published a newspaper titled the Typhis Pernambucano (Tiphys of the State of Pernambuco). (shrink)

The paper presents a renewed Habermasian view on transnational multi-stakeholder initiatives (MSIs) and assesses the institutional characteristics of the Equator Principles Association (EPA) from a deliberative democracy perspective. Habermas’ work has been widely adopted in the academic literature on the political responsibilities of (multinational) corporations (i.e., political corporate social responsibility), and also in assessing the democratic qualities of MSIs. Commentators, however, have noted that Habermas’ approach relies very much on ‘nation-state democracy’ and may not be applicable to democracy in MSIs—in (...) which nation-states are virtually absent. We argue that Habermas’ detailed conceptualization of the institutionalization of deliberative democracy can be applied to transnational MSIs if these initiatives can be said to have their own ‘dèmoi’ that can be represented in associational decision-making. Therefore, we develop a definition of the dèmos of an MSI based on the notion of collective agency. Subsequently, we explain how Habermas’ approach to democracy can be applied to MSIs and show that it has more to offer than hitherto has been uncovered. Our illustrative analysis of the EPA confirms the criticisms regarding this MSI which have recently been articulated by researchers and practitioners, but also yields new findings and possible avenues for the further development of the EPA: That is, although our assessment suggests that the EPA in its current state is still far from being a democratic MSI, the possibility of a sensible analysis of its democratic character indicates that transnational MSIs can, in principle, help to fill governance gaps in a democratic way. (shrink)

The aim of this paper is to give a description of the free algebras in some varieties of Glivenko MTL-algebras having the Boolean retraction property. This description is given (generalizing the results of [9]) in terms of weak Boolean products over Cantor spaces. We prove that in some cases the stalks can be obtained in a constructive way from free kernel DL-algebras, which are the maximal radical of directly indecomposable Glivenko MTL-algebras satisfying the equation in the title. We include (...) examples to show how we can apply the results to describe free algebras in some well known varieties of involutive MTL-algebras and of pseudocomplemented MTL-algebras. (shrink)

The aim of this paper is to give a description of the free algebras in some varieties of Glivenko MTL-algebras having the Boolean retraction property. This description is given (generalizing the results of [9]) in terms of weak Boolean products over Cantor spaces. We prove that in some cases the stalks can be obtained in a constructive way from free kernel DL-algebras, which are the maximal radical of directly indecomposable Glivenko MTL-algebras satisfying the equation in the title. We include (...) examples to show how we can apply the results to describe free algebras in some well known varieties of involutive MTL-algebras and of pseudocomplemented MTL-algebras. (shrink)

Many have taken Sellars’s critique of empiricism in “Empiricism and the Philosophy of Mind” (EPM) to be aimed at his teacher C. I. Lewis. But if so, why do the famous arguments of its opening sections carry so little force against Lewis’s views? Understandably, some respond by denying that Lewis’s epistemology is among the positions targeted by Sellars. But this is incorrect. Indeed, Sellars had earlier offered more trenchant (if already familiar) critiques of Lewis’s epistemology. What is original about EPM (...) is that it criticizes empiricist positions like Lewis’s not because of their foundationalism, but because of their psychologism about meaning. Since psychologism turns out to be unacceptable by Lewis’s own lights, EPM has a compelling (if implicit) critique of Lewis to offer after all, one that strikes at the heart of his philosophical system. (shrink)

It is argued that time's arrow is present in all equations of motion. But it is absent in the point particle approximations commonly made. In particular, the Lorentz-Abraham-Dirac equation is time-reversal invariant only because it approximates the charged particle by a point. But since classical electrodynamics is valid only for finite size particles, the equations of motion for particles of finite size must be considered. Those equations are indeed found to lack time-reversal invariance, thus ensuring an arrow of time. (...) Similarly, more careful considerations of the equations of motion for gravitational interactions also show an arrow of time. The existence of arrows of time in quantum dynamics is also emphasized. (shrink)

This paper is devoted to the algebraization of theories in which, as in Peano arithmetic, there is a formula, Theor(x), numerating the set of theorems, and satisfying Hilbert-Bernays derivability conditions. In particular, we study the diagonalizable algebras, which are been introduced by R. Magari in [6], [7]. We prove that for every natural number n, the n-freely generated algebra $\germ{J}_{n}$ is not functionally free in the equational class of diagonalizable algebras; we also prove that the diagonalizable algebra of Peano arithmetic (...) is not an element of the equational class generated by $\{\germ{J}_{n}\}$. (shrink)

Astral microtubules are rapidly elongated during anaphase and telophase in sea urchin eggs. The number of microtubules extending to the cell surface was calculated with a computer. For the calculations, microtubules were assumed to radiate from the astral center uniformly over angles. Although microtubules from two asters freely overlapped around the equator, the number per the unit area, i.e. the surface density, was larger in the polar region than in the equatorial region. The ratio of the theoretically calculated numbers in (...) the two regions was close to the ratio obtained from the ultrastructural observations by Asnes and Schroeder in 1979. When counted in the longitudinal section including two astral centers, the microtubule number was a little larger in the equatorial region than in the polar region. However, the numbers do not represent the surface density because the two-dimensional section contains only a small portion of all the microtubules spreading in the three-dimensional space. The fluorescence image for tubulin, in most cases, provides the microtubule distribution in the longitudinal section. Therefore, from such an image, we cannot judge whether the surface density of astral microtubules is larger at the pole or at the equator. (shrink)

This is the first in a series of papers in which a method of harmonic analysis in terms of functions over the groupSU(2) is applied to the description of interaction between matter and the electromagnetic field. Carmeli'sSU(2) formulation of Maxwell's equations is extended to anSU(2) formulation of the equations for the electromagnetic vector potential. The four functions which describe the vector potential are expanded in a generalized Fourier series [SU(2) harmonic analysis] and the equations for the coefficients are derived. These (...) equations are not independent of each other, but in a given order they can be solved consecutively one at a time. (shrink)

A certain class of geometric objects is considered against the background of a classical gauge field associated with an arbitrary structural Lie group. It is assumed that the components of these objects depend on the gauge potentials and their first derivatives, and also on certain gauge-dependent parameters whose properties are suggested by the interaction of an isotopic spin particle with a classical Yang-Mills field. It is shown that the necessary and sufficient conditions for the invariance of the given objects under (...) a finite gauge transformation are embodied in a set of three relations involving the derivatives of their components. As a special case these so-called invariance identities indicate that there cannot exist a gauge-invariant Lagrangian that depends on the gauge potentials, the interaction parameters, and the4-velocity components of a test particle. However, the requirement that the equations of motion that result from such a Lagrangian be gauge-invariant, uniquely determines the structure of these equations. (shrink)

In 1877, the young Alfred Espinas defended a philosophical study, ‘doctorat ès lettres’, at the Sorbonne University, entitled Des Sociétés animales. This was to become one of the principal sources of French organicist sociology. The paradox, however, is that this work seems to be fundamentally a study of natural science. Espinas tried to justify his position theoretically through two types of reciprocally exclusive and uncomplementary arguments. The first one consists in showing that only certain kinds of animal groupings belong legitimately, (...) if not academically, to sociology. The second one has a greater audacious and uncontrollable dimension. It consists in asserting that all pluricellular organisms are true societies. In this article we first focus on the role played by cellular theory in such a ‘sociologization’ of biology, concerning the extension of sociology. Second, we examine the importance of such confusion within the fields of extension, in aiming to explain the conceptual transfers between social sciences and life sciences, in the second half of the 19th century. (shrink)

Sara Confalonieri presents an overview of Cardano's mathematical treatises and, in particular, discusses the writings that deal with cubic equations. The author gives an insight into the latest of Cardano's algebraic works, the De Regula Aliza (1570), which displays the attempts to overcome the difficulties entailed by the casus irreducibilis. Notably some of Cardano's strategies in this treatise are thoroughly analyzed. Far from offering an ultimate account of De Regula Aliza, by one of the most outstanding scholars of the 16th (...) century, the present work is a first step towards a better understanding. Contents Inter-Dependencies Between the Families of Cubic Equations in the Ars Magna Ars Magna, Chapters XI-XXIII and the Casus Irreducibilis Getting Acquainted with the De Regula Aliza The Method of the Splittings in Aliza, Chapter I Target Groups Academics, researcher and students in the fields of mathematics, the history of mathematics, and epistemology. The Author Sara Confalonieri graduated in Philosophy at the Università degli Studi di Milano, in Mathematics at the Université Paris 6, and in Epistemology at the Université Paris 7, where she also obtained the PhD degree in history of mathematics on cubic equations during the Renaissance. At present, she takes part in a project on history of the didactic of mathematics in the 18th century at the Bergische Universität in Wuppertal as a post-doctoral researcher. (shrink)

This conceptual article aims to shed light on the significance of human spiritual dimension in the process of human resource development. It suggests spiritual intelligence as the missing link in the process of human development that should be identified and considered as an important factor for developed and morally qualified human resources. Moreover, this article also uncovered the growing interest of spiritual intelligence and its implications for HRD. The interest in spiritual intelligence in the body of knowledge has been established (...) in depth which assures that SI embedded in the fabric of the fields of organizational behaviour and psychology. The article emphasizes the vital influence of SI on bottom line of the organization, whereby, human resources can meaningfully contribute towards organization with improved performance. The conventional strategy of organizations in flourishing their employees is more on enhancement of individual’s knowledge, skills, abilities and emotions control. However, despite this immense interest in human capital, organizations tend to fail to have holistic approach of human resource development which eventually affects their performance. Further, the article indicates that without considering spiritual development of employees, the logic and emotions could not be the only ample source for human beings to perform utmost standard performances. Therefore, based on this, we conclude that the emerging notion of human spiritual quotient and its multi-dimensions must be included in HRD initiatives in order to have holistic mechanism. (shrink)