There are only five letters and two postcards which were written by Emmy Noether to P.S. Alexandroff that have been preserved. These will be edited in this paper. More than any other source, these letters and postcards give an insight into Emmy Noether's privacy, and her sympathy for the problems of her pen pal and colleagues. They illuminate her judgement of different colleagues, students, «mathematical grandchildren» and their papers. They also inform about relationships within the mathematicians' community and (...) the working atmosphere in Goettingen and the US after 1933. The author thanks Prof. Dr. Walter Purkert, Bonn, for the reference to the writings of Emmy Noether, and Prof. Dr. Albert Shiryaev, Moscow, for the kind publication permission. (shrink)

The mathematical framework of Relativistic Schrödinger Theory (RST) is generalized in order to include the self-interactions of the particles as an integral part of the theory (i.e. in a non-perturbative way). The extended theory admits a Lagrangean formulation where the Noether theorems confirm the existence of the conservation laws for charge and energy–momentum which were originally deduced directly from the dynamical equations. The generalized RST dynamics is applied to the case of some heavy helium-like ions, ranging from germanium (Z=32) (...) to bismuth (Z=83), in order to compute the interaction energy of the two electrons in their ground-state. The present inclusion of the electron self-energies into RST yields a better agreement of the theoretical predictions with the experimental data. (shrink)

Analysis of Emmy Noether's 1918 theorems provides an illuminating method for testing the consequences of coordinate generality, and for exploring what else must be added to this requirement in order to give general covariance its far-reaching physical significance. The discussion takes us through Noether's first and second theorems, and then a third related theorem due originally to F. Klein. Contact will also be made with the contributions of, principally, J.L. Anderson, A. Trautman, P.A.M. Dirac, R. Torretti and the (...) father of the whole business, A. Einstein. (shrink)

Gauge invariance of a manifestly covariant relativistic quantum theory with evolution according to an invariant time τ implies the existence of five gauge compensation fields, which we shall call pre-Maxwell fields. A Lagrangian which generates the equations of motion for the matter field (coinciding with the Schrödinger type quantum evolution equation) as well as equations, on a five-dimensional manifold, for the gauge fields, is written. It is shown that τ integration of the equations for the pre-Maxwell fields results in the (...) usual Maxwell equations with conserved current source. The analog of the O (3, 1) symmetry of the usual Maxwell theory is found to be O (3, 2) or O (4, 1), depending on the space-time Fourier spectrum of the field. We argue that the structure that is relevant to the description of radiation in interaction with matter evolving in a timelike sense is that of O (3, 2). The noncovariant form of the field equations is given; there are two fields of electric type and one (divergenceless) magnetic type field. The Noether currents are studied, and some remarks are made on second quantization. (shrink)

The project of this Précis de philosophie de la logique et des mathématiques (vol. 1 under the direction of F. Poggiolesi and P. Wagner, vol. 2 under the direction of A. Arana and M. Panza) aims to offer a rich, systematic and clear introduction to the main contemporary debates in the philosophy of mathematics and logic. The two volumes bring together the contributions of thirty researchers (twelve for the philosophy of logic and eighteen for the philosophy of mathematics), specialists in (...) the history or philosophy of logic or mathematics. Each volume consists of ten chapters; each chapter is about forty pages, is independent from the others and deals with a particular philosophical question about logic or mathematics. The objective is to offer to the French-speaking reader a reference book. On many of the issues addressed, this Précis offers the first clear and thorough synthesis that is available in French. -/- This book is intended for third year / master's students, but also for teachers of philosophy in secondary or higher education, for logicians and mathematicians willing to take a philosophical look at the fundamental concepts of their discipline, and for any reader interested in the basic issues discussed in the philosophy of logic and mathematics. Each chapter is self-contained, although some basic training in logic (or in mathematics, as the case may be) is required. The book should be looked at as a comprehensive framework for contemporary discussions in the philosophy of logic and mathematics, while also giving some guidance on the disciplinary content required by these discussions. -/- The first three chapters of the present volume (on the philosophy of mathematics) are devoted to the history of the philosophy of mathematics: from antiquity to the modern era, and from this period to the foundational crisis of the nineteenth century, to the twentieth century. Next, four chapters deal with the crucial questions for the philosophy of mathematics of the twentieth century: the opposition and/or comparison of set theory and category theory as foundational frameworks for mathematics; mathematical constructivism; the analysis of calculability; and Benaceraff's problem. The two following chapters are focused on the philosophy of mathematical practice, by treating the notion of ideals of proof, in particular explanation and purity, and the notion of informal proof and the use of visual artifacts in mathematical argumentation. Finally the last chapter deals with the applicability of mathematics, including the role of probability. -/- In Chapter 1, Sébastien Maronne and David Rabouin present the history of the philosophy of mathematics from antiquity to the modern era. The goal is to show that the philosophy of mathematics has a history as ancient as mathematics and philosophy itself, a history largely continuous with the latter, often by staying out of sync with respect to the former. In Chapter 2, Sébastien Gandon discusses the question of the foundations of mathematics from Kant to the end of the nineteenth century. By tying this question to Kant, he is able to show that the discussion of the foundations of mathematics that occupied a large part of these two centuries has much older roots. Accent is placed on the differences between the framework proposed by Kant for making sense of classical mathematics and the use made by Frege and then Russell of logical tools for giving a different reading of arithmetic and real analysis. The link between between these different conceptions and the evolution of mathematics itself is also underlined. -/- Chapter 3, written by Hourya Benis-Sinaceur and Mirna Džamonja, deals with the evolution of mathematics in the twentieth century, notably the structuralist turn of Dedekind, E. Noether, and Bourbaki, and certain more recent developments. They devote themselves, among other things, to explaining how these developments can be understood as responses to and extensions of questions posed during the foundational debate of the immediately preceding era. -/- In Chapter 4, Jean-Pierre Marquis and Jean-Jacques Szczeciniarz discuss the different foundational options coming from set theory and category theory. They discuss, among other things, Lawvere's program to replace ZF with an axiomatization of the category of sets, the latter judged better adapted to the needs of contemporary mathematics. Different reactions, as much philosophical as technical, raised by this program are also taken into account. -/- Constructive mathematics are the object of Chapter 5, in which Gerhard Heinzmann and Mark van Atten examine in a critical and comparative manner a variety of constructivisms, including intuitionism, constructive type theory, predicativism, and finitism. -/- In Chapter 6, Guido Gherardi and Maël Pegny present computability theory, stressing its philosophical consequences. They discuss the basic concepts of this theory, for the computability of both the natural numbers and the real numbers. They then tackle the theory of computational complexity. -/- In Chapter 7, Andrea Sereni and Fabrice Pataut present Benacerraf's problem, opposing every possible account of mathematical knowledge to the availability of a theory of truth founded on an abstract ontology of mathematical objects. They give an overview of the original problem and its reformulation by Hartry Field, and reconstruct the debate that this problem has raised, by meeting at once the major opposing positions today of the analytic affiliation of the philosophy of mathematics, as much those on the platonist side as on that of nominalism. -/- In Chapter 8, Valeria Giardino and Yacin Hamami treat certain crucial aspects of the philosophy of mathematical practice. They deal in particular with the notion of an informal proof and on the role of artifacts in mathematical reasoning. They consider how such proofs, making use of these means, can contribute to the understanding of theorems and mathematical theories, thanks also to the role of visualisation and the aid of computer tools. -/- Why do mathematics often give several proofs of the same theorem? This is the question that Andrew Arana raises in Chapter 9, introducing the notion of an epistemic ideal and discuss two such ideals, the explanatoriness and purity of proof. -/- Chapter 10 is devoted to the applicability of mathematics in the study of empirical phenomena. After summarizing the history of this question, going back to Plato and Aristotle and passing by Mill and Kant, Daniele Molinini and Marco Panza reconstruct the contemporary debate, in relation, among other things, to questions raised in the philosophy of science. -/- Two appendices complete the volume. In the first Frédéric Patras treats the French tradition in philosophy of mathematics of the 20th century. In the second, Maria Carla Galavotti discusses the notion of probability and its use in science. (shrink)

This collection considers algorithms at work, alongside black box control, platform society theory and the formation of subjectivities.

Résumé Depuis plusieurs années, habitants et militants de la vallée de Suse s’opposent à la construction d’une ligne à grande vitesse entre la France et l’Italie. La réaction des autorités est quasi-militaire mais le faible avancement des travaux ne justifie pas un tel emportement. La lutte expérimente pas à pas les nouveaux concepts de la construction du commun.

Marking the 50th anniversary of Pitirim A. Sorokin’s death, this Brief offers a critical analysis of the renowned sociologist’s theories while highlighting some of his more overlooked ones. Topics explored include cultural dynamics; the relationship between culture, society, and personality; social mobility; and the socio-cultural causality of time and space. In addition, this book updates these theories by discussing their relevance in current cultural contexts. The Brief aims to extend the work started by Sorokin on the promotion and application of (...) “integralism”, an approach that conceives the change of any sociocultural phenomena as the result of the combination of external and internal forces. It uses this method to analyse socio-cultural phenomena, propose new policy, and enhance the development of humanity from the point of view of culture. -/- This book also discusses sociology’s relationship with other sciences. In particular, it touches upon the interplay between sociology and psychology and pushes for a new scientific awareness that is transdisciplinary. The end point is a new vision of humanity and its development from a cultural context. -/- Social and Cultural Dynamics will be of interest to social scientists, sociologists, and psychologists as well as professionals in these disciplines. (shrink)

In this article we will study the pronominal system in Ortonese, which belongs to the central-southern Italo-Romance languages. The analysis we propose is contrastive: we will compare the data with the Italian to highlight their differences in terms of some morphosyntactic aspects. We will examine, the stressed and unstressed personal pronouns, emphasizing the placement of the combined pronouns with the compound tenses. Then, we will focus on the rest of the pronouns, such as demonstratives, possessives, quantifiers and indefinites, also pointing (...) out the uses of the clitics “ci” and “ne” and the presence of the pronoun “nome”, which does not exist in Italian. (shrink)

The condition of precariousness not only provides insights into a segment of the world of work or of a particular subject group, but is also a privileged standpoint for an overview of the condition of the social on a global scale. Because precariousness is multidimensional and polysemantic, it traverses contemporary society and multiple contexts, from industrial to class, gender, family relations as well as political participation, citizenship and migration. This book maps the differences and similarities in the ways precariousness and (...) insecurity in employment unfold and are subjectively experienced in regions and sectors that are confronted with different labour histories, legislations and economic priorities. Establishing a constructive dialogue amongst different global regions and across disciplines, the chapters explore the shift from precariousness to precariat and collective subjects as it is being articulated in the current global crisis. This edited collection aims to continue a process of mapping experiences by means of ethnographies, fieldwork, interviews, content analysis, where the precarious define their condition and explain how they try to withdraw from, cope with or embrace it. (shrink)

As humans interact in the world, they often orient one another's attention to objects through the use of spoken demonstrative expressions and head and/or hand movements to point to the objects. Although indicating behaviors have frequently been studied in lab settings, we know surprisingly little about how demonstratives and pointing are used to coordinate attention in large-scale space and in natural contexts. This study investigates how speakers of Quiahije Chatino, an indigenous language of Mexico, use demonstratives and pointing to give (...) directions to named places in large-scale space across multiple scales. The results show that the use and coordination of demonstratives and pointing change as the scale of search space for the target grows. At larger scales, demonstratives and pointing are more likely to occur together, and the two signals appear to manage different aspects of the search for the target: demonstratives orient attention primarily to the gesturing body, while pointing provides cues for narrowing the search space. These findings underscore the distinct contributions of speech and gesture to the linguistic composite, while illustrating the dynamic nature of their interplay.s in Spanish and Quiahije Chatino are provided as appendices.Se incluyen como apéndices resúmenes en español y en el chatino de San Juan Quiahije. SonGktyiCreCinH, ngyaqCskaEktyiCnoEndaHsonBnaFngaJnoIngyaqCloEktyiCreC, ngyaqCranFchaqExlyaKqoEchaqFjnyaJnoAndywiqArenqAKchinAKyqyaC. (shrink)

An overlap between the general relativist and particle physicist views of Einstein gravity is uncovered. Noether's 1918 paper developed Hilbert's and Klein's reflections on the conservation laws. Energy-momentum is just a term proportional to the field equations and a "curl" term with identically zero divergence. Noether proved a \emph{converse} "Hilbertian assertion": such "improper" conservation laws imply a generally covariant action. Later and independently, particle physicists derived the nonlinear Einstein equations assuming the absence of negative-energy degrees of freedom for (...) stability, along with universal coupling: all energy-momentum including gravity's serves as a source for gravity. Those assumptions imply that the energy-momentum is only a term proportional to the field equations and a symmetric curl, which implies the coalescence of the flat background geometry and the gravitational potential into an effective curved geometry. The flat metric, though useful in Rosenfeld's stress-energy definition, disappears from the field equations. Thus the particle physics derivation uses a reinvented Noetherian converse Hilbertian assertion in Rosenfeld-tinged form. The Rosenfeld stress-energy is identically the canonical stress-energy plus a Belinfante curl and terms proportional to the field equations, so the flat metric is only a convenient mathematical trick without ontological commitment. Neither generalized relativity of motion, nor the identity of gravity and inertia, nor substantive general covariance is assumed. The more compelling criterion of lacking ghosts yields substantive general covariance as an output. Hence the particle physics derivation, though logically impressive, is neither as novel nor as ontologically laden as it has seemed. (shrink)

It is argued that awareness of the distinction between dynamical and variational symmetries is crucial to understanding the significance of Noether's 1918 work. Specific attention is paid, by way of a number of striking examples, to Noether's first theorem, which establishes a correlation between dynamical symmetries and conservation principles.

This paper argues that Noether's axiomatic method in algebra cannot be assimilated to Weyl's late view on axiomatics, for his acquiescence to a phenomenological epistemology of correctness led Weyl to resist Noether's principle of detachment.

Attempts to find perennial elements in Aristotle’s cosmology are doomed to failure because his distinction of sub- and supra-lunary realms no longer holds. More fruitful approaches to the contemporary importance of Aristotelian cosmology must focus on parities of reasoning rather than content. This paper highlights the striking parallels between Aristotle’s use of symmetry arguments in cosmology and instances of Noether’s First Theorem in contemporary physics. Both observe simple motion, find symmetries in that motion, argue from those symmetries to notions (...) of conservation, and then conclude to cosmological structure. These parallels reveal an enduring relevance for Aristotelian cosmology that does not depend on positing an enduring content to his cosmological claims. (shrink)

A stochastic version of the Noether theorem is derived for systems under the action of external random forces. The concept of moment generating functional is employed to describe the symmetry of the stochastic forces. The theorem is applied to two kinds of random covariant forces. One of them generated in an electrodynamic way and the other is defined in the rest frame of the particle as a function of the proper time. For both of them, it is shown the (...) conservation of the mean value of a random drift momentum. The validity of the theorem makes clear that random systems can produce causal stochastic correlations between two faraway separated systems, that had interacted in the past. In addition possible connections of the discussion with the Ives Couder’s experimental results are remarked. (shrink)

The creation of algebraic topology required “all the energy and the temperament of Emmy Noether” according to topologists Paul Alexandroff and Heinz Hopf. Alexandroff stressed Noether's radical pro-Russian politics, which her colleagues found in “poor taste”; yet he found “a bright trait of character.” She joined the Independent Social Democrats in 1919. They were tiny in Göttingen until that year when their vote soared as they called for a dictatorship of the proletariat. The Minister of the Army and (...) many Göttingen students called them Bolshevist terrorists. Noether's colleague Richard Courant criticized USPD radicalism. Her colleague Hermann Weyl downplayed her radicalism and that view remains influential but the evidence favors Alexandroff. Weyl was ambivalent in parallel ways about her mathematics and her politics. He deeply admired her yet he found her abstractness and her politics excessive and even dangerous. (shrink)

The author is primarily concerned with the explanation of behavior in regard to (1) the mecanical model, (2) the effects of physical-organic processes on behavior, (3) the lack of understanding between philosophers and psychologists as to sufficient conditions for predicting a behavioral event, (4) conditions leading to expalantions of behavior that could predict behavior exclusive of any antecedent psychological behavior, and (5) variations of the mechanical-model introducing differing sorts of explanation. (staff).

Amazing as it may be, to this day few commentaries on the treatises of Plotinus' Enneads are written. The classic ninth treatise, for example, has hardly been studied. This treatise, however, is of vital importance, because it is in this work that for the first time in the Enneads, the One in its superform emerges and Plotinus dwells on the remarkable phenomenon of a 'mystical union' of the soul with the One. A thorough analysis of the argument and its development (...) next to philosophical and philo-logical support will be welcome to any reader of this in-triguing but difficult treatise. These aims are pursued in the main part of Meijer's work, the commentary. The first part of the book, preceding the commentary, examines the philosophical history of the concept of the One and its status in the first eight treatises. This new approach to the problem of the One leads to striking conclusions. It appears that while Plotinus was writing these first eight treatises, the concept of the One developed from that of a Supreme Entity of a Mesoplatonian character, viz. the upper part of the mind, to One of a Superone above mind. This casts an entirely new light on the position of the One in Plotinus and that of the ninth treatise itself. The third part not only examines the mystical union as pictured in the ninth treatise, but also provides a full scale discussion of Plotinus' descriptions of this union in his en-tire work. The degree of unification, viz. the question whether a part of the mystic self remains intact during the unification, is a matter of vigorous scholarly debate. Meijer shows that, in spite of some inconsistencies in his doctrine about the union, one must accept that Plotinus basically considered the union as a complete absorption of the soul into the Supreme Entity. (shrink)