Let G be a definably compact group in an o-minimal expansion of a real closed field. We prove that if dim(G\X) < dim G for some definable ${X \subseteq G}$ then X contains a torsion point of G. Along the way we develop a general theory for the so-called G-linear sets, and investigate definable sets which contain abstract subgroups of G.

In this article we consider some questions raised by F. Benoist, E. Bouscaren, and A. Pillay. We prove that infinitely $p$-divisible points on abelian varieties defined over function fields of transcendence degree one over a finite field are necessarily torsion points. We also prove that when the endomorphism ring of the abelian variety is $\mathbb{Z}$, then there are no infinitely $p$-divisible points of order a power of $p$.

In Anglophone educational research in the United States, the name Foucault has been more pointedly celebrated in some subfields such as curriculum studies relative to its more noticeable censorship in subfields such as history of education. This paper illustrates how such differential epistemological politics might be accounted for through reapproaching the challenges to historiography that Histoire de la Folie (Madness and Civilization) raised. Through the formalist lens of performative apophasis, and with attention to the dependencies of discourse that characterize narrative (...) prosthesis, this paper re‐engages the least referenced of Foucault's major histories in the educational field to bring into noticeability other ‘conditions of possibility’—ones that explicate how an apophatic turn might account for divergent reactions to less familiar philosophies of history and/or to ‘alternative’ approaches to documents through which history is now being narrated and critiqued in education and beyond. (shrink)

ABSTRACTThe torsion balance, an instrument that was first developed to demonstrate the high precision of physical science in the laboratory became a different sort of demonstration instrument in its brief vogue in the 1920s. This article considers intersecting stories of acquiring and testing the torsion balance as a field instrument in Canada, Britain and Australia. It examines the purchasing trip and fieldwork of A. H. Miller of the Dominion Observatory in 1928–1931, testing conducted by the British Geological Survey (...) in 1926–1930, and finally the Imperial Geophysical Experimental Survey of 1928–1930 in Australia. These different stories produce a kind of collective biography, illustrating well the variety of material and textual records that accrete around instruments, especially expensive ones. But the trials and travels of the torsion balance also point to large themes. By comparing the different ways an instrument becomes valuable, and to whom, these micro-histories reveal significant features of the developing identity of geophysics. They also show the interaction of different forms of scientific internationalism in the inter-war period. (shrink)

Using methods of geometric stability , we determine the structure of Abelian groups definable in ACFA, the model companion of fields with an automorphism. We also give general bounds on sets definable in ACFA. We show that these tools can be used to study torsion points on Abelian varieties; among other results, we deduce a fairly general case of a conjecture of Tate and Voloch on p-adic distances of torsion points from subvarieties.

We show that in an arbitrary o-minimal structure the following are equivalent: conjugates of a definable subgroup of a definably connected, definably compact definable group cover the group if the o-minimal Euler characteristic of the quotient is non zero; every infinite, definably connected, definably compact definable group has a non trivial torsion point.

Let M be an o-minimal expansion of an ordered field. Let φ be a formula in the language of ordered domains. In this note we establish some topological properties which are transferred from $\varphi^M$ to $\varphi^R$ and vice versa. Then, we apply these transfer results to give a new proof of a result of M. Edmundo-based on the work of A. Strzebonski-showing the existence of torsion points in any definably compact group defined in an o-minimal expansion of an ordered (...) field. (shrink)

The point of view expressed in the present research is directed towards the ideational “torsion” from rationalism to the “language-games” drawing up an analysis according to which one can notice the rationalist and post-rationalist aspects in the philosophy of communication, and the consequences of these perspectives, which could be of great interest as regards the philosophical concepts related to communication, to man or to the human community. As a matter of fact, “the torsion” is only apparent; it (...) cannot hold a dramatic change of the thinking range, from “rationalism” to “neo-positivism”, as regards the comment on Habermas’ theory of communication, as compared to Wittgenstein’s ideas about “the language-games” as central elements of human communication. Jürgen Habermas manifest a specific turn in his way of thinking, aiming at the contemporary modulation of the rationalist approach by means of inter-subjectivism orhumanism, and stressing the modulation of the logical approach, by means of “language-games” and “life-forms.”. (shrink)

The discipline of parallelization in the manifold of all possible measurement results is shown to be responsible for the existence of all quantum correlations, with the upper bound on their strength stemming from the maximum of possible torsion within all norm-composing parallelizable manifolds. A profound interplay is thus uncovered between the existence and strength of quantum correlations and the parallelizability of the spheres S^0, S^1, S^3, and S^7 necessitated by the four real division algebras. In particular, parallelization within a (...) unit 3-sphere is shown to be responsible for the existence of EPR and Hardy type correlations, whereas that within a unit 7-sphere is shown to be responsible for the existence of all GHZ type correlations. Moreover, parallelizability in general is shown to be equivalent to the completeness criterion of EPR, in addition to necessitating the locality condition of Bell. It is therefore shown to predetermine both the local outcomes as well as the quantum correlations among the remote outcomes, dictated by the infinite factorizability of points within the spheres S^3 and S^7. The twin illusions of quantum entanglement and non-locality are thus shown to stem from the topologically incomplete accountings of the measurement results. (shrink)

Not long ago, under the influence of Michel Foucault, one spoke of the conjunction of knowledge and power, but in this post-truth era power appears singularly uninterested in knowledge, even as the supporters of Donald Trump claim that he alone of all politicians speaks the truth. This essay proposes to examine the relations of power and knowledge under the present populist assault. This analysis begins in the work of Claude Lefort, who spoke of the separation of knowledge and power in (...) democracy’s symbolic regime, and is then counterposed to Ernesto Laclau’s understanding of ‘populist reason’ in order to explore the present torsion of this relation to the point where power can appear not just separated from, but opposed to knowledge. It will be argued that it is less a question of post-truth than of different forms of truth with different truth claims, borne by different imperatives, and tied to different forms of representation – truth claims that can, in relation to each other, be indifferent, complementary, or conflictual. With this in mind, the essay asks: what is the relation of the people to truth? Do those who claim to represent the people seek possession of a different kind of truth? What is the relation of populism to ideology? And what is populism’s relation to ‘post-modernism’? (shrink)

The obscured Thomas precessionof the special theory of relativity (STR) has been soared into prominence by exposing the mathematical structure, called a gyrogroup,to which it gives rise [A. A. Ungar, Amer. J. Phys.59,824 (1991)], and the role that it plays in the study of Lorentz groups [A. A. Ungar, Amer. J. Phys.60,815 (1992); A. A. Ungar, J. Math. Phys.35,1408 (1994); A. A. Ungar, J. Math. Phys.35,1881 (1994)]. Thomas gyrationresults from the abstraction of Thomas precession.As such, its study sheds light on (...) relativistic velocity spaces and their symmetries which are concealed in Thomas precession. In order to uncover new properties of relativistic gyrogroups, we employ in this article the group theoretic concepts of divisible groupsand two-torsion free groupsto construct midpointsin gyrogroups. Systems of successive midpoints then describe straight gyrolinesand suggest a new, natural distance function that involves a Thomas gyration. These, in turn, reveal a new, interesting geometry that underlies relativistic velocity spaces. In this resulting gyrogeometrythe straight gyrolines form geodesics under a distance function which turns out to be the Poincaré hyperbolic distance function relaxed by a Thomas gyration. These geodesics do obey the parallel axiom of Euclidean geometry. Ironically, (i) attempts to understand the parallel postulate of Euclidean geometry gave rise to hyperbolic geometry in which the parallel postulate disappears;(ii) hyperbolic geometry gave rise to Einstein's STR; (iii) Einstein's STR established the bizarre and counterintuitive relativistic effect called Thomas precession, the abstraction of which is called Thomas gyration; and (iv) Thomas gyration now repairs in this article the Poincaré distance function of hyperbolic geometry to the point where the parallel postulate reappears. (shrink)

The prediction of general relativity on the gravitational collapse of matter ending in a point is viewed as an absurdity of the kind to be expected in any consistent physical theory due to ultimate conflicts of the axioms of geometry with the properties of physical objects. The necessity to introduce a probability interpretation for the solution of partial differential equations in space time for quantum theory points to similar roots. It is pointed out that quantum theory in the very (...) small is not going to eliminate the problem, but macroscopic quantum effects in the large, modifying the properties of the horizon, may achieve it. Solutions such as wormholes allow as much empirical evidence as any science fiction. The present approach considers successive modifications of the field equations and equations of motion of gravitational theory by admixture of terms with higher derivatives. The rigorous application of a gauge principle combines Einstein's equations with the tensor analog of Maxwell's equations which are of third order for the metric. It is speculated that the natural presence of torsion in such a gauge theory is related to matter sources. (shrink)

The expression “ecological threat” refers to a dynamic of double intrusion: the intrusion of geological history in human history (the intrusion of Gaia) and the intrusion of human history in geological history (the Anthropocene). This double intrusion is founded on a series of major partitions (culture/nature; society/environment) that do not allow for the possibility of communication between the terms of these dichotomies unless it is in the form of reciprocal violation. In the article, the ontology of the flesh is used (...) in order to think the intrusion in a different way compared to the great partitions. Within a chiasmatic logic, the terms of each dichotomy are understood as inseparable moments of the same flesh which institutes a difference – inside/outside – through an infinite movement of folding and torsion. By thinking this common element, Merleau-Ponty’s ontology of the flesh enters in dialogue with Amerindian mythocosmologies of the “first Anthropocene.” In these mythocosmologies, a humanity-flesh – understood as a transformative, pre-individual, and metastable potential – gives birth, through differentiation, to the multiple points of view that populate the cosmos. This dialogue allows us to think about the socialization of Gaia and to trace the contours of a general ecology understood as a thought that operates between – or beyond – major partitions. (shrink)

The Flesh as the Folding of the OutsideDeleuze’s Reading of the last Merleau-PontyBy describing the flesh in terms of a “torsion” of “an Outside more distant than any exterior,” Deleuze in his 1986 book on Foucault sketches an ambivalent reading of Merleau-Ponty’s final philosophy. Insofar as it grants to the Outside an ontological primacy, Deleuze’s definition seems to indicate that the Flesh is not an originary agency, but rather a derived state of a primordial folding. If the flesh is (...) derived, then the inconstituability of the carnal fold, which Merleau-Ponty defends, would be radically challenged. But at the same time, the difficulty that Merleau-Ponty encounters in his final writings – that of giving an account of the specificity of my Flesh in relation to the Flesh of the world – would in this way perhaps be overcome. We shall show in fact that the absence of a specific ontological difference between the Flesh of the body and the Flesh of the world in The Visible and the Invisible – an absence that Deleuze points out when he invokes an “ideal coincidence” between the two kinds of flesh, could be avoided by recourse to the living Flesh conceived as stemming from a torsion of aprimordial Outside. To what extent is Deleuze, in his metaphysical reconstruction of Merleau-Ponty’s project, still faithful to this primordial Outside? To what extent does he twist this speculative reformulation in the direction of his own conception of life? These are the questions which my article would like to disentangle.La carne come piega del FuoriDeleuze lettore dell’ultimo Merleau-PontyDescrivendo, in un passo del suo libro su Foucault, la carne come torsione di un “Fuori più lontano di ogni mondo esterno”, Deleuze abbozza una lettura ambigua della filosofi a dell’ultimo Merleau-Ponty. In quanto concede al Fuori un primato ontologico, questa defi nizione deleuziana sembra costituire l’indice di una concezione secondo la quale la carne non sarebbe più un’istanza originaria, ma uno stato derivato da un piegarsi primordiale. Se così fosse, è l’incostituibilità della piega carnale, difesa da Merleau-Ponty, che verrebbe rimessa in questione. Al contempo, però, la difficoltà di rendere conto della specificità della mia carne rispetto alla carne del mondo verrebbe semplicemente aggirata. Come si tratterà di dimostrare, l’assenza di una differenza ontologica netta tra la carne del corpo e la carne del mondo ne Il visibile et l’invisibile, sottolineata da Deleuze nell’evocazione di una “coincidenza ideale” delle due carni,potrebbe venir risolta dal richiamo ad una carne ricavata dalla torsione di un Fuori primordiale. In che misura Deleuze, nella sua ricostruzione metafisica del progetto merleau-pontiano, si mantiene fedele ad esso? In che misura Deleuze inflette questa riformulazione speculativa in direzione della sua propria concezione della vita? Sono le questioni che il presente articolo si propone di affrontare. (shrink)

The Flesh as the Folding of the OutsideDeleuze’s Reading of the last Merleau-PontyBy describing the flesh in terms of a “torsion” of “an Outside more distant than any exterior,” Deleuze in his 1986 book on Foucault sketches an ambivalent reading of Merleau-Ponty’s final philosophy. Insofar as it grants to the Outside an ontological primacy, Deleuze’s definition seems to indicate that the Flesh is not an originary agency, but rather a derived state of a primordial folding. If the flesh is (...) derived, then the inconstituability of the carnal fold, which Merleau-Ponty defends, would be radically challenged. But at the same time, the difficulty that Merleau-Ponty encounters in his final writings – that of giving an account of the specificity of my Flesh in relation to the Flesh of the world – would in this way perhaps be overcome. We shall show in fact that the absence of a specific ontological difference between the Flesh of the body and the Flesh of the world in The Visible and the Invisible – an absence that Deleuze points out when he invokes an “ideal coincidence” between the two kinds of flesh, could be avoided by recourse to the living Flesh conceived as stemming from a torsion of aprimordial Outside. To what extent is Deleuze, in his metaphysical reconstruction of Merleau-Ponty’s project, still faithful to this primordial Outside? To what extent does he twist this speculative reformulation in the direction of his own conception of life? These are the questions which my article would like to disentangle.La carne come piega del FuoriDeleuze lettore dell’ultimo Merleau-PontyDescrivendo, in un passo del suo libro su Foucault, la carne come torsione di un “Fuori più lontano di ogni mondo esterno”, Deleuze abbozza una lettura ambigua della filosofi a dell’ultimo Merleau-Ponty. In quanto concede al Fuori un primato ontologico, questa defi nizione deleuziana sembra costituire l’indice di una concezione secondo la quale la carne non sarebbe più un’istanza originaria, ma uno stato derivato da un piegarsi primordiale. Se così fosse, è l’incostituibilità della piega carnale, difesa da Merleau-Ponty, che verrebbe rimessa in questione. Al contempo, però, la difficoltà di rendere conto della specificità della mia carne rispetto alla carne del mondo verrebbe semplicemente aggirata. Come si tratterà di dimostrare, l’assenza di una differenza ontologica netta tra la carne del corpo e la carne del mondo ne Il visibile et l’invisibile, sottolineata da Deleuze nell’evocazione di una “coincidenza ideale” delle due carni,potrebbe venir risolta dal richiamo ad una carne ricavata dalla torsione di un Fuori primordiale. In che misura Deleuze, nella sua ricostruzione metafisica del progetto merleau-pontiano, si mantiene fedele ad esso? In che misura Deleuze inflette questa riformulazione speculativa in direzione della sua propria concezione della vita? Sono le questioni che il presente articolo si propone di affrontare. (shrink)

The Flesh as the Folding of the OutsideDeleuze’s Reading of the last Merleau-PontyBy describing the flesh in terms of a “torsion” of “an Outside more distant than any exterior,” Deleuze in his 1986 book on Foucault sketches an ambivalent reading of Merleau-Ponty’s final philosophy. Insofar as it grants to the Outside an ontological primacy, Deleuze’s definition seems to indicate that the Flesh is not an originary agency, but rather a derived state of a primordial folding. If the flesh is (...) derived, then the inconstituability of the carnal fold, which Merleau-Ponty defends, would be radically challenged. But at the same time, the difficulty that Merleau-Ponty encounters in his final writings – that of giving an account of the specificity of my Flesh in relation to the Flesh of the world – would in this way perhaps be overcome. We shall show in fact that the absence of a specific ontological difference between the Flesh of the body and the Flesh of the world in The Visible and the Invisible – an absence that Deleuze points out when he invokes an “ideal coincidence” between the two kinds of flesh, could be avoided by recourse to the living Flesh conceived as stemming from a torsion of aprimordial Outside. To what extent is Deleuze, in his metaphysical reconstruction of Merleau-Ponty’s project, still faithful to this primordial Outside? To what extent does he twist this speculative reformulation in the direction of his own conception of life? These are the questions which my article would like to disentangle.La carne come piega del FuoriDeleuze lettore dell’ultimo Merleau-PontyDescrivendo, in un passo del suo libro su Foucault, la carne come torsione di un “Fuori più lontano di ogni mondo esterno”, Deleuze abbozza una lettura ambigua della filosofi a dell’ultimo Merleau-Ponty. In quanto concede al Fuori un primato ontologico, questa defi nizione deleuziana sembra costituire l’indice di una concezione secondo la quale la carne non sarebbe più un’istanza originaria, ma uno stato derivato da un piegarsi primordiale. Se così fosse, è l’incostituibilità della piega carnale, difesa da Merleau-Ponty, che verrebbe rimessa in questione. Al contempo, però, la difficoltà di rendere conto della specificità della mia carne rispetto alla carne del mondo verrebbe semplicemente aggirata. Come si tratterà di dimostrare, l’assenza di una differenza ontologica netta tra la carne del corpo e la carne del mondo ne Il visibile et l’invisibile, sottolineata da Deleuze nell’evocazione di una “coincidenza ideale” delle due carni,potrebbe venir risolta dal richiamo ad una carne ricavata dalla torsione di un Fuori primordiale. In che misura Deleuze, nella sua ricostruzione metafisica del progetto merleau-pontiano, si mantiene fedele ad esso? In che misura Deleuze inflette questa riformulazione speculativa in direzione della sua propria concezione della vita? Sono le questioni che il presente articolo si propone di affrontare. (shrink)

A connection viewed from the perspective of integration has the Bianchi identities as constraints. It is shown that the removal of these constraints admits a natural solution on manifolds endowed with a metric and teleparallelism. In the process, the equations of structure and the Bianchi identities take standard forms of field equations and conservation laws.The Levi-Civita (part of the) connection ends up as the potential for the gravity sector, where the source is geometric and tensorial and contains an explicit gravitational (...) contribution.Nonlinear field equations for the torsion result. In a “low-energy” approximation (linearity andlow energy-momentumtransfer), the postulate that only charge and velocities contribute to the source transforms these equations into the Maxwell system. Moreover, the affine geodesics become the equations of motion of special relativity with Lorentz force in the same approximation [J. G. Vargas,Found. Phys. 21, 379 (1991)]. The field equations for the torsion must then be viewed as applying to an electromagnetic/strong interaction.A classical unified theory thus arises where the underlying geometry confers their contrasting characters to Maxwell-Lorentz electrodynamics and to an Einstein's-like theory of gravity. The highly compact field equations must, however, be developed in phase-spacetime, since the connection is velocity-dependent, i.e., Finsler-like.Further opportunities for similarities with present-day physics are discussed: (a) teleparallelism allows for the formulation of the torsion sector of the theory as a flat space theory with concomitant point-dependent transformations; (b) spinors should replace Lorentz frames in their role as the subjects to which the connection refers; (c) the Dirac equation consistent with the frame bundle for a velocity-dependent metric with Lorentz signature generates a weak-like interaction in the torsion sector. (shrink)

Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. This geometry can be characterized by an orthonormal coframe ϑ α and a (metric compatible) Lorentz connection Γ α β . These two potentials yield the field strengths torsion T α and curvature R α β . Evans tried to infuse electromagnetic properties into this geometrical framework by putting the coframe ϑ α to be proportional to four extended (...) electromagnetic potentials $\mathcal{A}^{\alpha }$ ; these are assumed to encompass the conventional Maxwellian potential A in a suitable limit. The viable Einstein-Cartan (-Sciama-Kibble) theory of gravity was adopted by Evans to describe the gravitational sector of his theory. Including also the results of an accompanying paper by Obukhov and the author, we show that Evans’ ansatz for electromagnetism is untenable beyond repair both from a geometrical as well as from a physical point of view. As a consequence, his unified theory is obsolete. (shrink)

In an accompanying paper (I), it is shown that the basic equations of the theory of Lorentzian connections with teleparallelism (TP) acquire standard forms of physical field equations upon removal of the constraints represented by the Bianchi identities. A classical physical theory results that supersedes general relativity and Maxwell-Lorentz electrodynamics if the connection is viewed as Finslerian. The theory also encompasses a short-range, strong, classical interaction. It has, however, an open end, since the source side of the torsion field (...) equation is not geometric.In this paper, Kaehler's partial geometrization of the Dirac equation is taken as a starting point for the development of fully geometric Dirac equations via the correspondence principle given in I. For this purpose, Kaehler's calculus (where the spinors are differential forms) is generalized so that it also applies when the torsion is not zero. The point is then made that the forms can take values in tangent Clifford algebras rather than in tensor algebras. The basic “Eigenschaft” of the Kaehler calculus also is examined from the physical perspective of dimensional analysis.Geometric Dirac equations of great structural simplicity are finally inferred from the standard Dirac equation by using the aforementioned correspondence principle. The realm of application of the Dirac theory is thus enriched in principle, though only at an abstract level at this point: the standard spinors, which are scalar-valued forms in the Kaehler version of that theory, become Clifford-valued. In addition, the geometrization of the Dirac equation implies a geometrization of the Dirac current. When this current is replaced in the field equations for the torsion, the theory of Paper I becomes fully geometric. (shrink)

This corrigendum concerns [, § ] on ordered difference existentially closed valued fields where we overlooked the problem of immediate extensions.

Summary In this paper we examine the reaction of the Leiden low-temperature laboratory of Heike Kamerlingh Onnes to new ideas in quantum theory. Especially the contributions of Albert Einstein (1906) and Peter Debye (1912) to the theory of specific heat, and the concept of zero-point energy formulated by Max Planck in 1911, gave a boost to solid state research to test these theories. In the case of specific heat measurements, Kamerlingh Onnes's laboratory faced stiff competition from Walter Nernst's Institute (...) of Physical Chemistry in Berlin. In fact, Berlin got the better of it because Leiden lacked focus. After the liquefaction of helium in 1908, Kamerlingh Onnes transformed his laboratory into an international facility for low temperature research, and for this reason it was impossible to make headway with the specific heat measurements. In the case of zero-point energy, Leiden developed a magnetic research programme to test the concept. Initially the balance of evidence seemed to be tipping in favour of zero-point energy. After 1914, however, Leiden would desert the theory in fovour, of a concept from calssical physics. A curious move that illustrates Kamerlingh Onnes's discomfort with the new quantum theory. (shrink)

It is known today that Hegel's philosophy was at the center of the development of pragmatism. In particular, the relation of Dewey's philosophy to Hegel's has recently been studied with great attention1. Many studies have revealed that the German philosopher had a fundamental influence on the young John Dewey, particularly with regard to his theory of culture, for his logic, as well as for his psychology. These new readings propose a profoundly original view of Dewey and explain why he thought (...) of his philosophy as a "permanent Hegelian deposit".Our work aims to... (shrink)

Le présent article examine la façon dont John Dewey a entrepris de poser le problème de la valuation et de ses conséquences au sein de sa théorie de l’éducation. Plus spécifiquement, nous voudrions montrer que son effort pour repenser l’articulation des moyens et des fins du processus de valuation contribue à repenser l’enquête morale. Celle-ci, si elle fait alors l’objet d’une pédagogie qui met au centre l’expérience vécue du sujet, nous oblige à concevoir à nouveaux frais les valeurs que nous (...) accordons aux connaissances apprises. Notre analyse entend démontrer que : 1) de même que dans le domaine éthique, rien n’a de valeur en soi pour le sujet agissant. Mais que 2) la valuation de tout acte est déterminée en situation, alors, 3) dans le domaine de la pédagogie, aucune connaissance n’a de valeur en soi pour l’élève. 4) Ainsi la première tâche de l’enseignant.e est de former l’élève à des processus de valuation efficaces. Cela dans le but que celui-ci puisse à son tour, clairement, déterminer pour lui-même les connaissances qui auront de la valeur. Si notre hypothèse est juste alors cette tâche devient à la fois un point de départ important de la pédagogie pragmatiste et un impératif incontournable de l’éthique enseignante. -/- The present article examines how Dewey addressed the problem of value, as well as the consequences that this solution had for his educational theory. More specifically, I aim to show that Dewey’s effort to rethink means and ends within the process of valuation contributes to a recasting of moral inquiry. If moral inquiry becomes part of a pedagogy that focuses upon the lived experience of the subject, this compels us to rethink the value we attribute to acquired knowledge. My analysis will demonstrate 1) that even within the ethical domain, nothing has value in itself for the acting subject, but that 2) the value of all acts must be determined within specific situations, and therefore 3) within the domain of pedagogy, no knowledge has value in and of itself for the student. 4) Thus the first task of the teacher is to teach students how to evaluate questions of value, which will push them to determine for themselves what knowledge has value. If my hypothesis is correct, this task becomes simultaneously an important starting place for pragmatist pedagogy and a cornerstone of a new ethic of teaching. (shrink)

A totally ordered group G is essentially periodic if for every definable non-trivial convex subgroup H of G every definable subset of G is equal to a finite union of cosets of subgroups of G on some interval containing an end segment of H; it is coset-minimal if all definable subsets are equal to a finite union of cosets, intersected with intervals. We study definable sets and functions in such groups, and relate them to the quasi-o-minimal groups introduced in Belegradek (...) et al. . Main results: An essentially periodic group G is abelian; if G is discrete, then definable functions in one variable are ultimately piecewise linear. A group such that every model elementarily equivalent to it is coset-minimal is quasi-o-minimal , and its definable functions in one variable are piecewise linear. (shrink)

Given a simple non-trivial finite-dimensional Lie algebra L, fields $K_i$ and Chevalley groups $L(K_i)$ , we first prove that $\Pi_{\mathcal{U}} L(K_i)$ is isomorphic to $L(\Pi_{\mathcal{U}}K_i)$ . Then we consider the case of Chevalley groups of twisted type ${}^n\!L$ . We obtain a result analogous to the previous one. Given perfect fields $K_i$ having the property that any element is either a square or the opposite of a square and Chevalley groups ${}^n\!L(K_i)$ , then $\pu{}^n\!L(K_i)$ is isomorphic to ${}^n\!L(\pu K_i)$ . (...) We apply our results to prove the decidability of the set of sentences true in almost all finite groups of the form L(K) where K is a finite field and L a fixed untwisted Chevalley type. (shrink)

Given a model-complete theory of topological fields, we considered its generic differential expansions and under a certain hypothesis of largeness, we axiomatised the class of existentially closed ones. Here we show that a density result for definable types over definably closed subsets in such differential topological fields. Then we show two transfer results, one on the VC-density and the other one, on the combinatorial property NTP2.

We describe classes of existentially closed ordered difference fields and rings. We show an Ax-Kochen type result for a class of valued ordered difference fields.

With this proposal, we wish to revisit the Idea of the University in the perspective of the democratic project of the American philosopher and pragmatist John Dewey. Our hypothesis consists in the thesis that the deweyen project confronts the problem of the social distribution of knowledge, in the aim of giving us the means to transform the latter. In this way, if we consider that the university is part of this distribution through its student learning function, then our purpose is (...) to demonstrate that this learning is currently guided by an individual intelligence paradigm harms that the development of collective intelligence. For John Dewey, the latter is one of the central means of his democratic project which would reconcile the Idea of a University with real University institutions. Therefore, according to him, if universities want to contribute to the democratic project, we must adopt a new pedagogical orientation promoting individual and collective intelligence. (shrink)

"Philosophy for Children: a Way to Reconcile Disciplinary Teaching and School Life? Drawing mainly on John Dewey's writings, this contribution aims to extend the dualism of a traditional conception of education at the epistemological, pedagogical and organizational levels. This conception was already criticised by this author at the beginning of the 20th century and still remains widely present today among the school community. Through this approach, we demonstrate that the dualist approach is as many obstacles to be removed in the (...) process both to improve and rebuild a better education. The hypothesis defended here consists to demonstrate how philosophy for children, strengthened by its pragmatist heritage, can challenge these dualisms and thereby jeopardize the traditional conception of education. Keywords: John Dewey, philosophy of education, co-curriculum, school life, philosophy for children ". (shrink)

We show that if G is a group of finite Morley rank, then the verbal subgroup is of finite width, where w is a concise word. As a byproduct, we show that if G is any abelian-by-finite group, then Gn= is definable.

Le féminisme est un mouvement théorique et politique pluriel et en perpétuelle évolution. Aussi ce travail se situe dans les champs de la philosophie de l’éducation et plus particulièrement au sein des débats entre plusieurs courants philosophiques se réclamant du féminisme. Il cherche à évaluer l’intérêt de deux de ces approches philosophiques au regard de la construction d’une pédagogie féministe. Se trouve ainsi comparées l’approche de la théorie critique (proche du marxisme matérialiste et de l’école de Francfort) et l’approche pragmatiste (...) (issue des travaux de Jane Addams et John Dewey) par rapport au problème du “consciousness-raising” en pédagogie. Ce dernier présente en effet des difficultés à l’approche critique qui seront exposées dans la première partie de l’argumentation. L’hypothèse de notre travail est que le pragmatisme peut apporter des outils théoriques répondant à ses difficultés et venant ainsi compléter ceux de la théorie critique au profit de la pédagogie féministe. Ainsi la deuxième partie de notre argumentation se concentre sur l’intérêt épistémique de ces outils pédagogiques que propose le pragmatisme. Ces derniers sont rendus possibles par la valorisation épistémique de la perplexité et de l’empathie, et nous verrons en quoi ils permettent d’augmenter l’efficacité du “consciousness-raising” lors des pratiques pédagogiques quotidiennes. (shrink)

The reception of Dewey's work has suffered, in terms of his political philosophy, from a certain mistrust. First, in the field of education, Dewey's refusal to grant "ultimate" or "high" status to certain values, even those of the French Republic, has made him a mistrusted figure.1 Apart from the pedagogues of Education Nouvelle, which defied the then dominant "Cartesian tradition of the dualistic philosophy of reason" in France, Dewey was little studied before the 1960s. In 2013, Kambouchner perceived an opposition (...) between Dewey and Durkheim;2 however, the French reception of The Public and Its Problems in 1927 also suffered from suspicion and skepticism.3 To begin, there was suspicion with regard to this... (shrink)

This paper investigates how specific notions of gender and ethnicity are integrated into diversity discourses presented on 241 top European company websites. Large European companies increasingly disclose equality and diversity policies in statements on websites. Such statements may be used to promote an ethical image of the company in terms of how well it manages diversity and guards against discrimination. In this paper, we argue that diversity statement discourses are important as they play a key part in socially constructing how (...) diversity should be regarded in the company by minority and majority groups, as well as indicating corporate values to external stakeholders. Sometimes, the notions of gender or ethnic diversity are positioned as a liability in need of protection, whilst in others, as a source of competitive advantage. We find evidence of use of discursive tools such as problematisation, rationalisation, fixation, reframing and naturalisation of the notions of gender and ethnic diversity, reinforced by use of symbols, such as statistics, photographs, membership badges and awards. Few statements directly associate gender and ethnic diversity with enhanced corporate performance. We found that diversity statements sometimes appear to reinforce existing business stereotypes of women and people from ethnic minorities, and in a few discourses, create new ones, particularly evident in photographs illustrating the diversity web pages. (shrink)

We consider the reduct to the module language of certain theories of fields with a non surjective endomorphism. We show in some cases the existence of a model companion. We apply our results for axiomatizing the reduct to the theory of modules of non principal ultraproducts of separably closed fields of fixed but non zero imperfection degree.

Call a (strictly increasing) sequence (rn) of natural numbers regular if it satisfies the following condition: rn+1/rn→θ∈R>1∪{∞} and, if θ is algebraic, then (rn) satisfies a linear recurrence relation whose characteristic polynomial is the minimal polynomial of θ. Our main result states that (Z,+,0,R) is superstable whenever R is enumerated by a regular sequence. We give two proofs of this result. One relies on a result of E. Casanovas and M. Ziegler and the other on a quantifier elimination result. We (...) also show that (Z,+,0,<,R) is NIP whenever R is enumerated by a regular sequence that is ultimately periodic modulo m for all m>1. (shrink)

We revisit Kolchin's results on definability of differential Galois groups of strongly normal extensions, in the case where the field of constants is not necessarily algebraically closed. In certain classes of differential topological fields, which encompasses ordered or p‐valued differential fields, we find a partial Galois correspondence and we show one cannot expect more in general. In the class of ordered differential fields, using elimination of imaginaries in, we establish a relative Galois correspondence for relatively definable subgroups of the group (...) of differential order automorphisms. (shrink)