The article examines the current state of the mathematical education of the students-philosophers that depends on language of the humanitarian mathematics, evidence of its statements and methodological problem of the cognition of the mathematical facts. One of important tasks of philosophy of mathematical education consists in motivation of the need for training mathematics of students-philosophers. The main criterion of the usefulness of mathematics for philosophers is revealed in the ways of justification of its truth and completeness of reasoning of mathematical (...) statements. This reflects the attractiveness of mathematical knowledge for philosophers that is characterized by the fact that the truth is revealed along with a proof in mathematics. One of the main so-called ‘acupuncture points‘ of mathematical education of philosophers, as the author believes, is the language of modern mathematics. In General, the linguistic aspect is very important in modern science. The second ‘acupuncture point‘ of mathematical education of philosophers is the level of evidence claims. Third, according to the author, is responsible for knowledge of mathematical truths, is involved in not only our existence, but also transcendental knowledge. In the context of philosophy of the future of modern civilization, mathematics is indispensable as a necessary element of scientific and philosophical picture of the world. To support the conclusions the author draws a broad philosophical and scientific context. (shrink)

Acupuncture, the traditional Chinese practice of needling to alleviate pain, offers a striking case where scientific accounts in two cultures, East and West, diverge sharply. Yet the Chinese comfortably embrace the apparent ontological incommensurability. Their pragmatic posture resonates with the New Experimentalism in the West--but with some provocative differences. The development of acupuncture in China (and not in the West) further suggests general research strategies in the context of discovery. My analysis also exemplifies how one might fruitfully pursue (...) a comparative philosophy of science that explores how other cultures investigate and validate their conclusions about the natural world. (shrink)

Acupuncture, the traditional Chinese practice of needling to alleviate pain, offers a striking case where scientific accounts in two cultures, East and West, diverge sharply. Yet the Chinese comfortably embrace the apparent ontological incommensurability. Their pragmatic posture resonates with the New Experimentalism in the West--but with some provocative differences. The development of acupuncture in China further suggests general research strategies in the context of discovery. My analysis also exemplifies how one might fruitfully pursue a comparative philosophy of science (...) that explores how other cultures investigate and validate their conclusions about the natural world. (shrink)

Using medical imaging techniques, such as fMRI, the stimulation of certain acupuncture points can be shown to correlate with activity in corresponding regions of the brain. Identical activity is also seen if the acupoint is stimulated with a pulse of ultrasound rather than a needle. This article reviews the advantages offered by ultrasonic acupuncture and the impact on the practice of acupuncture.

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

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)

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)

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)

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)

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.

We study extensions of Presburger arithmetic with a unary predicate R and we show that under certain conditions on R, R is sparse and the theory of $\langle\mathbb{N}, +, R\rangle$ is decidable. We axiomatize this theory and we show that in a reasonable language, it admits quantifier elimination. We obtain similar results for the structure $\langle\mathbb{Q},+, R\rangle$.

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.

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)

In Dellunde et al. 997–1015), we determined the complete theory Te of modules of separably closed fields of characteristic p and imperfection degree e, eω{∞}. Here, for 0≠eω, we describe the closed set of the Ziegler spectrum corresponding to Te. Further, we establish a correspondence between certain submodules and n-types and we investigate several notions of dimensions and their relationships with the Lascar rank. Finally, we show that Te has uniform p.p. elimination of imaginaries and deduce uniform weak elimination of (...) imaginaries. (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)

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)

We consider first-order theories of topological fields admitting a model-completion and their expansion to differential fields . We give a criterion under which the expansion still admits a model-completion which we axiomatize. It generalizes previous results due to M. Singer for ordered differential fields and of C. Michaux for valued differential fields. As a corollary, we show a transfer result for the NIP property. We also give a geometrical axiomatization of that model-completion. Then, for certain differential valued fields, we extend (...) the positive answer of Hilbert’s seventeenth problem and we prove an Ax–Kochen–Ershov theorem. Similarly, we consider first-order theories of topological fields admitting a model-companion and their expansion to differential fields, and under a similar criterion as before, we show that the expansion still admits a model-companion. This last result can be compared with those of M. Tressl: on one hand we are only dealing with a single derivation whereas he is dealing with several, on the other hand we are not restricting ourselves to definable expansions of the ring language, taking advantage of our topological context. We apply our results to fields endowed with several valuations. (shrink)

We consider valued fields with a distinguished isometry or contractive derivation as valued modules over the Ore ring of difference operators. Under certain assumptions on the residue field, we prove quantifier elimination first in the pure module language, then in that language augmented with a chain of additive subgroups, and finally in a two-sorted language with a valuation map. We apply quantifier elimination to prove that these structures do not have the independence property.

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)

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 (investors, government, community, press etc.). 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)

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 construct a fibered dimension function in some topological differential fields.

Cet article se donne pour objectif de réfléchir à ce que la crise mondiale du Covid-19 a révélé de nos manières d’habiter les lieux où nous vivons, et parmi celles-ci, la pratique de la danse. La démarche adoptée ici est celle d’un dialogue entre trois courants philosophiques spécifiques : la phénoménologie, le pragmatisme et l’écoféminisme, au sujet de leur conception de l’expérience somatique, à la fois vécue, complexe et ordinaire. Nous cherchons ici les lignes communes à ces trois mouvements philosophiques, (...) dans le but d’esquisser une compréhensions nouvelle du corps, et par extension, une nouvelle approche de la danse par temps de crise pandémique. (shrink)

Cet article se donne pour objectif de réfléchir à ce que la crise mondiale du Covid-19 a révélé de nos manières d’habiter les lieux où nous vivons, et parmi celles-ci, la pratique de la danse. La démarche adoptée ici est celle d’un dialogue entre trois courants philosophiques spécifiques : la phénoménologie, le pragmatisme et l’écoféminisme, au sujet de leur conception de l’expérience somatique, à la fois vécue, complexe et ordinaire. Nous cherchons ici les lignes communes à ces trois mouvements philosophiques, (...) dans le but d’esquisser une compréhensions nouvelle du corps, et par extension, une nouvelle approche de la danse par temps de crise pandémique. (shrink)

We consider separably closed fields of characteristic $p > 0$ and fixed imperfection degree as modules over a skew polynomial ring. We axiomatize the corresponding theory and we show that it is complete and that it admits quantifier elimination in the usual module language augmented with additive functions which are the analog of the $p$-component functions.

The following strong form of density of definable types is introduced for theoriesTadmitting a fibered dimension functiond: given a modelMofTand a definable setX⊆Mn, there is a definable typepinX, definable over a code forXand of the samed-dimension asX. Both o-minimal theories and the theory of closed ordered differential fields are shown to have this property. As an application, we derive a new proof of elimination of imaginaries for CODF.