Since Piaget (1936), the concept of development has concerned the forms of adaptation deployed by the subject within his environment. Inspired by this constructivist perspective, many approaches, such as professional didactics (Pastré, 2011), problematization (Fabre, 2009, 2011) and investigation approaches (Grangeat, 2011, 2013) have advanced the idea of training through situations. As part of the socio-constructivist expectations of the latest teaching programs, we analyze teacher activity during a “débriefing after observation” (Villeret, 2008) about Moon phases conducted in primary school (...) class='Hi'>classes (Munoz & Villeret, 2012). In this article we examine whether “débriefing after observation” is a situation that allows for the development of teachers and pupils. We show that this activity allows pupils to learn, “problematize”, conceptualize and develop epistemologically based knowledge. It also allows the teacher to develop his skills to «do problematize» the pupils. These results allow us to discuss further the notion of «potential development situation» (Mayen, 1999) to complement it with the notions of “reactive and effective development situations”. (shrink)

The concept of the "new working class" was advanced by French Left radical sociologists 15 years ago, at a time when the social consequences of the revolution in science and technology under the conditions of governmentally intertwined monopoly capitalism had not yet become sufficiently clear. Bourgeois ideology hastened to interpret the social changes within the world of hired labor as the "dissolving" of the working class, its loss of revolutionary consciousness, and its integration into industrial society. Against this background, the (...) concept of the "new working class" stood out primarily because of its bearings on revolution: it asserted that the carrier of revolutionary ideas in the world today is precisely the working class, but not this class as a whole, only the portion of it associated with advanced branches of the economy. The concept of the "new working class" differed from the programs of the "New Left," with their spontaneous, emotional protest, in that it possessed a comprehensive, theoretical argumentum, reflecting both the changes in the economic and technological conditions of contemporary capitalism and the evolution of the social psychology of class consciousness. (shrink)

The class approach to the problem of educating a comprehensively developed personality under the conditions of developed socialist society requires careful consideration of the full complexity of the social structure of contemporary socialist society and the resultant concrete connections and interrelations of classes, social strata, and groups. A class approach requires that social reality be evaluated from the standpoint of the objective tendencies it embodies and the progressive possibilities of historical development; it relies on real social strata capable of (...) and concerned with implementing these potentials. (shrink)

A class of metric theories of gravitation on Minkowski spacetime is considered, which is—provided that certain assumptions (staying close to the original ideas of Einstein) are made—the almost most general one that can be considered. In addition to the Minkowskian metric G a dynamical metric H (called the Einstein metric)is defined by means of a second-rank tensor field S (referred to as gravitational potential).The theory is defined by a Lagrangian ℒ, from which the field equations as well as, e.g., the (...) energy-momentum tensor field for the gravitational field follow. The case of weak fields is considered explicitly. The static, spherically and time-inversal symmetric field is calculated, and as a first step to investigate the theory's viability the parameters are fitted to the experimental data of the perihelion advance and the deflection of light at the Sun. Finally the question of gauge freedoms in the gravitational potential is briefly discussed. (shrink)

What is it to be a woman? What is it to be a man? We start by laying out desiderata for an analysis of 'woman' and 'man': descriptively, it should link these gender categories to sex biology without reducing them to sex biology, and politically, it should help us explain and combat traditional sexism while also allowing us to make sense of the activist view that gendering should be consensual. Using a Putnam-style 'Twin Earth' example, we argue that none of (...) the existing analyses in the feminist literature succeeds in meeting all of our desiderata. Finally, we propose a positive account that we believe can satisfy all the desiderata outlined. According to our theory, the genders 'woman' and 'man' are individuated not by their contemporary connections to sex biology, but by their historical continuity with classes that were originally closely connected to sex biology. (shrink)

The aim is to defend the starting?point of Marx's theory of class, which is located in a definition of the working class in the Communist Manifesto. It is a definition solely in terms of separation from productive resources and a need to sell one's labour power, and it is closely connected with Marx's thesis that the population in capitalism has a tendency to polarize. That thesis conflicts with the widely?held belief in the growth of a large middle class, unaccounted for (...) by Marx. Moreover, recent critics such as Elster, Roemer, and Cohen have argued that this definition fails even in its own terms. The definition is refurbished so as to withstand these objections. But is there any point in using it? Does it serve to pick out the exploited producers as Marx intended? It does, once due attention is given to the idea of the collective worker, which is central in the volume of Capital which Marx himself published. That idea makes plain that it is an irreducibly corporate entity which is productive and subject to exploitation. The structural conditions for membership of that entity remove Marx's view from any simple identification of working?class membership with manual or lowly labour. (shrink)

A new approach to tackle Einstein equations for an isotropic and homogeneous Friedmann–Robertson–Walker Universe in the presence of a quintessence scalar field is devised. It provides a way to get a simple exact solution to these equations. This solution determines the quintessence potential uniquely and it differs from solutions which have been used to study inflation previously. It relays on a unification of geometry and dark matter implemented through the definition of a functional relation between the scale factor of the (...) Universe and the quintessence field. For a positive curvature Universe, this solution produces perpetual accelerated expansion rate of the Universe, while the Hubble parameter increases abruptly, attains a maximum value and decreases thereafter. The behavior of this cosmological solution is discussed and its main features are displayed. The formalism is extended to include matter and radiation. (shrink)

The chapter deals with the contrast between defining aspects of religious rigidity, a socio-historically derived counter-narrative, and anti-consumerism in Rastafarian philosophy and culture on one hand and the universal message and commercial success of the music on the other. After discussing the status of the genre as part of Jamaican national culture, the inherent socio-political claim of Reggae and Rastafarian culture are put in context with the conflicting claims of superiority and non-partiality that can frequently be found in the music. (...) Along the lines of religious doctrines in Rastafarian culture and the attempted spiritual transcendence of racism the chapter closes with an exploration of the genre's signature tropes of social justice and anti-materialism, also considering the less strictly defined identity-constructions of recent artists linked to the Reggae Revival movement. "Martin A. M. Gansinger's study of Reggae and class employs Rastafarianism as a key ingredient of both concepts. Gansinger contends that Rastafarianism offers a "spirituality-based consciousness" that lends itself to an egalitarian-driven social consciousness. Reggae's strong social, political and culture capital as a philosophy of liberation owes much to Rastafarianism, which, for all its contradictions, embodied in categories such as the "righteous" and the "wicked", as well as its segregationalist and patriarchal past, offers a means through which the music advances a socially transformative spirituality that may play a part in the rediscovery of a truly social consciousness." (Ian Peddie, Introduction to The Bloomsbury Handbook of Popular Music and Social Class). (shrink)

In this paper the familiar construction of the category of coalgebras for a cartesian comonad is extended to the setting of “algebraic set theory”. In particular, it is shown that, under suitable assumptions, several kinds of categories of classes are stable under the formation of coalgebras for a cartesian comonad, internal presheaves and comma categories.

When a professor from Middle Europe teaches Computer Ethics in the Middle East using a textbook from the US, cultural differences become apparent. A main challenge lies in avoiding cultural imperialism during teaching. In order to meet this challenge, personal portfolios have been used for course work. The course design as well as portfolio tasks are presented and experiences are discussed. Based on our experiences we recommend applying this approach to equally overcome effects of group dynamics in similar courses as (...) well as to bridge the generational gap that normally exists between students and professors. (shrink)

Since the onset of the latest United States (U.S.) recession (beginning in December 2007), the U.S. economy has been posting high unemployment levels consistently exceeding 8 percent. Of specific interest, the U.S. Department of Labor, Bureau of Labor Statistics (BLS), reports on a specific subset of the U.S. unemployed: the long‐term unemployed, defined as those who are unemployed for 27 weeks and over. Since December 2009, the share of the long‐term unemployed of the total U.S. unemployed has exceeded 40 percent (...) (through April 2012), the highest level since 1948 when data was first collected. A phenomenon of this recession is an alleged public bias by American private sector employers against hiring the long‐term unemployed, or even simply those unemployed. While the authors support the removal of discrimination against the unemployed in job advertisements, they cannot support the larger notion of including those who are unemployed as a protected class of employees. Becoming or being unemployed is a state that one can change, and based on the lack of research on how widespread this discrimination is (beyond anecdotal stories or limited research surveys), they believe that extending protection under equal employment opportunity legislation would be overreaching and inappropriate at this time. (shrink)

Argues that a set is the mereological whole of the singleton sets of its members (following Lewis's Parts of Classes), and that the singleton set of X is the state of affairs of X's having some unit-making property.

GEORGE BOOLE died one hundred years ago. This essay from Cork is intended as commemorative of a great man, for too long forgotten in the College he served so well.

We study classes of graded structures satisfying the properties of amalgamation, joint embedding and hereditariness. Given appropriate conditions, we can build a graded analogue of the Fraïssé limit. Some examples such as the class of all finite weighted graphs or the class of all finite fuzzy orders (evaluated on a particular countable algebra) will be examined.

The article presents an analysis of metaphorical names for yoga postures as well as other verbal and verbo-gestural means of communication used by yoga teachers to describe these co...

We study properties of certain subclasses of the Dedekind finite sets in set theory without the axiom of choice with respect to the comparability of their elements and to the boundedness of such classes, and we answer related open problems from Herrlich’s “The Finite and the Infinite.” The main results are as follows: 1. It is relatively consistent with ZF that the class of all finite sets is not the only finiteness class such that any two of its elements (...) are comparable. 2. The principle “Small Violations of Choice” —introduced by A. Blass—implies that the class of all Dedekind finite sets is bounded above. 3. “The class of all Dedekind finite sets is bounded above” is true in every permutation model of ZFA in which the class of atoms is a set, and in every symmetric model of ZF. 4. There exists a model of ZFA set theory in which the class of all atoms is a proper class and in which the class of all infinite Dedekind finite sets is not bounded above. 5. There exists a model of ZF in which the class of all infinite Dedekind finite sets is not bounded above. (shrink)

ABSTRACTVirtue ethics, a topic of growing interest in media ethics and philosophy more broadly, poses challenges for classroom instruction because it is rooted in long-term development of character. This article explores approaches for incorporating virtue into media ethics instruction and assessing associated student learning, based on an analysis of how students in a journalism ethics class demonstrated their understanding and application of virtues through activities tailored to virtue ethics. The analysis, in addition to suggesting the value of assignments such as (...) an exemplar paper for learning and assessment, highlights several challenges instructors should consider in both teaching and evaluating virtue instruction. (shrink)

In the paper A. I. Malcev's problem on the characterization of axioms for classes with strong homomorphisms is being solved.

To bring clearly before the mind what is meant by class and to distinguish this notion from all the notions to which it is allied, is one of the most difficult and important problems of mathematical philosophy.”When Russell wrote this in 1903, he could illustrate the difficulty of the problem by his own confusing attempt at a solution. He was able to demonstrate the importance of classes for mathematical philosophy in his later work: the definition of cardinal number as (...) a class of classes similar to a given class served him as a cornerstone for the derivation of mathematics from logic. (shrink)

Let Q be an equivalence relation whose equivalence classes, denoted Q[x], may be proper classes. A function L defined on Field(Q) is a labelling for Q if and only if for all x,L(x) is a set and L is a labelling by subsets for Q if and only if BG denotes Bernays-Gödel class-set theory with neither the axiom of foundation, AF, nor the class axiom of choice, E. The following are relatively consistent with BG. (1) E is true (...) but there is an equivalence relation with no labelling.(2) E is true and every equivalence relation has a labelling, but there is an equivalence relation with no labelling by subsets. (shrink)

In this thesis, we study the least fixed point principle in a constructive setting. A constructive theory of functions and sets has been developed by Feferman. This theory deals both with sets and with functions over sets as independent notions. In the language of Feferman's theory, we are able to formulate the least fixed point principle for monotone inductive definitions as: every operation on classes to classes which satisfies the monotonicity condition has a least fixed point. This is (...) called the principle of monotone inductive definition. Furthermore, we may formulate this principle in a uniform way as: there is an operation which maps a monotone operation to its least fixed point. This is called the principle of uniform monotone inductive definition. Feferman raised the question of the strength of the principle of monotone inductive definition when adjoined to his theory . This question is our primary concern in this thesis. ;Our main results are the consistency of both the principle of monotone inductive definition and the principle of uniform monotone inductive definition adjoined to his theory, and the proof theoretical equivalence between the principle of monotone inductive definition with Feferman's system without the inductive generation axiom and the system of the Pi-one-one Comprehension Axiom. Determination of the proof-theoretical strength of the principle of monotone inductive definition adjoined to Feferman's theory still remains open. ;The consistency of both the principle of monotone inductive definition and the principle of uniform monotone inductive definition with Feferman's theory will be achieved by constructing their models in set theoretical sense. The proof theoretical equivalence between the principle of monotone inductive definition with Feferman's system without the inductive generation axiom and the system of the Pi-one-one Comprehension Axiom can be obtained by a careful examination of the model construction for the principle of monotone inductive definition with Feferman's system without the inductive generation axiom, which is parallel to the model construction for the principle of monotone inductive definition with his theory. (shrink)

In Classes: A Marxist Critique, Paul Kamolnick has produced what may prove to be the most fundamental critique of Erik Olin Wright's class structure analysis to date.

We examine how degrees of computably enumerable equivalence relations under computable reduction break down into isomorphism classes. Two ceers are isomorphic if there is a computable permutation of ω which reduces one to the other. As a method of focusing on nontrivial differences in isomorphism classes, we give special attention to weakly precomplete ceers. For any degree, we consider the number of isomorphism types contained in the degree and the number of isomorphism types of weakly precomplete ceers contained (...) in the degree. We show that the number of isomorphism types must be 1 or ω, and it is 1 if and only if the ceer is self-full and has no computable classes. On the other hand, we show that the number of isomorphism types of weakly precomplete ceers contained in the degree can be any member of $[0,\omega ]$. In fact, for any $n \in [0,\omega ]$, there is a degree d and weakly precomplete ceers ${E_1}, \ldots,{E_n}$ in d so that any ceer R in d is isomorphic to ${E_i} \oplus D$ for some $i \le n$ and D a ceer with domain either finite or ω comprised of finitely many computable classes. Thus, up to a trivial equivalence, the degree d splits into exactly n classes.We conclude by answering some lingering open questions from the literature: Gao and Gerdes [11] define the collection of essentially FC ceers to be those which are reducible to a ceer all of whose classes are finite. They show that the index set of essentially FC ceers is ${\rm{\Pi }}_3^0$-hard, though the definition is ${\rm{\Sigma }}_4^0$. We close the gap by showing that the index set is ${\rm{\Sigma }}_4^0$-complete. They also use index sets to show that there is a ceer all of whose classes are computable, but which is not essentially FC, and they ask for an explicit construction, which we provide.Andrews and Sorbi [4] examined strong minimal covers of downwards-closed sets of degrees of ceers. We show that if $\left$ is a uniform c.e. sequence of non universal ceers, then $\left\{ {{ \oplus _{i \le j}}{E_i}|j \in \omega } \right\}$ has infinitely many incomparable strong minimal covers, which we use to answer some open questions from [4].Lastly, we show that there exists an infinite antichain of weakly precomplete ceers. (shrink)

First-order logic is known to have a severely limited expressive power on finite structures. As a result, several different extensions have been investigated, including fragments of second-order logic, fixpoint logic, and the infinitary logic L∞ωω in which every formula has only a finite number of variables. In this paper, we study generalized quantifiers in the realm of finite structures and combine them with the infinitary logic L∞ωω to obtain the logics L∞ωω, where Q = {Qi: iε I} is a family (...) of generalized quantifiers on finite structures. Using the logics L∞ωω, we can express polynomial-time properties that are not definable in L∞ωω, such as “there is an even number of x” and “there exists at least n/2 x” , without going to second-order logic. We show that equivalence of finite structures relative to L∞ωω can be characterized in terms of certain pebble games that are a variant of the Ehrenfeucht—Fraïssé games. We combine this game-theoretic characterization with sophisticated combinatorial tools from Ramsey theory, such as van der Waerden's Theorem and Folkman's Theorem, in order to investigate the scope and limits of generalized quantifiers in finite model theory. We obtain sharp lower bounds for expressibility in the logics L∞ωω and discover an intrinsic difference between adding finitely many simple unary generalized quantifiers to L∞ωω adding infinitely many. In particular, we show that if Qis a finite sequence of simple unary generalized quantifiers, then the equicardinality, or Härtig, quantifier is not definable in L∞ωω. We also show that the query “does the equivalence relation E have an even number of equivalence classes” is not definable in the extension L∞ωω of L∞ωω by the Härtig quantifier I and any finite sequence Q of simple unary generalized quantifiers. (shrink)

In several semantics for branching-time logic, the evaluation rules involve a quantification over the set of all histories in a given tree-like structure T. These semantics are often generalized by replacing these quantifications by quantifications over a bundle in T, that is, over a set of histories fulfilling suitable closure properties. According to this generalization, the basic semantical structures are pairs 〈T, B〉 in which B is a bundle in T.The problem of the definability of the class of complete bundled (...) trees, in a given class G, concerns the existence of a set Γ of formulas such that, for every bundled tree 〈T, B〉 in G, Γ is true in 〈T, B〉 if and only if B is the set of all histories in T. In Ockhamist branching-time logic, sets Γ corresponding to particular classes G have been found. It will be proved that Γ does not exist if G is the class of all bundled trees. (shrink)

Abstract The Marxian vulgate, which long dominated the historiography of the French Revolution, and which was broadly accepted in the social sciences, is no longer sustainable. But newer attempts to frame the issue of class in entirely linguistic terms, producing the claim that France had no bourgeoisie because few people explicitly described themselves as ?bourgeois,? are not entirely convincing. The Revolution brought into being, and helped to sustain, a new social group: the ?state bourgeoisie,? which defined itself by its education (...) and by state service, and which was socially cohesive and exclusive. Thus, the Revolution can be seen as ?bourgeois? not in the sense of having been caused by a rising bourgeoisie, but in the sense that it caused one to rise. (shrink)

Cultural concerns about race, class and beauty often intersect with mass-mediated depictions of the female body. Drawing on Foucault's theories about disciplining the public body, this article examines the changing public perception of Anna Nicole Smith from an ideal beauty to a white trash stereotype. This analysis argues that Smith's very public weight gains, her outrageous behaviour and her legal battle for her late husband's fortune is presented in the media as an example of inappropriate conduct for a white beauty (...) ideal and thus is repositioned as white trash culture. Central to this repositioning is the constant tabloid depiction of Smith as an ‘out of control’ grotesque. This article argues that contrary to the optimistic understanding of female grotesques as effective agents of cultural criticism and social change, Smith represents the female grotesque as an agent of cultural control that instructs middle-class women on how to avoid committing classed, racial and gendered transgressions. The article concludes that the case of Anna Nicole Smith functions as a cautionary tale that reinforces cultural standards of normalization. (shrink)

This paper discusses comparison classes—sets that relativize the interpretation of gradable adjectives, often specified with for-clauses as in John is smart for a linguist. Such a discussion ultimately lends support to the thesis that scales, degrees, measure functions, and linear orders are grammatically derived from more basic relations between individuals. Three accounts of comparison classes are compared and evaluated. The first proposes that such classes serve as an argument to a function that determines a standard of comparison. (...) The second maintains that these classes restrict the domain of a measure function used to map entities to degrees. The third proposes that these classes limit the kind of individuals that participate in a binary relation; this relation is then used in the construction of a scale and a measure function. It is this third account that is most consistent with the empirical data. It can explain how comparison classes fix a standard of comparison, induce presuppositions concerning the comparative subjects, and induce incommensurability in comparative constructions. (shrink)

Critics of contemporary metaphysics argue that it attempts to do the hard work of science from the ease of the armchair. Physics, not metaphysics, tells us about the fundamental facts of the world, and empirical psychology is best placed to reveal the content of our concepts about the world. Exploring and understanding the world through metaphysical reflection is obsolete. In this paper, I will show why this critique of metaphysics fails, arguing that metaphysical methods used to make claims about the (...) world are similar to scientific methods used to make claims about the world, but that the subjects of metaphysics are not the subjects of science. Those who argue that metaphysics uses a problematic methodology to make claims about subjects better covered by natural science get the situation exactly the wrong way around: metaphysics has a distinctive subject matter, not a distinctive methodology. The questions metaphysicians address are different from those of scientists, but the methods employed to develop and select theories are similar. In the first section of the paper, I will describe the sort of subject matter that metaphysics tends to engage with. In the second section of the paper, I will show how metaphysical theories are classes of models and discuss the roles of experience, common sense and thought experiments in the construction and evaluation of such models. Finally, in the last section I will discuss the way these methodological points help us to understand the metaphysical project. Getting the right account of the metaphysical method allows us to better understand the relationship between science and metaphysics, to explain why doing metaphysics successfully involves having a range of different theories, to understand the role of thought experiments involving fictional worlds, and to situate metaphysical realism in a scientifically realist context. (shrink)

Henle, Mathias, and Woodin proved in [21] that, provided that${\omega }{\rightarrow }({\omega })^{{\omega }}$holds in a modelMof ZF, then forcing with$([{\omega }]^{{\omega }},{\subseteq }^*)$overMadds no new sets of ordinals, thus earning the name a “barren” extension. Moreover, under an additional assumption, they proved that this generic extension preserves all strong partition cardinals. This forcing thus produces a model$M[\mathcal {U}]$, where$\mathcal {U}$is a Ramsey ultrafilter, with many properties of the original modelM. This begged the question of how important the Ramseyness of$\mathcal (...) {U}$is for these results. In this paper, we show that several classes of$\sigma $-closed forcings which generate non-Ramsey ultrafilters have the same properties. Such ultrafilters include Milliken–Taylor ultrafilters, a class of rapid p-points of Laflamme,k-arrow p-points of Baumgartner and Taylor, and extensions to a class of ultrafilters constructed by Dobrinen, Mijares, and Trujillo. Furthermore, the class of Boolean algebras$\mathcal {P}({\omega }^{{\alpha }})/{\mathrm {Fin}}^{\otimes {\alpha }}$,$2\le {\alpha }<{\omega }_1$, forcing non-p-points also produce barren extensions. (shrink)

Most human societies exhibit a distinct class structure, with an elite, middle classes, and a bottom class, whereas animals form simple dominance hierarchies in which individuals with higher fighting ability do not appear to form coalitions to “oppress” weaker individuals. Here, we extend our model of primate coalitions and find that a division into a bottom class and an upper class is inevitable whenever fitness-enhancing resources, such as food or real estate, are exploitable or tradable and the members of (...) the bottom class cannot easily leave the group. The model predicts that the bottom class has a near flat, low payoff and always comprises at least half the society. The upper class may subdivide into one or more middle class(es), resulting in improved payoff for the topmost members (elite). The model predicts that the bottom class on its own is incapable of mounting effective counter-coalitions against the upper class, except when receiving support from dissatisfied members of the middle class(es). Such counter-coalitions can be prevented by keeping the payoff to the lowest-ranked members of the middle classes (through concessions) well above that of the bottom class. This simple model explains why classes are also absent in nomadic hunter-gatherers and predominate in (though are not limited to) societies that produce and store food. Its results also agree well with various other known features of societies with classes. (shrink)

The naive theory of properties states that for every condition there is a property instantiated by exactly the things which satisfy that condition. The naive theory of properties is inconsistent in classical logic, but there are many ways to obtain consistent naive theories of properties in nonclassical logics. The naive theory of classes adds to the naive theory of properties an extensionality rule or axiom, which states roughly that if two classes have exactly the same members, they are (...) identical. In this paper we examine the prospects for obtaining a satisfactory naive theory of classes. We start from a result by Ross Brady, which demonstrates the consistency of something resembling a naive theory of classes. We generalize Brady’s result somewhat and extend it to a recent system developed by Andrew Bacon. All of the theories we prove consistent contain an extensionality rule or axiom. But we argue that given the background logics, the relevant extensionality principles are too weak. For example, in some of these theories, there are universal classes which are not declared coextensive. We elucidate some very modest demands on extensionality, designed to rule out this kind of pathology. But we close by proving that even these modest demands cannot be jointly satisfied. In light of this new impossibility result, the prospects for a naive theory of classes are bleak. (shrink)