The Neutrosophic Precalculus and the Neutrosophic Calculus can be developed in many ways, depending on the types of indeterminacy one has and on the method used to deal with such indeterminacy. This article is innovative since the form of neutrosophic binomial factorial theorem was constructed in addition to its refrains. Two other important theorems were proven with their corollaries, and numerical examples as well. As a conjecture, we use ten (indeterminate) forms in neutrosophic calculus taking an important (...) role in limits. To serve article's aim, some important questions had been answered. (shrink)

In his note [5] Hausner states a simple combinatorial principle, namely: $$(H)\left\{ {\begin{array}{*{20}c} {if f is a function a non - empty finite set \sigma into itself, p a} \\ {prime, f^p = i_\sigma and \sigma _0 the set of fixed points of f, then } \\ {\left| \sigma \right| \equiv \left| {\sigma _0 } \right|(mod p).} \\\end{array}} \right.$$ .He then shows how this principle can be used to prove:Fermat's little theorem,Cauchy's theorem for finite groups,Lucas' theorem for (...) binomial numbers.Letε=(0,1, ...),ℱ 1−1 the family of all one-to-one functions from a subset ofε intoε andℳ 1−1 the family of all p.r. (i.e., partial recursive) one-to-one functions from a subset ofε intoε. A subsetα of ε is finite, ifα is not equivalent to a proper subset under a function inℱ 1−1. The setα is calledisolated, if it is not equivalent to a proper subset under a function inℳ 1−1. An isolated set can also be defined as a subset ofε which has no infinite r.e. (i.e., recursively enumerable) subset. While every finite set is isolated, there are $c = 2^{\aleph _0 }$ infinite sets which are isolated; these sets are calledimmune. It is the purpose of this paper to generalize (H) to a principle (H*) for isolated sets and to show how (H*) can be used to prove generalizations of Fermat's little theorem and Cauchy's theorem for finite groups. We have been unable to generalize Lucas' theorem in a similar manner. (shrink)

During the first half of the nineteenth century, mathematical analysis underwent a transition from a predominantly formula-centred practice to a more concept-centred one. Central to this development was the reorientation of analysis originating in Augustin-Louis Cauchy's (1789–1857) treatment of infinite series in his Cours d’analyse. In this work, Cauchy set out to rigorize analysis, thereby critically examining and reproving central analytical results. One of Cauchy's first and most ardent followers was the Norwegian Niels Henrik Abel (1802–1829) who vowed to shed (...) some light on the vast darkness in analysis.This paper investigates some important aspects of Abel's contribution to the reorientation in analysis. In particular, it stresses the role for critical revision in the process of rigorization. By critically examining past practice, the new practice sought to explain the relative success of the previous—now outdated—approach. This is illustrated by discussing a number of issues related to Abel's new proof of the binomial theorem (1826) including his reactions to the exception that he encountered to one of the central theorems of Cauchy's theory.Following this discussion, the formation of new concepts as the result of critical revisions is illustrated by analysing the early history of the concept of absolute convergence. Thereby, it is shown how a new concept was distilled, investigated, put to use and eventually superseded. (shrink)

In this research article, we presented the idea of intuitionistic fuzzy incidence graphs along with their certain properties. The number of operations including Cartesian product, composition, tensor product, and normal product in an IFIGs are also investigated. The method to compute the degree of IFIGs obtained by CP, composition, tensor product, and the normal product is discussed. Some important theorems to calculate the degree of the vertices of IFIGs acquired by CP, composition, tensor product, and normal product are elaborated. An (...) application of CP and composition of two IFIGs in the textile industry to find the best combinations of departments expressing the highest percentage of progress and the lowest percentage of nonprogress is provided. A comparative analysis of our study with the existing study is discussed. Our study will be beneficial to comprehend and understand the further characteristics of IFIGs in detail. Another advantage of our study is that it will be helpful to find the maximum percentage of progress and minimum percentage of nonprogress in different departments of universities, garment factories, and hospitals. (shrink)

Before examining de Moivre's contributions to the science of mathematics, this article reviews the source materials, consisting of the printed works and the correspondence of de Moivre, and constructs his biography from them. The analytical part examines de Moivre's contributions and achievements in the study of equations, series, and the calculus of probability. De Moivre contributed to the continuing development from Viète to Abel and Galois of the theory of solving equations by means of constructing particular equations, the roots of (...) which can be written in the form $$\sqrt[n]{{a + \sqrt b }} + \sqrt[n]{{a - \sqrt b }}$$. He also discovered the reciprocal equations. In the course of this work de Moivre discovered an expression equivalent to (cos α+i sin α) n =cos n α+i sin n α and, following Cotes, he succeeded in expressing the nth roots of unity in trigonometric form. In the theory of series, de Moivre developed a polynomial theorem encom-passing Newton's binomial theorem and, in particular, a theorem of recurrent series useful in the calculus of probability. The demands of the calculus of probability led de Moivre to an approximation for the binomial coefficients $$\left( {_m^n } \right)$$ for large values of n. The interaction between de Moivre and James Stirling, particularly in regard to the asymptotic series for log (n!), is treated at length. This work supplied the foundation for de Moivre's limit theorem for the binomial distribution. The calculus of probability, which occupied him from 1708 onward, became in time ever more the center of de Moivre's inquiries. Proceeding from contemporary collections of gambling exercises, de Moivre, by introducing an explicit measure of probability for the so-called Laplace experiments, found the beginnings of a theory of probability. De Moivre expanded the classic application of probability calculus to games of chance by addressing himself to the problem of annuities and by adopting Halley's work with its conception of “Probability of life”. De Moivre was the first to publish a mathematically formulated law for the decrements of life derived from mortality tables. (shrink)

Common probability theories only allow the deduction of probabilities by using previously known or presupposed probabilities. They do not, however, allow the derivation of probabilities from observed data alone. The question thus arises as to how probabilities in the empirical sciences, especially in medicine, may be arrived at. Carnap hoped to be able to answer this question byhis theory of inductive probabilities. In the first four sections of the present paper the above mentioned problem is discussed in general. After a (...) short presentation of Carnap''s theory it is then shown that this theory cannot claim validity for arbitrary random processes. It is suggested that the theory be only applied to binomial and multinomial experiments. By application of de Finetti''s theorem Carnap''s inductive probabilities are interpreted as consecutive probabilities of the Bayesian kind. Through the introduction of a new axiom the decision parameter can be determined even if no a priori knowledge is given. Finally, it is demonstrated that the fundamental problem of Wald''s decision theory, i.e., the determination of a plausible criterion where no a priori knowledge is available, can be solved for the cases of binomial and multinomial experiments. (shrink)

With each sentential logic C, identified with a structural consequence operation in a sentential language, the class Matr * (C) of factorial matrices which validate C is associated. The paper, which is a continuation of [2], concerns the connection between the purely syntactic property imposed on C, referred to as Maehara Interpolation Property (MIP), and three diagrammatic properties of the class Matr* (C): the Amalgamation Property (AP), the (deductive) Filter Extension Property (FEP) and Injections Transferable (IT). The main (...) class='Hi'>theorem of the paper (Theorem 2.2) is analogous to the Wroski's result for equational classes of algebras [13]. It reads that for a large class of logics the conjunction of (AP) and (FEP) is equivalent to (IT) and that the latter property is equivalent to (MIP). (shrink)

The process of ‘logical differentiation’ was introduced by Peirce in 1870. Directly analogous to mathematical differentiation, it uses logical terms instead of mathematical variables. Here, this mysterious process receives new interpretations which serve to clarify Peirce’s use of logical terms. I introduce the logical terms, the operation of multiplication, the logical analogy to the binomial theorem, infinitesimal relatives, the concepts of numerical coefficients and the number associated with each term. I also analyse the algebraic development of ‘logical differentiation’ (...) and consider in depth one application of the process. (shrink)

Let l be a commutative field; Bauval [1] showed that the theory of the ring l[X1,...,Xm] is the same as the weak second-order theory of the field l. Now, l[X1,...,Xm] is the ring of the monoid m, so it may be asked what properties of m we can deduce from the theory of l[;m], that is, if l[m] is elementarily equivalent to the ring of monoid k[G], with k, a field and G, a monoid, what do we know not only (...) about the first-order theory of G but also about more properties of G. We prove that in this case G is isomorphic to m.Bauval [1, Theorem V.2.1] proved that if a factorial ring A is elementarily equivalent to l[;X1,...,Xm], then A is isomorphic to F[X1,...,Xm], with F being the field of invertible elements of A.Our result is different from this property because, a priori, the field k is not the field of invertible elements . Furthermore, k[G]; is not always factorial or Neotherian: if G is isomorphic to the cartesian product ∏i<ω, then the number of irreducible elements that divide elements that divide X is infinite, and the ideal generated by the monomials X is not finitely generated.We recall that to be factorial of Neotherian are not elementary properties. (shrink)

_Factory of Strategy_ is the last of Antonio Negri's major political works to be translated into English. Rigorous and accessible, it is both a systematic inquiry into the development of Lenin's thought and an encapsulation of a critical shift in Negri's theoretical trajectory. Lenin is the only prominent politician of the modern era to seriously question the "withering away" and "extinction" of the state, and like Marx, he recognized the link between capitalism and modern sovereignty and the need to destroy (...) capitalism and reconfigure the state. Negri refrains from portraying Lenin as a ferocious dictator enforcing the proletariat's reappropriation of wealth, nor does he depict him as a mere military tool of a vanguard opposed to the Ancien Régime. Negri instead champions Leninism's ability to adapt to different working-class configurations in Russia, China, Latin America, and elsewhere. He argues that Lenin developed a new political figuration in and beyond modernity and an effective organization capable of absorbing different historical conditions. He ultimately urges readers to recognize the universal application of Leninism today and its potential to institutionally--not anarchically--dismantle centralized power. (shrink)

In her influential article published in 2016, Alexandra Walsham, Professor of Modern History at the University of Cambridge, coined the metaphor that ‘Archives are the factories and laboratories of the historian’. Traditionally viewed as neutral storehouses of official records passively awaiting historians’ scrutiny, conceptions of archives have expanded in recent decades. Archives are now understood as complex social and cultural entities that actively participate in shaping understandings of the past. This paper examines shifting perspectives on the nature and functions of (...) archives through a critical analysis of key debates. Specifically, this paper adopts a hermeneutic lens to critically engage Walsham’s metaphor and move beyond its potential limitations through situated analysis and interpretation. This paper explores how archives are actively implicated in knowledge construction through their contents, organisational frameworks, and interactions with historians. Recognising archives as fragmented, culturally contingent remnants that mediate engagement with the past, the paper calls for collaborative, reflective approaches between archivists and historians. The paper also acknowledges historians’ subjective interpretive roles while advocating consultation of archivists’ contextual expertise. Ultimately, it advances methodological discussions on writing history through a nuanced appreciation of archives as dynamic mediators within historical research, not transparent conduits neutrally supplying facts. (shrink)

Factory farming continues to grow around the world as a low-cost way of producing animal products for human consumption. However, many of the practices associated with intensive animal farming have been criticized by public health professionals and animal welfare advocates. The aim of this essay is to raise three independent moral concerns with factory farming, and to explain why the practices associated with factory farming flourish despite the cruelty inflicted on animals and the public health risks imposed on people. I (...) conclude that the costs of factory farming as it is currently practiced far outweigh the benefits, and offer a few suggestions for how to improve the situation for animals and people. (shrink)

With the economy deindustrialized and the working class decentralized, a call for alternative horizons for resistance: the university and the art world. What was once the factory is now the university. As deindustrialization spreads and the working class is decentralized, new means of social resistance and political activism need to be sought in what may be the last places where they are possible: the university and the art world. Gerald Raunig's new book analyzes the potential that cognitive and creative labor (...) has in these two arenas to resist the new regimes of domination imposed by cognitive capitalism. Drawing on Gilles Deleuze's concept of “modulation” as the market-driven imperative for the constant transformation and reinvention of subjectivity, in Factories of Knowledge, Industries of Creativity, Raunig charts alternative horizons for resistance. Looking at recent social struggles including the university strikes in Europe, the Spanish ¡Democracia real YA! organization, the Arab revolts, and the Occupy movement, Raunig argues for a reassessment of the importance of cultural and knowledge production. The central role of the university, he asserts, is not as a factory of knowledge but as a place of creative disobedience. (shrink)

Objective: The aim of this study was to examine the psychometric properties and factorial structure of the Schema Mode Inventory for Eating Disorders (SMI-ED) in a disordered eating population. Method: 573 participants with disordered eating patterns as measured by the Eating Disorder Examination Questionnaire (EDE-Q) completed the 190-item adapted version of the Schema Mode Inventory (SMI). The new SMI-ED was developed by clinicians/researchers specializing in the treatment of eating disorders, through combining items from the original SMI with a set (...) of additional questions specifically representative of the eating disorder population. Psychometric testing included Confirmatory Factor Analysis (CFA) and internal consistency (Cronbach’s α). Multivariate Analyses of Covariance (MANCOVA) was also run to test statistical differences between the EDE-Q subscales on the SMI-ED modes, while controlling for possible confounding variables. Results: Factorial analysis confirmed an acceptable sixteen-related-factors solution for the SMI-ED, thus providing preliminary evidence for the adequate validity of the new measure based on internal structure. Concurrent validity was also established through moderate to high correlations on the modes most relevant to eating disorders with EDE-Q subscales. This study represents the first step in creating a psychometrically sound instrument for measuring schema modes in eating disorders, and provides greater insight into the relevant schema modes within this population. Conclusion: This research represents an important preliminary step toward understanding and labeling the schema mode model for this clinical group. Findings from the psychometric evaluation of SMI-ED suggest that this is a useful tool which may further assist in the measurement and conceptualization of schema modes in this population. (shrink)

The most compelling arguments for ethical veganism hinge on premise-pairs linking the serious wrongness of factory farming to that of buying its products: one premise claiming that buying those products stands in a certain relation to factory farming itself, and one claiming that entering into that relation with a seriously wrong practice is itself wrong. I argue that all such “linkage arguments” on offer fail, granting the serious wrongness of factory farming. Each relevant relation is such that if it holds (...) between factory farming and buying its products, then it holds between some seriously wrong practice and economic transactions of an absurd number and breadth. Hence, all these premise-pairs would, if true, generate unacceptable moral overreach; each premise-pair contains at least one unacceptable member, and the linkage arguments for ethical veganism fail. (shrink)

There is a theorem that shows that it is impossible for an algorithm to jointly satisfy the statistical fairness criteria of Calibration and Equalised Odds non-trivially. But what about the recently advocated alternative to Calibration, Base Rate Tracking? Here, we show that Base Rate Tracking is strictly weaker than Calibration, and then take up the question of whether it is possible to jointly satisfy Base Rate Tracking and Equalised Odds in non-trivial scenarios. We show that it is not, thereby (...) establishing an even more general impossibility theorem. (shrink)

Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems. (...) The level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists. (shrink)

In this paper, we present two proofs of the reciprocal butterfly theorem. The statement of the butterfly theorem is: Let us consider a chord PQ of midpoint M in the circle Ω(O). Through M, two other chords AB and CD are drawn, such that A and C are on the same side of PQ. We denote by X and U the intersection of AD respectively CB with PQ. Consequently, XM = YM. For the proof of this theorem, (...) see [1]. The reciprocal of the butterfly theorem has the following statement: In the circle Ω(O), let us consider the chords PQ, AB and CD which are concurrent in the point M≠O, such as the points A and C are on the same side of the line PQ. Let X and Y respectively be the intersections of the chord PQ with AD and BC respectively. If XM = YM, then M is the middle of the chord PQ. (shrink)

The ArgumentThis paper argues that science and technology studies need to adopt a much wider view of what counts as a laboratory. The factory, it is suggested, is as much a site of invention and intervention as the laboratory. As a site for the government of economic life, the factory is a laboratorypar excellence. One particular factory is studied — the Decatur, Illinois, plant of Caterpillar Inc. — as it is rethought and remade in accordance with ideals of cellular manufacturing, (...) Just-In-Time systems, customer-driven manufacturing, and competitor benchmarking. But it is not just the changes at the factory itself that are studied. The paper analyzes the linkages and relays between the redesign of a particular manufacturing plant and the plethora of calls for a revitalization of North American manufacturing industry and a new form of economic citizenship. The paper examines the remaking of a factory as anassemblage, a historically specific and temporarily stabilized complex of relations among ways of problematizing the factory in a multiplicity of locales. There are four steps to the changes analyzed here: a problematizing of the factory at the level of North American manufacturing as a whole in the 1980s; a problematizing of the notion of competitiveness at Caterpillar Inc, through the calculative practices of competitor benchmarking and related expertises; a diagraming of the ideal factory in systems terms; and the embedding of notions of the product, of competitiveness, and of a new economic citizenship in the “Assembly Highway” at the Decatur plant. Rethinking the factory took place within this assemblage of relations, rether than at any one site. (shrink)

Prior research has shown that various types of conventional multiword chunks are processed faster than matched novel strings, but it is unclear whether this processing advantage extends to variant multiword chunks that are less formulaic. To determine whether the processing advantage of multiword chunks accommodates variations in the canonical phrasal template, we examined the robustness of the processing advantage (i.e., predictability) of binomial phrases with non‐canonical conjunctions (e.g.,salt and also pepper; salt as well as pepper). Results from the cloze (...) study (Experiment 1) showed that there was a high tendency of producing the canonical conjunct (pepper), even in the binomials that contained non‐formulaic conjunctions. Consistent with these findings, results from two eye tracking studies (Experiments 2a and 2b) showed that canonical conjuncts were read faster than novel conjuncts that were matched on word length (e.g.,paprika), even in the binomials with variant conjunctions. This robust online processing advantage was replicated in a self‐paced reading study that compared all three conjunction types (Experiment 3). Taken together, these findings show that binomials with variant function words also receive facilitated processing relative to matched novel strings, even though both types of strings are neither conventional nor relatively frequent. Exploratory analyses revealed that this processing speed advantage was driven by the lexical–semantic association between the canonical conjuncts (salt–pepper), rather than lexical and phrasal frequency. Overall, these results highlight flexibility in the processing of multiword chunks that current models of multiword storage and processing must take into account. (shrink)

The process of assessing executive functions through behavioral observation scales is still under theoretical and empirical construction. This article reports on the analysis of the factorial structure of the EOCL-1 scale that assesses executive functions, as proposed by the theory developed by Luria, which has not been previously considered in this type of evaluation. In this scale, the executive functions taken into account are error correction, internal behavioral and cognition regulatory language, limbic system conscious regulation, decision making, future consideration (...) of consequences of actions, goal-directed behavior, inhibitory control of automatic responses, creation of new behavioral repertoires, and cognitive–behavioral activity verification. A variety of validity and reliability analyses were carried out, with the following results: an adequate internal consistency level of executive functions between α = 0.70 and α = 0.83, significant convergent validity with a scale that assesses frontal deficits between r = −0.07 and r = 0.28, and the scale’s construct validity that proposes a model with an executive central factor comparative fit index = 0.93, root mean square error of approximation = 0.04, standardized root mean square residual = 0.04, and x2 = 789.29, p = 0.001. The findings are discussed based on previous literature reports and in terms of the benefits of using a scale to assess the proposed executive functions. (shrink)

A system for the modal logic K furnishes a simple mechanical process for proving theorems.

With increasing attention on the role of parenting stress on family functioning and children’s development, one area that has been neglected is how such relations differ across cultures. Although sometimes viewed as homogeneous, Asian countries often have markedly different belief systems. Cross-cultural studies require instruments that have been validated in different socio-cultural contexts. The widely used parenting stress index-short form has been used in several locations. However, results regarding its factorial structure have been mixed. Furthermore, there are only a (...) few cross-cultural comparison studies. This study examined the factorial structure of an abridged version of the PSI-SF with data from Hong Kong and Thailand. The results from confirmatory factor analyses indicated that, in both cultures, a three-factorial structure provides the best model fit. Furthermore, we found evidence for partial metric invariance, suggesting that the test scores can be compared directly. Tests for convergent and discriminant validity revealed that the three factors were correlated with parent general distress, authoritative, authoritarian, and permissive parenting behaviors, in both cultures. These findings suggest that the abridged PSI-SF can provide a meaningful comparison of parenting stress between Hong Kong and Thailand. (shrink)

This paper examines the phenomenon of ‘baby factories’ as an abusive pattern of surrogacy and child adoption practices in Nigeria. Relying on a mixed qualitative approach that draws on extant literature and field-based personal insights, the paper posits that the economic, socio-cultural and psycho-emotional value of bearing and having a child, as well as the tacit disapproval of adoptive parenting by some cultures in Nigeria, have driven childless couples and adults into seeking child adoption through illicit and unconventional paths, such (...) as ‘baby factories’. The paper contends that the commercialization and non-regulation of surrogacy in Nigeria has created pretexts for the proliferation of ‘baby factories’, where babies are bought and sold, with pregnant girls and infants objectified as ‘stocks-in-trade’. To mitigate the phenomenon, it is expedient to regulate the bourgeoning illicit baby market in the country through proper legislation that is capable of moderating the excesses of surrogate and adoptive practices. (shrink)

Representation theorems are often taken to provide the foundations for decision theory. First, they are taken to characterize degrees of belief and utilities. Second, they are taken to justify two fundamental rules of rationality: that we should have probabilistic degrees of belief and that we should act as expected utility maximizers. We argue that representation theorems cannot serve either of these foundational purposes, and that recent attempts to defend the foundational importance of representation theorems are unsuccessful. As a result, we (...) should reject these claims, and lay the foundations of decision theory on firmer ground. (shrink)

Jury theorems are mathematical theorems about the ability of collectives to make correct decisions. Several jury theorems carry the optimistic message that, in suitable circumstances, ‘crowds are wise’: many individuals together (using, for instance, majority voting) tend to make good decisions, outperforming fewer or just one individual. Jury theorems form the technical core of epistemic arguments for democracy, and provide probabilistic tools for reasoning about the epistemic quality of collective decisions. The popularity of jury theorems spans across various disciplines such (...) as economics, political science, philosophy, and computer science. This entry reviews and critically assesses a variety of jury theorems. It first discusses Condorcet's initial jury theorem, and then progressively introduces jury theorems with more appropriate premises and conclusions. It explains the philosophical foundations, and relates jury theorems to diversity, deliberation, shared evidence, shared perspectives, and other phenomena. It finally connects jury theorems to their historical background and to democratic theory, social epistemology, and social choice theory. (shrink)

_Factory of Strategy_ is the last of Antonio Negri's major political works to be translated into English. Rigorous and accessible, it is both a systematic inquiry into the development of Lenin's thought and an encapsulation of a critical shift in Negri's theoretical trajectory. Lenin is the only prominent politician of the modern era to seriously question the "withering away" and "extinction" of the state, and like Marx, he recognized the link between capitalism and modern sovereignty and the need to destroy (...) capitalism and reconfigure the state. Negri refrains from portraying Lenin as a ferocious dictator enforcing the proletariat's reappropriation of wealth, nor does he depict him as a mere military tool of a vanguard opposed to the Ancien Régime. Negri instead champions Leninism's ability to adapt to different working-class configurations in Russia, China, Latin America, and elsewhere. He argues that Lenin developed a new political figuration in and beyond modernity and an effective organization capable of absorbing different historical conditions. He ultimately urges readers to recognize the universal application of Leninism today and its potential to institutionally -- not anarchically -- dismantle centralized power. (shrink)

The text is a continuation of the article of the same name published in the previous issue of Philosophical Alternatives. The philosophical interpretations of the Kochen- Specker theorem (1967) are considered. Einstein's principle regarding the,consubstantiality of inertia and gravity" (1918) allows of a parallel between descriptions of a physical micro-entity in relation to the macro-apparatus on the one hand, and of physical macro-entities in relation to the astronomical mega-entities on the other. The Bohmian interpretation ( 1952) of quantum mechanics (...) proposes that all quantum systems be interpreted as dissipative ones and that the theorem be thus derstood. The conclusion is that the continual representation, by force or (gravitational) field between parts interacting by means of it, of a system is equivalent to their mutual entanglement if representation is discrete. Gravity (force field) and entanglement are two different, correspondingly continual and discrete, images of a single common essence. General relativity can be interpreted as a superluminal generalization of special relativity. The postulate exists of an alleged obligatory difference between a model and reality in science and philosophy. It can also be deduced by interpreting a corollary of the heorem. On the other hand, quantum mechanics, on the basis of this theorem and of V on Neumann's (1932), introduces the option that a model be entirely identified as the modeled reality and, therefore, that absolutely reality be recognized: this is a non-standard hypothesis in the epistemology of science. Thus, the true reality begins to be understood mathematically, i.e. in a Pythagorean manner, for its identification with its mathematical model. A few linked problems are highlighted: the role of the axiom of choice forcorrectly interpreting the theorem; whether the theorem can be considered an axiom; whether the theorem can be considered equivalent to the negation of the axiom. (shrink)

For a set x, let ${\cal S}\left$ be the set of all permutations of x. We prove in ZF several results concerning this notion, among which are the following: For all sets x such that ${\cal S}\left$ is Dedekind infinite, $\left| {{{\cal S}_{{\rm{fin}}}}\left} \right| < \left| {{\cal S}\left} \right|$ and there are no finite-to-one functions from ${\cal S}\left$ into ${{\cal S}_{{\rm{fin}}}}\left$, where ${{\cal S}_{{\rm{fin}}}}\left$ denotes the set of all permutations of x which move only finitely many elements. For all sets (...) x such that ${\cal S}\left$ is Dedekind infinite, $\left| {{\rm{seq}}\left} \right| < \left| {{\cal S}\left} \right|$ and there are no finite-to-one functions from ${\cal S}\left$ into seq, where seq denotes the set of all finite sequences of elements of x. For all infinite sets x such that there exists a permutation of x without fixed points, there are no finite-to-one functions from ${\cal S}\left$ into x. For all sets x, $|{[x]^2}| < \left| {{\cal S}\left} \right|$. (shrink)

We are going to prove a key theorem that tells us just a bit more about the structure of the non-standard countable models of first-order Peano Arithmetic; and then we will very briefly consider whether any broadly philosophical morals can be drawn from the technical result.

Often, when one faces a choice between alternative actions, there are reasons both for and against each alternative. On one way of understanding these words, what one “ought to do all things considered (ATC)” is determined by the totality of these reasons. So, these reasons can somehow be “combined” or “aggregated” to yield an ATC verdict on these alternatives. First, various assumptions about this sort of aggregation of reasons are articulated. Then it is shown that these assumptions allow for the (...) proof of a “Reasons Aggregation Theorem” – parallel to John Harsanyi’s 1955 “Social Aggregation Theorem”. All reasons for action are grounded in reason-providing values; and, for every such reason-providing value, there is in principle a way of measuring how strongly this value counts against each alternative. The theorem tells us that the appropriate measure of how much reason ATC there is against each alternative is simply a weighted sum of the strengths with which these values count against that alternative; the agent ought not ATC to perform an action iff there is ATC more reason against it than against some available alternative. (shrink)

Many scholars of gender and migration assume that migration increases women’s household bargaining power, but this article argues that migration recreates and relies on patriarchal expectations that women return to household domestic labor. It draws on 16 months of ethnographic fieldwork with migrant factory women in China’s export processing zones as well as one migrant-sending community in China. Based on this fieldwork, I argue that despite young women’s desires to continue migrating for factory jobs, older generations perpetuate gendered views of (...) female migration as licentious and risky, in opposition to a dominant paradigm of proper femininity that relegates young women to household labor. They do this because migration creates an intergenerational dependence in migrant origin sites. Older women, unemployable in factories and deprived of state welfare support at home, rely on wage remittances from high-earning migrant sons and sons-in-law for subsistence. To ensure they receive remittances, they encourage daughters to marry higher-earning migrant men, then pressure these daughters to cease migrating in order to perform household domestic labor in support of migrant husbands. This finding reflects constraints on the opportunities that migration delivers to women: Not all women can migrate, and those who cannot must vie for control over migrant remittances. (shrink)

For a set x, let S(x) be the set of all permutations of x. We prove by the method of permutation models that the following statements are consistent with ZF: (1) There is an infinite set x such that |p(x)|<|S(x)|<|seq^1-1(x)|<|seq(x)|, where p(x) is the powerset of x, seq(x) is the set of all finite sequences of elements of x, and seq^1-1(x) is the set of all finite sequences of elements of x without repetition. (2) There is a Dedekind infinite set (...) x such that |S(x)|<|[x]^3| and such that there exists a surjection from x onto S(x). (3) There is an infinite set x such that there is a finite-to-one function from S(x) into x. (shrink)

There is a growing consensus that factory farming of animals — also known as CAFOs, or concentrated animal feeding operations — is morally wrong. The American animal rights movement, which in its early years focused largely on the use of animals in research, now has come to see that factory farming represents by far the greater abuse of animals. The numbers speak for themselves. In the United States somewhere between 20 million and 40 million birds and mammals are killed for (...) research every year. That might seem like a lot — and it far exceeds the number of animals killed for their fur, let alone the relatively tiny number used in circuses — but 40 million represents less than two days’ toll in America’s slaughterhouses, which kill about 10 billion animals each year. (shrink)

What was once the factory is now the university. As deindustrialization spreads and the working class is decentralized, new means of social resistance and political activism need to be sought in what may be the last places where they are possible: the university and the art world. Gerald Raunig's new book analyzes the potential that cognitive and creative labor has in these two arenas to resist the new regimes of domination imposed by cognitive capitalism. Drawing on Gilles Deleuze's concept of (...) "modulation" as the market-driven imperative for the constant transformation and reinvention of subjectivity, in Factories of Knowledge, Industries of Creativity, Raunig charts alternative horizons for resistance. Looking at recent social struggles including the university strikes in Europe, the Spanish ¡Democracia real YA! organization, the Arab revolts, and the Occupy movement, Raunig argues for a reassessment of the importance of cultural and knowledge production. The central role of the university, he asserts, is not as a factory of knowledge but as a place of creative disobedience. (shrink)

The aim of this manuscript is to discuss the reliability and the factorial, convergent and discriminant validities in measurement model of the 21-item Exercise Dependence Scale Revised used for diagnosing exercise addiction. A study was conducted among 695 Lebanese bilingual young adults who filled the English version of this questionnaire, along with a general questionnaire. This study showed that, despite an acceptable fit index confirming the 7-factor structure and invariance across gender, exercise duration and age groups; the EDS-R lacks (...) in reliability and convergent and discriminant validities in measurement model, due particularly to the “Reduction in other activities” subscale. The construction of the EDS-R is then to be discussed. (shrink)

We give a review and critique of jury theorems from a social-epistemology perspective, covering Condorcet’s (1785) classic theorem and several later refinements and departures. We assess the plausibility of the conclusions and premises featuring in jury theorems and evaluate the potential of such theorems to serve as formal arguments for the ‘wisdom of crowds’. In particular, we argue (i) that there is a fundamental tension between voters’ independence and voters’ competence, hence between the two premises of most jury theorems; (...) (ii) that the (asymptotic) conclusion that ‘huge groups are infallible’, reached by many jury theorems, is an artifact of unjustified premises; and (iii) that the (nonasymptotic) conclusion that ‘larger groups are more reliable’, also reached by many jury theorems, is not an artifact and should be regarded as the more adequate formal rendition of the ‘wisdom of crowds’. (shrink)

We write for the cardinality of the set of finite sequences of a set which is of cardinality. With the Axiom of Choice (), for every infinite cardinal where is the cardinality of the permutations on a set which is of cardinality. In this paper, we show that “ for every cardinal ” is provable in and this is the best possible result in the absence of. Similar results are also obtained for : the cardinality of the set of finite (...) sequences without repetition of a set which is of cardinality. (shrink)

This paper explores the psychometric properties of the Polish adaptation of the MBI-SS questionnaire, which measures academic burnout in students. The factorial structure of the tool was examined, and its validity was evaluated using a sample from Polish state universities (N=935). Findings suggest that the MBI-SS possesses strong psychometric parameters. Data supports the tool's 3-factor structure and internal consistency. However, there are reservations regarding one item (MBI_6). Consequently, the 15- item version of the MBI-SS is recommended as a suitable (...) tool for assessing burnout in Polish students. (shrink)