Objective Apeiron was founded in 1966 and has developed into one of the oldest and most distinguished journals dedicated to the study of ancient philosophy, ancient science, and, in particular, of problems that concern both fields. Apeiron is committed to publishing high-quality research papers in these areas of ancient Greco-Roman intellectual history; it also welcomes submission of articles dealing with the reception of ancient philosophical and scientific ideas in the later western tradition. The journal appears quarterly. Articles are peer-reviewed on (...) a double-blind basis. Topics ancient philosophy ancient science reception of ancient philosophical and scientific ideas in the later western tradition Article formats Original Articles. (shrink)

We survey recent developments in the theory of class forcing for- malized in the second-order set-theoretic setting.

First published in 1994. Routledge is an imprint of Taylor & Francis, an informa company.

This dissertation aims to analyze, clarify, and reconstruct the concept of class consciousness by developing a dialectical account of political agency at work in the concept. I defend a dialectical account of agency, that includes both the way in which individuals come together to form groups, but also the capacity of a collective to transform social conditions. I argue that this account of political agency is necessary in order to understand the possibility of social transformation or change. I trace (...) the development of the relationship between consciousness and agency in the early tradition of Western Marxism, focusing primarily on the account of class consciousness given by Georg Lukács in History and Class Consciousness. Against his account of the world historical agency of a unified proletariat, however, I defend Theodor Adorno’s insistence on nonidentity, and the importance of unreconciled groups in capitalist society. In order to understand these groups, such as the vanguard, party, or proletariat, we must understand the way in which individuals form groups, as well as their inherent collectivity. -/- My account of the political agency at work in the concept of class consciousness is broadly speaking pluralist. I argue that a multiplicity of methodologies is needed in order to arrive at a complete picture of the concept. I defend an account of class consciousness that is neither reductive nor deflationary with respect to other dimensions of social domination. This class forward approach seeks to build intersectional political coalitions in order to undertake revolutionary action. Successful revolutionary social transformation is never guaranteed in advance; however, the concept of class consciousness, reconstructed through the lens of political agency, offers conceptual resources to address the problems of today, for the sake of a better tomorrow. (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.

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.

An infinite binary sequence is complex if the Kolmogorov complexity of its initial segments is bounded below by a computable function. We prove that a Π₁⁰ class P contains a complex element if and only if it contains a wtt-cover for the Cantor set. That is, if and only if for every Y⊆ω there is an X in P such that X≥wtt Y. We show that this is also equivalent to the Π₁⁰ class's being large in some sense. (...) We give an example of how this result can be used in the study of scattered linear orders. (shrink)

This article argues that Brentano’s classification of mental phenomena is best understood against the background of the theories of natural classification held by Auguste Comte and John Stuart Mill. Section 1 offers a reconstruction of Brentano’s two-premise argument for his tripartite classification. Section 2 gives a brief overview of the reception and historical background of the classification project. Section 3 addresses the question as to why a classification of mental phenomena is needed at all and traces the answer back to (...) Mill’s view that psychological laws are class-specific. Section 4 and 5 connect the second premise of Brentano’s argument to Comte’s principle of comparative likeness and Mill’s insistance that class membership is determined by the possession of common characteristics. And section 6 briefly discusses the evidence Brentano provides for the first premise. (shrink)

This article presents a theoretical framework that views interpersonal power as interdependent with broader structures of gender and class inequalities. In contrast to oversimplified, gender-neutral or gender-static approaches, this approach illuminates the ways that structures of inequality are expressed in ideological hegemonies, which enhance, legitimate, and mystify the interpersonal power of privileged men relative to lower-status men and women in general. The discussion centers on how the relational construction of ascendant and subordinated masculinities provide men with different modes of (...) interpersonal power that, when exercised, construct and reaffirm interclass male dominance. Examples of how the construction of femininity can undermine women's interpersonal power and implications for other forms of masculinities and femininities are discussed. Examples are drawn from an analysis of conjugal power in the accounts of remarried individuals' first and second marriages to illustrate the main points of this perspective. (shrink)

I will discuss a variety of cases such that the subject's believing truly is somewhat of an accident, but less so than in a Gettier case. In each case, this is because her reasons are not ultimately undefeated full stop, but they are ultimately undefeated with certain qualifications. For example, the subject's reasons might be ultimately defeated considered in themselves but ultimately undefeated considered as a proper part of an inference to the best explanation that is undefeated without qualification. In (...) each section of the paper, I consider different qualifications and show how in each case we get an epistemic standing I call “coach-class knowledge”. First-class knowledge requires justifying reasons that are undefeated without qualification. Coach-class knowledge only requires qualified lack of defeat. I will use this distinction to bring debates over knowledge from falsehood and fake barns to an ecumenical resolution. In both cases, the subject enjoys coach-class rather than first-class knowledge. I will also show that the defeasible reasoning tradition can better account for graded accidental truth than safety theories. (shrink)

Les vingt dernières années ont vu l’apparition d’une convergence forte entre une démarche appliquée se consacrant à la création de corpus de grande taille, à leur codage et à leur étiquetage, et diverses théories linguistiques dont les analyses reposent sur de tels corpus. Pour l’analyse de conversation (ou linguistique interactionnelle) une telle convergence ne semble pas possible, car son approche est qualitative et s’appuie sur de « petits » corpus. De plus, un examen approfondi du contexte social des interactions recueillies (...) est nécessaire, qui ne peut donc se réduire à la collecte de métadonnées. Une question surgit immédiatement : la notion de « petit » corpus a une validité sur le plan épistémologique? Le présent article montre qu’une réponse positive peut être apportée à cette question et qu’il est possible de fonder en raison une pratique qui, le plus souvent, se drape sous les oripeaux de l’évidence. (shrink)

In this article we show that Morse-Kelley class theory provides us with an adequate framework for class forcing. We give a rigorous definition of class forcing in a model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$$$ \end{document} of MK, the main result being that the Definability Lemma can be proven without restricting the notion of forcing. Furthermore we show under which conditions the axioms are preserved. We conclude by proving that Laver’s Theorem does (...) not hold for class forcings. (shrink)

Elselijn Kingma argues that Christopher Boorse’s biostatistical theory (the BST) does not show how the reference classes it uses are objective and naturalistic. Recently, philosophers of medicine have attempted to rebut Kingma’s concerns. I argue that these rebuttals are theoretically unconvincing, and that there are clear examples of physicians adjusting their reference classes according to their prior knowledge of health and disease. I focus on the use of age-adjusted reference classes to diagnose low bone mineral density in children. In addition (...) to using the BST’s age, sex, and species, physicians also choose to use other factors to define reference classes, such as pubertal status, bone age, body size, and muscle mass. I show that physicians calibrate the reference classes they use according to their prior knowledge of health and disease. Reference classes are also chosen for pragmatic reasons, such as to predict fragility fractures. (shrink)

Food prices are a daily concern in many households’ decision-making, especially when people want to have healthier diets. Employing Bayesian Mindsponge Framework (BMF) analytics on a dataset of 710 Indonesian citizens, we found that people from wealthier households are less likely to have concerns about food prices. However, the degree of health considerations in food consumption was found to moderate against the above association. In other words, people of higher income-based social classes may worry more about food prices if they (...) care more about the health impacts of their food choices. These findings provide more insights for policymakers on the psychological aspects of promoting the balance between finance and health in food consumption. (shrink)

When classes of structures are not first-order definable, we might still try to find a nice description. There are two common ways for doing this. One is to expand the language, leading to notions of pseudo-elementary classes, and the other is to allow infinite conjuncts and disjuncts. In this paper we examine the intersection. Namely, we address the question: Which classes of structures are both pseudo-elementary and ${\mathcal {L}}_{\omega _1, \omega }$ -elementary? We find that these are exactly the classes (...) that can be defined by an infinitary formula that has no infinitary disjunctions. (shrink)

This paper presents a new approach to the class-theoretic paradoxes. In the first part of the paper, I will distinguish classes from sets, describe the function of class talk, and present several reasons for postulating type-free classes. This involves applications to the problem of unrestricted quantification, reduction of properties, natural language semantics, and the epistemology of mathematics. In the second part of the paper, I will present some axioms for type-free classes. My approach is loosely based on the (...) Gödel–Russell idea of limited ranges of significance. It is shown how to derive the second-order Dedekind–Peano axioms within that theory. I conclude by discussing whether the theory can be used as a solution to the problem of unrestricted quantification. In an appendix, I prove the consistency of the class theory relative to Zermelo–Fraenkel set theory. (shrink)

This article studies three most basic systems of truth as well as their subsystems over set theory ZF possibly with AC or the axiom of global choice GC, and then correlates them with subsystems of Morse–Kelley class theory MK. The article aims at making an initial step towards the axiomatic study of truth in set theory in connection with class theory. Some new results on the side of class theory, such as conservativity, forcing and some forms of (...) the reflection principle, are also presented. The equivalence results among systems of truth and classes obtained in this article are summarized in Theorem 104 , Theorem 107 and Theorem 108. (shrink)

The UK is an unequal society. Societies like these raise significant ethical questions for those who live in them. One is how they should respond to such inequality, and in particular, to its effects on those who are worst-off. In this article, I’ll approach this question by focusing on the obligations of a particular group of those who are best-off. I’ll defend the idea of morally objectionable class-based advantage, which I’ll call ‘class privilege’, argue that class privilege (...) can be non-culpable, and put forward an account of the obligations those with class privilege have. My main claim will be that those with class privilege have obligations to ‘offset’ their privilege, in something like the same way high emitters have obligations to offset their greenhouse gas emissions. (shrink)

Following the February Revolution in 1848, working-class women as well as men attempted to hold the government to its promise of the right to work, through street demonstrations, individual and collective demands for work, and participation in the national workshops that had been established in an attempt to address the problem of unemployment in the capital. In the process, these activists articulated what scholars have labelled as a democratic socialist vision of republicanism. In June of 1848, women participated in (...) the insurrection that sought to defend the vision of a social republic. While the republicanism of working-class men and bourgeois women such as George Sand has been examined, studies of working-class women in the first half of the nineteenth century have to this point focused on the romantic socialist influences that shaped their activities, in particular the Saint-Simonian movement. Drawing primarily on individual letters, police interrogations and newspaper reports, a vision of republicanism emerges that includes the ability for women to sustain their families through waged as well as household labour. This concept of republican virtue based itself not in suffrage but in women's capacity to act as both producers and consumers under just and equitable conditions. (shrink)

In our paper “A general characterization of the variable-sharing property by means of logical matrices”, a general class of so-called “Relevant logical matrices”, RMLs, is defined. The aim of this paper is to define a class of simpler Relevant logical matrices RMLs′serving the same purpose that RMLs, to wit: any logic verified by an RML′has the variable-sharing property and related properties predicable of the logic of entailment E and of the logic of relevance R.

The transition to twenty-first century post-industrial capitalism from the 'welfare' industrial capitalism of the twentieth century, has affected the ways in which class is lived in terms of relational inequality and the factors that structure identity. Class After Industry takes a complex realist approach to the dynamics of individual lives, places, the social structure and analyses their significance in terms of class. A wide range of quantitative and qualitative studies are drawn on to explore how 'life after (...) industry' shapes class, and the consequent potential for social change. The book will be of interest across the social sciences and beyond, to those concerned with how class forms might translate into political action. (shrink)

In his early writings, dealing mainly with problems of agricultural policy, Max Weber at times differentiates between “class” and “estate”, but in general he treats them as synonyms. Only after 1909, when he started to work on Economy and Society and Economic Ethic of the World Religions, he felt the necessity to use these concepts in a more clear-cut manner. “Classes” are only placed within the economic order, while “estates” belong to the social order and take shape through the (...) partition of «social prestige» or «honor», which in turn derives from different sources, including the religious ones. This essay explores the forms of religious stratification which arise from the knowledge of rituals and precedents, from the knowledge of the Sacred Scriptures, or from a specific knowledge of the conditions of possibility of redemption. (shrink)

In this paper we consider classes of finite structures where we have good control over the sizes of the definable sets. The motivating example is the class of finite fields: it was shown in [1] that for any formulain the language of rings, there are finitely many pairs (d,μ) ∈ω×Q>0so that in any finite fieldFand for any ā ∈Fmthe size |ø(Fn,ā)| is “approximately”μ|F|d. Essentially this is a generalisation of the classical Lang-Weil estimates from the category of varieties to that (...) of the first-order-definable sets. (shrink)

The article rebutts Michael Kremer’s contention that Russell’s contextual definition of set-theoretic language in Principia Mathematica constituted the ontological achievement of eliminating commitment to classes. Although Russell’s higher-order quantifiers, used in the definition, need not range over classes, none of the plausible substitutes provide a solid basis for eliminating them. This point is used to defend the presentation, in The Dawn of Analysis, of Russell’s logicist reduction, using a first-order version of naive set theory.

SC, CA, QA and QEA denote the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasi-polyadic algebras and quasi-polyadic equality algebras, respectively. Let ω ≤ α < β and let K ∈ {SC,CA,QA,QEA}. We show that the class of α -dimensional neat reducts of algebras in Kβ is not elementary. This solves a problem in [3]. Also our result generalizes results proved in [2] and [3].

This study, first published in 1986, provides a systematic account of the processes and structure of class formation in the major advanced capitalist societies. The focus is on the organizational mechanisms of class cohesion and division, theoretically deriving from a neo-Marxian perspective. Chapters consider the organization and structure of the ‘corporate ruling class’, the middle class and the working class, and are brought together in an overarching analysis of the organization of class in relation (...) to the state and the economy. This title will be of particular interest to students researching the impact of recession on societal structure and the processes of political class struggle, as well as those with a more general interest in the socio-economic theories of Marx, Engels and Weber. (shrink)

This paper is a critical examination of Vendler's well-known aspectual classes (states, activities, accomplishments, achievements). It is argued that it not classes that play a role in the explanation of aspectual phenomena but rather some specific semantic factors from which aspectual classes can be constructed, in particular factors inherent to the (lexical) verb and to the determiners of noun phrases.

SC, CA, QA and QEA denote the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasi-polyadic algebras and quasi-polyadic equality algebras, respectively. Let ω ≤ α < β and let K ∈ {SC,CA,QA,QEA}. We show that the class of α -dimensional neat reducts of algebras in Kβ is not elementary. This solves a problem in [3]. Also our result generalizes results proved in [2] and [3].

Marxian class theory has been unable to account for the most significant historical developments of the 20th century. The rise of fascism not only belied the hopes put in the revolutionary proletariat, it also brought into the center of the political stage those social strata which the class theory had relegated to, at best, secondary supporting roles. The triumph of the Bolshevik, revolution and the institutionalization and expansion of Soviet socialism has not only failed to issue into the (...) anticipated free, classless society, but has led to the creation of a new system of stratification and domination which is simply unthinkable within the classical Marxian framework. Late or advanced capitalism continues advancing in spite of all its crises and contradictions. (shrink)

We study smooth classes without the algebraic closure property. For such smooth classes we investigate the simplicity of the class of generic structures, in the context of Robinson theories.

The paper offers to substantiate a claim about the so-called Meritocratic Conception of how educational opportunities ought to be distributed. Such a conception holds an individual’s prospects for educational achievement may be a function of that individual’s talent or effort levels but should not be influenced by their social class background. The paper highlights the internal tension in the Meritocratic Conception between on the one hand a prohibition on the influence of social class on educational opportunities and on (...) the other a permission to allow unequal educational opportunities on the basis of talent and effort. This tension obtains because individuals’ talent and effort are themselves subject to influence by social class. The paper makes a positive case for an interpretation of the Meritocratic Conception that resolves this tension in favour of an egalitarian version, such that social class represents an objectionable determinant of unequal educational prospects even when its influence is mediated through the cultivation of talent and effort. This argument is further supported through an explanation that the character of social class as a systemic social source of the structure of individuals’ opportunities makes it an objectionable influence on educational opportunities. (shrink)

The dispute about the role of class in understanding the life situations of people of color has tended to be overpolarized, between a class reductionism and an “it's only race” position. Class processes shape racial groups’ life situations. Race and class are also distinct axes of injustice; but class injustice informs racial injustice. Some aspects of racial injustice can be expressed only in concepts associated with class (e.g., material deprivation, inferior education). But other aspects (...) of racial injustice or other harms, such as racial discrimination or stigma, are not reducible to class concepts and cannot be fully addressed through class-focused policies. Overall, any attempt to fully secure racial justice for a racial group will require a combination of race-focused and class-focused policies. Anti-racist outlooks often neglect or downplay either the normative or the explanatory significance of class, or both—for example, by overlooking or downplaying the dignitary harms of class and the material harms of race; missing the historical dimension of class injustice; masking class by a narrowing of the complex normative structure of racial disparities; or not recognizing that a class-focused initiative (like raising the minimum wage) can address substantial racial justice concerns, even though not all of them. “Systemic racism” terminology recognizes class explanatorily but suppresses it normatively. Charles Mills's influential notion of “white supremacy,” while a powerful tool for conceptualizing and illuminating racial injustice, can also contribute to minimizing or masking the justice-related impact of class, as do some of Mills's specific discussions of class in various writings. (shrink)

Let $\mathbf{I}(\mu,K)$ denote the number of nonisomorphic models of power $\mu$ and $\mathbf{IE}(\mu,K)$ the number of nonmutually embeddable models. We define in this paper the notion of a diverse class and use it to prove a number of results. The major result is Theorem B: For any diverse class $K$ and $\mu$ greater than the cardinality of the language of $K$, $\mathbf{IE}(\mu,K) \geq \min(2^\mu,\beth_2).$ From it we deduce both an old result of Shelah, Theorem C: If $T$ is (...) countable and $\lambda_0 > \aleph_0$ then for every $\mu > \aleph_0,\mathbf{IE}(\mu,T) \geq \min(2^\mu,\beth_2)$, and an extension of that result to uncountable languages, Theorem D: If $|T| < 2^\omega,\lambda_0 > |T|$, and $|D(T)| = |T|$ then for $\mu > |T|$, $\mathbf{IE}(\mu,T) \geq \min(2^\mu,\beth_2).$. (shrink)

In this paper we characterize, classify and axiomatize all universal classes of MV-chains. Moreover, we accomplish analogous characterization, classification and axiomatization for congruence distributive quasivarieties of MV-algebras. Finally, we apply those results to study some finitary extensions of the Łukasiewicz infinite valued propositional calculus.

In Gender, Class, and Freedom in Modern Political Theory, Nancy Hirschmann demonstrates not merely that modern theories of freedom are susceptible to gender and class analysis but that they must be analyzed in terms of gender and class in order to be understood at all. Through rigorous close readings of major and minor works of Hobbes, Locke, Rousseau, Kant, and Mill, Hirschmann establishes and examines the gender and class foundations of the modern understanding of freedom. Building (...) on a social constructivist model of freedom that she developed in her award-winning book The Subject of Liberty: Toward a Feminist Theory of Freedom, she makes in her new book another original and important contribution to political and feminist theory. Despite the prominence of "state of nature" ideas in modern political theory, Hirschmann argues, theories of freedom actually advance a social constructivist understanding of humanity. By rereading "human nature" in light of this insight, Hirschmann uncovers theories of freedom that are both more historically accurate and more relevant to contemporary politics. Pigeonholing canonical theorists as proponents of either "positive" or "negative" liberty is historically inaccurate, she demonstrates, because theorists deploy both conceptions of freedom simultaneously throughout their work. (shrink)

The question of what truths are necessary in the broadest possible sense is a difficult one to answer, as is the question of what the limits are to what is possible. (Most people would see these two questions as different sides of the same coin, of course, since many think the question of what is possible is just the question of what is not necessarily ruled out). We have three general sorts of strategies for determining whether something is necessary (or (...) possible). We can identify it in a class that we were previously sure was a class of things that are necessary – we might show it is a theorem of a logical system that we have confidence in, or that the sentence appears to be true simply in virtue of the meanings of the words, or that it is a true statement involving names or about natural kinds of the “necessary a posteriori” sort discussed by Kripke and Putnam, and there are perhaps other classes of claims which we are prepared to accept are necessary if true.1 Likewise, we might establish the possibility of something occurring by reference to a class of well-established or uncontroversial possibilities: e.g. we are inclined to think that it is possible (in the broadest sense) for an event to occur in the future if one of the same kind has occurred in the past. (shrink)