Let be the basic set theory that consists of the axioms of extensionality, emptyset, pair, union, powerset, infinity, transitive containment, Δ0‐separation and set foundation. This paper studies the relative strength of set theories obtained by adding fragments of the set‐theoretic collection scheme to. We focus on two common parameterisations of the collection: ‐collection, which is the usual collection scheme restricted to ‐formulae, and strong ‐collection, which is equivalent to ‐collection plus ‐separation. The main result of this paper shows that for (...) all, proves that there exists a transitive model of Zermelo Set Theory plus ‐collection, the theory is ‐conservative over the theory. It is also shown that (2) holds for when the Axiom of Choice is included in the base theory. The final section indicates how the proofs of (1) and (2) can be modified to obtain analogues of these results for theories obtained by adding fragments of collection to a base theory (Kripke‐Platek Set Theory with Infinity plus ) that does not include the powerset axiom. (shrink)

We identify complete fragments of the simple theory of types with infinity and Quine’s new foundations set theory. We show that TSTI decides every sentence ϕ in the language of type theory that is in one of the following forms: ϕ=∀x1r1⋯∀xkrk∃y1s1⋯∃ylslθ where the superscripts denote the types of the variables, s1>⋯>sl, and θ is quantifier-free, ϕ=∀x1r1⋯∀xkrk∃y1s⋯∃ylsθ where the superscripts denote the types of the variables and θ is quantifier-free. This shows that NF decides every stratified sentence ϕ in the language (...) of set theory that is in one of the following forms: ϕ=∀x1⋯∀xk∃y1⋯∃ylθ where θ is quantifier-free and ϕ admits a stratification that assigns distinct values to all of the variables y1,…,yl, ϕ=∀x1⋯∀xk∃y1⋯∃ylθ where θ is quantifier-free and ϕ admits a stratification that assigns the same value to all of the variables y1,…,yl. (shrink)

We present a novel, perspicuous framework for building iterated ultrapowers. Furthermore, our framework naturally lends itself to the construction of a certain type of order indiscernibles, here dubbed tight indiscernibles, which are shown to provide smooth proofs of several results in general model theory.

Given a model \ of set theory, and a nontrivial automorphism j of \, let \\) be the submodel of \ whose universe consists of elements m of \ such that \=x\) for every x in the transitive closure of m ). Here we study the class \ of structures of the form \\), where the ambient model \ satisfies a frugal yet robust fragment of \ known as \, and \=m\) whenever m is a finite ordinal in the sense (...) of \ Our main achievement is the calculation of the theory of \ as precisely \-\. The following theorems encapsulate our principal results:Theorem A. Every structure in \ satisfies \-\.Theorem B. Each of the following three conditions is sufficient for a countable structure \ to be in \: \ is a transitive model of \-\. \ is a recursively saturated model of \-\. \ is a model of \.Theorem C. Suppose \ is a countable recursively saturated model of \ and I is a proper initial segment of \ that is closed under exponentiation and contains \. There is a group embedding \ from \\) into \\) such that I is the longest initial segment of \ that is pointwise fixed by \ for every nontrivial \.\)In Theorem C, \\) is the group of automorphisms of the structure X, and \ is the ordered set of rationals. (shrink)

In this paper is used to denote Jensen's modification of Quine's ‘new foundations’ set theory () fortified with a type‐level pairing function but without the axiom of choice. The axiom is the variant of the axiom of counting which asserts that no finite set is smaller than its own set of singletons. This paper shows that proves the consistency of the simple theory of types with infinity (). This result implies that proves that consistency of, and that proves the consistency (...) of. (shrink)

Hamkins and Kikuchi (2016, 2017) show that in both set theory and class theory the definable subset ordering of the universe interprets a complete and decidable theory. This paper identifies the minimum subsystem of,, that ensures that the definable subset ordering of the universe interprets a complete theory, and classifies the structures that can be realised as the subset relation in a model of this set theory. Extending and refining Hamkins and Kikuchi's result for class theory, a complete extension,, of (...) the theory of infinite atomic boolean algebras and a minimum subsystem,, of are identified with the property that if is a model of, then is a model of, where M is the underlying set of, is the unary predicate that distinguishes sets from classes and is the definable subset relation. These results are used to show that that decides every 2‐stratified sentence of set theory and decides every 2‐stratified sentence of class theory. (shrink)

By a classical theorem of Harvey Friedman, every countable nonstandard model $\mathcal {M}$ of a sufficiently strong fragment of ZF has a proper rank-initial self-embedding j, i.e., j is a self-embedding of $\mathcal {M}$ such that $j[\mathcal {M}]\subsetneq \mathcal {M}$, and the ordinal rank of each member of $j[\mathcal {M}]$ is less than the ordinal rank of each element of $\mathcal {M}\setminus j[\mathcal {M}]$. Here, we investigate the larger family of proper initial-embeddings j of models $\mathcal {M}$ of fragments of (...) set theory, where the image of j is a transitive submodel of $\mathcal {M}$. Our results include the following three theorems. In what follows, $\mathrm {ZF}^-$ is $\mathrm {ZF}$ without the power set axiom; $\mathrm {WO}$ is the axiom stating that every set can be well-ordered; $\mathrm {WF}$ is the well-founded part of $\mathcal {M}$ ; and $\Pi ^1_\infty \text{-}\mathrm {DC}_\alpha $ is the full scheme of dependent choice of length $\alpha $.Theorem A.There is an $\omega $ -standard countable nonstandard model $\mathcal {M}$ of $\mathrm {ZF}^-+\mathrm {WO}$ that carries no initial self-embedding $j:\mathcal {M} \longrightarrow \mathcal {M}$ other than the identity embedding.Theorem B.Every countable $\omega $ -nonstandard model $\mathcal {M}$ of $\ \mathrm {ZF}$ is isomorphic to a transitive submodel of the hereditarily countable sets of its own constructible universe $L^{\mathcal {M}}$.Theorem C.The following three conditions are equivalent for a countable nonstandard model $\mathcal {M}$ of $\mathrm {ZF}^{-}+\mathrm {WO}+\forall \alpha \ \Pi ^1_\infty \text{-}\mathrm {DC}_\alpha $. There is a cardinal in $\mathcal {M}$ that is a strict upper bound for the cardinality of each member of $\mathrm {WF}$. $\mathrm {WF}$ satisfies the powerset axiom.For all $n \in \omega $ and for all $b \in M$, there exists a proper initial self-embedding $j: \mathcal {M} \longrightarrow \mathcal {M}$ such that $b \in \mathrm {rng}$ and $j[\mathcal {M}] \prec _n \mathcal {M}$. (shrink)

As we face the compounded crises of late capitalism - environmental catastrophe, pandemics, and technological transformation - who are the thinkers with a grasp on our world? McKenzie Wark surveys three areas at the cutting edge of current critical thinking: media ecologies, postcolonial ethnography, and the design of technologies. She introduces us to the ideas of seventeen major writers who, when brought together, contribute to the common task of knowing the world. Each chapter is a concise account of an (...) individual thinker, providing useful context and opening connections to the work of the others. (shrink)

In eastern spiritual traditions, samsara has long been associated with the cycle of birth and death. But what are the hidden depths of samsara, and just how far does it go?

Drawing on early work on ethical leadership, we argue that when leaders engage in leader moral hypocrisy (i.e., ethical promotion without ethical demonstration), followers can experience psychological reactance—a negative response to a perceived restriction of freedom—which can have negative downstream consequences. In a survey of employee–manager dyads (study 1), we demonstrate that leader moral hypocrisy is positively associated with follower psychological reactance, which increases follower deviance. In two subsequent laboratory experiments, we find similar patterns of results (study 2) and explore (...) potential alternative mechanisms (study 3). We demonstrate in a final experiment with working adults that the relationship between leader moral hypocrisy and psychological reactance is partly explained by increased perceptions of a leader’s use of power (study 4). We discuss the implications of our findings and advocate for further understanding of the risks associated with psychological reactance in response to leaders and other workplace situations. (shrink)

This book examines "Taylorean social theory," its sources, main characteristics and impact. Charles Taylor's meta-narrative of secularization in the West, prominently contained in his major work A Secular Age (2007), has brought new insight on the social and cultural factors that intervened in such process, the role of human agency, and particularly on the contemporary conditions of belief in North America and Europe. This study discusses what Taylor's approach has brought to the scholarly debate on Western secularization, which has been (...) carried on mostly in sociological terms. McKenzie interprets Taylor's views in a way that offers an original social theory. Such interpretation is possible with the help of sociologist Margaret Archer's "morphogenetic theory" and by making the most of Taylor's particular understanding of the method of the social sciences and of his philosophical views on human beings, knowledge and modernity. After exploring the philosophical and sociological sources informing Taylorean social theory and proposing its basic concepts and hermeneutic guidelines, the author compares it with two widespread theories of secularization: the now waning "orthodox" account and that proposed by Rational Choice Theory scholars, particularly prevalent in the United States. In doing so, the book shows in which ways Taylorean social theory supersedes them, what new issues it brings into the scholarly discussion, and what difficulties might limit its future development. (shrink)

This book presents the foundations of a general theory of algebras. Often called “universal algebra”, this theory provides a common framework for all algebraic systems, including groups, rings, modules, fields, and lattices. Each chapter is replete with useful illustrations and exercises that solidify the reader's understanding. The book begins by developing the main concepts and working tools of algebras and lattices, and continues with examples of classical algebraic systems like groups, semigroups, monoids, and categories. The essence of the book lies (...) in Chapter 4, which provides not only basic concepts and results of general algebra, but also the perspectives and intuitions shared by practitioners of the field. The book finishes with a study of possible uniqueness of factorizations of an algebra into a direct product of directly indecomposable algebras. There is enough material in this text for a two semester course sequence, but a one semester course could also focus primarily on Chapter 4, with additional topics selected from throughout the text. (shrink)

Unfortunately, business is often associated with unethical behavior. While research has offered a number of explanations for why business might encourage unethical behavior, we argue that how a person frames a situation may provide important insight. Drawing on the decision frame literature, the goal of the current research is to identify the differences in cognitive processing associated with two decision frames dominant in the business ethics literature—business and ethical—and, with that knowledge, examine ways to mitigate the detrimental influence of frame (...) on unethical behavior. We first demonstrate the causal link between frame and misrepresentation, and then identify several differences in cognitive processing—cost–benefit analyses, concern for others, and construal level—that distinguish business and ethical frames, and investigate their effects on misrepresentation. In our final set of studies, we demonstrate that the influence of these frames on misrepresentation can be altered by manipulating these cognitive processes, both mitigating and exacerbating a decision maker’s engagement in misrepresentation. We conclude by summarizing our findings and their potential impact on unethical behavior more broadly. (shrink)

A variant of the process dissociation procedure was coupled with a manipulation of response signal lag to assess whether manipulations of context affect one or both of the familiarity and search processes described by the dual process model of recognition. Participants studied a list of word pairs followed by a recognition test with target words presented in the same or different context, and in the same or different form as study . Participants were asked to recognize any target word regardless (...) of changes to form , or to only recognise words that were presented in the same form . The standard context reinstatement effect was evident even at the short response lags. Analyses of the estimates of the contributions of familiarity and search processes suggest that the context effect demonstrated here can be attributed in part to the influence of familiarity on recognition, whereas the effect on recollection was less clear. (shrink)

Any instance (i.e., event, behavior, trait) belongs to infinitely many reference classes, hence there are infinitely many base rates from which to choose. People clearly do not entertain all possible reference classes, however, so something must be limiting the search space. We suggest some possible mechanisms that determine which reference class is evoked for the purpose of judgment and decision.

he relationship between metaphysics and science has recently become the focus of increased attention. Ladyman and Ross, in particular, have accused even naturalistically inclined metaphysicians of pursuing little more than the philosophy of A-level chemistry and have suggested that analytic metaphysics should simply be discontinued. In contrast, we shall argue, first of all, that even metaphysics that is disengaged from modern science may offer a set of resources that can be appropriated by philosophers of physics in order to set physics (...) within an interpretational framework. Secondly, however, we shall urge that insofar as metaphysics is intended to be more than just a toolbox it needs to accommodate the implications of physics if many of its core claims are to be sustained. We shall illustrate this last point with a discussion of the nature of laws and modality in the context of modern physics. (shrink)

We introduce a dynamic model for evolutionary games played on a network where strategy changes are correlated according to degree of influence between players. Unlike the notion of stochastic stability, which assumes mutations are stochastically independent and identically distributed, our framework allows for the possibility that agents correlate their strategies with the strategies of those they trust, or those who have influence over them. We show that the dynamical properties of evolutionary games, where such influence neighborhoods appear, differ dramatically from (...) those where all mutations are stochastically independent, and establish some elementary convergence results relevant for the evolution of social institutions. (shrink)

Guy Debord, a key member of the avant garde movement known as the Situationist International, is best known for his concept of the society of the spectacle. Conceived in the sixties, the concept had at the time two variants, the concentrated and diffuse. Debord used these in those cold war times to describe the regimes of the image in both east and west under the same rubric. Later, he conceived of the rise of the integrated spectacle. Based on his experience (...) of France and Italy in the seventies, this concept explained regimes of the image that combined elements form both sides of the cold war divide, threading together the commodity fetishism of the west with the opaque actions of the state form the Soviet east. But what if a third period could be discerned, of what might be called the disintegrating spectacle? This concept might point the way to an analysis and critique of the image under twenty-first century conditions, where everyday life is super-saturated by the commodity, by digital media, and by the unravelling of the political form of social organization. (shrink)

A number of reports have suggested that patients who undergo deep brain stimulation may experience changes to their personality or sense of self. These reports have attracted great philosophical interest. This paper surveys the philosophical literature on personal identity and DBS and draws on an emerging empirical literature on the experiences of patients who have undergone this therapy to argue that the existing philosophical discussion of DBS and personal identity frames the problem too narrowly. Much of the discussion by neuroethicists (...) centers on the nature of the threat posed by DBS, asking whether it is best understood as a threat to personal identity, autonomy, agency, or authenticity, or as putting patients at risk of self-estrangement. Our aim in this paper is to use the empirical literature on patients’ experiences post-DBS to open up a broader range of questions - both philosophical and practical, and to suggest that attention to these questions will help to provide better support to patients, both before and after treatment. (shrink)

Les différentes institutions européennes sont nées pour résoudre les problèmes de la production du stade avancé du capitaliste ainsi que de son armature géopolitique. Plus qu’un régime d’accumulation, c’est d’abord une infrastructure – au sens marxiste vulgaire – qui permettait une production et une consommation industrielles en Europe et un commerce inégal avec le Sud. Mais que se passe-t-il si ce n’est même plus du capitalisme, mais un nouveau mode de production? Celui qui extrude hors de lui-même une infrastructure très (...) différente, à une échelle planétaire? La question se pose alors de savoir si les anciennes infrastructures institutionnelles de l’Europe peuvent être adaptées à cette nouvelle réalité économique et politique, celle d’un Stack informationnel caractéristique du capitalisme de plateformes. (shrink)

This chapter contains section titled: Kin Selection Reciprocity Group Selection Coercion Mutualism Byproduct Mutualism Local Interactions References.

Strong reciprocators possess two behavioural dispositions: they are willing to bestow benefits on those who have bestowed benefits, and they are willing to punish those who fail to bestow benefits according to some social norm. There is no doubt that peoples' behaviour, in many cases, agrees with what we would expect if people are strong reciprocators, and Fehr and Henrich argue that many people are, in fact, strong reciprocators. They also suggest that strongly reciprocal behaviour may be brought about by (...) specialised cognitive architecture produced by evolution. I argue that specialised cognitive architecture can play a role in the production of strongly reciprocal behaviour only in a very attenuated sense, and that the evolutionary foundations of strong reciprocity are more likely cultural than biological. (shrink)

This article examines two questions about scientists’ search for knowledge. First, which search strategies generate discoveries effectively? Second, is it advantageous to diversify search strategies? We argue pace Weisberg and Muldoon, “Epistemic Landscapes and the Division of Cognitive Labor”, that, on the first question, a search strategy that deliberately seeks novel research approaches need not be optimal. On the second question, we argue they have not shown epistemic reasons exist for the division of cognitive labor, identifying the errors that led (...) to their conclusions. Furthermore, we generalize the epistemic landscape model, showing that one should be skeptical about the benefits of social learning in epistemically complex environments. (shrink)

Let be a finite collection of finite algebras of finite signature such that SP( ) has meet semi-distributive congruence lattices. We prove that there exists a finite collection 1 of finite algebras of the same signature, , such that SP( 1) is finitely axiomatizable.We show also that if , then SP( 1) is finitely axiomatizable. We offer new proofs of two important finite basis theorems of D. Pigozzi and R. Willard. Our actual results are somewhat more general than this abstract (...) indicates. (shrink)

Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{K}$$ \end{document} be a finite collection of finite algebras of finite signature such that SP(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{K}$$ \end{document}) has meet semi-distributive congruence lattices. We prove that there exists a finite collection \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{K}$$ \end{document}1 of finite algebras of the same signature, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{K}_1 \supseteq (...) \mathcal{K}$$ \end{document}, such that SP(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{K}$$ \end{document}1) is finitely axiomatizable.We show also that if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$HS(\mathcal{K}) \subseteq SP(\mathcal{K})$$ \end{document}, then SP(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{K}$$ \end{document}1) is finitely axiomatizable. We offer new proofs of two important finite basis theorems of D. Pigozzi and R. Willard. Our actual results are somewhat more general than this abstract indicates. (shrink)

In a highly influential work, List and Pettit (Group Agency: The Possibility, Design, and Status of Corporate Agents, Oxford University Press, 2011) draw upon the theory of judgement aggregation to offer an argument for the existence of nonreductive group agents; they also suggest that nonreductive group agency is a widespread phenomenon. In this paper, we argue for the following two claims. First, that the axioms they consider cannot naturally be interpreted as either descriptive characterisations or normative constraints upon group judgements, (...) in general. This makes it unclear how the List and Pettit argument is to apply to real world group behaviour. Second, by examining empirical data about how group judgements are made by a powerful international regulatory board, we show how each of the List and Pettit axioms can be violated in ways which are straightforwardly explicable at the level of the individual. This suggests that group agency may best be understood as a pluralistic phenomenon, where close inspection of the dynamics of intragroup deliberation can reveal that what prima facie appears to be a nonreductive group agent is, in fact, reducible. (shrink)

For a variety of reasons, including the common use of deception in psychology experiments, participants often disbelieve experimenters' assertions about important task parameters. This can lead researchers to conclude incorrectly that participants are behaving non- normatively. The problem can be overcome by deriving and testing normative models that do not assume full belief in key task parameters. A real experimental example is discussed.

As a first step in involving user emotion in human‐computer interaction, a memory‐based expert system (JANUS; Kearney, 1991) was designed to interpret facial expression in terms of the signaled emotion. Anticipating that a VDU‐mounted camera will eventually supply face parameters automatically, JANUS now accepts manually made measurements on a digitized full‐face photograph and returns emotion labels used by college students. An intermediate representation in terms of face actions (e.g., mouth open) is also used. Production rules convert the geometry into these. (...) A dynamic memory (Kolodner, 1984; Schank, 1982) interprets the face actions in terms of emotion labels. The memory is dynamic in the sense that new emotion labels can be learned with experience. A prototype system has been implemented on a Sun 2/120 system using POPLOG. Validation studies on the prototype suggest that the interpretations achieved are generally consistent with those of college students without formal instruction in emotion signals. (shrink)