The HOD Dichotomy Theorem states that if there is an extendible cardinal, δ, then either HOD is “close” to V or HOD is “far” from V. The question is whether the future will lead to the first or the second side of the dichotomy. Is HOD “close” to V, or “far” from V? There is a program aimed at establishing the first alternative—the “close” side of the HOD Dichotomy. This is the program of inner model theory. In recent years the (...) third author has provided evidence that there is an ultimate inner model—Ultimate-L—and he has isolated a natural conjecture associated with the model—the Ultimate-L Conjecture. This conjecture implies that that the first alternative holds—HOD is “close” to V. This is the future in which pattern prevails. In this paper we introduce a very different program, one aimed at establishing the second alternative—the “far” side of the HOD Dichotomy. This is the program of large cardinals beyond choice. Kunen famously showed that if AC holds then there cannot be a Reinhardt cardinal. It has remained open whether Reinhardt cardinals are consistent in ZF alone. It turns out that there is an entire hierarchy of choiceless large cardinals of which Reinhardt cardinals are only the beginning, and, surprisingly, this hierarchy appears to be highly ordered and amenable to systematic investigation, as we shall show in this paper. The point is that if these choiceless large cardinals are consistent then the Ultimate-L Conjecture must fail. This is the future where chaos prevails. (shrink)

We show that Bounded Forcing Axioms (for instance, Martin's Axiom, the Bounded Proper Forcing Axiom, or the Bounded Martin's Maximum) are equivalent to principles of generic absoluteness, that is, they assert that if a $\Sigma_1$ sentence of the language of set theory with parameters of small transitive size is forceable, then it is true. We also show that Bounded Forcing Axioms imply a strong form of generic absoluteness for projective sentences, namely, if a $\Sigma^1_3$ sentence with parameters is forceable, then (...) it is true. Further, if for every real x, $x^{\sharp}$ exists, and the second uniform indiscernible is less than $\omega_2$ , then the same holds for $\Sigma^1_4$ sentences. (shrink)

I present an account of mental representation based upon the ‘SINBAD’ theory of the cerebral cortex. If the SINBAD theory is correct, then networks of pyramidal cells in the cerebral cortex are appropriately described as representing, or more specifically, as modelling the world. I propose that SINBAD representation reveals the nature of the kind of mental representation found in human and animal minds, since the cortex is heavily implicated in these kinds of minds. Finally, I show how SINBAD neurosemantics can (...) provide accounts of misrepresentation, equivocal representation, twin cases, and Frege cases. (shrink)

For each natural number n, let C(n) be the closed and unbounded proper class of ordinals α such that Vα is a Σn elementary substructure of V. We say that κ is a C(n)-cardinal if it is the critical point of an elementary embedding j : V → M, M transitive, with j(κ) in C(n). By analyzing the notion of C(n)-cardinal at various levels of the usual hierarchy of large cardinal principles we show that, starting at the level of superstrong (...) cardinals and up to the level of rank-into-rank embeddings, C(n)-cardinals form a much finer hierarchy. The naturalness of the notion of C(n)-cardinal is exemplified by showing that the existence of C(n)-extendible cardinals is equivalent to simple reflection principles for classes of structures, which generalize the notions of supercompact and extendible cardinals. Moreover, building on results of Bagaria et al. (2010), we give new characterizations of Vopeňka’s Principle in terms of C(n)-extendible cardinals. (shrink)

Gender, ‘race’, poverty, health and discourses of health reform in the context of globalization: a postcolonial feminist perspective in policy researchIn this paper, I draw on extant literature and my empirical work to discuss the impact of globalization and healthcare reform on the lives of women — those from countries of the South as well as of the North. First, I review briefly the economic hardships identified in different sectors of the population that have been attributed to how globalization is (...) now working. Second, I examine what these global processes mean for health, with particular focus on poverty, gender, racialization and health. Third, I reflect on how nurse scientists might develop research agendas in the 21st century that would foster social transformation and social justice for all people. The position taken here is not an indictment of globalization. Rather, I argue that globalization is a fact in all of our lives. There are positive aspects of globalization. There are also negative aspects which we must collectively address, given that the issues identified can have deleterious consequences for the world’s poor, women in particular. I suggest that, to construct knowledge for practice and praxis, research agendas of the future should be inclusive of subaltern voices. I argue that drawing on a postcolonial feminist epistemology might help us to define such agendas, and express the multilayered sociopolitical contexts of health and illness in advocacy with policy‐makers. (shrink)

Superstrong cardinals are never Laver indestructible. Similarly, almost huge cardinals, huge cardinals, superhuge cardinals, rank-into-rank cardinals, extendible cardinals, 1-extendible cardinals, 0-extendible cardinals, weakly superstrong cardinals, uplifting cardinals, pseudo-uplifting cardinals, superstrongly unfoldable cardinals, Σn-reflecting cardinals, Σn-correct cardinals and Σn-extendible cardinals are never Laver indestructible. In fact, all these large cardinal properties are superdestructible: if κ exhibits any of them, with corresponding target θ, then in any forcing extension arising from nontrivial strategically <κ-closed forcing Q∈Vθ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} (...) \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{Q} \in V_\theta}$$\end{document}, the cardinal κ will exhibit none of the large cardinal properties with target θ or larger. (shrink)

We introduce the large-cardinal notions of ξ-greatly-Mahlo and ξ-reflection cardinals and prove (1) in the constructible universe, L, the first ξ-reflection cardinal, for ξ a successor ordinal, is strictly between the first ξ-greatly-Mahlo and the first Π1ξ-indescribable cardinals, (2) assuming the existence of a ξ-reflection cardinal κ in L, ξ a successor ordinal, there exists a forcing notion in L that preserves cardinals and forces that κ is (ξ+1)-stationary, which implies that the consistency strength of the existence of a (ξ+1)-stationary (...) cardinal is strictly below a Π1ξ-indescribable cardinal. These results generalize to all successor ordinals ξ the original same result of Mekler–Shelah [A. Mekler and S. Shelah, The consistency strength of every stationary set reflects, Israel J. Math.67(3) (1989) 353–365] about a 2-stationary cardinal, i.e. a cardinal that reflects all its stationary sets. (shrink)

Millikan and Her Critics offers a unique critical discussion of Ruth Millikan's highly regarded, influential, and systematic contributions to philosophy of mind and language, philosophy of biology, epistemology, and metaphysics. These newly written contributions present discussion from some of the most important philosophers in the field today and include replies from Millikan herself.

John is currently thinking that the sun is bright. Consider his occurrent belief or judgement that the sun is bright. Its content is that the sun is bright. This is a truth- evaluable content (which shall be our main concern) because it is capable of being true or false. In virtue of what natural, scientifically accessible facts does John’s judgement have this content? To give the correct answer to that question, and to explain why John’s judgement and other contentful mental (...) states have the contents they do in virtue of such facts, would be to naturalize mental content. (shrink)

Recent events around the globe reflect the tensions and ethical dilemmas of the postmodern, postcolonial and neocolonial world that have far reaching implications for health, well-being, and human suffering. As we consider what is at stake, and what this means for local lives and human relationships, we need to examine whether the theories we draw on are adequate to further our understanding of health, and the social and material conditions of human suffering. In this paper I begin to explore the (...) question, ‘Can postcolonial feminist theories provide an inclusive scholarship that would further our understanding of human suffering and open up a path to healing?’ At issue here is whether this scholarship adds another dimension to a praxis-oriented nursing science. (shrink)

Reductive, naturalistic psychosemantic theories do not have a good track record when it comes to accommodating the representation of kinds. In this paper, I will suggest a particular teleosemantic strategy to solve this problem, grounded in the neurocomputational details of the cerebral cortex. It is a strategy with some parallels to one that Ruth Millikan has suggested, but to which insufficient attention has been paid. This lack of attention is perhaps due to a lack of appreciation for the severity of (...) the problem, so I begin by explaining why the situation is indeed a dire one. One of the main tasks for a naturalistic psychosemantic theory is to describe how the extensions of mental representations are determined. (Such a theory may also attempt to account for other aspects of the “meaning” of mental representations, if there are any.) Some mental representations, e.g. the concept of water, denote kinds (I shall be assuming this is non-negotiable). How is this possible? Unfortunately, I haven’t the space to canvass all the theories out there and show that each one fails to accommodate the representation of kinds, but I will point out the major types of problems that arise for the kinds of theories that, judging by the literature, are considered viable contenders.1 In general, the theories either attempt and fail to account for the representation of kinds, or they fall back on something like an intention to refer to a kind – not exactly the most auspicious move for a reductive theory. There are a number of problems that prevent non-teleosemantic theories from explaining how it is possible to represent kinds. A concept of a kind K must.. (shrink)

We give a level-by-level analysis of the Weak Vopěnka Principle for definable classes of relational structures ( $\mathrm {WVP}$ ), in accordance with the complexity of their definition, and we determine the large-cardinal strength of each level. Thus, in particular, we show that $\mathrm {WVP}$ for $\Sigma _2$ -definable classes is equivalent to the existence of a strong cardinal. The main theorem (Theorem 5.11) shows, more generally, that $\mathrm {WVP}$ for $\Sigma _n$ -definable classes is equivalent to the existence of (...) a $\Sigma _n$ -strong cardinal (Definition 5.1). Hence, $\mathrm {WVP}$ is equivalent to the existence of a $\Sigma _n$ -strong cardinal for all $n<\omega $. (shrink)

Michel Foucault was at times critical of the Marxist tradition, and at other times more sympathetic. After his dismissal of Marx in The Order of Things , he conceded the existence of a more compelling, non-humanist version of this discourse. Louis Althusser’s innovations are crucial for the existence of this second Marxism. While consideration of the relation between Foucault and Althusser varies between those who emphasize relations between State and capital, and conversely those who inscribe Marxist considerations into a micro-political (...) account, the distinction between the two thinkers takes place earlier in the development of their respective outlooks. Foucault initially emphasized Marxism as an anthropological eschatology; he revises this argument, commending the possibility of an epistemological mutation of history inherent in Marx’s thought. I locate crucial distinctions between Foucault and Althusser in the early work of the 1960s as inflecting relations in the seemingly more proximate work of the 1970s. In this approach, we can better examine Foucault’s non-Marxist contentions in order to consider the reciprocal distinctions and contributions between these two forms of anti-humanism, providing the necessary groundwork for debates regarding the nature of subjectivity, the State, and revolution. (shrink)

We strengthen a result of Harrington and Shelah by showing that, unless ω1 is an inaccessible cardinal in L, a relatively weak fragment of Martin's axiom implies that there exists a δ13 set of reals without the property of Baire.

We give a sharper version of a theorem of Rosický, Trnková and Adámek [13], and a new proof of a theorem of Rosický [12], both about colimits in categories of structures. Unlike the original proofs, which use category-theoretic methods, we use set-theoretic arguments involving elementary embeddings given by large cardinals such as $\alpha$-strongly compact and $C^{(n)}$-extendible cardinals.

This study considers the potential for influencing business students to become ethical managers by directing their undergraduate learning environment. In particular, the relationship between business students’ academic cheating, as a predictor of workplace ethical behavior, and their approaches to learning is explored. The three approaches to learning identified from the students’ approaches to learning literature are deep approach, represented by an intrinsic interest in and a desire to understand the subject, surface approach, characterized by rote learning and memorization without understanding, (...) and strategic approach, associated with competitive students whose motivation is the achievement of good grades by adopting either a surface or deep approach. Consistent with the hypothesized theoretical model, structural equation modeling revealed that the surface approach is associated with higher levels of cheating, while the deep approach is related to lower levels. The strategic approach was also associated with less cheating and had a statistically stronger influence than the deep approach. Further, a significantly positive relationship reported between deep and strategic approaches suggests that cheating is reduced when deep and strategic approaches are paired. These findings suggest that future managers and business executives can be influenced to behave more ethically in the workplace by directing their learning approaches. It is hoped that the evidence presented may encourage those involved in the design of business programs to implement educational strategies which optimize students’ approaches to learning towards deep and strategic characteristics, thereby equipping tomorrow’s managers and business executives with skills to recognize and respond appropriately to workplace ethical dilemmas. (shrink)

We study the preservation under projective ccc forcing extensions of the property of L(ℝ) being a Solovay model. We prove that this property is preserved by every strongly-̰Σ₃¹ absolutely-ccc forcing extension, and that this is essentially the optimal preservation result, i.e., it does not hold for Σ₃¹ absolutely-ccc forcing notions. We extend these results to the higher projective classes of ccc posets, and to the class of all projective ccc posets, using definably-Mahlo cardinals. As a consequence we obtain an exact (...) equiconsistency result for generic absoluteness under projective absolutely-ccc forcing notions. (shrink)

RESUMEN:Este trabajo tiene por objeto analizar la articulación entre la afirmación del carácter racional de la fe, esto es, su dimensión latitudinaria, el escepticismo epistemológico, y su derivación práctica en un concepto de tolerancia restringido al interior del protestantismo. Se subrayará, en este sentido, el carácter estratégico de la articulación entre racionalidad de la fe y escepticismo, en cuanto permite apelar a la ignorancia con vistas a la tolerancia, sin por ello dejar de sostener la interpretación protestante del cristianismo, en (...) detrimento de la interpretación católica.PALABRAS CLAVE:LOCKE - LATITUDINARISMO - ESCEPTICISMO - TOLERANCIA - PROTESTANTISMOABSTRACT:This paper aims to analyze the articulation between faith rationality assertion, i.e. its latitudinarian aspect, its epistemological skepticism, and its practical implication in a restricted concept of tolerance within Protestantism. In this regard, we will emphasize the strategic feature of the link between faith rationality and skepticism, as it allows appealing to ignorance towards tolerance, without dropping the Protestant interpretation of Christianity, to the detriment of Catholic interpretation.KEYWORDS:LOCKE - LATITUDINARIANISM - SKEPTICISM - TOLERATION - PROTESTANTISM. (shrink)

Why do sociological theorists remain uninterested in and resistant to feminist theory? Notwithstanding indications of increasing openness to feminist theory, journals and texts on sociological theory reflect a continuing pattern of neglect. I identify reasons for this pattern, including tensions resulting from the introduction of gender as a central analytical category: Not only does gender challenge the dichotomous categories that define sociology's boundaries and identity, it also displaces the discipline's central problematic of modernity. The significance of this displacement is apparent (...) when the discipline's responses to feminist and postmodernist theory are compared. I discuss the relevance of feminist theoretical work to contemporary issues in sociological theory, with specific attention to the synthetic nature of feminist theorizing, to work on rethinking power, resistance, and oppression, and to efforts to effect a conceptual shift from "either/or" to "both/and" thinking and to establish new grounds for assessing knowledge claims. (shrink)

We explore the consistency strength of Σ 3 1 and Σ 4 1 absoluteness, for a variety of forcing notions.

We study the preservation of the property of being a Solovay model under proper projective forcing extensions. We show that every strongly-proper forcing notion preserves this property. This yields that the consistency strength of the absoluteness of under strongly-proper forcing notions is that of the existence of an inaccessible cardinal. Further, the absoluteness of under projective strongly-proper forcing notions is consistent relative to the existence of a -Mahlo cardinal. We also show that the consistency strength of the absoluteness of under (...) forcing extensions with σ-linked forcing notions is exactly that of the existence of a Mahlo cardinal, in contrast with the general ccc case, which requires a weakly-compact cardinal. (shrink)

This comprehensive collection, bringing together significant essays by leading philosophers of the twentieth century, represents one prominent school of American thought philosophic naturalism. Naturalism holds that nature is objective and can be studied to gain knowledge that is not determined by methodology, perspective, belief, or theory. For the naturalist, "nature" is an all-encompassing concept; nothing is other than natural and any notion of a supernatural realm is rejected. Naturalism, however, cannot be equated with materialistic reductionism or strict determinism. Certain nonmaterial (...) aspects of human existence thoughts, feelings, meanings, values, beliefs, ideals, and free will are included within the scope of the naturalist's approach. (shrink)

We study the projective posets and their properties as forcing notions. We also define Martin's axiom restricted to projective sets, MA, and show that this axiom is weaker than full Martin's axiom by proving the consistency of ZFC + ¬lCH + MA with “there exists a Suslin tree”, “there exists a non-strong gap”, “there exists an entangled set of reals” and “there exists κ < 20 such that 20 < 2k”.

This is both a small and a large book. In number of pages it is modest, but it aspires to sort through a very large topic indeed. One of the challenges for a naturalist theology, which is to say a naturalist conception of the divine, and perhaps more importantly of the sacred, is to resolve the obvious problem of accommodating as an element of nature an entity that has for the most part been understood as supernatural. Yalcin’s book attempts to (...) do just that. Though I have some misgivings about this and that detail, which I will mention below, Yalcin succeeds, I would say, in articulating a coherent, plausible, creative, and wholly interesting understanding of the sacred on strictly naturalist grounds.It is... (shrink)

We consider several kinds of partition relations on the set ${\mathbb{R}}$ of real numbers and its powers, as well as their parameterizations with the set ${[\mathbb{N}]^{\mathbb{N}}}$ of all infinite sets of natural numbers, and show that they hold in some models of set theory. The proofs use generic absoluteness, that is, absoluteness under the required forcing extensions. We show that Solovay models are absolute under those forcing extensions, which yields, for instance, that in these models for every well ordered partition (...) of ${\mathbb{R}^\mathbb{N}}$ there is a sequence of perfect sets whose product lies in one piece of the partition. Moreover, for every finite partition of ${[\mathbb{N}]^{\mathbb{N}} \times \mathbb{R}^{\mathbb{N}}}$ there is ${X \in [\mathbb{N}]^{\mathbb{N}}}$ and a sequence ${\{P_{k} : k \in \mathbb{N}\}}$ of perfect sets such that the product ${[X]^{\mathbb{N}} \times \prod_{k}^{\infty}P_{k}}$ lies in one piece of the partition, where ${[X]^{\mathbb{N}}}$ is the set of all infinite subsets of X. The proofs yield the same results for Borel partitions in ZFC, and for more complex partitions in any model satisfying a certain degree of generic absoluteness. (shrink)

In order to consider the influence of tangible property on the exercise of political rights in the work of John Locke, we’ll analyze, first, the distribution and acreage measurement of the requirements for political participation and the exercise of public functions in The Fundamental Constitutions of Carolina ; secondly, the considerations on land ownership, as a means of production, and the wage labor in Chapter V of Two Treatises of Government , II; finally, we’ll analyze the patrimonial restrictions for the (...) access to political rights, as well as the suggested participation for workers in Some Considerations of the Lowering of Interest, and Raising the Value of Money. (shrink)

There is good evidence that the cerebral cortex is the seat of the human mind, so an understanding of representation in the cortex could help us understand the nature of mental representation. I argue that the cortex represents in the way that models do; it is an evolutionarily designed model-building machine. The cortex belongs to a general class of model-building machines that produce isomorphisms to structures in the environment by interacting with them. The representational content of a particular model produced (...) by such a machine is determined by the operational principles according to which the machine was designed, and the history of machine-environment interaction that resulted in the production of that model. ;I explore the possibility that the operational principles according to which the cerebral cortex was designed, i.e. aspects of its causal profile that were selected for, are those described by the SINBAD theory. The SINBAD theory implies that it is the biological function of the cortex to make its constituent neurons come to interact in a way that is isomorphic to regularities structured around "sources of correlation". In the context of this isomorphism, it is the function of a particular SINBAD cell to correspond to a particular source of correlation, the one that is responsible for that cell's tuning. In other words, the cortex builds models of environmental regularities structured around sources of correlation. ;Understanding mental representation as cortical representation of this kind allows us to explain a number of important and/or puzzling features of mental intentionality as we know it: the possibility of equivocation, misrepresentation, empty representation, and twin cases, the relation between concepts and inferential roles, how it is possible for us to acquire objective concepts and beliefs via our subjective and idiosyncratic senses, and the distinction between usefulness and truth. I conclude by outlining an account of the occurrent propositional attitudes as non-representational uses of a SINBAD model that has been built up through experience. Non-representational use is cashed out in terms of causal role. Together with an account of the non-occurrent attitudes, this yields an understanding of the nature of psychological explanation. (shrink)

The central idea is that the cerebral cortex is a model building machine, where regularities in the world serve as templates for the models it builds. First it is shown how this idea can be naturalized, and how the representational contents of our internal models depend upon the evolutionarily endowed design principles of our model building machine. Current neuroscience suggests a powerful form that these design principles may take, allowing our brains to uncover deep structures of the world hidden behind (...) surface sensory stimulation, the individuals, kinds, and properties that form the objects of human perception and thought. It is then shown how this account solves various problems that arose for previous attempts at naturalizing intentionality, and also how it supports rather than undermines folk psychology. As in the parable of the blind men and the elephant, the seemingly unrelated pieces of earlier theories (information, causation, isomorphism, success, and teleology) emerge as different aspects of the evolved model-building mechanism that explains the intentional features of our kind of mind. (shrink)

Contemporary pragmatic naturalism -- Reconciling pragmatism and naturalism -- Value of pragmatic naturalism -- Being and knowing -- Ontology of constitutive relations -- Particulars and relations -- Making sense of world making -- God and faith -- Art and knowledge -- Social experience -- Democratic challenge -- Democracy and its problems -- International relations and foreign policy -- Cosmopolitanism and humanism -- Pragmatic, naturalism, and the big narrative.

The Things in Heaven and Earth develops and applies the American philosophical naturalist tradition of the mid-20th century, specifically the work of three of the most prominent figures of what is called Columbia Naturalism: John Dewey, John Herman Randall Jr., and Justus Buchler. The book argues for the philosophical value and usefulness of this underappreciated tradition for a number of contemporary theoretical and practical issues, such as the modernist/postmodernist divide and debates over philosophical constructivism. Pragmatic naturalism offers a distinctive ontology (...) of constitutive relations. Relying on Buchler's ordinal ontology and on the relationality implicit in Dewey's instrumentalism, the book gives a detailed account of this approach in chapters that deal with issues in systematic ontology, epistemology, constructivism and objectivity, philosophical theology, art, democratic theory, foreign policy, education, humanism, and cosmopolitanism. (shrink)

If A ⊆ ω1, then there exists a cardinal preserving generic extension [MATHEMATICAL DOUBLE-STRUCK CAPITAL L][A ][x ] of [MATHEMATICAL DOUBLE-STRUCK CAPITAL L][A ] by a real x such that1) A ∈ [MATHEMATICAL DOUBLE-STRUCK CAPITAL L][x ] and A is Δ1HC in [MATHEMATICAL DOUBLE-STRUCK CAPITAL L][x ];2) x is minimal over [MATHEMATICAL DOUBLE-STRUCK CAPITAL L][A ], that is, if a set Y belongs to [MATHEMATICAL DOUBLE-STRUCK CAPITAL L][x ], then either x ∈ [MATHEMATICAL DOUBLE-STRUCK CAPITAL L][A, Y ] or Y (...) ∈ [MATHEMATICAL DOUBLE-STRUCK CAPITAL L][A ].The forcing we use implicitly provides reshaping of the given set A. (shrink)

Angelaki, Volume 17, Issue 2, Page 31-48, June 2012.

This chapter contains section titles: Proper Functions Representations: The Basic Teleosemantic Framework Concepts Externalism, Language, and Meaning Rationalism.

We prove two general results about the preservation of extendible and $C^{(n)}$ -extendible cardinals under a wide class of forcing iterations (Theorems 5.4 and 7.5). As applications we give new proofs of the preservation of Vopěnka’s Principle and $C^{(n)}$ -extendible cardinals under Jensen’s iteration for forcing the GCH [17], previously obtained in [8, 27], respectively. We prove that $C^{(n)}$ -extendible cardinals are preserved by forcing with standard Easton-support iterations for any possible $\Delta _2$ -definable behaviour of the power-set function on (...) regular cardinals. We show that one can force proper class-many disagreements between the universe and HOD with respect to the calculation of successors of regular cardinals, while preserving $C^{(n)}$ -extendible cardinals. We also show, assuming the GCH, that the class forcing iteration of Cummings–Foreman–Magidor for forcing $\diamondsuit _{\kappa ^+}^+$ at every $\kappa $ [10] preserves $C^{(n)}$ -extendible cardinals. We give an optimal result on the consistency of weak square principles and $C^{(n)}$ -extendible cardinals. In the last section prove another preservation result for $C^{(n)}$ -extendible cardinals under very general (not necessarily definable or weakly homogeneous) class forcing iterations. As applications we prove the consistency of $C^{(n)}$ -extendible cardinals with $\mathrm {{V}}=\mathrm {{HOD}}$, and also with $\mathrm {GA}$ (the Ground Axiom) plus $\mathrm {V}\neq \mathrm {HOD}$, the latter being a strengthening of a result from [14]. (shrink)

We address Steel’s Programme to identify a ‘preferred’ universe of set theory and the best axioms extending $\mathsf {ZFC}$ by using his multiverse axioms $\mathsf {MV}$ and the ‘core hypothesis’. In the first part, we examine the evidential framework for $\mathsf {MV}$, in particular the use of large cardinals and of ‘worlds’ obtained through forcing to ‘represent’ alternative extensions of $\mathsf {ZFC}$. In the second part, we address the existence and the possible features of the core of $\mathsf {MV}_T$ (where (...) T is $\mathsf {ZFC}$ +Large Cardinals). In the last part, we discuss the hypothesis that the core is Ultimate-L, and examine whether and how, based on this fact, the Core Universist can justify V=Ultimate-L as the best (and ultimate) extension of $\mathsf {ZFC}$. To this end, we take into account several strategies, and assess their prospects in the light of $\mathsf {MV}$ ’s evidential framework. (shrink)

Recent evidence from the social neuroscience of empathy suggests that there is core neural circuitry underlying empathy in humans, and important roles for top—down and bottom—up processes in the production and regulation of empathic experience. Less well understood is how cultural and genetic forces give rise to empathy and prosocial behavior within and across groups. Here I argue that culture-gene coevolutionary theory may play an important role in understanding how and when empathy is experienced, and that future research in cultural (...) neuroscience is needed to understand how cultural and genetic factors shape empathic neural response. (shrink)

After discussing the limitations inherent to all set-theoretic reflection principles akin to those studied by A. Lévy et. al. in the 1960s, we introduce new principles of reflection based on the general notion of Structural Reflection and argue that they are in strong agreement with the conception of reflection implicit in Cantor’s original idea of the unknowability of the Absolute, which was subsequently developed in the works of Ackermann, Lévy, Gödel, Reinhardt, and others. We then present a comprehensive survey of (...) results showing that different forms of the new principle of Structural Reflection are equivalent to well-known large cardinal axioms covering all regions of the large-cardinal hierarchy, thereby justifying the naturalness of the latter. (shrink)