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)

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)

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)

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)

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.

Community ecology entered the 1970s with the belief that niche theory would supply a general theory of community structure. The lack of wide-spread empirical support for niche theory led to a focus on models specific to classes of communities such as lakes, intertidal communities, and forests. Today, the needs of conservation biology for metrics of “ecological health” that can be applied across types of communities prompts a renewed interest in the possibility of general theory for community ecology. Disputes about the (...) existence of general patterns in community structure trace at least to the 1920s and continue today almost unchanged in concept, although now expressed through mathematical modeling. Yet, a new framework emerged in the 1980s from findings that community composition and structure depend as much on the processes that bring species to the boundaries of a community as by processes internal to a community, such as species interactions and co-evolution. This perspective, termed “supply-side ecology”, argued that community ecology was to be viewed as an “organic earth science” more than as a biological science. The absence of a general theory of the earth would then imply a corresponding absence of any general theory for the communities on the earth, and imply that the logical structure of theoretical community ecology would consist of an atlas of models special to place and geologic time. Nonetheless, a general theory of community ecology is possible similar in form to the general theory for evolution if the processes that bring species to the boundary of a community are analogized to mutation, and the processes that act on the species that arrive at a community are analogized to selection. All communities then share some version of this common narrative, permitting general theorems to be developed pertaining to all ecological communities. Still, the desirability of a general theory of community ecology is debatable because the existence of a general theory suppresses diversity of thought even as it allows generalizations to be derived. The pros and cons of a general theory need further discussion. (shrink)

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)

Ethicists and others who study and teach the social implications of science and technology are faced with a formidable challenge when they seek to address “emerging technologies.” The topic is incredibly important, but difficult to grasp because not only are the precise issues often unclear, what the technology will ultimately look like can be difficult to discern. This paper argues that one particularly useful way to overcome these difficulties is to engage with their natural science and engineering colleagues in laboratories. (...) Through discussions and interactions with these colleagues ethicists can simultaneously achieve three important objectives. First they can get a great deal of assistance in their research into the social implications of future technologies by talking with people that are actively creating those futures. Second their presence in the lab and the discussions that result can be a very powerful method for educating not only students, but faculty about the ramifications of their work. And third, because the education is directly linked to the students’ everyday work it is likely that it will not just be a theoretical exercise, but have direct impact on their practice. (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)

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)

Frege is celebrated as an arch-Platonist and arch-realist. He is renowned for claiming that truths of arithmetic are eternally true and independent of us, our judgments and our thoughts; that there is a third realm containing nonphysical objects that are not ideas. Until recently, there were few attempts to explicate these renowned claims, for most philosophers thought the clarity of Frege's prose rendered explication unnecessary. But the last ten years have seen the publication of several revisionist interpretations of Frege's writings (...) — interpretations on which these claims receive a very different reading. In Frege on Knowing the Third Realm, Tyler Burge attempts to undermine this trend. Burge argues that Frege is the very Platonist most have thought him — that revisionist interpretations of Frege's Platonism, mine among them, run afoul of the words on Frege's pages. This paper is a response to Burge's criticisms. I argue that my interpretation is more faithful than Burge's to Frege's texts. (shrink)

Does Frege have a metatheory for his logic? There is an obvious and uncontroversial sense in which he does. Frege introduces and discusses his new logic in natural language; he argues, in response to criticisms of Begriffsschrift, that his logic is superior to Boole's by discussing formal features of both systems. In so far as the enterprise of using natural language to introduce, discuss, and argue about features of a formal system is metatheoretic, there can be no doubt: Frege has (...) a metatheory. There is also an obvious and uncontroversial sense in which Frege does not have a metatheory for his logic. The model theoretic semantics with which we are familiar today are a post-Fregean development. The question I address in this paper is, does Frege have a metatheory in the following sense: do his justifications of his basic laws and rules of inference employ, or even require, ineliminable use of a truth predicate and metalinguistic variables? My answer is ‘no’ on both counts. I argue that Frege neither uses, nor has any need to use, a truth predicate or metalinguistic variables in his justifications of his basic laws and rules of inference. Quine's famous explanation of the need for semantic ascent simply does not apply to Frege's logic. The purpose of the discussions that are typically understood as constituting Frege's metatheory is, rather, elucidatory. And once we see what the aim of these particular elucidations is, we can explain Frege's otherwise puzzling eschewal of the truth predicate in his discussions of the justification of the laws and rules of inference. (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”.

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)

This article briefly outlines some of the key problems with the way in which the moral realm has traditionally been understood and analysed. I propose two alternative views of what is morally interesting and applicable to nursing practice and I indicate that instability has its upsides. I begin with a moral tale – a 'Good Samaritan' story – which raises fairly usual questions about the nature of morality but also the more philosophically fundamental question about the relationship between subjectivity and (...) moral agency. I then consider this relationship from the perspectives of two twentieth century philosophers: Emmanuel Levinas and Michel Foucault. Levinas' basic point is that the experience of ethical subjectivity is made possible through others: the demand to respond to the existence of others is the basic social structure that precedes individual freedom. If Levinas posits intersubjectivity as a fundamental or primitive feature of the moral realm, Foucault poses an even more basic question: how have moral subjects and relations of obligation been constituted? The aim of ethical inquiry, for Foucault, is to describe the network of discourses, institutions, relations, and practices through which certain kinds of subjects are constituted and constitute themselves, e.g. as a kind of person who can act morally. Finally, I consider some recent research in philosophy of nursing which illustrates how Levinasian and/or Foucauldian perspectives can deepen understanding of nurses' moral practices, specifically, the work of Norwegian public health nurses, Canadian pediatric nurses, and Irish midwives. I suggest that in spite of the instability of morality in general and the particular ethical challenges that face nurses, there are grounds for hope and possible strategies for living in unstable times. (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)

Why did Frege look for the foundations of arithmetic in logic? Robin Jeshion has argued against several proposed answers, mine among them, and offered one of her own. In response, I argue that (i) Jeshion's own interpretation does not work: it is unsupported by the text and fails to answer the question; (ii) while it is not my view that Frege is motivated solely by philosophical concerns, his motivation cannot be divorced from his belief that foundations for science must show (...) whether its truths are analytic or synthetic, a priori or a posteriori; (iii) it must (for Frege) be evident from the content of a primitive truth to which of these categories the truth belongs. (shrink)

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

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)

Philosophical inquiries into the nature of consciousness have long been intrinsically tied to questions regarding the nature of the self. Although philosophers of mind seldom make reference to the role of cultural context in shaping consciousness, since antiquity culture has played a notable role in philosophical conceptions of the self. Western philosophers, from Plato to Locke, have emphasized an individualistic view of the self that is autonomous and consistent across situations, while Eastern philosophers, such as Lao Tzu and Confucius, have (...) argued for a collectivistic view of the self, one that is interconnected to others and embedded within specific social contexts and situations. Here we argue that a comprehensive theory of consciousness needs to account for the role of cultural context and its bidirectional interaction with neural and genetic mechanisms in shaping a variety of conscious phenomena, from visual perception to self- awareness. We review recent evidence of cultural variation in neurobiological mechanisms underlying these phenomena and discuss the implications of these cultural neuroscience findings for the study of consciousness. (shrink)

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)

I argued that Frege does not have a metatheory in the following sense: the justifications he offers for his basic laws and rules of inference neither employ nor require a truth-predicate or metalinguistic variables. In ‘Does Frege Use a Truth-predicate in his "Justification" of the Laws of Logic?’, Dirk Greimann disputes this. As Greimann interprets Frege, (i) Frege's remarks commit him to giving a metatheoretic justification of the basic laws and rules of his logic, and (ii) Frege actually gives such (...) a justification in the early sections of Grundgesetze—although the truth-predicate that Frege employs is a non-standard one: it is neither a predicate that holds of all and only true sentences nor a predicate that holds of all and only true thoughts. I argue that Greimann's interpretation is not, in the end, true to the text, and that his non-standard view of what is required of a Tarskian truth-predicate is ultimately not viable. (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)