The Halpern–Läuchli theorem, a combinatorial result about trees, admits an elegant proof due to Harrington using ideas from forcing. In an attempt to distill the combinatorial essence of this proof, we isolate various partition principles about products of perfect Polish spaces. These principles yield straightforward proofs of the Halpern–Läuchli theorem, and the same forcing from Harrington’s proof can force their consistency. We also show that these principles are not ZFC theorems by showing that they put lower bounds on the size (...) of the continuum. (shrink)

What is addiction? Why do some people become addicted while others do not? Is the addict rational? In this book, Craig Hanson attempts to answer these questions and more. Using insights from the beginnings of philosophy to contemporary behavioral economics, Hanson attempts to assess the variety of ways in which we can and cannot, understand addiction. Special consideration is given to a challenging (and controversial) proposal dubbed “hyperbolic discounting.” Hanson proposes some modifications to the hyperbolic discounting view (...) that permit it to explain not only addiction, but also a variety of psychological maladies, such as self-deception. (shrink)

Generic language (e.g., “tigers have stripes”) leads children to assume that the referenced category (e.g., tigers) is inductively informative and provides a causal explanation for the behavior of individual members. In two preregistered studies with 4- to 7-year-old children (N = 497), we considered the mechanisms underlying these effects by testing how correcting generics might affect the development of these beliefs about novel social and animal kinds (Study 1) and about gender (Study 2). Correcting generics by narrowing their scope to (...) a single individual limited beliefs that the referenced categories could explain what their members would be like while broadening the scope to a superordinate category (Study 2) uniquely limited endorsement of gender norms. Across both studies, correcting generics did not alter beliefs about feature heritability and had mixed effects on inductive inferences, suggesting that additional mechanisms (e.g., causal reasoning about shared features) contribute to the development of full-blown essentialist beliefs. These results help illuminate the mechanisms by which generics lead children to view categories as having rich inductive and causal potential; in particular, they suggest that children interpret generics as signals that speakers in their community view the referenced categories as meaningful kinds that support generalization. The findings also point the way to concrete suggestions for how adults can effectively correct problematic generics (e.g., gender stereotypes) that children may hear in daily life. (shrink)

We have been discussing some of the fundamental features of the classical calculus of probability. The equiprobability of rival events was seen to be a major assumption of the calculus. Moreover, it is an assumption which the pure mathematician need not bother to justify. He need only present his formal system as follows.

The current studies (N = 255, children ages 4–5 and adults) explore patterns of age‐related continuity and change in conceptual representations of social role categories (e.g., “scientist”). In Study 1, young children's judgments of category membership were shaped by both category labels and category‐normative traits, and the two were dissociable, indicating that even young children's conceptual representations for some social categories have a “dual character.” In Study 2, when labels and traits were contrasted, adults and children based their category‐based induction (...) decisions on category‐normative traits rather than labels. Study 3 confirmed that children reason based on category‐normative traits because they view them as an obligatory part of category membership. In contrast, adults in this study viewed the category‐normative traits as informative on their own (not only as a cue to obligations). Implications for continuity and change in representations of social role categories will be discussed. (shrink)

Motivated by a characterization of weakly compact cardinals due to Todorcevic, we introduce a new cardinal characteristic, the C-sequence number, which can be seen as a measure of the compactness of a regular uncountable cardinal. We prove a number of ZFC and independence results about the C-sequence number and its relationship with large cardinals, stationary reflection, and square principles. We then introduce and study the more general C-sequence spectrum and uncover some tight connections between the C-sequence spectrum and the strong (...) coloring principle U(. . .), introduced in Part I of this series. (shrink)

We investigate questions involving Aronszajn trees, square principles, and stationary reflection. We first consider two strengthenings of introduced by Brodsky and Rinot for the purpose of constructing κ‐Souslin trees. Answering a question of Rinot, we prove that the weaker of these strengthenings is compatible with stationary reflection at κ but the stronger is not. We then prove that, if μ is a singular cardinal, implies the existence of a special ‐tree with a cf(μ)‐ascent path, thus answering a question of Lücke.

The Sickness unto Death is commonly regarded as one of Kierkegaard's most important works – but also as one of his most difficult texts to understand. It is a meditation on Christian existentialist themes including sin, despair, religious faith and its redemptive power, and the relation and difference between physical and spiritual death. This volume of new essays guides readers through the philosophical and theological significance of the work, while clarifying the complicated ideas that Kierkegaard develops. Some of the essays (...) focus closely on particular themes, others attempt to elucidate the text as a whole, and yet others examine it in relation to other philosophical views. Bringing together these diverse approaches, the volume offers a comprehensive understanding of this pivotal work. It will be of interest to those studying Kierkegaard as well as existentialism, religious philosophy, and moral psychology. (shrink)

The appearance and intensive development of a socialist orientation as a distinctive form of noncapitalist development of formerly oppressed countries and peoples are among the outstanding phenomena of our time and require the most serious theoretical and methodological interpretation. The national-democratic revolutions that have taken place in these countries have removed the bases of imperialist and feudal domination, interrupted the rise of capitalism at its earliest level, and embarked on a noncapitalist path of social progress. A gradual process bringing the (...) orientation toward socialism into convergence with a people's democratic development of society began in the course of radical reorganization of precapitalist or early capitalist structures. (shrink)

Viale introduced covering matrices in his proof that SCH follows from PFA. In the course of the proof and subsequent work with Sharon, he isolated two reflection principles, CP and S, which, under certain circumstances, are satisfied by all covering matrices of a certain shape. Using square sequences, we construct covering matrices for which CP and S fail. This leads naturally to an investigation of square principles intermediate between □κ and □ for a regular cardinal κ. We provide a detailed (...) picture of the implications between these square principles. (shrink)

A loose analogy relates the work of Laplace and Hilbert. These thinkers had roughly similar objectives. At a time when so much of our analytic effort goes to distinguishing mathematics and logic from physical theory, such an analogy can still be instructive, even though differences will always divide endeavors such as those of Laplace and Hilbert.

With all the research on mind/brain connections these days -- Your brain in lust or love! While gambling or feeling envious! While meditating, praying, or having an out-of-body experience! -- it’s natural to wonder about ’big questions’ about the relationships among the mind, the brain, and God. For instance, some people have taken the findings that some spiritual experiences have neural correlates to mean that the hand of God is at work in the brain. Others have interpreted the same research (...) to mean that spiritual experiences are "just" neural, and thus evidence against the existence of God or other supernatural forces. These debates are updated versions of longstanding philosophical and religious wrestlings with how God and nature might or might not intertwine. What’s your own gut view, right now, as a kind of snapshot: Do you think that God is involved in some way in your thoughts and feelings? In your most intimate sense of being? In this essay, we’ll explore what mind, brain, and. (shrink)

We continue our study of strongly unbounded colorings, this time focusing on subadditive maps. In Part I of this series, we showed that, for many pairs of infinite cardinals $\theta < \kappa $, the existence of a strongly unbounded coloring $c:[\kappa ]^2 \rightarrow \theta $ is a theorem of $\textsf{ZFC}$. Adding the requirement of subadditivity to a strongly unbounded coloring is a significant strengthening, though, and here we see that in many cases the existence of a subadditive strongly unbounded coloring (...) $c:[\kappa ]^2 \rightarrow \theta $ is independent of $\textsf{ZFC}$. We connect the existence of subadditive strongly unbounded colorings with a number of other infinitary combinatorial principles, including the narrow system property, the existence of $\kappa $ -Aronszajn trees with ascent paths, and square principles. In particular, we show that the existence of a closed, subadditive, strongly unbounded coloring $c:[\kappa ]^2 \rightarrow \theta $ is equivalent to a certain weak indexed square principle $\boxminus ^{\operatorname {\mathrm {ind}}}(\kappa, \theta )$. We conclude the paper with an application to the failure of the infinite productivity of $\kappa $ -stationarily layered posets, answering a question of Cox. (shrink)

[Anne:] “I can't, I'm in the depths of despair. Can you eat when you are in the depths of despair?”“I've never been in the depths of despair, so I can't say,” said Marilla.“Weren't you? Well did you ever try to imagine you were in the depths of despair?”” No, I didn't.”“Then I don't think you can understand what it's like. It's a very uncomfortable feeling indeed. When you try to eat a lump comes right up in your throat and you (...) can't swallow anything, not even if it was a chocolate caramel.”—L.M. Montgomery, Anne of Green Gables.Emotion, as a “suprarational” property, transcends rationality in that it can be thought of as a group, contextual rather than as a solely individual trait, and thus is a higher order property, as the above quote suggests. This proposal arises from a metatheoretical analysis of models available to broach questions of emotion. I use metatheoretical in the sense of both the context of theory production and the theory of theory. From the first arose the idea that emotion, through the use of irrationality, has surfaced as a working equivalent to inexplicability or rational relativity, and can be modelled more adequately as suprarational, with a unique nature in its own right. The latter led me to propose that the concept of emotion as contextual, a higher order group level property, is possible and tentatively profitable. (shrink)

How do people gather samples of evidence to learn about the world? Adults often prefer to sample evidence from diverse sources—for example, choosing to test a robin and a turkey to find out if something is true of birds in general. Children below age 9, however, often do not consider sample diversity, instead treating non‐diverse samples (e.g., two robins) and diverse samples as equivalently informative. The current study (N = 247) found that this discontinuity stems from developmental changes in standards (...) for evaluating evidence—younger children chose to learn from samples that best approximate idealized views of what category members are supposed to be like (e.g., the fastest cheetahs), with a gradual shift across age toward samples that cover more within‐category variation (e.g., cheetahs of varying speeds). These findings have implications for the relation between conceptual structure and inductive reasoning, and for the mechanisms underlying inductive reasoning more generally. (shrink)

Parallogic models the relationship between mind and context. It, as does the excerpt above, suggests that systems of logic are context specific and therefore parallel. This model points out that perceived departures in mental process, reasoning, may be more apparent than real. It also suggests a new way to conceive of mental illness by separating breakdowns in mental process from shifts in mental process.

When attempting to answer the question, in the context of clinical healthcare, one might be tempted to leap to either of two rather obvious, but seemingly contradictory conclusions. On the one hand, we might have a general impression of religion not making much of a distinctive and clear difference, at least in the actions and outcomes of most cases of clinical interaction. Those of us in the bioethics world of discourse are likely to think only of the less common cases (...) of Christian Scientists, Jehovah's Witnesses, Orthodox Jews, or certain religious groups who seem to the majority of the population to hold especially sectarian, if not beliefs about medical matters. The so-called mainstream religious groups do not get much attention because they largely don't cause much trouble ; they have learned to bracket their religious commitments from at least any professional settings ; or they don't hold views entailing consequences any different from those of most nonbelieving, generally upright individuals. Furthermore, although religious believers may have some distinctive views, these views don't often noticeably manifest themselves in distinctive or significant ways. (shrink)

We address three questions raised by Cummings and Foreman regarding a model of Gitik and Sharon. We first analyze the PCF-theoretic structure of the Gitik–Sharon model, determining the extent of good and bad scales. We then classify the bad points of the bad scales existing in both the Gitik–Sharon model and other models containing bad scales. Finally, we investigate the ideal of subsets of singular cardinals of countable cofinality carrying good scales.

In this paper I argue that there can be genuine (as opposed to merely verbal) disputes about whether a sentence form is logically true or an argument form is valid. I call such disputes ?cases of deviance?, of which I distinguish a weak and a strong form. Weak deviance holds if one disputant is right and the other wrong, but the available evidence is insufficient to determine which is which. Strong deviance holds if there is no fact of the matter. (...) In section 2 I argue that weak deviance need not be trivial and may even be interesting. Section 3 considers what it could mean to say that logic is determined by a theory, especially a theory of meaning, an idea that arises in section 2. In section 4 I discuss the dispute between classical and relevance logicians over entailment and argue that it is a case of strong deviance. Finally, in section 5 I show that the result of the previous section is not absolute but relative to the background logic used in reaching it. (shrink)

For Henry the question ‘Can the truth be learned?’ is as much an aporia as it was for Kierkegaard, and both thinkers ask this question not in order to solve some abstract or pedantic epistemological issue but because the truth they seek is the one that is appropriate to human beings and their salvation. This paper examines Henry’s and Kierkegaard’s answers to the question of how the truth is learned, and in the course of this examination will necessarily have occasion (...) to compare the two thinkers’ accounts of paradox and the phenomenality of Christ, two themes that bring into focus the nature of truth in both thinkers. The paper begins with an analysis of Henry’s theory of two truths, one of the world and the other of life. These two truths collide in the crucial eleventh chapter of I Am the Truth, which elucidates Henry’s understanding of paradox and the role it plays in his phenomenology. Finally, the paper entertains some questions for his theory that a Kierkegaardian might raise. Throughout it can be seen that despite his appreciation of Kierkegaard, Henry’s account of paradox and the specific mode of revelation that is appropriate to the Christ deviates from the Dane’s theory. Furthermore, it would seem that in a similar fashion their understandings of what counts as a paradox ultimately differ in such a way that Henry’s supposed paradoxes turn out to be by his own admission merely apparent, whereas for Kierkegaard (and perhaps in this respect his theory is a bit closer to ordinary intuitions about what it means for a truth to be paradoxical), paradox is an ineradicable feature of the highest kind of truth as reason confronts it. The thesis then that for Henry paradox and the tension between two kinds of truth are merely apparent whereas for Kierkegaard they are intensified is not merely of interest in establishing a proper reading of each respective thinker; it affects our understanding of the phenomenological notions of world, truth, and the absolute as well as establishing divergences of considerable theological interest. What is at stake is the exact status of the kind of truth phenomenology will privilege and the bearing that this question has upon the nature of the world and phenomenality. (shrink)

We give a formalism for approximate isomorphism in continuous logic simultaneously generalizing those of two papers by Ben Yaacov [2] and by Ben Yaacov, Doucha, Nies, and Tsankov [6], which are largely incompatible. With this we explicitly exhibit Scott sentences for the perturbation systems of the former paper, such as the Banach‐Mazur distance and the Lipschitz distance between metric spaces. Our formalism is simultaneously characterized syntactically by a mild generalization of perturbation systems and semantically by certain elementary classes of two‐sorted (...) structures that witness approximate isomorphism. As an application, we show that the theory of any ‐tree or ultrametric space of finite radius is stable, improving a result of Carlisle and Henson [8]. (shrink)

A way to a self-consistent physically acceptable formulation of quantum gravity field theory is found. The simplified model of quantized conformally-flat gravity and a massive scalar field is analyzed.

Workplace incivility is a current challenge in organizations, including smaller firms, as is the development of programs that enhance employees’ treatment of coworkers and ethical decision making. Ethics programs in particular might attenuate tendencies toward interpersonal misconduct, which can harm ethical reasoning. Consequently, this study evaluated the relationships among the presence of ethics codes and employees’ locus of control, social aversion/malevolence, and ethical judgments of incivility using information secured from a sample of businesspersons employed in smaller organizations. Results indicated that (...) ethics code presence was associated with a more internal locus of control and stronger ethical judgment of workplace incivility. Social aversion/malevolence was negatively related to ethical judgment, and internal locus of control was positively related to ethical judgment. Smaller firms should develop ethics codes to manage individuals’ perceptions of control, thus encouraging enhanced ethical reasoning in situations that involve the mistreatment of coworkers; they should also monitor counterproductive tendencies that harm such reasoning and precipitate incivility. (shrink)

Reverse inference in cognitive neuropsychology has been characterized as inference to ‘psychological processes’ from ‘patterns of activation’ revealed by functional magnetic resonance or other scanning techniques. Several arguments have been provided against the possibility. Focusing on Machery’s presentation, we attempt to clarify the issues, rebut the impossibility arguments, and propose and illustrate a strategy for reverse inference. 1 The Problem of Reverse Inference in Cognitive Neuropsychology2 The Arguments2.1 The anti-Bayesian argument3 Patterns of Activation4 Reverse Inference Practiced5 Seek and Ye Shall (...) Find, Maybe6 Conclusion. (shrink)

We introduce a natural two-cardinal version of Bagaria’s sequence of derived topologies on ordinals. We prove that for our sequence of two-cardinal derived topologies, limit points of sets can be characterized in terms of a new iterated form of pairwise simultaneous reflection of certain kinds of stationary sets, the first few instances of which are often equivalent to notions related to strong stationarity, which has been studied previously in the context of strongly normal ideals. The non-discreteness of these two-cardinal derived (...) topologies can be obtained from certain two-cardinal indescribability hypotheses, which follow from local instances of supercompactness. Additionally, we answer several questions posed by the first author, Holy and White on the relationship between Ramseyness and indescribability in both the cardinal context and in the two-cardinal context. (shrink)