An outline is given of the proof that the consistency of a κ⁺-Mahlo cardinal implies that of the statement that I[ω₂] does not include any stationary subsets of Cof(ω₁). An additional discussion of the techniques of this proof includes their use to obtain a model with no ω₂-Aronszajn tree and to add an ω₂-Souslin tree with finite conditions.

Continuing William Mitchell's investigations of how we understand, reason about, anduse images, The Reconfigured Eye provides the first systematic, critical analysis of the digitalimaging revolution.

In [4], Kunen used iterated ultrapowers to show that ifUis a normalκ-complete nontrivial ultrafilter on a cardinalκthenL[U], the class of sets constructive fromU, has only the ultrafilterU∩L[U] and this ultrafilter depends only onκ. In this paper we extend Kunen's methods to arbitrary sequencesUof ultrafilters and obtain generalizations of these results. In particular we answer Problem 1 of Kunen and Paris [5] which asks whether the number of ultrafilters onκcan be intermediate between 1 and 22κ. If there is a normalκ-complete ultrafilterUonκsuch (...) that {α <κ: α is measurable} ∈Uthen there is an inner model with exactly two normal ultrafilters onκ, and ifκis super-compact then there are inner models havingκ+ +,κ+or any cardinal less than or equal toκnormal ultrafilters.These methods also show that several properties ofLwhich had been shown to hold forL[U] also hold forL[U]: using an idea of Silver we show that inL[U] the generalized continuum hypothesis is true, there is a Souslin tree, and there is awell-ordering of the reals. In addition we generalize a result of Kunen to characterize the countaby complete ultrafilters ofL[U]. (shrink)

We give a short proof of a lemma which generalizes both the main lemma from the original construction in the author’s thesis of a model with no ω2-Aronszajn trees, and also the “Key Lemma” in Hamkins’ gap forcing theorems. The new lemma directly yields Hamkins’ newer lemma stating that certain forcing notions have the approximation property.

We use a $\kappa^{+}-Mahlo$ cardinal to give a forcing construction of a model in which there is no sequence $\langle A_{\beta} : \beta \textless \omega_{2} \rangle$ of sets of cardinality $\omega_{1}$ such that $\{\lambda \textless \omega_{2} : \existsc \subset \lambda & (\bigcupc = \lambda otp(c) = \omega_{1} & \forall \beta \textless \lambda (c \cap \beta \in A_{\beta}))\}$ is stationary.

We prove several results giving lower bounds for the large cardinal strength of a failure of the singular cardinal hypothesis. The main result is the following theorem: Theorem. Suppose κ is a singular strong limit cardinal and 2κ λ where λ is not the successor of a cardinal of cofinality at most κ. If cf > ω then it follows that o λ, and if cf = ωthen either o λ or {α: K o α+n} is confinal in κ for (...) each n ε ω.We also prove several results which extend or are related to this result, notably Theorem. If 2ω ω1 then there is a sharp for a model with a strong cardinal.In order to prove these theorems we give a detailed analysis of the sequences of indiscernibles which come from applying the covering lemma to nonoverlapping sequences of extenders. (shrink)

If there is no inner model with a cardinal κ such that o(κ) = κ ++ then the set K ∩ H ω 1 is definable over H ω 1 by a Δ 4 formula, and the set $\{J_\alpha[\mathscr{U}]: \alpha of countable initial segments of the core model K = L[U] is definable over H ω 1 by a Π 3 formula. We show that if there is an inner model with infinitely many measurable cardinals then there is a model (...) in which $\{J_\alpha [\mathscr{U}]: \alpha is not definable by any Σ 3 formula, and K ∩ H ω 1 is not definable by any boolean combination of Σ 3 formulas. (shrink)

We reprove Gitik's theorem that if the GCH holds and o(κ) = κ + 1 then there is a generic extension in which κ is still measurable and there is a closed unbounded subset C of κ such that every $\nu \in C$ is inaccessible in the ground model. Unlike the forcing used by Gitik. the iterated forcing $R_{\lambda +1}$ used in this paper has the property that if λ is a cardinal less then κ then $R_{\lambda + 1}$ can (...) be factored in V as $R_{\kappa + 1} = R_{\lambda + 1} \times R_{\lambda + 1, \kappa}$ where $\mid R_{\lambda +1}\mid \leq \lambda^+$ and $R_{\lambda + 1, \kappa}$ does not add any new subsets of λ. (shrink)

Mitchell, W.J., An infinitary Ramsey property, Annals of Pure and Applied Logic 57 151–160. We prove that the consistency of a measurable cardinal implies the consistency of a cardinal κ>+ satisfying the partition relations κ ω and κ ωregressive. This result follows work of Spector which uses the same hypothesis to prove the consistency of ω1 ω. We also give some examples of partition relations which can be proved for ω1 using the methods of Spector but cannot be proved (...) for cardinals κ>+ without a much stronger hypothesis. (shrink)

Assume that there is no transitive class model of [Formula: see text] with a Woodin cardinal. Let [Formula: see text] be a singular ordinal such that [Formula: see text] and [Formula: see text]. Suppose [Formula: see text] is a regular cardinal in K. Then [Formula: see text] is a measurable cardinal in K. Moreover, if [Formula: see text], then [Formula: see text].

Woodin has shown that if there is a measurable Woodin cardinal then there is, in an appropriate sense, a sharp for the Chang model. We produce, in a weaker sense, a sharp for the Chang model using only the existence of a cardinal \ having an extender of length \.

This article addresses five research questions: What specific behaviors are described in the literature as ethical or unethical? What percentage of business people are believed to be guilty of unethical behavior? What specific unethical behaviors have been observed by bank employees? How serious are the behaviors? Are experiences and attitudes affected by demographics? Conclusions suggest: There are seventeen categories of behavior, and that they are heavily skewed toward internal behaviors. Younger employees have a higher level of ethical consciousness than older (...) employees. The longer one works for a company, the more one may look to job security as a priority; this can lead to rationalizing or overlooking apparently unethical behaviors. More emphasis is needed on internal behaviors with particular attention on the impact that external behaviors have on internal behaviors. (shrink)

These essays represent an important contribution to modern philosophical theology. They begin with an appreciation of Basil Mitchell's work and then discuss the role of reason in the justification of Christian theism, giving special attention to the nature of informal reasoning in religion and science. The latter essays examine particular arguments raised by specific religious concepts, covering such topics as the problem of evil, conspicuous sanctity, atonement, and the Eucharist. Drawn from a wide spectrum of philosophers and theologians, the (...) contributors include Maurice Wiles, Grace M. Jantzen, Gordon Kaufman, J.R. Lucas, Rom Harr'e, Richard Swinburne, and Michael Dummett. (shrink)

Lower subjective socioeconomic status (SSS) and higher personal relative deprivation (PRD) relate to poorer health. Both constructs concern people’s perceived relative social position, but they differ in their emphasis on the reference groups people use to determine their comparative disadvantage (national population vs. similar others) and the importance of resentment that may arise from such adverse comparisons. We investigated the relative utility of SSS and PRD as predictors of self-rated physical and mental health (e.g., self-rated health, stress, health complaints). Across (...) 6 studies, self-rated physical and mental health were on the whole better predicted by measures of PRD than by SSS while controlling for objective socioeconomic status (SES), with SSS rarely contributing unique variance over and above PRD and SES. Studies 4 to 6 discount the possibility that the superiority of PRD over SSS in predicting health is due to psychometric differences (e.g., reliability) or response biases between the measures. (shrink)

Despite the salient experience of encoding threatening events, these memories are prone to distortions and often non-veridical from encoding to recall. Further, threat has been shown to preferentially disrupt the binding of event details and enhance goal-relevant information. While extensive work has characterised distinctive features of emotional memory, research has not fully explored the influence threat has on temporal memory, a process putatively supported by the binding of event details into a temporal context. Two primary competing hypotheses have been proposed; (...) that threat can impair or enhance temporal memory. We analysed two datasets to assess temporal memory for an in-person haunted house experience. In study 1, we examined the temporal structure of memory by characterising memory contiguity in free recall as a function of individual levels of heart rate as a proxy of threat. In study 2, we replicated marginal findings of threat-related increases in memory contiguity found in study 1. We extended these findings by showing threat-related increases in recency discriminations, an explicit test of temporal memory. Together, these findings demonstrate that threat enhances temporal memory regarding free recall structure and during explicit memory judgments. (shrink)

This state-of-the-art overview reflects the rich variety of approaches and disciplines embraced by contemporary communication studies. The book consists of thirteen original essays by some of the most prominent communication scholars, including Ien Ang, Deidre Boden, David Crowley, James M. Collins, Klaus Krippendorff, William Leiss, Denis McQuail, William Melody, Joshua Meyrowitz, David Mitchell, Mark Poster, Majid Tehranian, John B. Thompson and Teun A. van Dijk.

A tension between perspectives that emphasize deterministic versus stochastic processes has sparked controversy in ecology since pre-Darwinian times. The most recent manifestation of the contrasting perspectives arose with Hubbell’s proposed “neutral theory”, which hypothesizes a paramount role for stochasticity in ecological community composition. Here we shall refer to the deterministic and the stochastic perspectives as the niche-based and neutral-based research programs, respectively. Our goal is to represent these perspectives in the context of Lakatos’ notion of a scientific research program. We (...) argue that the niche-based program exhibits all the characteristics of a robust, progressive research program, including the ability to deal with disconfirming data by generating new testable predictions within the program. In contrast, the neutral-based program succeeds as a mathematical tool to capture, as epiphenomena, broad-scale patterns of ecological communities but appears to handle disconfirming data by incorporating hypotheses and assumptions from outside the program, specifically, from the niche-based program. We conclude that the neutral research program fits the Lakatosian characterization of a degenerate research program. (shrink)

This volume brings together eminent theologians, philosophers and political theorists to discuss such questions as how religious understandings have shaped the moral landscape of contemporary culture; the possible contributions of theology and theologically informed moral argument to contemporary public life; the problem of religious and moral discourse in a pluralistic society; and the proper relationship between religion and culture.

The study of anarchism as a philosophical, political, and social movement has burgeoned both in the academy and in the global activist community in recent years. Taking advantage of this boom in anarchist scholarship, Nathan J. Jun and Shane Wahl have compiled twenty-six cutting-edge essays on this timely topic in New Perspectives on Anarchism.

If there is no inner model with a cardinal $\kappa$ such that $o = \kappa^{++}$ then the set $K \cap H_{\omega_1}$ is definable over H$_{\omega_1}$ by a $\Delta_4$ formula, and the set $\{J_\alpha[\mathscr{U}] : \alpha < \omega_1\}$ of countable initial segments of the core model $K = L[\mathscr{U}]$ is definable over $H_{\omega_1}$ by a $\Pi_3$ formula. We show that if there is an inner model with infinitely many measurable cardinals then there is a model in which $\{J_\alpha [\mathscr{U}] : \alpha (...) < \omega_1\}$ is not definable by any $\Sigma_3$ formula, and $K \cap H_{\omega_1}$ is not definable by any boolean combination of $\Sigma_3$ formulas. (shrink)

Can poem and picture collaborate successfully in a composite art of text and design? Or does one art inevitably dominate the other? W.J.T. Mitchell maintains that Blake's illuminated poems are an exception to Suzanne Langer's claim that "there are no happy marriages in art—only successful rape." Drawing on over one hundred reproductions of Blake's pictures, this book shows that neither the graphic nor the poetic aspect of his composite art consistently predominates: their relationship is more like an energetic rivalry, (...) a dialogue between vigorously independent modes of expression. W.J.T. Mitchell is Professor of English and Art and Design at the University of Chicago and editor of Critical Inquiry. Originally published in 1978. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

Over the last two decades J.N. Williams has developed an account of the absurdity of such utterances as Its raining but I dont believe it that is both intuitively plausible and applicable to a wide variety of forms that this so-called Moorean absurdity can take. His approach is also noteworthy for making only minimal appeal to principles of epistemic or doxastic logic in its account of such absurdity. We first show that Williams places undue emphasis upon assertion and belief: It (...) is similarly absurd for a person to accept a proposition P as a supposition for the sake of argument while denying that her state of mind is one of supposing P, yet Williams has no account of this. Williams approach is then modified to account for such a case. That modification employs a principle of doxastic logic that is at least plausible as the one on which Williams relies, while being unlike his principle in applying to cases other than belief. (shrink)

This letter responds to the essay “Securing the Trustworthiness of the FDA to Build Public Trust in Vaccines,” by Leah Z. Rand, Daniel P. Carpenter, Aaron S. Kesselheim, Anushka Bhaskar, Jonathan J. Darrow, and William B. Feldman, in the special report “Time to Rebuild: Essays on Trust in Health Care and Science,” in the September‐October 2023 issue of the Hastings Center Report.

Supervaluationism is often described as the most popular semantic treatment of indeterminacy. There’s little consensus, however, about how to fill out the bare-bones idea to include a characterization of logical consequence. The paper explores one methodology for choosing between the logics: pick a logic thatnorms beliefas classical consequence is standardly thought to do. The main focus of the paper considers a variant of standard supervaluational, on which we can characterizedegrees of determinacy. It applies the methodology above to focus ondegree logic. (...) This is developed first in a basic, single-premise case; and then extended to the multipremise case, and to allowdegreesof consequence. The metatheoretic properties of degree logic are set out. On the positive side, the logic is supraclassical—all classical valid sequents are degree logic valid. Strikingly, metarules such as cut and conjunction introduction fail. (shrink)

The authors respond to a letter by Mitchell Berger in the March‐April 2024 issue of the Hastings Center Report concerning their essay “Securing the Trustworthiness of the FDA to Build Public Trust in Vaccines.”.

Cognitive science is an interdisciplinary research endeavor focusing on human cognitive phenomena such as memory, language use, and reasoning. It emerged in the second half of the 20th century and is charting new directions at the beginning of the 21st century. This chapter begins by identifying the disciplines that contribute to cognitive science and reviewing the history of the interdisciplinary engagements that characterize it. The second section examines the role that mechanistic explanation plays in cognitive science, while the third focuses (...) on the importance of mental representations in specifically cognitive explanations. The fourth section considers the interdisciplinary nature of cognitive science and explores how multiple disciplines can contribute to explanations that exceed what any single discipline might accomplish. The conclusion sketches some recent developments in cognitive science and their implications for philosophers. (shrink)