We show that it is consistent, relative to n ∈ ω supercompact cardinals, for the strongly compact and measurable Woodin cardinals to coincide precisely. In particular, it is consistent for the first n strongly compact cardinals to be the first n measurable Woodin cardinals, with no cardinal above the n th strongly compact cardinal being measurable. In addition, we show that it is consistent, relative to a proper class of supercompact cardinals, for the strongly compact cardinals and the cardinals which (...) are both strong cardinals and Woodin cardinals to coincide precisely. We also show how the techniques employed can be used to prove additional theorems about possible relationships between Woodin cardinals and strongly compact cardinals. (shrink)

Greek Papyri in the British Museum: Catalogue, Vol. III. Edited by F. G. Kenyon and H. I. Bell. London: H. Frowde and others, 1907. Pp. lxxiv+388. 100 Collotype Facsimiles, in Portfolio. £2 2s.

Before establishing his mature interpretation of infinitesimals as fictions, Gottfried Leibniz had advocated their existence as actually existing entities in the continuum. In this paper I trace the development of these early attempts, distinguishing three distinct phases in his interpretation of infinitesimals prior to his adopting a fictionalist interpretation: (i) (1669) the continuum consists of assignable points separated by unassignable gaps; (ii) (1670-71) the continuum is composed of an infinity of indivisible points, or parts smaller than any assignable, with no (...) gaps between them; (iii) (1672- 75) a continuous line is composed not of points but of infinitely many infinitesimal lines, each of which is divisible and proportional to a generating motion at an instant (conatus). In 1676, finally, Leibniz ceased to regard infinitesimals as actual, opting instead for an interpretation of them as fictitious entities which may be used as compendia loquendi to abbreviate mathematical reasonings. (shrink)

Blessed be the Lord God of Israel, for he has visited his people, he has come to their rescue and he has raised up a power for salvation in the House of his servant David.” Thus exclaimed the Lanercost chronicler after recounting the glorious deeds of King Edward III at Crécy and Calais in 1346–47. By the middle years of his reign Edward was already commonly seen as the divinely inspired instrument of English salvation, the epitome of Old Testament kingship, (...) and an exemplar for Christian princes. English writers and artists made enthusiastic comparisons with Samson and David, with Arthur and Charlemagne. Edward was frequently portrayed as the great boar which, according to certain well-known political prophecies, would subdue England's enemies and restore the kingdom to its former greatness. (shrink)

The narrative ethicist imagines life as multiple points of view, each reflecting a distinct imagination and each more or less capable of comprehending other points of view and how they imagine. Each point of view is constantly being acted out and then modified in response to how others respond. People generally have good intentions, but they get stuck realizing those intentions. Stories stall when dialogue breaks down. People stop hearing others' stories, maybe because those others have quit telling their stories. (...) The narrative ethicist's job is to help people generate new imaginations that can restart dialogues. (shrink)

Studies in philosophy: I. Tufts, J.H. On moral evolution. II. Willcos, W.F. The expansion of Europe in its influence upon population. III. Woods, R.A. Democracy a new unfolding of human power. IV. Sharp, F.C. An analysis of the moral judgment. V. Woodbridge, F.J.E. The problem of consciousness. VI. Norton, E.L. The intellectual element in music. VII. Raub, W.L. Pragmatism and Kantianism. VIII. Lyman, E.W. The influence of pragmatism upon the status of theology.--Studies in psychology: IX. Delabarre, E.B. Influence of surrounding (...) objects on the apparent direction of a line. X. Swift, E.J. Beginning a language; a contribution to the psychology of learning. XI. Pierce, A.H. An appeal from the prevailing doctrine of a detached subconsciousness. XII. Woodworth, R.S. The cause of a voluntary movement. XIII. Burnett, C.T. An experimental test of the classical theory of volition. (shrink)

This commentary discusses 12 stories about receiving ethics consultation in hospitals. Five stories are by physicians, three by nurses, and four by family members; three of the writers have training in bioethics. Some writers requested the consultation, others experienced the consultation as an imposition forced upon them, and in two cases, the story is about the absence of any consultation service. Three types of narrative are found to structure the stories: the genuine dilemma narrative, the institutional intransigence narrative, and the (...) relational care narrative. Throughout, the question is what makes for a valuable consultation, and the general answer is whether consultation enables the development of mutually supportive relationships. (shrink)

Peer review is a topic of considerable concern to many researchers, and there is a correspondingly large body of research on the topic. This issue of Science and Engineering Ethics presents recent work on peer review that is both grounded in empirical science and is applicable to policy decisions. This research raises two basic questions; (a) how does current peer review operate, and (b) how can it be improved? Topics addressed include descriptions of how peer review is used in Federal (...) agencies. whether peer review leads to better manuscripts, demographic characteristics of authors or reviewers (status or institutional affiliation), blinding of reviewers, authors, or results, reliability and consistency of reviews, accepting a paper before the study is done, simultaneous submission, and use of dispute resolution procedures such as scientific dialectical and pleading protocols. (shrink)

This essay discusses how two physicians in Britain's National Health Service describe and analyze the conditions of their work: how algorithms and protocols structure the care they can provide and create the dilemmas they and their patients face. In these issues, the NHS is a canary in the mineshaft of contemporary Western health care. NHS practices are understood as how states and state-like entities, Leviathans, seek to render their subjects _legible_; in this instance, to make both physicians and patients transparently (...) visible to surveillance and administration by standardizing medical work and patient need. Physicians respond by engaging in workarounds, finding ways to provide care despite systemic restrictions. (shrink)

. From a proper class of supercompact cardinals, we force and obtain a model in which the proper classes of strongly compact and strong cardinals precisely coincide. In this model, it is the case that no strongly compact cardinal \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\kappa$\end{document} is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $2^\kappa = \kappa^+$\end{document} supercompact.

Contemporary health care often lacks generosity of spirit, even when treatment is most efficient. Too many patients are left unhappy with how they are treated, and too many medical professionals feel estranged from the calling that drew them to medicine. Arthur W. Frank tells the stories of ill people, doctors, and nurses who are restoring generosity to medicine--generosity toward others and to themselves. The Renewal of Generosity evokes medicine as the face-to-face encounter that comes before and after diagnostics, pharmaceuticals, (...) and surgeries. Frank calls upon the Roman emperor Marcus Aurelius, philosopher Emmanuel Levinas, and literary critic Mikhail Bakhtin to reflect on stories of ill people, doctors, and nurses who transform demoralized medicine into caring relationships. He presents their stories as a source of consolation for both ill and professional alike and as an impetus to changing medical systems. Frank shows how generosity is being renewed through dialogue that is more than the exchange of information. Dialogue is an ethic and an ideal for people on both sides of the medical encounter who want to offer more to those they meet and who want their own lives enriched in the process. The Renewal of Generosity views illness and medical work with grace and compassion, making an invaluable contribution to expanding our vision of suffering and healing. (shrink)

Starting from cardinals κ κ is measurable, we construct a model for the theory “ZF + n < ω[DCn] + ω + 1 is a measurable cardinal”. This is the maximum amount of dependent choice consistent with the measurability of ω + 1, and by a theorem of Shelah using p.c.f. theory, is the best result of this sort possible.

Can a supercompact cardinal κ be Laver indestructible when there is a level-by-level agreement between strong compactness and supercompactness? In this article, we show that if there is a sufficiently large cardinal above κ, then no, it cannot. Conversely, if one weakens the requirement either by demanding less indestructibility, such as requiring only indestructibility by stratified posets, or less level-by-level agreement, such as requiring it only on measure one sets, then yes, it can.

If κ < λ are such that κ is a strong cardinal whose strongness is indestructible under κ -strategically closed forcing and λ is weakly compact, then we show thatA = {δ < κ | δ is a non-weakly compact Mahlo cardinal which reflects stationary sets}must be unbounded in κ. This phenomenon, however, need not occur in a universe with relatively few large cardinals. In particular, we show how to construct a model where no cardinal is supercompact up to a (...) Mahlo cardinal in which the least supercompact cardinal κ is also the least strongly compact cardinal, κ 's strongness is indestructible under κ -strategically closed forcing, κ 's supercompactness is indestructible under κ -directed closed forcing not adding any new subsets of κ, and δ is Mahlo and reflects stationary sets iff δ is weakly compact. In this model, no strong cardinal δ < κ is indestructible under δ -strategically closed forcing. It therefore follows that it is relatively consistent for the least strong cardinal κ whose strongness is indestructible under κ -strategically closed forcing to be the same as the least supercompact cardinal, which also has its supercompactness indestructible under κ -directed closed forcing not adding any new subsets of κ. (shrink)

A correction to this paper has been published: https://doi.org/10.1007/s10912-021-09698-y.

1. Introduction. It is generally admitted that a large part of man's knowledge is based on inductive arguments. Hence any philosophical theory concerning the nature of inductive arguments constitutes an epistemological theory. Any such philosophical theory of induction must, if it is to be satisfactory, take adequate account of Hume's criticism of inductive arguments. One way of treating his criticism is to say that the validity of inductive arguments is in an important sense relative to some broad factual assumptions about (...) the general nature of the universe and that these general factual assumptions are presupposed in a certain way by the users of inductive arguments. Let us call any theory of this general type a postulate theory of induction. (shrink)

Suppose λ > κ is measurable. We show that if κ is either indestructibly supercompact or indestructibly strong, then A = {δ < κ | δ is measurable, yet δ is neither δ + strongly compact nor a limit of measurable cardinals} must be unbounded in κ. The large cardinal hypothesis on λ is necessary, as we further demonstrate by constructing via forcing two models in which ${A = \emptyset}$ . The first of these contains a supercompact cardinal κ and (...) is such that no cardinal δ > κ is measurable, κ’s supercompactness is indestructible under κ-directed closed, (κ +, ∞)-distributive forcing, and every measurable cardinal δ < κ is δ + strongly compact. The second of these contains a strong cardinal κ and is such that no cardinal δ > κ is measurable, κ’s strongness is indestructible under < κ-strategically closed, (κ +, ∞)-distributive forcing, and level by level inequivalence between strong compactness and supercompactness holds. The model from the first of our forcing constructions is used to show that it is consistent, relative to a supercompact cardinal, for the least cardinal κ which is both strong and has its strongness indestructible under κ-directed closed, (κ +, ∞)-distributive forcing to be the same as the least supercompact cardinal, which has its supercompactness indestructible under κ-directed closed, (κ +, ∞)-distributive forcing. It further follows as a corollary of the first of our forcing constructions that it is possible to build a model containing a supercompact cardinal κ in which no cardinal δ > κ is measurable, κ is indestructibly supercompact, and every measurable cardinal δ < κ which is not a limit of measurable cardinals is δ + strongly compact. (shrink)

We construct models for the level by level equivalence between strong compactness and supercompactness in which for κ the least supercompact cardinal and δ ≤ κ any cardinal which is either a strong cardinal or a measurable limit of strong cardinals, 2δ > δ+ and δ is < 2δ supercompact. In these models, the structure of the class of supercompact cardinals can be arbitrary, and the size of the power set of κ can essentially be made as large as desired. (...) This extends and generalizes [5, Theorem 2] and [4, Theorem 4]. We also sketch how our techniques can be used to establish a weak indestructibility result. (shrink)

We force and construct a model in which level by level equivalence between strong compactness and supercompactness holds, along with certain additional combinatorial properties. In particular, in this model, ♦ δ holds for every regular uncountable cardinal δ, and below the least supercompact cardinal κ, □ δ holds on a stationary subset of κ. There are no restrictions in our model on the structure of the class of supercompact cardinals.

A question of Woodin asks if κ is strongly compact and GCH holds below κ, then must GCH hold everywhere? One variant of this question asks if κ is strongly compact and GCH fails at every regular cardinal δ < κ, then must GCH fail at some regular cardinal δ ≥ κ? Another variant asks if it is possible for GCH to fail at every limit cardinal less than or equal to a strongly compact cardinal κ. We get a negative (...) answer to the first of these questions and positive answers to the second of these questions for a supercompact cardinal κ in the context of the absence of the full Axiom of Choice. (shrink)

A scholarly edition of Volume 2 of The Clarendon Edition of the Works of John Locke: A Paraphrase and Notes on the Epistles of St. Paul by Arthur Wainwright. The edition presents an authoritative text, together with an introduction, commentary notes, and scholarly apparatus.

We show that the consistency of the theories “ holds below ” + “there is an injection ” + “both and fail” and + “ holds below ” + “there is an injection ” + “ satisfies the tree property” follow from the appropriate supercompactness hypotheses. These provide answers in a choiceless context to certain long‐standing open questions concerning, weak square, approachability, and the tree property. There is nothing special about, and the injection into can be from any ordinal λ (...) (which means that pcf theory can fail badly in the models constructed if ). (shrink)

But even with respect to inductive arguments there are a number of different philosophical problems. One is to make explicit the fundamental or most general pattern or patterns of inductive argument. Once these patterns are known a second and third problem arise. The second is to justify man's use of and faith in inductive arguments. And the third is to formulate some general propositions about nature which could reasonably be accepted by users of inductive arguments and which when added to (...) the premises of these arguments make them explicitly deductive. (shrink)

Hermann Lotze has truly said that “among all the errors of the human mind” the “strangest” is doubting its “own existence,” or regarding it “at second hand as the product of an external Nature” which can be known only “indirectly” while the mind knows itself directly. Yet this denial is found both in the Occident and in the Orient. Moreover, while in the latter it stems largely from an extreme form of idealism in terms of a reductionistic pantheism, in the (...) former it is almost altogether the result of an analytical, reductive naturalism. More specifically, in the West this impersonalistic tendency has really been the result of two movements which have merged in certain contemporary schools. (shrink)

This paper presents a framework that editors, peer reviewers, and authors can use to identify and resolve efficiently disputes that arise during peer review in scientific journals. The framework is called a scientific dialectical brief. In this framework, differences among authors and reviewers are formatted into specific assertions and the support each party provides for its position. A literature review suggests that scientists use five main types of support; empirical data, reasoning, speculation, feelings, and status. It is suggested that the (...) scientific dialectical brief format can streamline the review process by facilitating rapid differentiation between stronger and weaker support, so that valuable time can be focused on the better-substantiated claims. The paper concludes with some suggestions for implementation. (shrink)

We obtain 2 models in which AC is false and in which there are long sequences of consecutive large cardinals.

Action explanations like ‘I am heading to the ferry because the bridge is closed,’ are supposed to require restatement: ‘I am... because I believe the bridge is closed,’ because (i) the objective claim may be false though the intended explanation is correct, and (ii) because objective circumstances have to be cognitively mediated if they are to bear on action. This supposition is rejected here. Restatements cannot withdraw the objective claim without withdrawing the explanation. In the context of reason‐giving, belief statements (...) do not function as assertions about the inner life. The fact that belief statements may be true though the belief itself is false creates the illusion of distinctive subject matters. The illusion is exploited by conceptions of belief positing stored representations. Even if there were such representations, retrieved for the sake of expressing previously acquired beliefs, the expression of belief must endorse p and cannot merely advert to the existence and content of a representation. The reverse of the standard philosophical view about restatement is actually correct. Wherever an agent correctly adduces a belief that an objective circumstance obtains in explaining his action, a de‐psychologizing restatement that merely makes the objective claim must be ascribable to the agent. (shrink)

A question of Woodin asks if $\kappa$ is strongly compact and GCH holds for all cardinals $\delta < \kappa$ , then must GCH hold everywhere. We get a negative answer to Woodin's question in the context of the negation of the Axiom of Choice.

We examine combinatorial aspects and consistency strength properties of almost Ramsey cardinals. Without the Axiom of Choice, successor cardinals may be almost Ramsey. From fairly mild supercompactness assumptions, we construct a model of ZF + ${\neg {\rm AC}_\omega}$ in which every infinite cardinal is almost Ramsey. Core model arguments show that strong assumptions are necessary. Without successors of singular cardinals, we can weaken this to an equiconsistency of the following theories: “ZFC + There is a proper class of regular almost (...) Ramsey cardinals”, and “ZF + DC + All infinite cardinals except possibly successors of singular cardinals are almost Ramsey”. (shrink)