One task of logic, Peirce held, is to classify arguments so as to determine the validity of each kind. His own classification is interesting because it includes a novel type of argument in addition to the two traditionally recognized types. It is the purpose of this paper to discuss what Peirce thought to be sufficiently distinctive about abduction to warrant calling it a new kind of argument. But since one finds in his writings on abduction a number of different views (...) it is first necessary to make a few remarks concerning the unity of Peirce's thought. (shrink)

We examine the number of normal measures a successor cardinal can carry, in universes in which the Axiom of Choice is false. When considering successors of singular cardinals, we establish relative consistency results assuming instances of supercompactness, together with the Ultrapower Axiom (introduced by Goldberg in [12]). When considering successors of regular cardinals, we establish relative consistency results only assuming the existence of one measurable cardinal. This allows for equiconsistencies.

We prove two theorems concerning indestructibility properties of the first two strongly compact cardinals when these cardinals are in addition the first two measurable cardinals. Starting from two supercompact cardinals $\kappa _1 < \kappa _2$, we force and construct a model in which $\kappa _1$ and $\kappa _2$ are both the first two strongly compact and first two measurable cardinals, $\kappa _1$ ’s strong compactness is fully indestructible, and $\kappa _2$ ’s strong compactness is indestructible under $\mathrm {Add}$ for any (...) ordinal $\delta $. This provides an answer to a strengthened version of a question of Sargsyan found in [17, Question 5]. We also investigate indestructibility properties that may occur when the first two strongly compact cardinals are not only the first two measurable cardinals, but also exhibit nontrivial degrees of supercompactness. (shrink)

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)

We summarize the known methods of producing a non-supercompact strongly compact cardinal and describe some new variants. Our Main Theorem shows how to apply these methods to many cardinals simultaneously and exactly control which cardinals are supercompact and which are only strongly compact in a forcing extension. Depending upon the method, the surviving non-supercompact strongly compact cardinals can be strong cardinals, have trivial Mitchell rank or even contain a club disjoint from the set of measurable cardinals. These results improve and (...) unify Theorems 1 and 2 of [5], due to the first author. (shrink)

This general type of view may be characterized more fully by using the notion of an inductive method. All scientists use approximately the same inductive method, which we will call the standard inductive method. This method is based on the rule of induction by simple enumeration, which may be roughly stated as follows: if it is known only that a certain property Ψ has accompanied another property Φ in a number of instances, then the larger this number of instances the (...) higher the probability that the next occurrence of Φ will be accompanied by Ψ. Though scientists actually reason inductively in accord with this rule, it is important that there are logically consistent inductive methods based on alternative rules. We will describe two of these briefly. The inverse inductive method assigns probabilities according to the rule that if it is known only that Ψ has accompanied Φ a number of times, then the larger the number of instances the lower the probability that the next occurrence of Φ will be accompanied by Ψ. The random predictive method assigns to the proposition that the next occurrence of Φ will be accompanied by Ψ a probability completely independent of the number of times that Ψ has accompanied Φ in the past.. (shrink)

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)

We construct two models containing exactly one supercompact cardinal in which all non-supercompact measurable cardinals are strictly taller than they are either strongly compact or supercompact. In the first of these models, level by level equivalence between strong compactness and supercompactness holds. In the other, level by level inequivalence between strong compactness and supercompactness holds. Each universe has only one strongly compact cardinal and contains relatively few large cardinals.

In At the Will of the Body , Arthur Frank told the story of his own illnesses, heart attack and cancer. That book ended by describing the existence of a "remission society," whose members all live with some form of illness or disability. The Wounded Storyteller is their collective portrait. Ill people are more than victims of disease or patients of medicine they are wounded storytellers. People tell stories to make sense of their suffering when they turn their diseases (...) into stories, they find healing. Drawing on the work of authors such as Oliver Sacks, Anatole Broyard, Norman Cousins, and Audre Lorde, as well as from people he met during the years he spent among different illness groups, Frank recounts a stirring collection of illness stories, ranging from the well-known--Gilda Radner's battle with ovarian cancer--to the private testimonials of people with cancer, chronic fatigue syndrome, and disabilties. Their stories are more than accounts of personal suffering: they abound with moral choices and point to a social ethic. Frank identifies three basic narratives of illness in restitution, chaos, and quest. Restitution narratives anticipate getting well again and give prominence to the technology of cure. In chaos narratives, illness seems to stretch on forever, with no respite or redeeming insights. Quest narratives are about finding that insight as illness is transformed into a means for the ill person to become someone new. (shrink)

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

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.

Because statements like ‘This object is soluble in aqua regia’ involve the causal modalities, we call them causal dispositional statements. Now while this involvement has long been recognized, no thorough examination of its exact nature has ever been made. One purpose of this paper is to begin such an examination. In Sec. 2 we will suggest an analysis of causal dispositional statements, and in Sec. 3 we will discuss some philosophic issues to which this analysis is relevant.

We construct two models in which the least strongly compact cardinal κ is also the least strong cardinal. In each of these models, κ satisfies indestructibility properties for both its strong compactness and strongness.

During Abraham Nussbaum's first year of medical school, he participated in a white coat ceremony and was invested, literally, with a white coat that is symbolic of entry into the medical profession. He was also given a book, an anthology of writings on medicine that Nussbaum describes as having a "wistful quality" and being "engaging but reverential" ; the dust jacket featured a Norman Rockwell painting. He later went to a second-hand bookstore and traded the anthology for Abraham Verghese's 1994 (...) memoir, My Own Country, an excerpt from which was in the anthology. For Nussbaum, struggling to figure out what it means to be a doctor, Verghese's writing "portrays the physician as the storyteller of his... (shrink)

We show the consistency, relative to the appropriate supercompactness or strong compactness assumptions, of the existence of a non-supercompact strongly compact cardinal $\kappa _0$ (the least measurable cardinal) exhibiting properties which are impossible when $\kappa _0$ is supercompact. In particular, we construct models in which $\square _{\kappa ^+}$ holds for every inaccessible cardinal $\kappa $ except $\kappa _0$, GCH fails at every inaccessible cardinal except $\kappa _0$, and $\kappa _0$ is less than the least Woodin cardinal.

This review of Jay Baruch's Tornado of Life: A Doctor's Journey through Constraints and Creativity in the ER considers the book's contributions, including its explorations of the clinical dilemma of working with patients’ stories that are fragmented, how easily clinicians can miss crucial parts of patients’ stories and how that affects care, and the “agonizing compromises” between what patients need and what institutions can provide. Baruch acknowledges, without any self‐indulgence, the shame that his work causes him, given the limitations of (...) what he can do. (shrink)

Narrative ethics holds that if you ask someone what goodness is, as a basis of action, most people will first appeal to various abstractions, each of which can be defined only by other abstractions that in turn require further definition. If you persist in asking what each of these abstractions actually means, eventually that person will have to tell you a story and expect you to recognize goodness in the story. Goodness and badness need stories to make them thinkable and (...) to translate them into individual and collective actions. Yet after more than two decades of considering the issue, I do not believe that a collection of stories can by itself guide actions in ways that are sufficient to respond to ethical troubles in institutional settings. The question will always remain open for me, but my present belief is that narrative bioethics is always hyphenated, in the sense that guidance from stories needs to be allied with other ethical guidance. Each side of the hyphen qualifies the other side. The hyphenation I will argue for in this essay is “narrative-deontology.”. (shrink)

We construct a variety of inner models exhibiting features usually obtained by forcing over universes with large cardinals. For example, if there is a supercompact cardinal, then there is an inner model with a Laver indestructible supercompact cardinal. If there is a supercompact cardinal, then there is an inner model with a supercompact cardinal κ for which 2κ = κ+, another for which 2κ = κ++ and another in which the least strongly compact cardinal is supercompact. If there is a (...) strongly compact cardinal, then there is an inner model with a strongly compact cardinal, for which the measurable cardinals are bounded below it and another inner model W with a strongly compact cardinal κ, such that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H^{V}_{\kappa^+} \subseteq {\rm HOD}^W}$$\end{document}. Similar facts hold for supercompact, measurable and strongly Ramsey cardinals. If a cardinal is supercompact up to a weakly iterable cardinal, then there is an inner model of the Proper Forcing Axiom and another inner model with a supercompact cardinal in which GCH + V = HOD holds. Under the same hypothesis, there is an inner model with level by level equivalence between strong compactness and supercompactness, and indeed, another in which there is level by level inequivalence between strong compactness and supercompactness. If a cardinal is strongly compact up to a weakly iterable cardinal, then there is an inner model in which the least measurable cardinal is strongly compact. If there is a weakly iterable limit δ of <δ-supercompact cardinals, then there is an inner model with a proper class of Laver-indestructible supercompact cardinals. We describe three general proof methods, which can be used to prove many similar results. (shrink)

Let φ1 stand for the statement V = HOD and φ2 stand for the Ground Axiom. Suppose Ti for i = 1, …, 4 are the theories “ZFC + φ1 + φ2,” “ZFC + ¬φ1 + φ2,” “ZFC + φ1 + ¬φ2,” and “ZFC + ¬φ1 + ¬φ2” respectively. We show that if κ is indestructibly supercompact and λ > κ is inaccessible, then for i = 1, …, 4, Ai = df{δ κ is inaccessible. We show it is also (...) the case that if κ is indestructibly supercompact, then Vκ⊨T1, so by reflection, B1 = df{δ κ is inaccessible, we demonstrate that it is possible to construct a model in which κ is indestructibly supercompact and for every inaccessible cardinal δ < κ, Vδ⊨T1. It is thus not possible to prove in ZFC that Bi = df{δ < κ∣δ is an inaccessible limit of inaccessible cardinals and Vδ⊨Ti} for i = 2, …, 4 is unbounded in κ if κ is indestructibly supercompact. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. (shrink)

In this paper, we show that certain choiceless models of ZF originally constructed using an almost huge cardinal can be constructed using cardinals strictly weaker in consistency strength.

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)

We construct models containing exactly one supercompact cardinal in which level by level inequivalence between strong compactness and supercompactness holds. In each model, above the supercompact cardinal, there are finitely many strongly compact cardinals, and the strongly compact and measurable cardinals precisely coincide.

.In this paper, we first prove several general theorems about strongness, supercompactness, and indestructibility, along the way giving some new applications of Hamkins’ lottery preparation forcing to indestructibility. We then show that it is consistent, relative to the existence of cardinals κ<λ so that κ is λ supercompact and λ is inaccessible, for the least strongly compact cardinal κ to be the least strong cardinal and to have its strongness, but not its strong compactness, indestructible under κ-strategically closed forcing.

. 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.

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)

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)