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

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)

If κ < λ are such that κ is indestructibly supercompact and λ is 2λ supercompact, it is known from [4] that {δ < κ | δ is a measurable cardinal which is not a limit of measurable cardinals and δ violates level by level equivalence between strong compactness and supercompactness}must be unbounded in κ. On the other hand, using a variant of the argument used to establish this fact, it is possible to prove that if κ < λ are (...) such that κ is indestructibly supercompact and λ is measurable, then {δ < κ | δ is a measurable cardinal which is not a limit of measurable cardinals and δ satisfies level by level equivalence between strong compactness and supercompactness}must be unbounded in κ. The two aforementioned phenomena, however, need not occur in a universe with an indestructibly supercompact cardinal and sufficiently few large cardinals. In particular, we show how to construct a model with an indestructibly supercompact cardinal κ in which if δ < κ is a measurable cardinal which is not a limit of measurable cardinals, then δ must satisfy level by level equivalence between strong compactness and supercompactness. We also, however, show how to construct a model with an indestructibly supercompact cardinal κ in which if δ < κ is a measurable cardinal which is not a limit of measurable cardinals, then δ must violate level by level equivalence between strong compactness and supercompactness. (shrink)

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.

We show that the theories “ZFC \ There is a supercompact cardinal” and “ZFC \ There is a supercompact cardinal \ Level by level inequivalence between strong compactness and supercompactness holds” are equiconsistent.

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)

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)

. 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.

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)

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)

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.

Increasingly, medicine is used to remodel, revise, and revamp as much as to heal and mend. It is tempting to say that people make merely personal choices about these new uses. But such choices have implications for everybody, and they ought to be made cautiously, slowly, and in a way that opens them to discussion.

We show that for all natural numbers n, the theory “ZF + DC $_{\aleph_n}$ + $\aleph_{\omega}$ is a Rowbottom cardinal carrying a Rowbottom filter” has the same consistency strength as the theory “ZFC + There exists a measurable cardinal”. In addition, we show that the theory “ZF + $\aleph_{\omega_1}$ is an ω 2-Rowbottom cardinal carrying an ω 2-Rowbottom filter and ω 1 is regular” has the same consistency strength as the theory “ZFC + There exist ω 1 measurable cardinals”. We (...) also discuss some generalizations of these results. (shrink)

Conflict can profoundly affect individuals and their groups. Oftentimes, conflict involves a clash between one side seeking change and increased gains through victory and the other side defending the status quo and protecting against loss and defeat. However, theory and empirical research largely neglected these conflicts between attackers and defenders, and the strategic, social, and psychological consequences of attack and defense remain poorly understood. To fill this void, we model (1) the clashing of attack and defense as games of strategy (...) and reveal that (2) attack benefits from mismatching its target's level of defense, whereas defense benefits from matching the attacker's competitiveness. This suggests that (3) attack recruits neuroendocrine pathways underlying behavioral activation and overconfidence, whereas defense invokes neural networks for behavioral inhibition, vigilant scanning, and hostile attributions; and that (4) people invest less in attack than defense, and attack often fails. Finally, we propose that (5) in intergroup conflict, out-group attack needs institutional arrangements that motivate and coordinate collective action, whereas in-group defense benefits from endogenously emerging in-group identification. We discuss how games of attack and defense may have shaped human capacities for prosociality and aggression, and how third parties can regulate such conflicts and reduce their waste. (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)

We establish an Easton theorem for the least supercompact cardinal that is consistent with the level by level equivalence between strong compactness and supercompactness. In both our ground model and the model witnessing the conclusions of our theorem, there are no restrictions on the structure of the class of supercompact cardinals. We also briefly indicate how our methods of proof yield an Easton theorem that is consistent with the level by level equivalence between strong compactness and supercompactness in a universe (...) with a restricted number of large cardinals. We conclude by posing some related open questions. (shrink)

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)

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)

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.

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

We prove a consistency result about square principles and stationary reflection which generalises the result of Ben-David and Magidor [4].

It is known that if $\kappa < \lambda$ are such that κ is indestructibly supercompact and λ is 2λ supercompact, then level by level equivalence between strong compactness and supercompactness fails. We prove a theorem which points towards this result being best possible. Specifically, we show that relative to the existence of a supercompact cardinal, there is a model for level by level equivalence between strong compactness and supercompactness containing a supercompact cardinal κ in which κ’s strong compactness is indestructible (...) under κ-directed closed forcing. (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.

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)

We give a new proof using iterated Prikry forcing of Magidor's theorem that it is consistent to assume that the least strongly compact cardinal is the least supercompact cardinal.

A collection of stories by bioethicists writing about their own illnesses displays the importance of microethics. From this perspective, ethics happens not in the application of principles to specific decisions, but rather in the moment-to-moment flow of clinical interaction, as healthcare workers and patients make decisions, especially in their use of language. Microethical issues that are common to multiple stories are described as dense junctures of ethical concern. Three junctures are discussed in detail: conflicts between medical and patient rationalities, issues (...) of how clinicians represent patients, and practices of truth telling. These junctures are illustrated with examples from the bioethicists’ personal stories of treatment. (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)

This symposium contribution presents three vignettes of resistance to COVID-19 public health measures in Alberta, Canada, where I live. These show resolutely individualistic attitudes toward health and a desire to understand the pandemic as a one-off aberration. I then suggest four ways that the work of bioethics needs to change. These begin with situating the pandemic within the context of global climate emergency and end with how a new polarization diminishes possibilities for the rational dialogue that bioethics has here-to-fore assumed (...) people would engage in. (shrink)

Assuming Con, a model in which there are unboundedly many regular cardinals below Θ and in which the only regular cardinals below Θ are limit cardinals was previously constructed. Using a large cardinal hypothesis far beyond Con, we construct in this paper a model in which there is a proper class of regular cardinals and in which the only regular cardinals in the universe are limit cardinals.