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)

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..

This volume has 41 chapters written to honor the 100th birthday of Mario Bunge. It celebrates the work of this influential Argentine/Canadian physicist and philosopher. Contributions show the value of Bunge’s science-informed philosophy and his systematic approach to philosophical problems. The chapters explore the exceptionally wide spectrum of Bunge’s contributions to: metaphysics, methodology and philosophy of science, philosophy of mathematics, philosophy of physics, philosophy of psychology, philosophy of social science, philosophy of biology, philosophy of technology, moral philosophy, social and political (...) philosophy, medical philosophy, and education. The contributors include scholars from 16 countries. Bunge combines ontological realism with epistemological fallibilism. He believes that science provides the best and most warranted knowledge of the natural and social world, and that such knowledge is the only sound basis for moral decision making and social and political reform. Bunge argues for the unity of knowledge. In his eyes, science and philosophy constitute a fruitful and necessary partnership. Readers will discover the wisdom of this approach and will gain insight into the utility of cross-disciplinary scholarship. This anthology will appeal to researchers, students, and teachers in philosophy of science, social science, and liberal education programmes. 1. Introduction Section I. An Academic Vocation Section II. Philosophy Section III. Physics and Philosophy of Physics Section IV. Cognitive Science and Philosophy of Mind Section V. Sociology and Social Theory Section VI. Ethics and Political Philosophy Section VII. Biology and Philosophy of Biology Section VIII. Mathematics Section IX. Education Section X. Varia Section XI. Bibliography. (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)

Photo by Tingey Injury Law Firm on Unsplash ABSTRACT The coverage of healthcare costs allegedly brought about by people’s own earlier health-adverse behaviors is certainly a matter of justice. However, this raises the following questions: justice for whom? Is it right to take people’s past behaviors into account in determining their access to healthcare? If so, how do we go about taking those behaviors into account? These bioethical questions become even more complex when we consider them in the context of (...) a commitment to publicly funded, universal healthcare coverage. INTRODUCTION Healthcare coverage of lifestyle-related conditions is certainly a matter of justice. However, this raises the following justice-related question: Is it right to consider people’s past behaviors in determining their access to healthcare? If so, the methods of taking those behaviors into account must be fair and justifiable. This bioethical question becomes even more complex when we consider it in the context of a commitment to publicly funded, universal healthcare coverage. This paper takes an old, classic debate, evaluates newer approaches, and offers an argument favoring a combined approach which alters the liberal-egalitarian solution to account for social justice. ANALYSIS I. Causes of Disease If healthcare coverage were universal, irrespective of socioeconomic status and lifestyle, people would contribute to the cost of remedying the lifestyle-induced health problems of others. In the West, lifestyle-related diseases are burdensome.[i] This paper approaches this concern from a western lens that incorporates both a European tradition of “social safety nets” and an American tradition of personal freedoms. By taking such an approach, solutions to the consequences of one’s past behavior burdening others must consider an individual’s personal freedom to choose to act as he or she wishes, with the distributive social and economic equality of the many. The concept of disease caused by lifestyle and diet is proven. Many health conditions include behavioral risk factors. Multi-pack smoking increases the risk of chronic lung disease, while obesity increases the risk of type 2 diabetes. Inattention to high blood pressure, high cholesterol, and a lack of exercise leads to increased risks of coronary artery disease.[ii] While poor lifestyle choices certainly influence these conditions, their causes are multifactorial, and it is difficult to say that any single string of poor choices led to their development. In a scenario where two men excessively eat fast food for 20 years, several discrete factors impact whether any of them might suffer an ischemic-embolic stroke or not. Genetics, circumstances, and activity will also contribute to outcomes. II. Alcohol-Related End-Stage Liver Disease One paper suggests that alcohol-related end-stage liver disease (ARESLD) differs from other multifactorial disorders as alcohol alone causes the disease.[iii] It justifies attributing personal responsibility to patients with ARESLD because the condition develops only after the cumulative effects of large quantities of alcohol consumed from years to decades.[iv] However, the paper undermines its position by admitting that even the susceptibility to becoming an alcoholic has some degree of genetic predisposition.[v] Given the extreme scarcity of donor livers, some patients may be prioritized over others on the transplant waiting list. Since donor livers cannot be given to everyone, transplanting a liver into an alcoholic may result in death for competing candidates whose liver disease was not their fault. All else being equal, if bioethicists avoid claiming moral deficiency or judgment, those with apparently self-inflicted ARESLD will not be deprived of treatment but will have a lower priority for transplant.[vi] In contrast, another position suggests that it is often difficult to define what behaviors are punishable as these are largely personal and value-laden.[vii] Still, people do not support using their own resources to support the consequences of others’ poor choices, no matter how objective.[viii] In democratic societies, one must take into consideration community morals and values.[ix] Even if we were to punish people for their health-adverse behaviors, we could not logistically employ the vigorous and sustained efforts necessary to determine whose actions are morally weak.[x] III. The Liberal-Egalitarian Proposal One past argument proposes a liberal-egalitarian solution to manage personal responsibility for so-called “lifestyle diseases.”[xi] This Rawlsian system combines the European-style “social safety net” commitment to social and economic equality with the American liberal notion of pluralist toleration and personal freedoms. This idealized system aims to hold people responsible for their choices rather than the consequences to mitigate the downside of blaming those who might not be blameworthy. The approach avoids determining the questionable nature of luck and personal responsibility for health outcomes, fairness in the distribution of economic burden, and the intrusiveness required to practically determine who acts in a morally wrong and health-adverse way. The liberal-egalitarian model, a theory of distributive justice, has two facets: the liberal principle that people should be held accountable for their choices and the egalitarian principle that people who make the same choices should have the same outcomes.[xii] This model attempts to fuse responsibility with equity by seeking to reward good behavior and tax bad behavior rather than punish the consequences of the action and navigate who deserves treatment. For instance, the hospital bedside is not the appropriate place to introduce responsibility for one’s health outcomes.[xiii] This appeals to the reality that, at that time, discerning the true causes of disease was not plausible and to humanity in avoiding a heartless and cruel approach. An argument in favor of the liberal-egalitarian model considers its method of implementation. This approach assumes that the healthcare system treats all individuals regardless of their choices or ability to cover costs. The liberal-egalitarian model also assumes that a certain adverse health condition is related, statistically speaking, to the consumption of a certain good and that good can be taxed. As such, it proposes to tax the consumption of that good to finance the collective burden which arises from that good’s consumption rather than require individuals to pay for their own treatment. In the example of ARESLD, the recommended solution would be taxing all alcohol. While a systematic infrastructure is not explicit, there is the implication that a per-unit tax can be imposed on alcohol so the total tax revenue would make up for the additional healthcare costs due to consumption.[xiv] Upholding the principle that all people who make the same choices should face the same costs, all consumers of alcohol would pay the same tax, regardless of factors such as genetic predisposition to alcoholism, lifestyle, or expected cost of treatment. Upholding the principle of individual responsibility, this model does not deny treatment to anyone, neutralizing factors outside that individual’s control by imposing the tax ex-ante. Other people are not burdened by those who consume the good. People who consume alcohol face a burden proportional to the amount consumed. This tax-based implementation is justified so long as the tax is not prohibitively high for the average consumer. Further, the model mitigates concerns over the intrusiveness of ascribing morality to health-adverse behaviors. IV. Moral and Social Arguments Against the Liberal-Egalitarian Position Arguments against the liberal-egalitarian model concerns its many assumptions. First, this model assumes that consumption of such goods is directly related to the health outcome and that these goods can be taxed.[xv] Certain people genetically predisposed to alcoholism would be predisposed to consume more alcohol. The model falls short when applied to scenarios where health outcomes are not consumption-based, such as engaging in unsafe sex or abstaining from healthy lifestyle choices like exercise. Second, some might argue that the liberal-egalitarian model fails to remain neutral. Residual moral judgments tied to consumption choices introduce non-neutrality. Although taxation in free societies is determined by democratic procedures rather than by individuals in the healthcare system, moral and value-based judgments will be implicit in deciding what behaviors are taxable, such as the purchase of cigarettes. Third, the liberal-egalitarian model fails to determine whether one’s behavior is autonomous, as socio-cultural-economic factors may influence it and behavior is more a product of society, peer pressure, or income. Those also may reflect systemic inequalities. Therefore, this model, which rewards, or taxes based solely on decisions, regardless of their consequences and motivations, fails to consider that a person’s decisions may not be completely autonomous. V. Libertarian Arguments Against the Liberal-Egalitarian Model a. State Intrusiveness as Counter to the Liberal-Egalitarian Model Last, there is a libertarian worry that if the state guarantees universal healthcare coverage to all people, the state will have to become highly intrusive and investigate people’s morals.[xvi] At least one-third of all disease burden in North America, Europe, and the Asia-Pacific is attributable to lifestyle measures such as tobacco smoking, alcohol consumption, high cholesterol, and obesity.[xvii] With these various lifestyles, it is not likely to agree on what conduct to tax or condemn.[xviii] The fine-toothed comb required to determine whether each citizen has been engaging in these behaviors would intrude on daily life and personal freedom. Libertarians champion the argument that impractical intrusiveness would result from universal healthcare, and such a degree of intrusiveness would likely be universally unacceptable.[xix] The liberal-egalitarian model mitigates the libertarian worry about state intrusiveness as it does not involve prying into one’s life and choices other than taxing goods. A liberal state should ideally be neutral to how people decide to live their lives. In all, libertarians can rest assured that the liberal-egalitarian tax-based model, through its ex-ante implementation, will require no prying state eyes. States that provide universal healthcare coverage and wish to condemn certain misconduct do not need to become overly intrusive to carry out measures to hold individuals accountable. b. Fairness Another libertarian worry regarding the guarantee of universal healthcare coverage in the context of lifestyle-driven diseases is that the public will be burdened unfairly with covering others’ ill-advised mistakes or bad luck. An ideal system to address this worry would link treatment or payment for treatment with whatever behavior caused that need.[xx] The distribution of burdens should be linked to how different individuals contributed to the creation of those burdens. Applied to health policy, we should ask how the need for a certain treatment arose when determining how to distribute its cost.[xxi] The liberal-egalitarian model aspires to hold individuals responsible for their choices, not for the consequences of such choices. This model significantly mitigates the libertarian worry over unfair burdens for covering other people’s mistakes or social conditions, which lead to those bad outcomes, by ensuring to not burden others with any of the costs for the treatment of people who decide to engage in certain health-adverse behaviors. The aforementioned taxation-based system would only tax those who also engage in the health-adverse behavior through consumption, and that tax directly pays for the necessary collective treatment. As such, those who do not consume the good are not involved with the payment scheme, while those who do consume the good are responsible for payment in a matter proportional to the amount of the good they have consumed. VI. Universal Coverage Taking a step back, one should consider whether these worries regarding the coverage of apparently self-inflicted health conditions in the context of universal healthcare are worthwhile issues. One perspective raises what is called the culturally imagined objection — an idea erroneously held by many that sick people, especially those who are poor and uneducated, bring these illnesses upon themselves due to poor decision-making and irresponsible risk-taking.[xxii] This perspective critiques the uniquely American view that, since individuals are free to choose their lifestyles, they should bear the costs of their lifestyle.[xxiii] Taking this argument further, some (perhaps the strongly libertarian) would say that the poor health status among many individuals is the price individuals must pay for their American way of life and the liberty and freedom to live as they wish. However, people should not completely punish individuals for their health-adverse behaviors because these choices are largely pre-determined by a person’s socioeconomic influences.[xxiv] The outcomes from these allegedly ill-advised behaviors, which largely affect poorer people, are not just poor behavior but rather a public health crisis. Perhaps the state and its people should take collective responsibility and cover the costs of treatment for those health outcomes without question, as a form of public service. Rather than worrying about accountability and taxing bad behavior or intrusiveness into personal decisions, some might argue that people need to collectively take responsibility for reducing the overarching systemic inequalities and covering the associated treatment costs as a measure of public health. VII. Proposed Solution Given the strengths of the liberal-egalitarian model and taking into account libertarian and social justice-oriented objections, an ideal solution for the coverage of lifestyle-related health problems needs to consider the complex relationship between a person’s behaviors and their apparent health outcomes. It must consider how society as a whole passes judgment on behaviors and how to take into account that many health-adverse decisions are not truly autonomous decisions, as various genetic and socioeconomic factors influence them. An ideal solution combines the liberal-egalitarian tax-based model with the social justice concerns of universal coverage. Whatever the cost for the treatment of medical issues resulting in part or entirely from lifestyle and diet, taxes collected from spending associated with the behavior (like the purchase of alcohol, junk food, and cigarettes) ex-ante should fund 50 percent of the cost of treatment, while the universal healthcare taxation scheme should include the other 50 percent. Such a system would provide an incentive to avoid the purchases that can lead to unhealthy consumption and make healthier choices, slightly punish and discourage such purchases through taxation, yet not overly punish people whose outcomes may have more to do with socioeconomic factors and genetics. Adding public responsibility demonstrates acknowledgement that health care is in the public interest and can mitigate public health inequalities. This solution would fuse personal responsibility with the public responsibility of state-sponsored social improvement while ensuring that all people have fair access to necessary treatment, no matter their ability to pay. CONCLUSION The 50-50 system this paper proposes reflects both justice and personal responsibility in covering healthcare costs allegedly brought about by people’s own health-adverse behaviors. By allocating tax revenue from consumption that contributes or even alone causes poor health outcomes, such a system incorporates personal responsibility. By using general tax revenue for health care, such a system would meet the libertarian requirement of providing care without any moral investigation of past behaviors and the social justice consideration of providing health care to those who may have unwittingly ventured into ill-health due to systemic injustice, socioeconomics, or genetics. - [i] Cappelen, A. W. (2005). Responsibility in health care: A liberal egalitarian approach. Journal of Medical Ethics, 31(8), 476–480. https://doi.org/10.1136/jme.2004.010421 [ii] Moss, A. H. (1991). Should alcoholics compete equally for liver transplantation? JAMA: The Journal of the American Medical Association, 265(10), 1295–1298. https://doi.org/10.1001/jama.1991.03460100097032 [iii] Moss, p. 1295-1298. [iv] Moss, p. 1296. [v] Moss, p. 1295-1298. [vi] Moss, p. 1295-1298. [vii] Cohen, C. IS THIS SUPPOSED TO BE COHEN AND BENJAMIN (1991). Alcoholics and liver transplantation. JAMA: The Journal of the American Medical Association, 265(10), 1299–1301. https://doi.org/10.1001/jama.1991.03460100101033 [viii] Cohen, p. 1299-1301. [ix] Moss, p. 1297. [x] Cohen, p. 1300. [xi] Cappelen, p. 478-480. [xii] Cappalen, p. 478-480. [xiii] Cappelen, p.479. [xiv] Cappelen, p. 479. [xv] Cappelen, p. 479 [xvi] Cohen, p. 1301. [xvii] Cappelen, p. 478. [xviii] Cohen, p. 1299-1301. [xix] Cohen, p. 1301. [xx] Cappelen, p. 476-480. [xxi] Cappelen, p. 476-480. [xxii] Kawachi, I. (2005). Why the United States is not number one in Health. Healthy, Wealthy, and Fair, 18–33. https://doi.org/10.1093/acprof:oso/9780195170665.003.0013 [xxiii] Kawachi, p. 18-33. [xxiv] Kawachi, p. 18-33. (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)

Using the analysis developed in our earlier paper, we show that every uncountable cardinal in Gitik's model of in which all uncountable cardinals are singular is almost Ramsey and is also a Rowbottom cardinal carrying a Rowbottom filter. We assume that the model of is constructed from a proper class of strongly compact cardinals, each of which is a limit of measurable cardinals. Our work consequently reduces the best previously known upper bound in consistency strength for the theory math formula (...) + “All uncountable cardinals are singular” + “Every uncountable cardinal is both almost Ramsey and a Rowbottom cardinal carrying a Rowbottom filter”. (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)

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)

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)

Arthur Collins's succinct, revisionist exposition of Kant's _Critique of Pure Reason_ brings a new clarity to this notoriously difficult text. Until recently most readers, ascribing broadly Cartesian assumptions to Kant, have concluded that the _Critique_ advances an idealist philosophy, because Kant calls it "transcendental idealism" and because the work abounds in apparent confirmations of that interpretation. Collins maintains not only that this reading of Kant is false but also that it conceals Kant's real achievements. To counter it, he addresses (...) the themes and passages in the _Critique_ that seem to require an idealist thesis and shows how they may be better understood without ascribing any idealist philosophy to Kant. His account coheres with Kant's explicit "refutations" of idealism, it fits Kant's rejection of the imputation of idealism to him by early critics and readers, and it validates Kant's contention that the second edition of the _Critique_ changes the expression but not the doctrine of the first. (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.

. 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.

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)

Combining techniques of the first author and Shelah with ideas of Magidor, we show how to get a model in which, for fixed but arbitrary finite n, the first n strongly compact cardinals κ 1 ,..., κ n are so that κ i for i = 1,..., n is both the i th measurable cardinal and κ + i supercompact. This generalizes an unpublished theorem of Magidor and answers a question of Apter and Shelah.

We show the consistency, relative to a supercompact cardinal, of the least measurable cardinal being both strongly compact and fully Laver indestructible. We also show the consistency, relative to a supercompact cardinal, of the least strongly compact cardinal being somewhat supercompact yet not completely supercompact and having both its strong compactness and degree of supercompactness fully Laver indestructible.

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

We show relative to strong hypotheses that patterns of compact cardinals in the universe, where a compact cardinal is one which is either strongly compact or supercompact, can be virtually arbitrary. Specifically, we prove if V “ZFC + Ω is the least inaccessible limit of measurable limits of supercompact cardinals + ƒ : Ω → 2 is a function”, then there is a partial ordering P V so that for , There is a proper class of compact cardinals + If (...) ƒ = 0, then the αth compact cardinal is not supercompact + If ƒ = 1, then the αth compact cardinal is supercompact”. We then prove a generalized version of this theorem assuming κ is a supercompact limit of supercompact cardinals and ƒ : κ → 2 is a function, and we derive as corollaries of the generalized version of the theorem the consistency of the least measurable limit of supercompact cardinals being the same as the least measurable limit of nonsupercompact strongly compact cardinals and the consistency of the least supercompact cardinal being a limit of strongly compact cardinals. (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)

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)

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 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)

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)

If κ < λ are such that κ is indestructibly supercompact and λ is measurable, then we show that both A = {δ < κ | δ is a measurable cardinal which is not a limit of measurable cardinals and δ carries the maximal number of normal measures} and B = {δ < κ | δ is a measurable cardinal which is not a limit of measurable cardinals and δ carries fewer than the maximal number of normal measures} are 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 carry fewer than the maximal number of normal measures. 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 carry the maximal number of normal measures. If we weaken the requirements on indestructibility, then this last result can be improved to obtain a model with an indestructibly supercompact cardinal κ in which every measurable cardinal δ < κ carries the maximal number of normal measures. (shrink)

"More than any thing else technology creates our world. It creates our wealth, our economy, our very way of being," says W. Brian Arthur. Yet, until now the major questions of technology have gone unanswered. Where do new technologies come from -- how exactly does invention work? What constitutes innovation, and how is it achieved? Why are certain regions -- Cambridge, England, in the 1920s and Silicon Valley today -- hotbeds of innovation, while others languish? Does technology, like biological (...) life, evolve? How do new industries, and the economy itself, emerge from technologies? In this groundbreaking work, pioneering technology thinker and economist W. Brian Arthur sets forth a boldly original way of thinking about technology that gives answers to these questions. The Nature of Technology is an elegant and powerful theory of technology's origins and evolution. It achieves for the progress of technology what Thomas Kuhn's The Structure of Scientific Revolutions did for scientific progress. Arthur explains how transformative new technologies arise and how innovation really works. Conventional thinking ascribes the invention of technologies to "thinking outside the box," or vaguely to genius or creativity, but Arthur shows that such explanations are inadequate. Rather, technologies are put together from pieces -- themselves technologies -- that already exist. Technologies therefore share common ancestries and combine, morph, and combine again to create further technologies. Technology evolves much as a coral reef builds itself from activities of small organisms -- it creates itself from itself; all technologies are descended from earlier technologies. Drawing on a wealth of examples, from historical inventions to the high-tech wonders of today, and writing in wonder fully engaging and clear prose, Arthur takes us on a mind-opening journey that will change the way we think about technology and how it structures our lives. (shrink)

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.

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)

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.

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)

Using Steel's recent result that assuming AD, in L[R] below Θ, κ is regular $\operatorname{iff} \kappa$ is measurable, we mimic below Θ certain earlier results of Gitik. In particular, we construct via forcing a model in which all uncountable cardinals below Θ are singular and a model in which the only regular uncountable cardinal below Θ is ℵ 1.

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.

We obtain an equiconsistency for a weak form of universal indestructibility for strongness. The equiconsistency is relative to a cardinal weaker in consistency strength than a Woodin cardinal. Stewart Baldwin's notion of hyperstrong cardinal. We also briefly indicate how our methods are applicable to universal indestructibility for supercompactness and strong compactness.

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.

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 force and obtain three models in which level by level equivalence between strong compactness and supercompactness holds and in which, below the least supercompact cardinal, GCH fails unboundedly often. In two of these models, GCH fails on a set having measure 1 with respect to certain canonical measures. There are no restrictions in all of our models on the structure of the class of supercompact cardinals.

We show that it is consistent, relative to a supercompact limit of supercompact cardinals, for the least strongly compact cardinal k to be both the least measurable cardinal and to be > 2k supercompact.