The property on the filter in Definition 1, a kind of large cardinal property, suffices for the proof in Liu Shelah [LiSh484] and is proved consistent as required there (see Conclusion 6). A natural property which looks better, not only is not obtained here, but is shown to be false (in Claim 7). On earlier related theorems see Gitik Shelah [GiSh310]. On such games see e.g. [Je], [Sh-b], [Sh-f].

Building upon earlier work of Donna Carr, Don Pelletier, Chris Johnson, Shu-Guo Zhang and others, we show that a normal ideal J on Pκ is strongly normal if and only if J+→< 2 for every μ < κ, and we describe the least normal ideal J on Pκ such that J+ →< 2.

Using previous work of Baumgartner, Shelah and others, we describe, for each infinite cardinal θκ, the smallest κ-normal ideal J on Pκ such that.

For every uncountable regular cardinalκ and any cardinalλ≧κ,P κ λ denotes the set $\left\{ {x \subseteqq \lambda :\left| x \right|< \kappa } \right\}$ . Furthermore, < denotes the binary operation defined inP κ λ byxideal overP κ λ extending the ideal dual to the filter generated by $\left\{ {\left\{ {x \in P_\kappa \lambda :y \subseteqq x} \right\}:y \in P_\kappa \lambda } \right\}$ . For any idealI overP (...) κ λ,I + denotes the setP κ λ−I, andI * the filter dual toI.An idealI overP κ λ is said to benormal iff every functionf:P κ λ→λ with the property that {x∈P κ λ:f(x)∈x}∈I + is constant on a set inI +.I is said to bestrongly normal iff every functionf:P κ λ→P κ λ with the property that {x∈P κ λ:x∩xκ≠Ø∧f(x)normal ideal is normal. However, the converse of this is false.In this paper, we completely characterize those pairs (κ, λ) for whichP κ λ bears a strongly normal ideal, and describe the smallest such ideal for these pairs. As well, we show that for each of these pairs, the operator∇ < defined on the set of all ideals overP κ λ by where $$\nabla _< \left\{ {X_a :a \in P_\kappa \lambda } \right\} = \left\{ {x \in P_\kappa \lambda :x \cap \kappa = \phi \vee \left( {\exists a< x} \right)\left( {x \in X_a } \right)} \right\}$$ is idempotent. Our results include the following theorems. (shrink)

Idealization is a reasoning strategy that biologists use to describe, model and explain that purposefully departs from features known to be present in nature. Similar to other strategies of scientific reasoning, idealization combines distinctive strengths alongside of latent weaknesses. The study of ontogeny in model organisms is usually executed by establishing a set of normal stages for embryonic development, which enables researchers in different laboratory contexts to have standardized comparisons of experimental results. Normal stages are a form of (...) idealization because they intentionally ignore known variation in development, including variation associated with phenotypic plasticity (e.g. via strict control of environmental variables). This is a tension between the phenomenon of plasticity and the practice of staging that has consequences for evolutionary developmental investigation because variation is conceptually removed as a part of rendering model organisms experimentally tractable. Two compensatory tactics for mitigating these consequences are discussed: employing a diversity of model organisms and adopting alternative periodizations. (shrink)

It is a priori on many accounts of colour concepts that something is red if and only if it is such that it would look red to normal observers in normal circumstances: it is such that it would look red, as we can say, under normal conditions of observation. And as this sort of formula is widely applied to colour concepts, so similar schemas are commonly defended in relation to a variety of other concepts too. Not only (...) are colour concepts connected in such a fashion with human responses, so by many accounts are secondary quality concepts in general; aesthetic concepts, moral concepts and evaluative concepts of all kinds; modal concepts that serve to pick out the possible and the necessary; and so on. The fashion for resorting to such formulas should not be surprising. Most of us suppose that whether a given, ostensively introduced term has a certain semantic value – whether, for example, it designates a certain property – ought to show up in people’s tending to use it of things, and only of things, that apparently have that property. The obvious way of expressing this expectation is to require that the use of the ostensive term covary with the presence of the property in conditions that are normal in some sense for detecting that property. Thus there is prima facie reason to hold, and hold as an a priori matter, that for any ostensively introduced term, ‘P’, something is P if and only if it is such that it would seem P – people would be disposed to use ‘P’ to ascribe the corresponding property to it – under normal conditions of observation. The schemas invoked under this motivation may vary in many different ways, of course. First, they may not connect the bare or simple reality of being P with a normalised human response, as Philosophical Studies 96: 21–44, 1999. © 1999 Kluwer Academic Publishers. Printed in the Netherlands. 22. (shrink)

People’s beliefs about normality play an important role in many aspects of cognition and life (e.g., causal cognition, linguistic semantics, cooperative behavior). But how do people determine what sorts of things are normal in the first place? Past research has studied both people’s representations of statistical norms (e.g., the average) and their representations of prescriptive norms (e.g., the ideal). Four studies suggest that people’s notion of normality incorporates both of these types of norms. In particular, people’s representations of (...) what is normal were found to be influenced both by what they believed to be descriptively average and by what they believed to be prescriptively ideal. This is shown across three domains: people’s use of the word ‘‘normal” (Study 1), their use of gradable adjectives (Study 2), and their judgments of concept prototypicality (Study 3). A final study investigated the learning of normality for a novel category, showing that people actively combine statistical and prescriptive information they have learned into an undifferentiated notion of what is normal (Study 4). Taken together, these findings may help to explain how moral norms impact the acquisition of normality and, conversely, how normality impacts the acquisition of moral norms. (shrink)

The concept of normal is so familiar that it can be hard to imagine contemporary life without it. Yet the term entered everyday speech only in the mid-twentieth century. Before that, it was solely a scientific term used primarily in medicine to refer to a general state of health and the orderly function of organs. But beginning in the middle of the twentieth century, normal broke out of scientific usage, becoming less precise and coming to mean a balanced (...) condition to be maintained and an ideal to be achieved. In Normality, Peter Cryle and Elizabeth Stephens offer an intellectual and cultural history of what it means to be normal. They explore the history of how communities settle on any one definition of the norm, along the way analyzing a fascinating series of case studies in fields as remote as anatomy, statistics, criminal anthropology, sociology, and eugenics. Cryle and Stephens argue that since the idea of normality is so central to contemporary disability, gender, race, and sexuality studies, scholars in these fields must first have a better understanding of the context for normality. This pioneering book moves beyond binaries to explore for the first time what it does—and doesn’t—mean to be normal. (shrink)

Starting with a measurable cardinal κ of the Mitchell order κ++ we construct a model with a precipitous ideal on ℵ1 but without normal precipitous ideals. This answers a question by T. Jech and K. Prikry. In the constructed model there are no Q-point precipitous filters on ℵ1, i. e. those isomorphic to extensions of Cubℵ1.

What is considered normal determines clinical practice in medicine and has implications at an individual level, doctor-patient relationship and health care policies. With the increase in medical information and technical abilities it is urgent to have a clear concept of normality in medicine so that crucial discussions can be held with unequivocal terms.The different meanings for normality were analyzed throughout the literature and grouped according to their relevance in the academic community in models, namely the Biostatistical Theory (BST), Health, (...) Ideal, Process and Biological advantage. The BST is the most established naturalistic approach, however normal variability can arguably constitute a problem. Health is similar and raises the question of setting the boundaries of pathology. Normality as an Ideal is an useful tool but is naturally unrealistic. As a Process it is comprehensible but is hard to frame for practical purposes. If considered as a Biological Advantage, seems intuitive but abnormality should tend to disappear.After, three examples were presented to discuss these models. They were Anemia, Psychiatric diseases and Psychopathy. In the case of Anemia the BST was applied and the arbitrary boundaries but with social impact were exposed. Psychiatric diseases was discussed under the process of self-organization and non-suffering ideal. With Psychopathy the boundaries of biological advantage are questioned.This review appeals to the importance of redesigning of the concept of normality in medicine according to current times and stresses the importance of integrating concepts such as variability and autonomy. (shrink)

We study normal ideals on Pκ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${P_{\kappa} }$$\end{document} that are defined in terms of games of uncountable length.

It is well known that saturation of ideals is closely related to the “antichain-catching” phenomenon from Foreman–Magidor–Shelah [10]. We consider several antichain-catching properties that are weaker than saturation, and prove:If${\cal I}$is a normal ideal on$\omega _2 $which satisfiesstationary antichain catching, then there is an inner model with a Woodin cardinal;For any$n \in \omega $, it is consistent relative to large cardinals that there is a normal ideal${\cal I}$on$\omega _n $which satisfiesprojective antichain catching, yet${\cal I}$is not saturated. (...) This provides a negative answer to Open Question number 13 from Foreman’s chapter in the Handbook of Set Theory. (shrink)

We study a normal ideal on Pκ that is defined in terms of games.

The main result of this paper is that if κ is not a weakly Mahlo cardinal, then the following two conditions are equivalent: 1. P(κ)/ J is κ+-complete. 2. J is a prenormal ideal. Our result is a generalization of an announcement made in [Z]. We say that J is selective iff for every J-function f: κ → κ there is a set X ∈ J such that f∣(κ - X) is one-to-one. Our theorem provides a positive partial answer (...) to a question of B. Weglorz from [BTW, p. 90], viz.: is every selective ideal J, with P(κ)/J κ+-complete, isomorphic to a normal ideal? The theorem is also true for fine ideals on $\lbrack\lambda\rbrack^{<\kappa}$ for any κ ≤ λ, i.e. if κ is not a weakly Mahlo cardinal then the Boolean algebra $\mathscr{P} (\lbrack\lambda\rbrack^{<\kappa})/\mathscr{J}$ is λ+-complete iff J is a prenormal ideal (in the sense of $\lbrack\lambda\rbrack^{<\kappa})$. (shrink)

The main result of this paper is that if $\kappa$ is not a weakly Mahlo cardinal, then the following two conditions are equivalent: 1. $\mathscr{P}(\kappa)/ \mathscr{J}$ is $\kappa^+$-complete. 2. $\mathscr{J}$ is a prenormal ideal. Our result is a generalization of an announcement made in [Z]. We say that $\mathscr{J}$ is selective iff for every $\mathscr{J}$-function $f: \kappa \rightarrow \kappa$ there is a set $X \in \mathscr{J}$ such that $f\mid(\kappa - X)$ is one-to-one. Our theorem provides a positive partial answer (...) to a question of B. Weglorz from [BTW, p. 90], viz.: is every selective ideal $\mathscr{J}$, with $\mathscr{P}(\kappa)/\mathscr{J} \kappa^+$-complete, isomorphic to a normal ideal? The theorem is also true for fine ideals on $\lbrack\lambda\rbrack^{<\kappa}$ for any $\kappa \leq \lambda$, i.e. if $\kappa$ is not a weakly Mahlo cardinal then the Boolean algebra $\mathscr{P} (\lbrack\lambda\rbrack^{<\kappa})/\mathscr{J}$ is $\lambda^+$-complete iff $\mathscr{J}$ is a prenormal ideal (in the sense of $\lbrack\lambda\rbrack^{<\kappa})$. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Ideal of Shared Decision Making Between Physicians and PatientsDan W. Brock (bio)IntroductionShared treatment decision making, with its division of labor between physician and patient, is a common ideal in medical ethics for the physician-patient relationship.1 Most simply put, the physician's role is to use his or her training, knowledge, and experience to provide the patient with facts about the diagnosis and about the prognoses without treatment (...) and with alternative treatments. The patient's role in this division of labor is to provide the values—his or her own conception of the good—with which to evaluate these alternatives, and to select the one that is best for himself or herself. As a rough guide to practice, this is a reasonable conception; most of the time it is likely to produce sound treatment decisions. However, as an ideal it is too simplistic, and is subject to several challenges that I will explore in this paper.Some challenges relate to the physician's role. This facts/values division of labor seems to assume that the physician can and should provide the facts about treatment alternatives in a value-neutral form. But some have questioned whether the sciences on which medicine is based are, or can be, value free. Moreover, the concepts of health and disease, and of the normal and pathological, are held by many to be value laden. And even if it is possible for physicians to provide only value-neutral facts to the patient, should the physicians' role be restricted in this way?Other challenges that I will present in the paper are to the patient's role [End Page 28] as provider of the values for the evaluation of the different treatment alternatives. One defense of this role is based on the claim that physicians are not in a position to know reliably what is in a patient's best interests (Buchanan, forthcoming). I believe at least as influential—even if often not explicitly stated—is an extreme subjectivism about values that assumes that the patient's own ultimate values, which define his or her own conception of the good, are incorrigible. By incorrigible, I mean they cannot be mistaken. In the standard case in which treatment is pursued for the patient's benefit, this extreme subjectivism is thought to support the patient's values guiding treatment decision making and treatment. I will explore this incorrigibility claim and will argue that on each of the main philosophical conceptions of the good for persons it is indefensible and should not be the basis for shared treatment decision making.Underlying this view of the physician-patient division of labor are assumptions and beliefs about the nature and relation of facts and values, and science and ethics, that are largely the legacy of a logical positivism that has long since been rejected by most philosophers. It is time that these unstable foundations for our normative ideal of the physician-patient relation were finally removed and replaced with more defensible underpinnings.Two Models of the Physician-Patient RelationshipPositivists insisted on a relatively sharp distinction between descriptive or empirical claims and science, on the one hand, and evaluative claims and ethics, on the other.2 Descriptive statements and the claims of science were to be true or false according to whether they in fact correctly described and explained the world. By remaining properly descriptive or empirical, science could, at least in principle, be entirely value neutral or value free.In its more extreme versions, positivism held that ethical judgments lacked cognitive content, but were instead expressions of emotions or attitudes, and as such could be neither true nor false, correct or mistaken. Because no evaluative statements were held to be logically entailed by any descriptive or empirical statements, moral reasoning was thought to be properly understood not as reasoning but as attempts at nonrational persuasion.3 Many drew from this an extreme subjectivism in ethics along the lines of what I have called above the incorrigibility thesis—there is no meaningful sense in which an individual's ultimate values defining his or her own conception of the good life could be mistaken, false, or unfounded.These... (shrink)

In discussions surrounding epistemology and rationality, it is often useful to assume an agent is rational or ideally rational. Often, this ideal rationality assumption is spelled out along the following lines: -/- 1. The agent believes everything about a situation which the evidence entitles her to believe and nothing which it does not. -/- 2. The agent believes all the logical consequences of any of her beliefs. -/- 3. The agent knows her own mind: if she believes P, she (...) believes that she believes P; and if she doesn't believe P, she believes that she doesn't believe P. -/- 4. The agent believes nothing of the form 'P and it is not the case that P.' -/- 5. If an agent's background belief-set satisfies 1-4 and if rationality requires the agent to add P to her belief-set, then the resulting belief-set will also satisfy 1-4. -/- While individually plausible, there are cases in which holding on to 1-5 generates paradox. Some resolve such paradoxical cases by granting 1-5 but arguing while ideally rational agents can exist, they can't possibly ever find themselves in such a situation: such case descriptions are epistemically incoherent. Others allow that rational agents can coherently find themselves in such odd circumstances, and argue that it's more reasonable to weaken our concept of ideal rationality and give up premise (2) above. However, this strategy has also been rejected. My aim in this paper is to defend the utility of positing an ideally rational agent in such paradoxical circumstances. I argue in such cases we should give up (2), in particular the assumption that (necessarily) if an ideally rational agent believes both P and the conditional, if P then Q, then she believes Q.. What's important is to hold on to the goal of positing ideal rationality: to maximize the amount of true or probably true information a thinker can justifiably believe in a given circumstance. Normally that will mean holding on to (2), but these unusual paradoxical cases are best handled by giving up (2). (shrink)

We describe a recipe for generating normal ideals on successors of singular cardinals. We show that these ideals are related to many weakenings of □ that have appeared in the literature. Our main purpose, however, is to provide an organized list of open questions related to these ideals.

Given an ideal $I$ , let $\mathbb{P}_{I}$ denote the forcing with $I$ -positive sets. We consider models of forcing axioms $MA(\Gamma)$ which also have a normal ideal $I$ with completeness $\omega_{2}$ such that $\mathbb{P}_{I}\in \Gamma$ . Using a bit more than a superhuge cardinal, we produce a model of PFA (proper forcing axiom) which has many ideals on $\omega_{2}$ whose associated forcings are proper; a similar phenomenon is also observed in the standard model of $MA^{+\omega_{1}}(\sigma\mbox{-closed})$ obtained from (...) a supercompact cardinal. Our model of PFA also exhibits weaker versions of ideal properties, which were shown by Foreman and Magidor to be inconsistent with PFA. Along the way, we also show (1) the diagonal reflection principle for internally club sets ( $\mathit{DRP}(IC_{\omega_{1}})$ ) introduced by the author in earlier work is equivalent to a natural weakening of “there is an ideal $I$ such that $\mathbb{P}_{I}$ is proper”; and (2) for many natural classes $\Gamma$ of posets, $MA^{+\omega_{1}}(\Gamma)$ is equivalent to an apparently stronger version which we call $MA^{+\operatorname{Diag}}(\Gamma)$. (shrink)

Multiply realizable kinds are scientifically problematic, for it appears that we should not expect discoveries about them to hold of other members of that kind. As such, it looks like MR kinds should have no place in the ontology of the special sciences. Many resist this conclusion, however, because we lack a positive account of the role that certain realization-unrestricted terms play in special science explanations. I argue that many such terms actually pick out idealizing models. Idealizing explanation has many (...) of the features normally associated with explanation by MR kinds. As idealized models are usually mere possibilia, such explanations do not run afoul of the metaphysical problems that plague MR kinds. (shrink)

We show that a cardinal κ is a (strongly) Mahlo cardinal if and only if there exists a nontrivial κ-complete κ-normal ideal on κ. Also we show that if κ is Mahlo and λ ≥ κ and $\lambda^{ then there is a nontrivial κ-complete κ-normal fine ideal on P κ (λ). If κ is the successor of a cardinal, we consider weak κ-normality and prove that if κ = μ + and μ is a regular cardinal (...) then (1) $\mu^{ if and only if there is a nontrivial κ-complete weakly κ-normal ideal on κ, and (2) if $\mu^{ then there is a nontrivial κ-complete weakly κ-normal fine ideal on P κ (λ). (shrink)

The notion of an ideal reasoner has several uses in epistemology. Often, ideal reasoners are used as a parameter of (maximum) rationality for finite reasoners (e.g. humans). However, the notion of an ideal reasoner is normally construed in such a high degree of idealization (e.g. infinite/unbounded memory) that this use is unadvised. In this dissertation, I investigate the conditions under which an ideal reasoner may be used as a parameter of rationality for finite reasoners. In addition, (...) I present and justify the research program of computational epistemology, which investigates the parameter of maximum rationality for finite reasoners using computer simulations. (shrink)

We study the distributivity of the bounded ideal on Pkλ and answer negatively to a question of Johnson in [13]. The size of non-normal ideals with the partition property is also studied.

The aim of this chapter is to understand how sortals determine what aesthetic properties an object has. It is argued that Frank Sibley’s notion of an ideal of beauty does not help us to achieve that aim. Instead, it is argued, the special aesthetic relevance of sortals is better understood by reference to the (non-aesthetic) ideas of normality and functionality associated with sortals. In passing, the paper also argues that there must be a maximum degree of beauty if non-comparative (...) judgments of beauty are possible, as they seem to be. (shrink)

It is a theorem of Rowbottom [12] that ifκis measurable andIis a normal prime ideal onκ, then for eachλ<κ,In this paper a natural structural property of ideals, distributivity, is considered and shown to be related to this and other ideal theoretic partition relations.The set theoretical terminology is standard and background results on the theory of ideals may be found in [5] and [8]. Throughoutκwill denote an uncountable regular cardinal, andIa proper, nonprincipal,κ-complete ideal onκ.NSκis the ideal (...) of nonstationary subsets ofκ, andIκ= {X⊆κ∣∣X∣<κ}. IfA∈I+ −I), then anI-partitionofAis a maximal collectionW⊆,P ∩I+so thatX∩ Y ∈IwheneverX, Y∈W, X≠Y. TheI-partitionWis said to be disjoint if distinct members ofWare disjoint, and in this case, fordenotes the unique member ofWcontainingξ. A sequence 〈Wα∣α<η} ofI-partitions ofAis said to be decreasing if wheneverα<β<ηandX∈Wβthere is aY∈Wαsuch thatX⊆Y.. (shrink)

In this paper, we propose a general constraint on theories of knowledge that we call ‘normalism’. Normalism is a view about the epistemic threshold that separates knowledge from mere true belief; its basic claim is that one knows only if one has at least a normal amount of epistemic support for one’s belief. We argue that something like normalism is required to do full justice to the normative role of knowledge in many key everyday practices, such as assertion, inquiry, (...) and testimony. The view of normality we employ to flesh out this claim is inspired by experimental work on the folk notion of normality, which suggests that folk judgments of what is ‘normal’ are based upon both statistical averages as well as normative ideals within the relevant target domain. Adopting this notion of normality to set the threshold for knowledge results in a view upon which knowledge is routinely available on an everyday basis without being a merely trivial achievement. We explore several interesting consequences of this view, including the implication that the threshold for knowing may change as, e.g., the ease of availability of information in an epistemic community changes over time. The result is a ‘shifty’ view of knowledge which nonetheless retains more stability than standard contextualist or pragmatic encroachment approaches. (shrink)

In this paper we show that if there is a weakly normal ideal on κ then for each $\eta < \kappa, E^\eta_\kappa$ fails. This greatly improves a theorem of C. A. Johnson.

The aim of the paper is to propose an understanding of idealization in terms of Nowak’s unitarian metaphysics. Two natural interpretations of the procedure are critically discussed and rejected as inadequate. The first account of idealization is unable to explain why idealized factors cease to exert influence on the investigated magnitude. The second account of idealization solves this problem but does so at the cost of blurring the distinction between idealization and abstruction. Moreover, it faces the consequence that the process (...) of idealization instead of leading to a sharper understanding of phenomena will normally result in making the picture more and more probabilistic. I propose a third account of idealization in unitarian terms that solves all three problems. (shrink)

This study aims to introduce a modal extension M4CC of Arieli, Avron, and Zamansky's ideal paraconsistent four-valued logic 4CC as a Gentzen-type sequent calculus and prove the Kripke-completeness and cut-elimination theorems for M4CC. The logic M4CC is also shown to be decidable and embeddable into the normal modal logic S4. Furthermore, a subsystem of M4CC, which has some characteristic properties that do not hold for M4CC, is introduced and the Kripke-completeness and cut-elimination theorems for this subsystem are proved. (...) This subsystem is also shown to be decidable and embeddable into S4. (shrink)

We give some general criteria, when κ-complete forcing preserves largeness properties-like κ-presaturation of normal ideals on λ (even when they concentrate on small cofinalities). Then we quite accurately obtain the consistency strength "NS λ is ℵ 1 -preserving". for λ > ℵ 2.

We strengthen a theorem of Gitik and Shelah [6] by showing that if κ is either weakly inaccessible or the successor of a singular cardinal and S is a stationary subset of κ such that $NS_{\kappa} \upharpoonright S$ is saturated then $\kappa \S$ is fat. Using this theorem we derive some results about the existence of fat stationary sets. We then strengthen some results due to Baumgartner and Taylor [2], showing in particular that if I is a $\lambda^{+++}-saturated$ normal (...) ideal on $P_{\kappa} \lambda$ then the conditions of being $\lambda^{+}-preserving$ , weakly presaturated, and presaturated are equivalent for I. (shrink)

According to recent scholarship within queer theory, heterosexuality maintains itself as a class by employing its epistemological authority for identifying and defining homosexuals. Heterosexuality is thus an ideological abstraction that privileges those with social and material advantages, rather than an accurate description of the actual, and thus heteronormative descriptions of sexuality correspond to Charles W. Mills’ description of ideal-as-idealized theory. Since ideological arguments cannot be overturned simply by appeals to rational debate, to what can we turn to subvert the (...) sense of entitlement and rightness that heteronormativity provides? Recent feminist philosophers have stressed the distinction between guilt as emotional self-assessment and existential guilt. Taking up Kierkegaard’s existential account of guilt, I claim that in order to advance a non-ideal theory of desire, which grounds critique in actual conditions, it is important to consider the nature of subjective attachments to exclusive, idealized conceptions of the ‘normal.’. (shrink)

This article raises the question of ‘normality’ today and the fracturing of health ideals along new lines of enablement and function. In particular the study asks if ‘functional’ and ‘dysfunctional’ are displacing ‘normal’ and ‘pathological’ as master biopolitical binarisms, and if so, what distinctions can be drawn between them. The discourse of ‘function’ and ‘dysfunction’ is certainly ubiquitous in two areas of research and practice: gerontology and sexology. In the former case ‘functional health’ is linked to successful aging represented (...) by technical tests around activities of daily living (ADLs) and risk-assessment profiles. In the latter case, sexual function and dysfunction have become all-encompassing markers of heterosexual competence, now largely detached from reproductive imperatives, but refashioned as integral to responsible and successful self-management. Presenting examples from both cases, the article concludes that functionality, circulating under the signs of ‘normal’, ‘natural’ and ‘healthy’, furnishes economic, technological, educational, professional, pharmacological and policy fields with a rich intellectual, practical and regulatory resource. (shrink)

With less than 0# two generic extensions ofL are identified: one in which ${\aleph_1}$ , and the other ${\aleph_2}$ , is almost precipitous. This improves the consistency strength upper bound of almost precipitousness obtained in Gitik M, Magidor M (On partialy wellfounded generic ultrapowers, in Pillars of Computer Science, 2010), and answers some questions raised there. Also, main results of Gitik (On normal precipitous ideals, 2010), are generalized—assumptions on precipitousness are replaced by those on ∞-semi precipitousness. As an application (...) it is shown that if δ is a Woodin cardinal and there is an ${f:\omega_1 \to \omega_1}$ with ${\|f\|=\omega_2}$ , then after ${Col(\aleph_2,\delta)}$ there is a normal precipitous ideal over ${\aleph_1}$ . The existence of a pseudo-precipitous ideal over a successor cardinal is shown to give an inner model with a strong cardinal. (shrink)

When Cicero uncovered and suppressed the Catilinarian Conspiracy as consul in 63 B.c., supporters hailed him ‘father of his country’ and proposed that he be awarded the oak crown normally given to a soldier who had saved the life of a comrade in battle . Our sources connect these honours with earlier heroes such as Romulus, Camillus and Marius, but the Elder Pliny writes as if Cicero was the first before Caesar and the Emperors to be given the title pater (...) patriae. Pliny's point may revolve around Senatorial initiative, and assuming this to be the case he really should have stressed that Cicero received the informal support of a limited number of Senators only, whereas Caesar and the Emperors were honoured by formal vote of the entire Senate. Perhaps Pliny was fooled by the prominence of those who spoke on Cicero's behalf, such as Cato, Catulus and Gellius Publicola. Opponents, on the other hand, angrily rejected calls that Cicero be recognised as the saviour of the state. In their eyes his execution of the Catilinarians marked him as a cruel tyrant. Metellus Nepos proposed Pompey's recall from the East in order to free Rome from Cicero's tyranny. Aside from echoes of patria potestas, it seems obvious that the Romans were thinking in terms of the conventional Greek antithesis between the good king who is like a father to his people and the selfish tyrant who treats his subjects as slaves. The Younger Pliny employs the same basic ideas in his Panegyricus: the cruel tyrant Domitian suppressed freedom and desired honour as a god ; the gentle Trajan is a citizen and father not a tyrant and master . Tacitus has this basic distinction in mind too. Nevertheless, as is well known, Pliny regularly addresses Trajan not as ‘father’ but as ‘master’ in Book 10 of his Letters. This was plainly an acceptable practice on the social plane, if not quite yet on the political. Augustus, Tiberius and Claudius indicated their opposition to dominus as a title for themselves, evidently for its connotations of autocracy and servitude. Domitian, damned as a tyrant, was accused of demanding to be addressed as dominus et deus. The title dominus existed from at least the first century A.d. as a common form of polite address between inferiors and superiors of free birth, not only between masters and slaves. It gradually gained acceptance as an official title of the Emperor through the second century and was advertised widely by the Severi. And yet its tone throughout this period could also be critical when understood in terms of the good king/tyrant antithesis. (shrink)

Em consideração às posturas de Kuhn e seus críticos, voltaremos nossa atenção para refletirmos sobre a possibilidade de uma ciência normal. A pergunta motivadora do problema central deste texto será: Há realmente uma ciência normal no sentido proposto por Kuhn? Pretendemos oferecer uma resposta que anuirá parcialmente com o ideal kuhniano de ciência normal.

Burke proved that the generalized nonstationary ideal, denoted by NS, is universal in the following sense: every normal ideal, and every tower of normal ideals of inaccessible height, is a canonical Rudin‐Keisler projection of the restriction of NS to some stationary set. We investigate how far Burke's theorem can be pushed, by analyzing the universality properties of NS with respect to the wider class of ‐systems of filters introduced by Audrito and Steila. First we answer a (...) question of Audrito and Steila, by proving that ‐systems of filters do not capture all kinds of set‐generic embeddings. We provide a characterization of supercompactness in terms of short extenders and canonical projections of NS, without any reference to the strength of the extenders; as a corollary, NS can consistently fail to canonically project to arbitrarily strong short extenders. We prove that ω‐cofinal towers of normal ultrafilters, e.g., the kind used to characterize I2 and I3 embeddings, are well‐founded if and only if they are canonical projections of NS. Finally, we provide a characterization of “ is Jónsson” in terms of canonical projections of NS. (shrink)

In an attempt to explore further the Madelung fluid-like representation of quantum mechanics, we derive the small perturbation equations of the fluid with respect to its basic states. The latter are obtained from the Madelung transform of the Schrödinger equation eigenstates. The fundamental eigenstates of de Broglie monochromatic matter waves are then shown to be mapped into the simple basic states of a fluid with constant density and velocity, where the latter is the de Broglie group velocity. The normal (...) modes with respect to these basic states are derived and found to also satisfy the de Broglie dispersion relation. Despite being dispersive waves, their propagation mechanism is equivalent to that of sound waves in a classical ideal adiabatic gas. We discuss the physical interpretation of these results. (shrink)

The ideal of autonomy has a positive and a negative aim. Its positive aim is to create the conditions in which more and more people can be more and more autonomous. Its negative aim is to prevent actions that cause serious harm and are normally both immoral and criminal. These two aims are incompatible. Increasing autonomy increases the frequency of crimes and decreasing the frequency of crimes requires decreasing autonomy. The incompatibility of these two aims has radical implications for (...) much current thinking about criminal justice. (shrink)

Let $\mathcal {I}$ be an ideal on $\omega $. For $f,\,g\in \omega ^{\omega }$ we write $f \leq _{\mathcal {I}} g$ if $f(n) \leq g(n)$ for all $n\in \omega \setminus A$ with some $A\in \mathcal {I}$. Moreover, we denote $\mathcal {D}_{\mathcal {I}}=\{f\in \omega ^{\omega }: f^{-1}[\{n\}]\in \mathcal {I} \text { for every } n\in \omega \}$ (in particular, $\mathcal {D}_{\mathrm {Fin}}$ denotes the family of all finite-to-one functions).We examine cardinal numbers $\mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathcal {I}} \times \mathcal (...) {D}_{\mathcal {I}}))$ and $\mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathrm {Fin}}\times \mathcal {D}_{\mathrm {Fin}}))$ describing the smallest sizes of unbounded from below with respect to the order $\leq _{\mathcal {I}}$ sets in $\mathcal {D}_{\mathrm {Fin}}$ and $\mathcal {D}_{\mathcal {I}}$, respectively. For a maximal ideal $\mathcal {I}$, these cardinals were investigated by M. Canjar in connection with coinitial and cofinal subsets of the ultrapowers.We show that $\mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathrm {Fin}} \times \mathcal {D}_{\mathrm {Fin}})) =\mathfrak {b}$ for all ideals $\mathcal {I}$ with the Baire property and that $\aleph _1 \leq \mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathcal {I}} \times \mathcal {D}_{\mathcal {I}})) \leq \mathfrak {b}$ for all coanalytic weak P-ideals (this class contains all $\bf {\Pi ^0_4}$ ideals). What is more, we give examples of Borel (even $\bf {\Sigma ^0_2}$ ) ideals $\mathcal {I}$ with $\mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathcal {I}} \times \mathcal {D}_{\mathcal {I}}))=\mathfrak {b}$ as well as with $\mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathcal {I}} \times \mathcal {D}_{\mathcal {I}})) =\aleph _1$.We also study cardinals $\mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathcal {J}} \times \mathcal {D}_{\mathcal {K}}))$ describing the smallest sizes of sets in $\mathcal {D}_{\mathcal {K}}$ not bounded from below with respect to the preorder $\leq _{\mathcal {I}}$ by any member of $\mathcal {D}_{\mathcal {J}}\!$. Our research is partially motivated by the study of ideal-QN-spaces: those cardinals describe the smallest size of a space which is not ideal-QN. (shrink)

Theoretical works in economics usually have a core consisting of proofs that a “model-economy” has certain properties. The economist constructs a model that can be looked on as a description of an economy, and then proves that certain relations hold in this economy and/or that certain relations in this economy depend on certain specific characteristics. The model-economy is usually described as simplified or idealized.