Let P be any one of the following combinatorial properties: weak P-pointness, weak (semi-) Q-pointness, weak (semi-)selectivity, ω-closedness. We deal with the following two questions: (1) What is the least cardinal κ such that there exists an ideal with κ many generators that does not have the property P? (2) Can one extend every ideal with the property P to a prime ideal with the property P?

In lieu of an abstract, here is a brief excerpt of the content:Kennedy Institute of Ethics Journal 10.1 (2000) 103-108 [Access article in PDF] Letters "Small Sacrifices" in Stem Cell Research Madam: I agree with Professors McGee and Caplan (in their article "The Ethics and Politics of Small Sacrifices in Stem Cell Research," KIEJ, June 1999) that the question of the nature and status of the source of stem cells must be addressed. However, in their eagerness to convince us of (...) the smallness of the sacrifices, I think the authors use some unfortunate rhetorical devices and move much too quickly over some necessary distinctions.The rhetorical display is unfortunate if the article is intended to be a fair and rational development of an argument--e.g., those who hold a position in opposition to the authors do not argue they "inveigh." The section on the political area of the controversy seems particularly dismissive of other's positions.However, I will focus on just two areas where I think a more nuanced consideration would make the question of the moral legitimacy of the "small sacrifices" of embryos less obvious than the authors' rhetoric would suggest.First, they claim that opponents of such research assume some sort of "super status" for an embryo. The rights generally conceded to born human beings may not be as "weak" as they characterize. But even considering only the "negative right against unwarranted violence," I think the authors misdescribe the situation. Contrary to their assertion, I do not know when "adults and even children are... forced to give life... in the defense or at least interest of the community's highest ideals and most pressing interests" (p. 153). Could they be speaking of capital punishment, justified in the name of protecting the community? But then why mention children?It is true that not everyone can be guaranteed every means to preserving and enhancing life. But this limitation on positive rights is not a "forced giving." Adults may be compelled to risk life--e.g. in a draft for the sake of a war. But, again, the more or less justifiable imposition of a risk is not the same as selecting out one particular individual or class to be directly killed. Neither adults nor born children are compelled to be killed for the sake of organ "donation," even if a greater number might be saved. If one grants equivalent status to the embryo (as the authors seem to do here for the sake of argument), opponents do not have to claim a "super status" for embryos, just the ordinary human right not to be killed even for "compassionate" motives.A second area where I think the authors move too quickly is in their impoverished definition of the essential humanity of the early embryo as exhaustively represented by the physical structure of its DNA. The authors seem to recognize [End Page 103] that, ordinarily, there is more to personhood than sheer physical structure. For example, they mention memories and habits (p. 154). They could also speak of relationships, attitudes, and the like. Since an early embryo has no such components of personality as we experience it, the authors hold that its identity could only be contained in its DNA. Since this DNA is preserved, even spread far and wide, by the use of stem cells, it almost seems as if we are doing the early embryo a favor by breaking it up.However, just because the embryo does not have any conscious memories or other attributes of character or personality, that does not mean its identity is constituted only by its physical structure described statically. The early embryo is not just a bundle of discrete structures, and its DNA is not just an inert lump made up of certain smaller lumps. Both the embryo and its DNA are active. Thus the identity of even an early embryo includes both its current processes and the innate potential for further activity and development. Although lacking a conscious will, the early embryo is already in a sense an agent, already doing things--growing, changing, and heading toward something that... (shrink)

The field of business ethics has shown little attention to the dynamics of memory in maintaining moral character. Yet memory is a complex process that involves the repression of some experiences in order to protect the moral integrity of the personality. Without the capacity to repress what one's moral conscience would not accept, the mind can be overtaken by neurotic ambivalence and moral confusion. In the context of business competition, where the pressures for potential gains and losses can be immense, (...) long repressed desires can receive renewed strength resulting in a weakening of moral constraint. In this essay, I use the psycho-analytic theory of repression to investigate the complex, psychological vicissitudes of human memory. The theory of repression is a particularly powerful tool to investigate the moral implications of memory because memories which are repressed - i.e., forbidden consciousness - are done so at the behest of the individual's moral ideals. Experiences that offend these ideals or threaten the integrity of the ego can be repressed. Repression, then, is an infallible index of moral judgement. I will apply the theory of repression to the characters in and story line of Arthur Miller's play "Death of a Salesman" to elucidate the relationship between memory and ethics in business. "Death of a Salesman" is well suited for this purpose because the memories of the main characters are central to the play and are inextricably linked to the moral challenge competition in business poses. (shrink)

This contemporary examination of moral theory succinctly covers the full range of theoretical positions, from extreme particularism to moral ideals. Students are challenged to think critically about abstract theories and to use acquired knowledge to support moral experience. In this comprehensive approach to the study of ethics the student is exposed to numerous positions, asked to consider their strengths and weaknesses, and guided to understand how typically opposed theories can jointly aid moral decision making.

We answer a question of Cummings and Magidor by proving that the P-ideal dichotomy of Todorčević refutes ${\square}_{\kappa, \omega}$ for any uncountable $\kappa$. We also show that the P-ideal dichotomy implies the failure of ${\square}_{\kappa, < \mathfrak{b}}$ provided that $cf(\kappa) > {\omega}_{1}$.

When visual attention is directed away from a stimulus, neural processing is weak and strength and precision of sensory data decreases. From a computational perspective, in such situations observers should give more weight to prior expectations in order to behave optimally during a discrimination task. Here we test a signal detection theoretic model that counter-intuitively predicts subjects will do just the opposite in a discrimination task with two stimuli, one attended and one unattended: when subjects are probed to discriminate (...) the unattended stimulus, they rely less on prior information about the probed stimulus’ identity. The model is in part inspired by recent findings that attention reduces trial-by-trial variability of the neuronal population response and that they use a common criterion for attended and unattended trials. In five different visual discrimination experiments, when attention was directed away from the target stimulus, subjects did not adjust their response bias in reaction to a change in stimulus presentation frequency despite being fully informed and despite the presence of performance feedback and monetary and social incentives. This indicates that subjects did not rely more on the priors under conditions of inattention as would be predicted by a Bayes-optimal observer model. These results inform and constrain future models of Bayesian inference in the human brain. (shrink)

In this paper, we study some new examples of ideals on $$\omega $$ with maximal Tukey type (that is, maximal among partial orders of size continuum). This discussion segues into an examination of a refinement of the Tukey order—known as the weak Rudin–Keisler order—and its structure when restricted to these ideals of maximal Tukey type. Mirroring a result of Fremlin (Note Mat 11:177–214, 1991) on the Tukey order, we also show that there is an analytic P-ideal above all (...) other analytic P-ideals in the weak Rudin–Keisler order. (shrink)

We show that if κ is an infinite successor cardinal, and λ > κ a cardinal of cofinality less than κ satisfying certain conditions, then no ideal on Pκ is weakly λ+-saturated. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Knowing Persons is an original study of Plato's account of personhood. For Plato, embodied persons are images of a disembodied ideal. The ideal person is a knower. Hence, the lives of embodied persons need to be understood according to Plato's metaphysics of imagery. For Gerson, Plato's account of embodied personhood is not accurately conflated with Cartesian dualism. Plato's dualism is more appropriately seen in the contrast between the ideal disembodied person and the embodied one than in the (...) contrast between mind or soul and body. (shrink)

Ideal interpretation is understanding a text in the best possible way. It is usually used when the text has a canonical status, such as the Bible or the U.S. Constitution. We argue that Zhu Xi’s view about interpreting the Four Books and Ronald Dworkin’s view about constitutional interpretation are examples of ideal interpretation and that their basic principles are similar. Each holds, roughly, that their target text contains moral truth; that the author’s mind requires the mediation of learning; (...) that the purpose of interpretation is not only to lead the reader to the moral truth but to become a better person; that all propositions are about the same moral truth or about political justice; that the interpretation ultimately must come from oneself, purged of prejudices; and that the only correct interpretation is one that captures the original meaning. (shrink)

In this unique work, James P. Sterba argues that traditional ethics has yet to confront the three significant challenges posed by environmentalism, feminism, and multiculturalism. He maintains that while traditional ethics has been quite successful at dealing with the problems it faces, it has not addressed the possibility that its solutions to these problems are biased in favor of humans, men, and Western culture. In Three Challenges to Ethics: Environmentalism, Feminism, and Multiculturalism, Sterba examines each of these challenges. In the (...) case of environmentalism, he argues that traditional ethics must incorporate conflict resolution principles that favor nonhumans over humans in a significant range of cases. In terms of feminism, he maintains that traditional ethics should rule out gendered family structures and implement an ideal of androgyny. In regard to multiculturalism, he contends that traditional ethics must endorse an ethics that is secular in character and that can survive an extensive comparative evaluation of both Western and non-Western moral ideals and cultures. The only textbook devoted to this topic, Three Challenges to Ethics is an engaging text for introductory courses in ethics and moral problems and is also interesting and provocative reading for scholars and general readers. (shrink)

Tradução para o português do ensaio "Social Morality and Individual Ideal”. Publicado originalmente em Philosophy: The Journal of the Royal Institute of Philosophy, vol. XXXVI, n. 136, p. 1-17, Jan. 1961. Republicado em: STRAWSON, P. F. Freedom and Resentment and Other Essays. Londres: Methuen, 1974. [Routledge, 2008, p. 26-44]. ]. Publicado na coletânea: Ensaios sobre a filosofia de Strawson: com a tradução de Liberdade e ressentimento & Moralidade social e ideal individual. Organizadores: Jaimir Conte & Itamar Luís Gelain. (...) Editora da UFSC, 2015. ISBN: 9788532807250. (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)

Men make for themselves pictures of ideal forms of life. Such pictures are various and may be in sharp opposition to each other; and one and the same individual may be captivated by different and sharply conflicting pictures at different times. At one time it may seem to him that he should live—even that a man should live —in such-and-such a way; at another that the only truly satisfactory form of life is something totally different, incompatible with the first. (...) In this way, his outlook may vary radically, not only at different periods of his life, but from day to day, even from one hour to the next. It is a function of so many variables: age, experiences, present environment, current reading, current physical state are some of them. As for the ways of life that may thus present themselves at different times as each uniquely satisfactory, there can be no doubt about their variety and opposition. The ideas of self-obliterating devotion to duty or to the service of others; of personal honour and magnanimity; of asceticism, contemplation, retreat; of action, dominance and power; of the cultivation of “an exquisite sense of the luxurious”; of simple human solidarity and co-operative endeavour; of a refined complexity of social existence; of a constantly maintained and renewed affinity with natural things—any of these ideas, and a great many others too, may form the core and substance of a personal ideal. (shrink)

This book considers the common human predicament that we often choose an action other than the one we perceive to be best. Philosophers know this problem as _akrasia_. The author develops a nuanced understanding of the nature and causes of _akrasia_ by integrating the best insights of Socrates, Aristotle, Augustine, and Aquinas, and several contemporary philosophers.

Weak measurements offer new insights into the behavior of quantum systems. Combined with post-selection, quantum mechanics predicts a range of new experimentally testable phenomena. In this paper I consider weak measurements performed on time-dependent pre- and post-selected ensembles, with emphasis on the decay of excited states. The results show that the standard exponential decay law is a limiting case of a more general law that depends on both the time of post-selection and the choice of final state. The (...) generalized law is illustrated for two interesting choices of post-selection. (shrink)

We locate winning strategies for various ${\mathrm{\Sigma }}_{3}^{0}$ -games in the L-hierarchy in order to prove the following: Theorem 1. KP+Σ₂-Comprehension $\vdash \exists \alpha L_{\alpha}\ models"\Sigma _{2}-{\bf KP}+\Sigma _{3}^{0}-\text{Determinacy}."$ Alternatively: ${\mathrm{\Pi }}_{3}^{1}\text{\hspace{0.17em}}-{\mathrm{C}\mathrm{A}}_{0}\phantom{\rule{0ex}{0ex}}$ "there is a β-model of ${\mathrm{\Delta }}_{3}^{1}-{\mathrm{C}\mathrm{A}}_{0}\text{\hspace{0.17em}}\text{\hspace{0.17em}}+\text{\hspace{0.17 em}}{\mathrm{\Sigma }}_{3}^{0}$ -Determinacy." The implication is not reversible. (The antecedent here may be replaced with ${\mathrm{\Pi }}_{3}^{1}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left({\mathrm{\Pi }}_{3}^{1}\right)-{\mathrm{C}\mathrm{A}}_{0}:\text{\hspace{0.17em}}{\mathrm{\Pi }}_{3}^{1}$ instances of Comprehension with only ${\mathrm{\Pi }}_{3}^{1}$ -lightface definable parameters—or even weaker theories.) Theorem 2. KP +Δ₂-Comprehension +Σ₂-Replacement + ${\mathrm{\Sigma }}_{3}^{0}\phantom{\rule{0ex}{0ex}}$ -Determinacy. (Here AQI (...) is the assertion that every arithmetical quasi-inductive definition converges.) Alternatively: $\Delta _{3}^{1}{\rm CA}_{0}+{\rm AQI}\nvdash \Sigma _{3}^{0}$ -Determinacy. Hence the theories: ${\mathrm{\Pi }}_{3}^{1}-{\mathrm{C}\mathrm{A}}_{0},\text{\hspace{0.17em}}{\mathrm{\Delta }}_{3}^{1}-{\mathrm{C}\mathrm{A}}_{0}+\text{\hspace{0.17em}}{\mathrm{\Sigma }}_{3}^{0}-\mathrm{D}\mathrm{e}\mathrm{t}\phantom{\rule{0ex}{0ex}}$ -Det, ${\mathrm{\Delta }}_{3}^{1}-{\mathrm{C}\mathrm{A}}_{0}+\mathrm{A}\mathrm{Q}\mathrm{I}$ , and ${\mathrm{\Delta }}_{3}^{1}-{\mathrm{C}\mathrm{A}}_{0}\phantom{\rule{0ex}{0ex}}$ are in strictly descending order of strength. (shrink)

Ideal for introductory ethics courses, The Moral Life: An Introductory Reader in Ethics and Literature, Fifth Edition, brings together an extensive and varied collection of ninety-one classical and contemporary readings on ethical theory and practice. Integrating literature with philosophy in an innovative way, this unique anthology uses literary works to enliven and make concrete the ethical theory or applied issues addressed. It also emphasizes the personal dimension of ethics, which is often ignored or minimized in ethics anthologies. The readings (...) are enhanced by chapter introductions, study questions, suggestions for further reading, and biographical sketches. The fifth edition adds ten new readings, eight of which appear in two new chapters: Feminist Ethics and the Ethics of Care and Global Economic Justice. An updated Companion Website at www.oup.com/us/pojman provides self-quizzes, essay questions, and helpful links for students and reading summaries, a test bank, and PowerPoint-based lecture slides for instructors. (shrink)

We look at a hierarchical arrangement of ideals in an MV -algebra. The principal classes of ideals studied are the maximals, the primes, the local and perfect ideals and the semi-locals. Beyond these special classes of ideals are the general ideals. Herein we study some relationships among these classes and, more specifically, the products of ideals of these classes. Among the results obtained are the square of a prime ideal is a local ideal, the finite product of prime (...) ideals is a semilocal ideal. We also show that the set of local ideals shares many of the properties of the class of prime ideals, as the Lying Over Theorem and the Going Up Theorem. (shrink)

We define theories of bounded arithmetic, whose definable functions and relations are exactly those in certain complexity classes. Based on a recursion-theoretic characterization of NC in Clote , the first-order theory TNC, whose principal axiom scheme is a form of short induction on notation for nondeterministic polynomial-time computable relations, has the property that those functions having nondeterministic polynomial-time graph Θ such that TNC x y Θ are exactly the functions in NC, computable on a parallel random-access machine in polylogarithmic parallel (...) time with a polynomial number of processors.0 We then define three theories of weak second-order arithmetic which respectively characterize relations in the classes of alternating logarithmic time, logspace and nondeterministic logspace. (shrink)

Are the political ideals of liberty and equality compatible? This question is of central and continuing importance in political philosophy, moral philosophy, and welfare economics. In this book, two distinguished philosophers take up the debate. Jan Narveson argues that a political ideal of negative liberty is incompatible with any substantive ideal of equality, while James P. Sterba argues that Narveson's own ideal of negative liberty is compatible, and in fact leads to the requirements of a substantive (...) class='Hi'>ideal of equality. Of course, they cannot both be right. Thus, the details of their arguments about the political ideal of negative liberty and its requirements will determine which of them is right. Engagingly and accessibly written, their debate will be of value to all who are interested in the central issue of what are the practical requirements of a political ideal of liberty. (shrink)

Classics of Philosophy, 2/e, is the most comprehensive anthology of writings in Western philosophy in print. Spanning 2500 years of thought, it is ideal for introduction to philosophy and history of philosophy courses that are structured chronologically. More than seventy works by forty-two philosophers as well as fragments from the Pre-Socratics are included, offering students and general readers alike an extensive and economical collection of the major works of the Western tradition. This anthology contains the most important writings from (...) Thales to Rawls; seventeen of these are complete works, while the others are judiciously abridged so that little of value to the student is lost. Unabridged works include such classics as Plato's The Apology, Descartes's Meditations on First Philosophy, Leibniz's The Monadology, Hume's An Enquiry Concerning Human Understanding, Kant's Foundation for the Metaphysic of Morals, Mill's Utilitarianism, Russell's A Free Man's Worship, Sartre's Existentialism and Humanism, and Rawls's "Justice as Fairness." A lucid introduction, including a brief biographical sketch, accompanies each of the featured philosophers. Classics of Philosophy, 2/e, provides an extensive view of the most significant stages of growth in Western philosophy, including its birth with the Pre-Socratics as well as its contemporary developments. The second edition includes new selections by Augustine, Berkeley, Hume, Wollstonecraft, Nagel, and Foot. (shrink)

Tradução para o português do ensaio "Freedom and Resentment”, de P. F. Strawson. Publicado originalmente em Proceedings of the British Academy, v. 48, 1960. Republicado em Freedom and Resentment and Other Essays. Londres: Methuen, 1974. [Routledge, 2008, p. 2-28]. Publicado na coletânea: Ensaios sobre a filosofia de Strawson: com a tradução de Liberdade e ressentimento & Moralidade social e ideal individual. Organizadores: Jaimir Conte & Itamar Luís Gelain. Editora da UFSC, 2015. ISBN: 9788532807250.

Pursuing the proof-theoretic program of Friedman and Simpson, we begin the study of the metamathematics of countable linear orderings by proving two main results. Over the weak base system consisting of arithmetic comprehension, II 1 1 -CA0 is equivalent to Hausdorff's theorem concerning the canonical decomposition of countable linear orderings into a sum over a dense or singleton set of scattered linear orderings. Over the same base system, ATR0 is equivalent to a version of the Continuum Hypothesis for linear (...) orderings, which states that every countable linear ordering either has countably many or continuum many Dedekind cuts. (shrink)

IΣ n andBΣ n are well known fragments of first-order arithmetic with induction and collection forΣ n formulas respectively;IΣ n 0 andBΣ n 0 are their second-order counterparts. RCA0 is the well known fragment of second-order arithmetic with recursive comprehension;WKL 0 isRCA 0 plus weak König's lemma. We first strengthen Harrington's conservation result by showing thatWKL 0 +BΣ n 0 is Π 1 1 -conservative overRCA 0 +BΣ n 0 . Then we develop some model theory inWKL 0 and (...) illustrate the use of formalized model theory by giving a relatively simple proof of the fact thatIΣ 1 provesBΣ n+1 to be Π n+2-conservative overIΣ n . Finally, we present a proof-theoretic proof of the stronger fact that theΠ n+2 conservation result is provable already inIΔ 0 + superexp. ThusIΣ n+1 proves 1-Con (BΣ n+1) andIΔ 0 +superexp proves Con (IΣ n )↔Con(BΣ n+1). (shrink)

One of the predominant debates in AI Ethics is the worry and necessity to create fair, transparent and accountable algorithms that do not perpetuate current social inequities. I offer a critical analysis of Reuben Binns’s argument in which he suggests using public reason to address the potential bias of the outcomes of machine learning algorithms. In contrast to him, I argue that ultimately what is needed is not public reason per se, but an audit of the implicit moral assumptions of (...) societies within which algorithms are built and applied. Public justification is appealing since it offers us the possibility to align the decision-making outcomes of the algorithm with the core moral values of stakeholders within a constitutional democratic society. My concern is that the common moral principles that form the foundation of public reason are not necessarily neutral, as they still express specific moral ideals and normative standards even if there is moral agreement by society as a whole, or among different stakeholders within society. Appealing to such normative standards may thus still lead to algorithmic outcomes being biased as common moral values may very well still be discriminatory even though they are formed from a consensus, and even if public reason is applied as a kind of filter for potential algorithmic outcomes. Hence, I argue that these implicit moral norms within society that we take as a given in public reasoning, need to be audited from generation to generation in order to effectively mitigate potential algorithmic bias. (shrink)

The weak objectification of physical properties is shown to yield the same probabilistic implications as strong objectification and can therefore be refuted on the basis of suitable interference experiments. An alternative test of hypothetical objectification statements, as they occur in the EPR experiment, is based on joint probabilities and the ensuing Bell inequalities. Quantum mechanics turns out to be partially compatible with Bell's inequalities even in cases where weak objectification is excluded by interference.

Aron Gurwitsch claims that the field of consciousness is invariantly organized in a theme, thematic field, margin pattern. However, at least two perceptual presentations, chaos and boundlessness, are not ordered in accordance with this pattern. The question this study poses then is the following: given Gurwitsch's field-theory of experiential organization, what is the structure, status, and function of chaos and boundlessness in the field of consciousness? ;Using Gurwitsch's field-theory organization as a base, the structure of thematic chaos and then of (...) thematic boundlessness is articulated: the first by contrasting the field-theories of Gurwitsch and James, the second by contrasting Gurwitsch and Kant. It is concluded that in both cases no thematic Gestalt-coherence and no thematic field as relevant context is presented. ;In terms of status and function, chaos and boundlessness are interpreted as necessary limits. These "limit cases" are not "ideal limits" since they are possible perceptual presentations. Also, limit is taken to mean a two-edged presentation, one that is both an ending and a beginning. Interpreting Gurwitsch, we conclude that both cases are epistemological endings, since they represent a necessary end to the ordinary perception of things. Interpreting James, we conclude that it is possible that thematic chaos is also a metaphysical beginning in experience, since it is that experience in which reality is presented as underived and original. Interpreting Kant, we conclude that it is possible that boundlessness is also an ethical beginning in experience, since it is that experience in which the most original feeling of our sense of humanity is presented. ;We show that chaos and boundlessness each have their own unique field-organization, that they function as two-edged limits involving epistemological concerns on the one hand and metaphysical and ethical concerns respectively on the other, and that their structure and status as limits in the field of consciousness are not contingent but necessary. (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)

At the beginning of the twentieth century in the Russian-speaking philosophical space philosophical projects emerged which brought ontology and gnoseology closer together. One can observe this process, for example, in the philosophical doctrines of the Russian intuitivists Nikolay Lossky and Semyon Frank. I demonstrate that the emergence of these doctrines and the development of their onto-gnoseological categorial apparatus were mainly connected with the criticism of the Neo-Kantian theory of cognition and the possibility of transcendent knowledge as such. The main sources (...) of my study are The Intuitive Basis of Knowledge and The World as an Organic Whole by N. O. Lossky and The Object of Knowledge and The Unknowable by S. L. Frank. My investigation makes it possible to treat Lossky’s categorial framework as the representation of a system of levels of the universe each of which is characterised by two aspects: the ontological, i.e. it is part of the unity of the world, and the gnoseological, i.e. it has an independent cognitive significance. Frank considers categories to be an organic part of the ontological proof of intuitivism. A common trend in the construction of categorial schemes by Lossky and Frank is their striving to combine gnoseological and ontological descriptions of categories. The key difference is the way an onto-gnoseological system as a whole is justified. In revealing the contradictions in Lossky’s conception, I proceed from the critical remarks of S. A. Askoldov, pointing out that these contradictions stem from an absolutisation of intuition in cognition, the renunciation of the idea of gnoseological transcendence, incompleteness of the theory of immanence and discordance between onto-gnoseological categories. Askoldov’s critical comments clarify the substantive features of Lossky’s theory and the essence of the transformations carried out in Frank’s absolute ideal-realism. (shrink)

Did the Greeks believe in their mythology? The answer is difficult, for “believe” means so many things… Not everyone believed that Minos continued to be a judge in Hell or that Theseus defeated the Minotaur, and they knew that poets “lie.” Nevertheless, their manner of not believing gave reason for concern, for Theseus was no less real in their eyes. It is simply necessary to “purify myth with reason’“ and to reduce the biography of the companion of Hercules to its (...) historic kernel. As for Minos, after a prodigious mental effort, Thucydides extracts the same kernel from his subject: “Of all those whom we know only by hearsay, Minos was the first to have a fleet.” The father of Phaedra, the husband of Pasiphaë is nothing more than a king who was master of the sea. The purification of the mythical by the logos is not an episode in the eternal struggle, from the beginning to Voltaire and Renan, between superstition and reason, a struggle which was the glory of Greek genius. The myth and the logos, despite Nestle, are not simple opposites like truth and error. Myth was a subject of serious reflections, and the Greeks had not yet finished with it six centuries after the Sophist movement which has been called their Aufklärung. Far from being a triumph of reason, the purging of myth by logos is a very dated program whose absurdity is surprising. Why did the Greeks make themselves unhappy for nothing by seeking to separate the wheat from the chaff instead of rejecting in one gesture the fantasy of both Theseus and the Minotaur, the very existence of a fabulous Minos as well as the implausible qualities with which the myth endows this Minos? (shrink)

We study the degree of (weak) Q-pointness, and that of (weak) P-pointness, of ideals on a regular infinite cardinal.

This dissertation offers a critical discussion of the prioritisation of ‘the right’ in John Rawls’s theory of justice. Rawls’s theory of justice – ‘justice as fairness’ – is arguably one of the best illustrations of the prioritisation of ‘the right’ in current political literature. However, his theory has been criticised by a diversity of thinkers for its implied structural relation between ‘the right’ and ‘the good’. Some theorists argue that conceptually ‘the good’ can never be derived from ‘the right’; others (...) argue that, even if it were possible, the social implications of such a conceptualisation would devastating as it would result in a so-called “community of strangers” (Rorty 1988, 273). In this dissertation, I argue that be on the one hand, theories that prioritise ‘the right’– such as ‘justice as fairness’ – enable the attractive possibility of the multiple coexistence of ‘comprehensive goods’. This is attractive as it upholds the liberating ethos: ‘I have the freedom to determine my own ends’. This possibility is attributed to the fact of neutrality, which characterises the priority of ‘the right’. The claim of neutrality is embedded in the ideal that political principles can be developed prior to and independently of any content of ‘the good’. This is then supposed to justify the claim that political principles are non-reliant on comprehensive moral ideals. In this way, the prioritisation of ‘the right’, as evident in ‘justice as fairness’, supposedly enables citizens to construct impartial universal principles that govern their society. Yet, on the other hand, I question the degree of neutrality present in ‘justice as fairness’. I argue that ‘justice as fairness’, although its justification is independent of a singular moral truth, is not neutral concerning ‘the good’. In fact, the moral values encapsulated in the priority of ‘the right’, I argue, set the conditions of justification of all doctrines of ‘the good’ because any idea of ‘the good’ that embodies contradictory values to those encapsulated in the priority of ‘the right’ would necessarily be excluded from a Rawlsian society. Therefore, I argue that Rawls’s theory of justice cannot be said to take into account “a diversity of conflicting and irreconcilable yet reasonable comprehensive doctrines” (Rawls 2001, 34); as moral values are already implied in the prioritising of ‘the right’. In light of how Rawls’s theory of justice is simultaneously neutral and prescriptive regarding ‘the good’, I suggest a re-problematisation of the debate on the relationship between ‘the right’ and ‘the good’. The literature on theories that prioritise ‘the right’ or ‘the good’ seems to imply such theories either embody the one or the other methodological approach. I argue that this debate has been presented as a false dichotomy and, as such, the debate itself seems to be exhausted, because it creates a kind of natural impasse. Therefore, I suggest recasting the debate in terms of representing ‘the right’ and ‘the good’ as two methodological positions on a continuum, that are at the same time both more or less gradually similar and divergent from one another. The purpose of this continuum is to demonstrate that notions such as neutrality, objectivity and comprehensiveness are not clear-cut. (shrink)

D. Z. Phillips is a leading figure in advocating a Wittgensteinian approach to the philosophical study of religion. His writings exert an important influence on contemporary philosophy of religion, giving a new direction to the philosophical discussion of religious belief and practice. Although his work has prompted much - often critical - comment, a thorough investigation has not been forthcoming. Grammars of Faith fills that gap. The book pays close attention to Wittgenstein's own remarks on religious belief, arranging them against (...) the background of his broader philosophical methodology, as well as to the efforts of the early Wittgensteinians at providing a more comprehensive Wittgensteinian philosophy of religion. Central to this study are Phillips's understanding of philosophical enquiry as a form of contemplation, and his descriptive accounts of religious belief. By means of a careful and methodical examination of Phillips's oeuvre, the study seeks to present a fair assessment of Phillips's position, showing not only its weaknesses, but also its strength. (shrink)

In this one-of-a-kind text, George P. Fletcher, a renowned legal theorist, offers a provocative yet accessible overview of the basics of legal thought. The first section of the book is designed to introduce the reader to fundamental concepts such as the rule of law and deciding cases under the law. It continues with an analysis of the values of justice, desert, consent, and equality, as they figure into our judgment of legal cultures in terms of soundness and legitimacy. The final (...) chapters address the problems of morality and consistency in the law. In each case the author not only introduces the basic ideas but considers important arguments in the contemporary literature and raises original claims of his own. Ideally suited for courses in the philosophy of law, legal issues, and jurisprudence, Basic Concepts of Legal Thought fills a void in the literature, as there is no other volume that both eases law students into the mysteries of legal philosophy and provides an introduction to the legal mind for non-lawyers. (shrink)