Hilbert took to using ideal elements in the 1890's, in both algebraic number theory and geometry. His Zahlbericht of 1897 popularized the concept of the ideal introduced by Dedekind in 1871 (which in turn formalized the concept of "ideal number" introduced by Kummer in the 1840's). His geometric work likewise followed a long history of ideal elements, some that originated in geometry and others that originated elsewhere and were applied to geometry. Important examples were:Piero (...) della Francesca's Ideal City.Points at infinity in projective geometry, originating in the 1430s from the "vanishing points" in perspective drawing.Imaginary points in algebraic geometry, originating from the imaginary numbers used by .. (shrink)

Domain extension in mathematics occurs whenever a given mathematical domain is augmented so as to include new elements. Manders argues that the advantages of important cases of domain extension are captured by the model-theoretic notions of existential closure and model completion. In the specific case of domain extension via ideal elements, I argue, Manders’s proposed explanation does not suffice. I then develop and formalize a different approach to domain extension based on Dedekind’s Habilitationsrede, to which Manders’s account (...) is compared. I conclude with an examination of three possible stances towards extensions via ideal elements. (shrink)

Roscoe Pound, former dean of Harvard Law School, delivered a series of lectures at the University of Calcutta in 1948. In these lectures, he criticized virtually every modern mode of interpreting the law because he believed the administration of justice had lost its grounding and recourse to enduring ideals. Now published in the U.S. for the first time, Pound's lectures are collected in Liberty Fund's The Ideal Element in Law, Pound's most important contribution to the relationship between law and (...) liberty. The Ideal Element in Law was a radical book for its time and is just as meaningful today as when Pound's lectures were first delivered. Pound's view of the welfare state as a means of expanding government power over the individual speaks to the front-page issues of the new millennium as clearly as it did to America in the mid-twentieth century. Pound argues that the theme of justice grounded in enduring ideals is critical for America. He views American courts as relying on sociological theories, political ends, or other objectives, and in so doing, divorcing the practice of law from the rule of law and the rule of law from the enduring ideal of law itself. Roscoe Pound is universally recognized as one of the most important legal minds of the early twentieth century. Considered by many to be the dean of American jurisprudence, Pound was a former Justice of the Supreme Court of Nebraska and served as dean of Harvard Law School from 1916 to 1936. Please note: This title is available as an ebook for purchase on Amazon, Barnes and Noble, and iTunes. (shrink)

This contribution sheds light on the role of infinite idealization in structural analysis, by exploring how infinite elements and finite element methods are combined in civil engineering models. This combination, I claim, should be read in terms of a ‘complementarity function’ through which the representational ideal of completeness is reached in engineering model-building. Taking a cue from Weisberg’s definition of multiple-model idealization, I highlight how infinite idealizations are primarily meant to contribute to the prediction of structural behavior in (...) Multiphysics approaches. (shrink)

This contribution sheds light on the role of infinite idealization in structural analysis, by exploring how infinite elements and finite element methods are combined in civil engineering models. This combination, I claim, should be read in terms of a ‘complementarity function’ through which the representational ideal of completeness is reached in engineering model-building. Taking a cue from Weisberg’s definition of multiple-model idealization, I highlight how infinite idealizations are primarily meant to contribute to the prediction of structural behavior in (...) Multiphysics approaches. (shrink)

This paper deals with the connection between the Boyle-Mariotte-law and the Van der Waals-law from the perspective of the Structuralist Theory Conception as well as the Pragmatic Idealization Concept. It was inspired by an interesting paper by Martti Kuokkanen and Timo Tuomivaara, recently published in this journal.1 One result of the Kuokkanen-Tuomivaara-paper is that the Boyle-Mariotte-law is not an idealized law and therefore not an idealized special case of the Van der Waals-law, but that its models can be expanded to (...) the models of an idealized special case of the Van der Waals-law. From the perspective of idealized diachronic theory-elements and -nets the second part of this result shall be questioned. (shrink)

ArgumentHistorians have accorded a privileged status to the analytic ideal of elements as a distinctive marker of “modern” chemistry. Boyle’s and Lavoisier’s have been used to characterize their modernity, which has in turn justified their status as the founding fathers of modern chemistry. It has been difficult, however, to establish a viable connection between these two fathers or the genealogy of their definitions. I argue in this paper that French didactic tradition gave rise to the definition Boyle stated (...) in the Sceptical Chymist, or the analytic/philosophical ideal of elements. He did not endorse the definition he gave, but criticized its lack of analytic rigor and philosophical sophistication. His critique served as a negative heuristic, leading to Nicolas Lemery’s analytic ideal of “chemical principles” as distinct from “natural principles.” Lemery’s definition survived in French didactic tradition, as is evidenced in Macquer’s and Guyton’s textbooks which provided direct precedents for Lavoisier’s analytic ideal of “elements or principles.”. (shrink)

Introduction. Bert HAMMINGA and Neil DE MARCHI: Préface. Bert HAMMINGA and Neil DE MARCHI: Idealization and the Defence of Economics: Notes Toward a History. Part I: General Observations on Idealization in Economics. Kevin D. HOOVER: Six Queries about Idealization in an Empirical Context. Bernard WALLISER: Three Generalization Processes for Economic Models. Steven COOK and David HENDRY: The Theory of Reduction in Econometrics. Maarten C.W. JANSSEN: Economic Models and Their Applications. Adolfo GARCÍA DE LA SIENRA: Idealization and Empirical Adequacy in Economic (...) Theory. Izabella NOWAKOWA and Leszek NOWAK: On Correspondence between Economic Theories. Uskali MÄKI: Isolation, Idealization and Truth in Economics. Part II: Case Studies of Idealization in Economics. Nancy CARTWRIGHT: Mill and Menger: Ideal Elements and Stable Tendencies. Wolfgang BALZER: Exchange Versus Influence: A Case of Idealization. Kees COOLS, Bert HAMMINGA, Theo A.F. KUIPERS: Truth Approximation by Concretization in Capital Structure Theory. Daniel M. HAUSMAN: Paul Samuelson as Dr. Frankenstein: When an Idealization Runs Amuck. Hugo A. KEUZENKAMP: What if an Idealization is Problematic? The Case of the Homogeneity Condition in Consumer Demand. Werner DIEDERICH: Nowak on Explanation and Idealization in Marx's 'Capital'. Gérard JORLAND: Idealization and Transformation. Jack BIRNER: Idealizations and Theory Development in Economics. Some History and Logic of the Logic Discovery. Discussions. Leszek NOWAK: The Idealizational Methodology and Economics. Replies to Diederich, Hoover, Janssen, Jorland and Mäki. (shrink)

The standing screens on the title is the oldest work extant of KANO Motonobu's work as folding screens of thick colored flowers and birds with golden background. This thesis designates that the scenery and the motif of the work are in correspondence with both descriptions of the scenery of Pure Land in several Buddhist scriptures and the design of actual gardens. Firstly, a peacock on the right hand screen is focused to indicate the bird connotes the elements of auspicious (...) birds in Buddhism, such as Mahamayuri and Kalavinka.Secondly, the elements of the scenery in the work, such as the four seasons at the same time ∼ the depiction of perpetuity ∼ and the existence of a pond, are identified with the description of Pure Land in Kwan-mu-liang-shou-ching and Ta-wuliang-shou-ching. These elements of the garden in the work are placed similarly to the Pure Land style gardens, which are illustrated in "Center and Surrounds of Kyoto" 's. In consideration of the above factors, the conclusion that, in the work, KANO Motonobu succeeded to portray the ideal garden by combining the scenery of Pure Land and that of actual gardens, is drawn. (shrink)

In this paper, we argue for an instrumental form of existence, inspired by Hilbert’s method of ideal elements. As a case study, we consider the existence of contradictory objects in models of non-classical set theories. Based on this discussion, we argue for a very liberal notion of existence in mathematics.

The terms “ideal theory” and “nonideal theory” are used in contemporary Anglophone political philosophy to identify alternative methodological approaches for justifying normative claims. Each term is used in multiple ways. In this article Alison M. Jaggar disentangles several versions of ideal and nonideal theory with a view to determining which elements may be helpful in designing models of real-world justice that are contextually relevant, morally plausible, and practically feasible.

Idealizations are ubiquitous in physics. They are distortions or falsities that enter into theories, laws, models, and scientific representations. Various questions suggest themselves: What are idealizations? Why do we appeal to idealizations and how do we justify them? Are idealizations essential to physics and, if so, in what sense and for which purpose? How can idealizations provide genuine understanding? If our motivation for believing in the existence of unobservable entities like electrons and quarks is that they are indispensable to our (...) best theories, should we also believe in the existence of indispensable idealizations? This Element will tackle such questions and offer an opinionated and selective introduction to philosophical issues concerning idealizations in physics. Topics to be covered include the concept of and reasons for introducing idealization, abstraction, and approximation, possible taxonomy and justification, and application to issues of mathematical Platonism, scientific realism, and scientific understanding. (shrink)

Moral theory has generally focused on resolving ethical dilemmas by identifying ethically sound options. Whether the focus is on consequences, duties, principles or virtues, ethical cases are often approached in ways that assume morally sound solutions can be found and followed. Such ‘ideal morality’ assumes that moral goodness is always possible, leaving people confident they have done the right thing. Such an approach becomes inadequate in disaster settings where any good solution is often difficult to see. This paper examines (...) recent work on nonideal moral theory as a useful model for disaster bioethics. This approach views moral dilemmas as situations where no choice is ideal and every option involves some element of unavoidable wrongdoing. Rather than straining for ideal answers, this approach acknowledges that sometimes the lesser of two evils is the best that can be done. Such situations inevitably lead to feelings of regret or guilt, commonly encountered in discussions of disaster bioethics. This paper explores the practical implications of nonideal approaches for disaster responders working in tragic situations. (shrink)

Two approaches to understanding the idealizations that arise in the Aharonov–Bohm effect are presented. It is argued that a common topological approach, which takes the non-simply connected electron configuration space to be an essential element in the explanation and understanding of the effect, is flawed. An alternative approach is outlined. Consequently, it is shown that the existence and uniqueness of self-adjoint extensions of symmetric operators in quantum mechanics have important implications for philosophical issues. Also, the alleged indispensable explanatory role of (...) said idealizations is examined via a minimal model explanatory scheme. Last, the idealizations involved in the AB effect are placed in a wider philosophical context via a short survey of part of the literature on infinite and essential idealizations. (shrink)

Ideals are important in social reality, but they have been neglected in theories of law, politics, and morality. This book has the role of ideals as its central theme. More specifically, it argues that ideals are necessary to understand pluralism, that they are key elements in controversy and debate, and that they enable development. It combines theoretical analysis of the concept of ideals with discussion of concrete debates and cases, including philosophical debates about politics and equality, sociological studies of (...) the diverse interpretations of the rule of law, and accounts of the development of environmental law and privacy law. Thus, the functioning of ideals is critically examined, showing the merits and limitations of an ideal-oriented approach. (shrink)

The Elements of Philosophy: Readings from Past and Present offers an extensive collection of classic and contemporary readings, organized topically into five main sections: Religion and Belief, Moral and Political Philosophy, Metaphysics and Epistemology, Philosophy of Mind and Language, and Life and Death. Within these broad areas, readings are arranged in clusters that address both traditional issues--such as the existence of God, justice and the state, knowledge and skepticism, and free will--and contemporary topics--including God and science, just war theory, (...) vegetarianism, and time travel. Carefully chosen selections from a wide range of pre-20th-century philosophers are paired with writings from more than fifty leading contemporary philosophers and thinkers. The traditional philosophers represented range from Plato and Aristotle to Immanuel Kant and A.J. Ayer; the contemporary philosophers include Saul Kripke, David Lewis, Thomas Nagel, Derek Parfit, Hilary Putnam, Robert Nozick, Judith Jarvis Thomson, John Rawls, Bernard Williams, and Susan Wolf. Also included are selections from linguist Noam Chomsky, physicist Albert Einstein, and psychologist William James. Edited by a team of scholars who are also highly esteemed instructors, The Elements of Philosophy is uniquely student-friendly. A team of undergraduate philosophy majors played a central role in helping to select topics, choose readings, and identify terms likely to require clarification. In response to their suggestions, the volume includes detailed introductions to each section, explanatory footnotes that define unfamiliar terms and concepts, an extensive glossary, and a guide to further resources. A companion Instructor's Manual, available on CD, offers article summaries, suggested essay questions, reading guides, model handouts, and sample syllabi. One of the most extensive and expansive anthologies available, The Elements of Philosophy is an ideal choice for both general and targeted introductory philosophy courses. (shrink)

The concept of Galilean Idealization is based on a pragmatically grounded relation between universes of so-called real and idealized entities. The concept was developed in the course of a critical discussion of different explications of the concept of idealization (e.g. by W. F. Barr, C. G. Hempel and L. Nowak), these being attempts to specify sufficient syntactic and semantic criterions for idealization. But this line of argument shall not be followed here. Instead, first the concept of Pragmatic Idealization, and as (...) its special case the Galilean one, is presented (1.) and certain aspects of the application of an idealized theory are discussed (2.). Then, working within the Strucuralist View of theories, definitions of the idealized variants of the diachronic theory-element and theory-net are presented (3.). (shrink)

The test of civilization is the power of drawing the most benefit out of cities." Ralph Waldo Emerson What is the role of the urban experience in the construction of American democratic ideals? By looking at the disparate visions of a just society advanced by Jefferson and Hamilton, this paper will attempt to provide an account of the historical role of the urban experience in the construction of the American vision of democracy. Then, through the works of John Dewey and (...) Lewis Mumford (and Robert Westbrook's account of their continuing disagreements), the essay will address some of the issues stemming from the role of urban experience in the processes of moral development. Then, through the work of Whitman, it will be argued that the urban experience is a necessary condition for the adequate development of democratic ideals. The essay will conclude with a brief analysis of some of the important elements of the urban experience, and their respective contributions to the construction of democratic values. (shrink)

Is there a unique way to de-idealize models? If not, how might the possible ways of reducing the distortion between models and reality differ from each other? Based on an empirical case study conducted in financial markets, this paper discusses how a popular valuation model (the Discounted Cash Flow model) idealizes reality and how the market participants de-idealize it in concrete market situations. In contrast to Cartwright's view that economic models are generally over-constrained, this paper suggests that valuation models are (...) under-constrained. This serves as the reason why the relaxation of simplifying assumptions and concretization do not work as methods of de-idealization. The paper finds that financial market participants de-idealize models using commentary that takes the form of judgment. As a conclusion, a hypothesis is formulated that proposes that the more underdetermined the model is the bigger role narrative and other pragmatic elements play in the process of model application. (shrink)

This paper discusses non-ideal theory as guidance for making bad situations better by morally permissible means. It distinguishes constructive theorizing, which suggests ways of improving specific kinds of bad situation, from cautionary theory, which concerns moral risks of actions under bad conditions. Reflective moral judgment yields cautionary precepts, identifying presumptively unjustifiable modes of action. The paper illustrates the application of precepts cautioning about coercion and the exposure of others to significant risks, by considering the 1955–1956 bus boycott in Montgomery, (...) Alabama, and the ‘Children’s Crusade’ of the 1963 Birmingham desegregation campaign. All such campaigns involve coercive elements, but the paper argues that coercion was not a morally significant factor in either case. Endangerment is another matter: given the violent, sometimes lethal, reactions to civil rights actions under Jim Crow, those two campaigns’ endangerment of innocent persons must be taken very seriously, especially as it concerns Birmingham. And, in fact, potentially lethal anti-reform violence occurred during each campaign. Relevant factors include the preparation and understanding of young participants and the difference in risk that is assumed by engaging in peaceful, nonviolent public actions. (shrink)

This article problematizes the republican reliance on contemporary ‘states as they are’ as protectors and guarantors of the republican notion of freedom as non-domination. While the principle of freedom as non-domination constitutes an advance over the liberal principle of freedom as non-interference, its reliance on the national, territorial, legal-technical and extra-economic contemporary state prevents the theoretical uncovering of its full potential. The article argues that to make the most of the principle of freedom as non-domination, a strong Athenian element is (...) required. The democratic confederalist project that is being experimented with by Syrian Kurds in the cantons of Rojava, it is maintained, can contribute theoretically and practically to this republican ideal through its democratic and participatory mechanisms, despite fundamental challenges it has to face. (shrink)

Mauricio Suárez and Agnes Bolinska apply the tools of communication theory to scientific modeling in order to characterize the informational content of a scientific model. They argue that when represented as a communication channel, a model source conveys information about its target, and that such representations are therefore appropriate whenever modeling is employed for informational gain. They then extract two consequences. First, the introduction of idealizations is akin in informational terms to the introduction of noise in a signal; for in (...) an idealization we introduce ‘extraneous’ elements into the model that have no correlate in the target. Second, abstraction in a model is informationally equivalent to equivocation in the signal; for in an abstraction we “neglect” in the model certain features that obtain in the target. They conclude that it becomes possible in principle to quantify idealization and abstraction in informative models, although precise absolute quantification will be difficult to achieve in practice. (shrink)

We say that $\mathcal {I}$ is an ideal independent family if no element of ${\mathcal {I}}$ is a subset mod finite of a union of finitely many other elements of ${\mathcal {I}}.$ We will show that the minimum size of a maximal ideal independent family is consistently bigger than both $\mathfrak {d}$ and $\mathfrak {u},$ this answers a question of Donald Monk.

Steve Biko is one of the most important liberation activists of his time. Yet, his theoretical contribution is not well understood or appreciated. This article reconstructs Biko’s political ideas and introduces a new integrated reading and interpretation of his writings, speeches, and recorded interviews. It argues that Biko’s Black consciousness ideal should not only be read as engaging an activist movement or programme but, also, as encompassing an original theoretical framework grounded in a communalist ethos of Biko’s own conceptual (...) development. It argues that Biko’s Black consciousness ideal sought to relate racialised oppression to a historically centred communalist solution framed by two interlocking structural elements—rightful power and free community. The article argues that only by a theoretical and normative consideration of these elements, on Biko’s own conceptual terms, do we get a coherent understanding of Biko’s distinctive view of free postcolonial society. (shrink)

J.S. Mackenzie surveys Western philosophy from Socrates to the New Realists in an uncomplicated and approachable style. Originally published in 1917, this text serves as a useful introduction to philosophy and well-summarises the key theories of great philosophers throughout the centuries and their bearing on early twentieth-century thought. It is ideal for students of Philosophy, both for beginners and the more advanced.

Besides the book under review here, the “30-Second” series of books includes numerous titles such as those on anatomy, architecture, astronomy, the Bible, brain, economics, maths, mythology, philosophies, politics, psychology, religion, and theories.Together with eight contributors, each a leading authority with a proven track record for successfully explaining science to a general audience, Eric Scerri, Lecturer in Chemistry at the University of California, Los Angeles; founder and editor of this journal; and the undisputed world authority on the history and philosophy (...) of the periodic table, has edited this most attractive addition to the series.The chemical elements, the separate building blocks of our physical universe, lend themselves ideally to this 30-second approach. In his introduction to the volume Scerri briefly sketches the plan of the book and discusses the evolution of the periodic table from Dmitri Ivanovich Mendeleev’s original proposal to the latest developments in the .. (shrink)

This paper shows that Cassirer’s philosophy of mathematics underwent a significant transformation by the end of the 1920s. This transformation was due to Cassirer’s reception of the ‘foundational crisis’ within mathematics itself. David Hilbert’s conception of the ‘ideal elements’ of mathematics attracted Cassirer’s particular attention. Indeed, he sought a ‘transcendental deduction’ of these elements. Reflection on this issue is therefore essential to providing an adequate interpretation of the later Cassirer’s enterprise in the philosophy of mathematics.

In this paper, I examine Kant’s reception of and solution to the problem of the unity of the political will. I propose that Kant distances himself from the modern paradigmatic foundations of sovereignty principally with his theses of the ideality of the general will and of the apriority of the justification of popular sovereignty. My interpretative hypothesis is that Kant solves the problem by grounding sovereignty in a conceptual element which is new in the history of political philosophy, i. e. (...) the a priori unified omnilateral will. In section IV, I explain why my reading of the ideality of the general will can respond to seemingly plausible objections arising from Kant’s own texts and how it works in the face of concrete political states of affairs. (shrink)

The article that discusses the issue of culturalism as an element of the idea of representation tries to examine a concept, which claims to represent reality through conceptualization, from scratch, or by going to the bottom in a manner of excavation. Foucault's archaeology was chosen as the most suitable method for this excavation activity. Because the archaeological method does not make a historical or meta-historical claim beyond the truth; it does not impose the necessary violence of the method on its (...) object. It grasps its object in its singularity, and most importantly, it thinks and suggests that the truth is no more than an invention. This archaeological study on the concept of culture tries to reveal the difference between the current meaning of the concept and its etymological origin and to grasp it in its singularity. In this way, the problematic relationship between the concepts that man invented and applied while engaging in understanding things that are happening around him will be revealed. Conceptualization is inherent in the idea of truth, which is based on absolutism and is no more than an invention, while ultimately subordinating the particular to the universal. While the article reveals the intolerance of the act of dichotomous thinking, which operates as a product of the effort to represent the truth, as in the nature-culture distinction, it acts according to the approach known as deconstruction in social sciences. In a representative thought, truth is what can actually be represented, presenting itself to the observer as an object of display. The fact that the understanding of truth is based on essentialist principles such as absolute, unchangeable, fixed, universal thanks to Plato makes an idealized representation inevitable. In fact, intellectual endeavors such as conceptualization, abstraction, and generalization mean the idealization of the concrete, singular, and unique by detaching it from its context. It can be said that underlying the idea of representation is the belief that the human mind can grasp the essence of things and therefore can represent them in thought, depending on the idea that truth is rational. As is, it is a thought that tries to keep realism in its hands, blesses it, and strives with all its might to declare its divine absolutism. Ultimately, while the mechanism of representation operates for the stable, it acts with the aim of establishing dominance. The distinction between the representative and the represented is ultimately the product of an anthropocentric perspective. Thanks to this distinction, it is inevitable that everything except the observer subject becomes the object of study. This point of view, believed to be one and universal, requires the fixation of the object of study. It can be said that the idea of representation, which signifies the ideal of absolute truth, underlies today's issues that are based on differences, such as language, religion, race, and gender, that have always been on the world agenda. As the products of representative thought, both binary categorization based on distinction such as nature and culture, and the concept that implies a direct relationship between thought and the outside world, realism is a state of alienation in which whatever is related to the human being ceases to belong to it and is used against it. The reification made possible by the distinction between the representative and the represented is actually nothing but alienation. It can be said that the rooted problem of the world of thought and the peoples of the world since Platonism is that reification and commodification have become so universal that they seem almost like natural, organic entities, and forms. The attempt of representative thought, which confines external reality to the conceptual world, to impose a framework on reality, breaks the connection with reality, and moreover, by being guided by concepts and abstractions, it builds iron cages around the human being. The insistence of Western thought on representation, no matter if it is true or false, no matter it is accepted or not, has led to the radical consequence of the abolition of certainty over reality. Today, the world of thought has evolved from the representation of the truth, which implies the idea that there is a necessary connection between the order of things and the order of words, to the reality of representation, where the boundary between reality and image is abolished, the reality is aestheticized and transformed into images, and society ultimately becomes cultural. With an entry into the cultural turn, everything has become cultural and conventional in the postmodern period. (shrink)

Faik Kurtulmuş’s exploration of the epistemic basic structure (EBS) invites us to think about the generation, dissemination, and absorption of knowledge in a society, emphasizing the role of institutions in determining epistemic outcomes. Moreover, Kurtulmuş—in joint work with Gürol Irzık—offers a normative take on the EBS from the viewpoint of the theory of justice and does not shy away from drawing specific policy recommendations. Thus, a powerful, innovative concept is used to extend an influential theory and draw out its practical (...) implications. What more is there to wish for? A project of such ambition inevitably faces serious challenges. I address the issue of the alignment between the ideal and non-ideal elements of Kurtulmuş’s theory with an eye toward the practicalities of social reform. My central claim is that the philosophers striving to promote distributive epistemic justice need to think carefully about whom they intend to address with their proposals and how to persuade such addressees. I also maintain that emphasis on a holistic approach to social reform represents a major hindrance to its pragmatic success. (shrink)

We consider the theory Thprin of Boolean algebras with a principal ideal, the theory Thmax of Boolean algebras with a maximal ideal, the theory Thac of atomic Boolean algebras with an ideal where the supremum of the ideal exists, and the theory Thsa of atomless Boolean algebras with an ideal where the supremum of the ideal exists. First, we find elementary invariants for Thprin and Thsa. If T is a theory in a first order (...) language and α is a linear order with least element, then we let Sentalg be the Lindenbaum-Tarski algebra with respect to T, and we let intalg be the interval algebra of α. Using rank diagrams, we show that Sentalg ⋍ intalg, Sentalg ⋍ intalg ⋍ Sentalg, and Sentalg ⋍ intalg. For Thmax and Thac we use Ershov's elementary invariants of these theories. We also show that the algebra of formulas of the theory Tx of Boolean algebras with finitely many ideals is atomic. (shrink)

Virtual objects, such as online shops, the elements that go to make up virtual life in computer games, virtual maps, e-books, avatars, cryptocurrencies, chatbots, holograms, etc., are a phenomenon we now encounter at every turn: they have become a part of our life and our world. Philosophers—and ontologists in particular—have sought to answer the question of what, exactly, they are. They fall into two camps: some, pointing to the chimerical character of virtuality, hold that virtual objects are like dreams, (...) illusions and fictions, while others, citing the real impact of virtuality on our world, take them to be real—an actual part of the real world, just like other real objects. In this article, we defend the thesis that both sides are wrong. Using Roman Ingarden’s phenomenological ontology, we advocate a position according to which a virtual object is a computationally grounded intentional object that has its existential foundation in computational processes, which are compliant with a certain model of computation. We point out that virtuality is framed by some kind of ideal mathematical objects: i.e., mathematical models of computation, which in turn fall, each of them, under their respective ideas. We also refer to the idea of natural computation, which in conjunction with the ontological analysis carried out leads to the thesis that an object can be more or less virtual. (shrink)

Introduction : changing forms of global order. Towards a multipolar world ; The paradox of our times ; Economic liberalism and international market integration ; Security ; The impact of the global financial crisis ; Shared problems and collective threats ; A cosmopolitan approach ; Democratic public law and sovereignty ; Summary of the book ahead -- Cosmopolitanism : ideas, realities and deficits. Globalization ; The global governance complex ; Globalization and democracy : five disjunctures ; Cosmopolitanism : ideas and (...) trajectories ; Cosmopolitan realities ; Addressing the institutional deficit : reframing the market -- Principles of cosmopolitan order. Cosmopolitan principles ; Thick or thin cosmopolitanism? ; Cosmopolitan justifications ; From cosmopolitan principles to cosmopolitan law -- Cosmopolitan law and institutional requirements. The idea of cosmopolitan law ; Institutional requirements ; In sum ; Political openings -- Violence, law and justice in a global age. Reframing human activity : international law, rights and responsibilities ; 9/11, war and justice ; Islam, the Kantian heritage and double standards ; Concluding reflections -- Reframing global governance : apocalypse soon or reform!. The paradox of our times ; Why be concerned with global challenges? ; Deep drivers and governance challenges ; Global governance : contemporary surface trends ; Problems and dilemmas of global problem-solving ; Strengthening global governance ; Global governance and the democratic question ; Multilevel citizenship, multilayered democracy -- Parallel worlds : the governance of global risks in finance, security and the environment. Global governance and the paradox of our times ; The global governance of finance ; The global governance of security ; The global governance of the environment ; Conclusion : crisis, politicization and reform -- Democracy, climate change and global governance. Democracy I : the democratic nation-state and climate change ; Democracy II : global governance and climate change ; The policy debate : squaring the circle? ; The political elements of a democratic global deal ; Democracy and the policy menu ahead. (shrink)

The field K((G)) of generalized power series with coefficients in the field K of characteristic 0 and exponents in the ordered additive abelian group G plays an important role in the study of real closed fields. Conway and Gonshor (see [2, 4]) considered the problem of existence of non-standard irreducible (respectively prime) elements in the huge "ring" of omnific integers, which is indeed equivalent to the existence of irreducible (respectively prime) elements in the ring K((G ≤ 0 )) (...) of series with non-positive exponents. Berarducci (see [1]) proved that K((G ≤ 0 )) does have irreducible elements, but it remained open whether the irreducibles are prime i.e.; generate a prime ideal. In this paper we prove that K((G ≤ 0 )) does have prime elements if G = (R, +) is the additive group of the reals, or more generally if G contains a maximal proper convex subgroup. (shrink)

(English abstract further below.) -/- Wer denkt, Polyamorie erfordere ein geringeres Maß an Verpflichtung als Zweierbeziehungen, der liegt gründlich daneben. Wie aber gestaltet sich polyamoröse wechselseitige Verpflichtung idealerweise? In diesem Beitrag untersuche ich, ob sich ein bestimmtes, auf Iris Murdochs Konzeption von Liebe als gerechter Aufmerksamkeit beruhendes Ideal wechselseitiger Verpflichtung in romantischen Partnerschaften fruchtbar auf polyamoröse Beziehungsgeflechte anwenden lässt. Ich beginne damit, Murdochs im deutschsprachigen Raum kaum rezipierte Liebeskonzeption ausführlich darzustellen und diese dabei von Simone Weils Position abzugrenzen, der (...) Murdoch wesentliche Elemente entnimmt. In einem zweiten Schritt skizziere ich das von Murdochs Position inspirierte Ideal wechselseitiger Verpflichtung. In Auseinandersetzung mit Überlegungen, die John Enman-Beech und Julienne Obadia mit Blick auf die in polyamorösen Beziehungsgeflechten verbreitete Praxis angestellt haben, Beziehungsvereinbarungen einzugehen, werbe ich drittens für die skizzierte Idealkonzeption, indem ich zeige, dass sich mit ihr den von Enman-Beech und Obadia aufgeworfenen Herausforderungen, die sich im Zuge intrapolykularer Beziehungsvereinbarungen stellen, in zwei Hinsichten mit Erfolg begegnen lässt. Erstens hebe ich hervor, dass eine am skizzierten Ideal orientierte Praxis bereits die Art von prozeduralen Normen implementiert, auf deren Bedeutung Enman-Beech zu Recht hinweist. Zweitens argumentiere ich dafür, dass das skizzierte Ideal nicht den Schwierigkeiten ausgesetzt ist, die sich nach Obadia mit denjenigen Elementen intrapolykularer Beziehungsvereinbarungen verbinden, die sie als Vertragskomplex bezeichnet, und ein weniger pessimistisches Bild davon nahelegt, wie vermittelst solcher Beziehungsvereinbarungen konstituierte Individuen aufzufassen sind. -/- ENGLISH ABSTRACT: In this paper, I focus on a certain ideal conception of how lovers may commit to each other in polyamorous relationships. Drawing on an analysis of Iris Murdoch’s adaptation of Simone Weil’s ideas, I sketch what I have elsewhere called the ideal lovers’ pledge—a conception of a commitment between lovers that is spelled out in terms of Weil’s and Murdoch’s shared notion of love as just attention. I then argue that this conception is well-suited to meet certain challenges that arise in the context of thinking about relationship agreements in polyamorous relationships, challenges that have been brought out in recent work by John Enman-Beech and Julienne Obadia. First, I show that practices of forging relationship agreements in polyamorous relationships that are oriented toward the ideal I propose will naturally implement the kind of procedural norms that Enman-Beech rightly highlights. Second, I argue that the ideal I propose does not generate the kinds of problems that according to Obadia arise due to a constellation of assumptions that she thinks underlie the practice of forging relationship agreements in polyamorous relationships – a constellation she dubs the contract complex. The proposed ideal thus suggests an alternative under-standing of such agreements and implies a less pessimistic account of what kind of individuals are constituted by way of forging such agreements. (shrink)

For Locke, Professor Konvitz suggests, political sovereignty is dependent upon the existence of a social contract between the sovereign, the legislature, and the people who, through this contract, agree to be governed. It is the right of the governed, acting as a whole, to revolt against their government when it no longer protects their natural rights and to seek a new government that will act in accordance with these rights. It is further the right of individuals within such a society (...) to refuse to act in accordance with specific laws that offend their personal conscience, but they should be prepared to suffer consequences for violating such laws. In the latter concept, Locke, Professor Konvitz asserts, has anticipated the essential elements of the concept of civil disobedience. (shrink)

Who am I? What is my purpose in life? These are timeless questions. Indian philosophy and the yoga tradition offer a comprehensive understanding of the human being, from its conception of the mind to the nature of the soul, a path of self-discovery and doorway to inner liberation. With a fresh and modern interpretation of the five elements: earth, water, air, fire, and space, readers are presented with a practical and assessable approach to knowing themselves more deeply, illuminating how (...) we might see other people with more compassion, tolerance, and acceptance. Chapters are organized by each element and include thoughtful, accessible exercises and practices to bring the reader into greater inner and outer balance. With a framework that integrates the physical body with the inner terrain of the subtle bodies, the book is an ideal guide for yoga practitioners and teachers to explore a modern interpretation of ancient wisdom. For contemporary spiritual seekers and individuals with no background or experience with yoga, Yoga and the Five Elements offers an imminently practical approach to self-development. (shrink)

This edition of Houston Stewart Chamberlain's Politische Ideale reveals the historical significance of Chamberlain in German conservative political philosophy. Contrasting the vital nationalistic state with the sterile commercialism of liberal democracies, moral freedom with the unruly selfishness of democratic parties, and the decaying culture of the Anglo-Saxon peoples with the relatively pure Teutonic, Chamberlain evokes in this work the principal elements of a genuinely conservative state.

The main purpose Robert Alexy tries to achieve with The argument from Injustice and all the other works he wrote on the same topic is to prove, against legal positivism, that law is a bidimensional concept comprising both a real or institutional dimension and an ideal one. As we know, positivism believes that law is valid for formal or factual reasons that just contingently, this is the inclusive variant, may incorporate moral elements; otherwise Professor Alexy believes that law, (...) the concept of law, is to be defined such that, alongside these fact oriented-properties, moral elements must be included. This paper is intended to analyse the core of Professor Alexy’s connection argument between factual and ideal dimensions of the law, in order to support this central conclusion: his theory is only perfectly acceptable as a theory “of and about” democratic and constitutional legal systems, and not if intended as a theory “of and about” the concept of law. (shrink)

The ideal of the bodhisattva was crucial in the development of the Mah y na branch of the Buddhist tradition. It provided a meeting ground for cardinal Mah y nist doctrines concerning praj, karun and ś nvat, as well as introducing into Buddhism more overtly religious elements which help to account for its popular appeal in those areas where the Mah y na took hold. The vow of the bodhisattva to forego entry into nirv na until all beings (...) “down to the last blade of grass” have been delivered raises several apparent contradictions and condundrums; these disappear in the light of a proper understanding of the pivotal Mah y nist doctrine of ś nvat. This paper examines the relationship of the bodhisattva ideal to the metaphysic of sunyata and discusses the place of this ideal in the spiritual economy of the Mah y na. (shrink)

Elekes proved that any infinite-fold cover of a σ-finite measure space by a sequence of measurable sets has a subsequence with the same property such that the set of indices of this subsequence has density zero. Applying this theorem he gave a new proof for the random-indestructibility of the density zero ideal. He asked about other variants of this theorem concerning I-almost everywhere infinite-fold covers of Polish spaces where I is a σ-ideal on the space and the set (...) of indices of the required subsequence should be in a fixed ideal ${{\mathcal{J}}}$ on ω. We introduce the notion of the ${{\mathcal{J}}}$ -covering property of a pair ${({\mathcal{A}}, I)}$ where ${{\mathcal{A}}}$ is a σ-algebra on a set X and ${{I \subseteq \mathcal{P}(X)}}$ is an ideal. We present some counterexamples, discuss the category case and the Fubini product of the null ideal ${\mathcal{N}}$ and the meager ideal ${\mathcal{M}}$ . We investigate connections between this property and forcing-indestructibility of ideals. We show that the family of all Borel ideals ${{\mathcal{J}}}$ on ω such that ${\mathcal{M}}$ has the ${{\mathcal{J}}}$ -covering property consists exactly of non weak Q-ideals. We also study the existence of smallest elements, with respect to Katětov–Blass order, in the family of those ideals ${\mathcal{J}}$ on ω such that ${\mathcal{N}}$ or ${\mathcal{M}}$ has the ${\mathcal{J}}$ -covering property. Furthermore, we prove a general result about the cases when the covering property “strongly” fails. (shrink)

An intriguing though little noticed trend within moral theology over the last half century or so is the move towards re-conceptualising moral norms previously considered mandatory into ideals. The ideal-normative turn has been taken by official Catholic and Anglican ecclesial documents, in both cases as regards the closely related matters of marital permanence and extra/post-marital unions. Yet the turn has occurred with little or no scrutiny of the distinction at its heart, that between ideal and mandatory norms. This (...) article applies the distinction to an analysis of New Testament moral normativity, with particular focus on teachings on marriage. Through this examination core elements of New Testament normativity are clarified and the credibility of the ideal-normative turn as it pertains to marital permanence is thereby challenged. (shrink)

Some realists in political theory deny that the notion of feasibility has any place in realist theory, while others claim that feasibility constraints are essential elements of realist normative theorising. But none have so far clarified what exactly they are referring to when thinking of feasibility and political realism together. In this article, we develop a conception of the realist feasibility frontier based on an appraisal of how political realism should be distinguished from non-ideal theories. In this realist (...) framework, political standards are feasible if they meet three requirements: they are politically intelligible, contextually recognisable as authoritative, and contestable. We conclude by suggesting that our conception of realist feasibility might be compatible with utopian demands, thereby possibly finding favour with realists who otherwise refuse to resort to the notion of feasibility. (shrink)

In formal semantics, structure is treated as the essential ingredient in the creation of sentence meaning from individual word meaning. This book introduces some of the foundational concepts, principles and techniques in the formal semantics of natural language and outlines the mathematical principles that underlie linguistics meaning. Using English examples, Yoad Winter presents the most useful tools and concepts of formal semantics in an accessible style and includes a variety of practical exercises so that readers can learn to utilize these (...) tools effectively. For readers with an elementary background in set theory and linguistics or with an interest in mathematical modelling, this fascinating study is an ideal introduction to natural language semantics. Designed as a quick yet thorough introduction to one of the most vibrant areas of research in modern linguistics today this volume reveals the beauty and elegance of the mathematical study of meaning. (shrink)