This is a short expository account of the regularity lemma for stable graphs proved by the authors, with some comments on the model theoretic context, written for a general logical audience.

We show how to build various models of first-order theories, which also have properties like: tree with only definable branches, atomic Boolean algebras or ordered fields with only definable automorphisms. For this we use a set-theoretic assertion, which may be interesting by itself on the existence of quite generic subsets of suitable partial orders of power λ + , which follows from ♦ λ and even weaker hypotheses . For a related assertion, which is equivalent to the morass see Shelah (...) and Stanley [16]. The various specific constructions serve also as examples of how to use this set-theoretic lemma. We apply the method to construct rigid ordered fields, rigid atomic Boolean algebras, trees with only definable branches; all in successors of regular cardinals under appropriate set- theoretic assumptions. So we are able to answer the following algebraic question. Saltzman's Question . Is there a rigid real closed field, which is not a subfield of the reals? (shrink)

Assuming 0 ♯ does not exist, we present a combinatorial approach to Jensen's method of coding by a real. The forcing uses combinatorial consequences of fine structure (including the Covering Lemma, in various guises), but makes no direct appeal to fine structure itself.

For a centerless group G, we can define its automorphism tower. We define G α : G 0 = G, G α+1 = Aut(G α ) and for limit ordinals ${G^{\delta}=\bigcup_{\alpha<\delta}G^{\alpha}}$ . Let τ G be the ordinal when the sequence stabilizes. Thomas’ celebrated theorem says ${\tau_{G}<(2^{|G|})^{+}}$ and more. If we consider Thomas’ proof too set theoretical (using Fodor’s lemma), we have here a more direct proof with little set theory. However, set theoretically we get a parallel theorem without (...) the Axiom of Choice. Moreover, we give a descriptive set theoretic approach for calculating an upper bound for τ G for all countable groups G (better than the one an analysis of Thomas’ proof gives). We attach to every element in G α , the αth member of the automorphism tower of G, a unique quantifier free type over G (which is a set of words from ${G*\langle x\rangle}$ ). This situation is generalized by defining “(G, A) is a special pair”. (shrink)

This paper grew as a continuation of [Sh462] but in the present form it can serve as a motivation for it as well. We deal with the same notions, all defined in 1.1, and use just one simple lemma from there whose statement and proof we repeat as 2.1. Originally entangledness was introduced, in [BoSh210] for example, in order to get narrow boolean algebras and examples of the nonmultiplicativity of c.c-ness. These applications became marginal when other methods were found (...) and successfully applied (especially Todorčevic walks) but after the pcf constructions which made their début in [Sh-g] and were continued in [Sh462] it seems that this notion gained independence.Generally we aim at characterizing the existence of strong and weak entangled orders in cardinal arithmetic terms. In [Sh462, §6] necessary conditions were shown for strong entangledness which in a previous version was erroneously proved to be equivalent to plain entangledness. In §1 we give a forcing counterexample to this equivalence and in §2 we get those results for entangledness (certainly the most interesting case). A new construction of an entangled order ends this section. In §3 we get weaker results for positively entangledness, especially when supplemented with the existence of a separating point (Definition 2.2). An antipodal case is defined in 3.10 and completely characterized in 3.11. Lastly we outline in 3.12 a forcing example showing that these two subcases of positive entangledness comprise no dichotomy. The work was done during the fall of 1994 and the winter of 1995. The second author proved Theorems 1.2, 2.14, the result that is mentioned in Remark 2.11 and what appears in this version as Theorem 2.10(a) with the further assumptionden(I)θ< μ. The first author is responsible for waving off this assumption (actually by showing that it holds in the general case), for Theorems 2.12 and 2.13 in Section 2 and for the work which is presented in Section 3. (shrink)

In this article, we develop and clarify some of the basic combinatorial properties of the new notion of n-dependence recently introduced by Shelah. In the same way as dependence of a theory means its inability to encode a bipartite random graph with a definable edge relation, n-dependence corresponds to the inability to encode a random -partite -hypergraph with a definable edge relation. We characterize n-dependence by counting φ-types over finite sets, and in terms of the collapse of random ordered -hypergraph (...) indiscernibles down to order-indiscernibles. (shrink)

We set up a general context in which one can prove Sauer-Shelah type lemmas. We apply our general results to answer a question of Bhaskar [1] and give a slight improvement to a result of Malliaris and Terry [7]. We also prove a new Sauer-Shelah type lemma in the context of op-rank, a notion of Guingona and Hill [4].

We give a simplified proof of the main lemma in “Ramsey filters and the reaping number—Con” by Goldstern and Shelah.

We outline a framework for analyzing episodes from the history of science in which the application of mathematics plays a constitutive role in the conceptual development of empirical sciences. Our starting point is the inferential conception of the application of mathematics, recently advanced by Bueno and Colyvan. We identify and discuss some systematic problems of this approach. We propose refinements of the inferential conception based on theoretical considerations and on the basis of a historical case study. We demonstrate the usefulness (...) of the refined, dynamical inferential conception using the well-researched example of the genesis of general relativity. Specifically, we look at the collaboration of the physicist Einstein and the mathematician Grossmann in the years 1912--1913, which resulted in the jointly published ``Outline of a Generalized Theory of Relativity and a Theory of Gravitation,'' a precursor theory of the final theory of general relativity. In this episode, an independently developed mathematical theory, the theory of differential invariants and the absolute differential calculus, was applied in the process of physical theorizing aiming at finding a relativistic theory of gravitation. We argue that the dynamical inferential conception not only provides a natural framework to describe and analyze this episode, but it also generates new questions and insights. We comment on the mathematical tradition on which Grossmann drew, and on his own contributions to mathematical theorizing. We argue that the dynamical inferential conception allows us to identify both the role of heuristics and of mathematical resources as well as the systematic role of problems and mistakes in the reconstruction of episodes of conceptual innovation and theory change. (shrink)

How is it possible that emotions in the community can be influenced by media? According to the paper’s concept, this is only understandable if we accept with Marshall McLuhan that media and the human body are not separable. There is no divide. The medium is the message expressed through the body/human being. This has preconditions, because the connection must be based on an analog principle that serves as the transmitter. This lies in non-discursive affectively relevant forms and an equally affectively (...) evaluative mode of perception, as empirical research now confirms. On this basis, as Daniel N. Stern shows, people operate “with vigorous goal-directedness to assure social interactions.” This points to the second premise, that every body/human being – infallibly – perceives a promise in communion with others, namely that of happiness, security, and community. This concept has far-reaching implications for how communities understand themselves, as the research of poststructuralists and frame theorists demonstrates, and as the trial and death of Socrates in ancient Athens attests. (shrink)

Vorbemerkungen: Die Exponenten der spekulativen Ästhetik in der Mitte des 19. Jahrhunderts vertreten die Ansicht, dass eine Begegnung mit den verschiedenen Gegenstandsbereichen der Welt und unsere Einordnung in diese Weltbezüge nur gelingen kann, wenn nicht alles rein zufällig und verschieden ist, sondern vielmehr in einer alles übergreifenden Einheit zusammengehört und einer höheren Idee folgt. […] [Denn] das Schöne steht für den höheren Sinn von allem, was ist und geschieht. In Übereinstimmung mit diesem Grundsatz, jedoch auf völlig anderen Grundlagen, kommen zu (...) jener Zeit Vorstellungen auf, in denen es um den konkreten Nachweis des Schönen, Wahren und Guten in allem geht und damit darum, den betreffenden Wert der Dinge aus ihnen selbst abzuleiten. Es sind die Vertreter der Formwissenschaft, die im Sinne einer exakten Wissenschaft danach streben, diesen Nachweis des Wertes eines jeden (und von allem) aus dem Gegebenen selbst zu erschließen. […]. (shrink)

The exponential rise in transgender self-identification invites consideration of what constitutes an ethical response to transgender individuals’ claims about how best to promote their well-being. In this paper, we argue that ‘accepting’ a claim to medical transitioning in order to promote well-being would be in the person’s best interests iff at the point of request the individual is correct in their self-diagnosis as transgender (i.e., the distress felt to reside in the body does not result from another psychological and/or societal (...) problem) such that the medical interventions they are seeking will help them to realise their preferences. If we cannot assume this—and we suggest that we have reasonable grounds to question an unqualified acceptance in some cases—then ‘acceptance’ potentially works against best interests. We propose a distinction between ‘acceptance’ and respectful, in-depth exploration of an individual’s claims about what promotes their well-being. We discuss the ethical relevance of the unconscious mind to considerations of autonomy and consent in working with transgender individuals. An inquisitive stance, we suggest, supports autonomous choice about how to realise an embodied form that sustains well-being by allowing the individual to consider both conscious and unconscious factors shaping wishes and values, hence choices. (shrink)

Since the beginning of the 20th Century to the present day, it has rarely been doubted that whenever formal aesthetic methods meet their iconological counterparts, the two approaches appear to be mutually exclusive. In reality, though, an ahistorical concept is challenging a historical analysis of art. It is especially Susanne K. Langer´s long-overlooked system of analogies between perceptions of the world and of artistic creations that are dependent on feelings which today allows a rapprochement of these positions. Krois’s insistence on (...) a similar point supports this analysis. - I - Unbestritten bis heute gilt, formwissenschaftliche und ikonologische Methoden scheinen sich grundsätzlich auszuschließen, da die ersteren auf ahistorischen und die letzteren auf historischen Grundlagen aufbauen. Dem entgegen soll mit diesem Beitrag gezeigt werden, wie insbesondere die Forschungen Susanne K. Langers und ergänzend diejenigen von John M. Krois eine Annäherung beider Positionen ermöglichen. (shrink)

La obra de Sauer abre paso a la formación del saber ambiental de nuestro tiempo y contribuye a su desarrollo en América Latina. El artículo sigue una serie de temas profundizados por el autor, y concluye recordándonos que el aterrador impacto del moderno mundo Occidental, no cancela la verdad de que el la historia del hombre ha sido marcadamente pluralista, y que no existen leyes generales de la sociedad, sino únicamente acuerdos culturales.

Neither the art historians Panofsky and Warburg nor the philosopher Cassirer had any interest with their cultural-historical research in fact-based, historical questions. An approach that had become common in the 19th century due to the loss of validity of the speculative aesthetics. On the contrary, instead of this substantial understanding as the documentary concept represents, these researchers focused on a functional understanding of art historical sources. Nevertheless, in contrast to this starting point, Panofsky invented a methodological procedure, the so-called iconological (...) method, which in turn led back to a documentary-focused historical analysis of artistic artefacts that is still recognized today. The goal is to rediscover the original background of Panofsky´s method. This should make it clear that the original idea of the image concept pursued by Warburg and Cassirer, which had been lost or obscured by the aftermath of National Socialism in Germany, can be made fruitful in a new light today. This path may open up iconology to “image science”/Bildwissenschaft and thus transform the former from a purely historical approach to an understanding relevant to cultural processes and thus to human action. (shrink)

Everyday media consumption leaves no doubt that the perception of moving images from various media is characterized by experience and understanding. Corresponding research in this field has shown that the stimulus patterns flooding in on us are not only processed mentally, but also bodily. Building on this, the following study argues that incoming stimuli are processed not only visually, but multimodally, with all senses, and moreover affectively. The classical binding of a sensory organ to a medium, on whose delimitation the (...) common understanding of multimodality is based, is thus abolished. Can arguments for this assumption be found? Building on the research of cultural anthropologist Ernst Cassirer and his successors, the two American philosophers Susanne K. Langer and John M. Krois, and supported by research from the life sciences in which, in parallel, the arts also play an important role in understanding image formation, as in the work of Heinz Werner and, following on from this, in the more recent research of the child psychologist Daniel N. Stern in collaboration with mirror neuron research by the group of neuroscientists around Giacomo Rizzolatti in Parma, justifications for this will be provided. What the multimodal processing of film images is concretely based on will finally be made clear by means of an exemplary analysis of a video film by the Swiss artist Pipilotti Rist. It aims to prove, that the prerequisites for the thesis can only lie in the fact, that both the modes of perception (visual, tactile, auditory, olfactory, gustatory) as well as the medially conditioned modes of image formation are based on non-discursive, formal-abstract structures that are also processed affectively. At the same time, the analysis thus shows how the selection and composition of the vital experienced forms can provide information about the socio-culturally shaped self-image of the producer and the viewer. (shrink)

To relate theories of affordance and frame with the tradition of formal aesthetics, philosophical iconology and the life sciences (keyword Vitality Semiotics) is the starting point of the paper. According to this approach, the structural preconditions of images, as determined by materials, techniques and the composition of the design means, become essential. Through these structures, the producers are able to set impulses that become decisive for the interpretation of space and time or the "scene" as a dynamic event. Against the (...) social and cultural background of the recipients the "scene" gains a meaning to their life. This means to understand the productʼs conception and composition as an affordance which determines the framework of the reception conditions. The benefit of this approach lies in the identification of changes in the self-understanding and thus of trends in to new standards of societies. This is to be illustrated by Exekiasʼ drinking bowl around 540/30 BC in Munich. (shrink)

Notini et al 1 offer a timely addition in the wake of a significant increase in young people identifying as transgender and gender diverse. The authors focus specifically on the case of 18-year-old Phoenix’s request for ongoing puberty suppression to affirm a non-binary gender identity. A central issue raised by Phoenix’s predicament, and that I suggest we can extend to ethical consideration of requests for other types of medical intervention by binary and non-binary TGD individuals, is whether we should ‘affirm’ (...) the claims made by TGD young people about what promotes their well-being. As a clinician working with TGD young people who have undergone a range of medical interventions to align their bodies with their gender identity, my starting presumption is that it is important to respect what people think will help them: there are some TGD young people for whom, all things considered, medical interventions to affirm gender identity promote their well-being. Well-being has become an important conceptual currency in ethical debates and lies at the core of the authors’ analysis of Phoenix’s case. While the authors do not ground their argument in favour of OPS in a specific theory of well-being, welfarist considerations 2 appear to underpin …. (shrink)

Notini _et al_ 1 offer a timely addition in the wake of a significant increase in young people identifying as transgender and gender diverse. The authors focus specifically on the case of 18-year-old Phoenix’s request for ongoing puberty suppression to affirm a non-binary gender identity. A central issue raised by Phoenix’s predicament, and that I suggest we can extend to ethical consideration of requests for other types of medical intervention by binary and non-binary TGD individuals, is whether we should ‘affirm’ (...) the claims made by TGD young people about what promotes their well-being. As a clinician working with TGD young people who have undergone a range of medical interventions to align their bodies with their gender identity, my starting presumption is that it is important to respect what people think will help them: there are some TGD... (shrink)

Implicit cognition is cognition that happens automatically and (typically) non-consciously. In moral psychology, implicit cognition is almost always understood in terms of dual process models of moral judgment. In this chapter, we address the question whether implicit moral judgment is usefully cashed out in terms of automatic (“type 1”) processes, and what the limitations of this approach are. Our chapter has six sections. In (1), we provide a brief overview of dual process models of domain-general (moral and non-moral) cognition. (2) (...) reviews a recent debate regarding the soundness of dual process models to begin with. Section (3) is about dual process accounts of moral judgment specifically. The last three sections then survey attempts to go beyond a simplistic automatic/controlled (“type 2”) distinction in conceptualizing implicit moral cognition. Recently, three main theoretical approaches have emerged, which all revolve around the questions whether type 2 processing can successfully penetrate implicit moral cognition. First, rational learning approaches highlight how episodes of moral learning can feed back into and shape our moral intuitions (4). Second, so-called triple process models suggest that automatic cognitive outputs can under certain circumstances be reined in by reflective cognition (5). Finally, recent evidence shows that moral reasoning is not as impotent as earlier developments in empirical moral psychology claimed to demonstrate (6). (shrink)

Aesthetics versus Art History? Ernst Cassirer as Mediator in an ongoing Controversy on the Relevance of Art for Life. Against the background of Ernst Cassirer’s cultural philosophy, art studies are to be classified as cultural studies. Central to this is Cassirer’s philosophy as the basis for answering a question that has been posed by the methods of formal aesthetics and iconology since the 19th century but is still unanswered today, namely the question of the relevance of the arts for life. (...) In this way, aesthetics/Kunstwissenschaft and art history gain a new meaning as cultural studies beyond their achievements in the humanities and in epistemology. (shrink)

What is reality? It is postmodern or poststructuralist philosophers like Roland Barthes, who realized that it only seems that the media present reality in the form of facts, because they actually spread myths. Accordingly, Jacques Derrida made it clear that communication via media is not based on logic, but is characterized by a significant “différance” between a “marque” (trace) of the past and the expectations of the future. Both agreed, that the initial misunderstanding of the concept of reality must be (...) uncovered or "deconstructed". This is more than necessary for them, because media, be it pictures or language, in truth convey values that are culturally and socially significant. They ‘iterate’ these values subliminally, because what shows up are only placeholders and thus mere forms (“structures of graphematic”) that are superficially realised as facts (“stereotypes”). In this way, according to Barthes, we all accept without question the values hidden behind them, so that they can gain a normative power that unconsciously guides our thinking, our decisions and our actions. Afterwards, it is Judith Butler who critically asked: How can we ever escape from this? Given the power of the subliminal dominant discourses, she saw the only effective solution “im Umdeuten” (in reinterpretation) of their subliminal values. In order to finally escape this “parasitic existence at the ritual”, the media philosopher Walter Benjamin already suggested to trigger "Chockwirkungen” (shock effects) in the viewer. It is the German painter Karin Kneffel, so it shall be shown, who has realized this with her series Fruits and Interiors in the most beautiful photorealistic strategy. (shrink)

Do we communicate with pictures? If so, the text asks, what about their complex, dynamic appearances? Are they part of the communication process? By analysing a cover image of the journal Jugend from 1896 and by consulting the research on the logic of pictures (“Eigenlogik”) in Bildwissenschaft, Iconology and Cultural Anthropology these questions shall be persued. The analysis suggests, that instead of consenting the results of epistemological aesthetic research a new understanding of pictures shall be implemented: They can be considered (...) as parts of cultural semiotic processes. That means, it is not the view of something (epistemology) but the view of someone (culture) that is shown by the pictures. - I - -/- Kommunizieren wir über Bilder? Falls das zutrifft, stellt sich die Frage, ob daran auch deren komplexe dynamische Erscheinungsweise Anteil hat? Über die Analyse eines Titelblatts der Zeitschrift Jugend von 1896 und die Betrachtung der Forschungen zur Eigenlogik von Bildern in Bildwissenschaft, Ikonologie und Kultureller Anthropologie soll diesen Fragen nachgegangen werden. Die Auswertung veranlasst, sich von der klassischen, erkenntnisorientierten, ästhetischen Theorie zu distanzieren und sie als kulturtheoretische, semiotische Theorie neu zu fassen. Die Neuausrichtung wird im Verständnis des Gehalts der Bilder im medialen Transfer greifbar: Statt in einer Ansicht von etwas (Erkenntniswert), so eröffnet sich, liegt er in einer Ansicht über etwas (Meinung/Kulturwert). (shrink)

The paper follows the thesis, that the perception of real or virtual media shares the anthropological state of "Ausdruckswahrnehmung" or perception of expression (Ernst Cassirer). This kind of perception does not represent a distant, neutral point of view, but one that is guided by feelings or "vitality affects" (Daniel N. Stern). The prerequisites, however, for triggering these feelings/"vitality affects" are not recognizable objects or motifs, but rather their sensually evaluable “abstract representations” or their formal logical structures. In contrast to aesthetic (...) feelings, however, they affect not only our feelings of lust or unlust or our knowledge (formal aesthetics) but also our actions (semiotics). So, when I extend aesthetic experiences to semiotic effects, I will talk about vitality semiotics. This new concept is of consequence, because the thesis of the responsibility of the producer is based on these effects. This is to be carried out by analyzing and presenting the approach of the Bauhaus master Josef Albers. (shrink)

Is it true that there is an analogy between modes of creation and such of perception? Respective to the cultural anthropological research of Ernst Cassirer, Susanne K. Langer and John M. Krois and by the analysis of a tape of the Swiss video-artist Pipilotti Rist this initial thesis of Formal Aesthetics shall be supported. - I - -/- Lässt sich die Behauptung stützen, dass zwischen Gestaltungsweisen und Wahrnehmungsweisen eine Analogie besteht? Aufbauend auf den kulturanthropologischen Forschungen von Ernst Cassirer, Susanne K. (...) Langer und John M. Krois sowie der Analyse eines Tapes der Schweizer Videokünstlerin Pipilotti Rist gilt es diese ursprünglich von der formalen Ästhetik aufgeworfene These zu untermauern. (shrink)

It is proved to be consistent relative to a measurable cardinal that there is a uniform ultrafilter on the real numbers which is generated by fewer than the maximum possible number of sets. It is also shown to be consistent relative to a supercompact cardinal that there is a uniform ultrafilter on \ which is generated by fewer than \ sets.

We propose a fundamental challenge to the feasibility of moral progress: most extant theories of progress, we will argue, assume an unrealistic level of cognitive control people must have over their moral judgments for moral progress to occur. Moral progress depends at least in part on the possibility of individual people improving their moral cognition to eliminate the pernicious influence of various epistemically defective biases and other distorting factors. Since the degree of control people can exert over their moral cognition (...) tends to be significantly overestimated, the prospects of moral progress face a formidable problem, the force of which has thus far been underappreciated. In the paper, we will provide both conceptual and empirical arguments for this thesis, and explain its most important implications. (shrink)

Global sourcing largely occurs from so-called emerging markets and developing economies. In these contexts, substantial leverage effects for sustainability in supply chains can be expected by reducing adverse impacts on society and minimising related risks. For this ethical end, an adequate understanding of the respective sourcing contexts is fundamental. This case study of South Africa’s mining sector uses institutional theory and the notion of institutional uncertainty to empirically analyse the challenges associated with establishing social sustainability. The case study research is (...) informed by 39 semi-structured interviews with top management representatives and various state and non-state decision makers in SA. Our findings suggest that sustainability in the institutional field is mainly shaped by the Social and Labour Plan institution, induced by state actors and mining companies’ practices. However, four weakening factors were identified that adversely affect this regulative institution, drive institutional uncertainty and allow for mining companies’ gradual decoupling. Contrastingly, complementing pressures of non-state actors limit institutional uncertainty and push toward mainstreaming the stipulations of the institution. This study contributes to the business ethics literature by providing an in-depth exploration of institutional uncertainty’s drivers and barriers within an upstream SC setting and shedding light on multiple actors’ interplay and relevance in sector-wide sustainability. The findings are condensed into three main propositions as well as an analytical framework as a basis for follow-up research. This case study helps practitioners understand and manage complexity that results from actor plurality and institutional uncertainty in EMDEs. (shrink)

When it comes to improving the health of the general population, mHealth technologies with self-monitoring and intervention components hold a lot of promise. We argue, however, that due to various factors such as access, targeting, personal resources or incentives, self-monitoring applications run the risk of increasing health inequalities, thereby creating a problem of social justice. We review empirical evidence for “intervention-generated” inequalities, present arguments that self-monitoring applications are still morally acceptable, and develop approaches to avoid the promotion of health inequalities (...) through self-monitoring applications. (shrink)

_Alessandra Lemma - Winner of the Levy-Goldfarb Award for Child Psychoanalysis!_ The contemporary relevance of psychoanalysis is being increasingly questioned; _Off the Couch_ challenges this view, demonstrating that psychoanalytic thinking and its applications are both innovative and relevant, in particular to the management and treatment of more disturbed and difficult to engage patient groups. Chapters address: clinical applications in diverse settings across the age range the relevance of psychoanalytic thinking to the practice of CBT, psychosomatics and general psychiatry the (...) contribution of psychoanalytic thinking to mental health policy and the politics of conflict and mediation. This book suggests that psychoanalysis has a vital position within the public health sector and discusses how it can be better utilised in the treatment of a range of mental health problems. It also highlights the role of empirical research in providing a robust evidence base. _Off the Couch_ will be essential reading for those practicing in the field of mental health and will also be useful for anyone involved in the development of mental health and public policies. It will ensure that practitioners and supervisors have a clear insight into how psychoanalysis can be applied in general healthcare. (shrink)

When it comes to improving the health of the general population, mHealth technologies with self-monitoring and intervention components hold a lot of promise. We argue, however, that due to various factors such as access, targeting, personal resources or incentives, self-monitoring applications run the risk of increasing health inequalities, thereby creating a problem of social justice. We review empirical evidence for “intervention-generated” inequalities, present arguments that self-monitoring applications are still morally acceptable, and develop approaches to avoid the promotion of health inequalities (...) through self-monitoring applications. (shrink)

In light of recent empirical data, many psychologists and philosophers have turned away from rationalism about moral judgment and embraced sentimentalism. In the process, they have rejected the classical “moral signature” as a way of distinguishing moral from conventional norms in favor of a sentimentalist approach to carving out the moral domain. In this paper, we argue that this sentimentalist turn has been made prematurely. Although we agree that the experiments reveal that the classical approach is flawed, we propose to (...) replace it with an alternative, according to which a norm is moral precisely if it is justifiable to all. This does not hold for most norms based on disgust or loyalty to a particular community. We accommodate the fact that such norms are not merely conventional by introducing a third domain, the domain of ethics. Our proposal reveals that (psychological) rationalism is still a viable option, as a lot of the experimental evidence that features emotions concerns the domain of ethics rather than morality. (shrink)

We prove some consistency results about and δ, which are natural generalisations of the cardinal invariants of the continuum and . We also define invariants cl and δcl, and prove that almost always = cl and = cl.