ALTHOUGH the content of Alexander Gottlieb Baumgarten's Aesthetica seems to be familiar in German philosophical circles, it is relatively unknown outside Germany. Most of us are aware that it was Baumgarten who coined the name "aesthetics" for the new philosophical discipline his Aesthetica was intended to establish; but as for the content of that work, our acquaintance is likely to be indirect, through two remarks of Kant. Explaining his own use of "Transcendental Aesthetic" in the Critique of Pure Reason, (...) Kant criticizes Baumgarten's "abortive attempt... to bring the critical treatment of the beautiful under rational principles and so to raise its rules to the rank of a science". In the Critique of Judgment, it is generally assumed to be Baumgarten Kant has in mind when, arguing that judgments of beauty are not cognitive or "logical" judgments, he criticizes the view that beauty is perfection known confusedly or indistinctly. Combining Kant's remark with Leibniz's view that beauty is--or, more precisely, flows from--perfection, we might conclude that Baumgarten simply lowered beauty from the level of distinct to that of confused concepts and tried to deduce its rules from the concept of perfection. If this was indeed Baumgarten's project, we might well ask to be excused from pursuing the subject further. (shrink)

I. The framework. 1, Aristotle's project and methods. 2, The perceptual capacity of the soul. 3, The sensory apparatus. 4, The common sense and the related capacities -- II. The terminology. 1, Overlooked occurrences of the phrase 'common sense'. 2, De anima III.1 425a27. 3, De partibus animalium IV.10 686a31. 4, De memoria et reminiscentia 1 450a10. 5, De anima III.7 431b5. 6, Conclusions on the terminology -- III. Functions of the common sense. 1, Simultaneous perception and cross-modal binding. 2, (...) Perceptual discrimination. 3, Waking, sleep, and control of the senses. 4, Perceiving that what we see and hear, and monitoring of the senses. 5, Other roles of the common sense -- Conclusion. (shrink)

Engagements with Contemporary Literary and Critical Theory is a wide-ranging but accessible introduction that illuminates the field of theory through a variety of useful and relevant examples. Covering all key theories and theorists, this book looks at the relation of theory to form, discourses, subjectivity, media and networks, and environments. Organized thematically, Engagements with Contemporary Literary and Critical Theory illuminates the field by focusing on the concepts and methodologies of key thinkers, while also providing historical introductions that contextualize the latest (...) developments with regard to forms; discourses; subjectivities and embodiments; media, networks, and machines; and animals, affects, objects, and environments. Each chapter includes examples from a canonical novel, a contemporary text, and a new media artefact, while textboxes regularly introduce additional emerging or overlooked theorists of interest. An ideal guide for undergraduates studying literary theory, this book will give readers the background they need to continue their own fruitful explorations of this vibrant field of study. (shrink)

By means of multi-agent simulations, it investigates the truth and consensus-conduciveness of controversial debates. The book brings together research in formal epistemology and argumentation theory.

The ideal of value free science states that the justification of scientific findings should not be based on non-epistemic (e.g. moral or political) values. It has been criticized on the grounds that scientists have to employ moral judgements in managing inductive risks. The paper seeks to defuse this methodological critique. Allegedly value-laden decisions can be systematically avoided, it argues, by making uncertainties explicit and articulating findings carefully. Such careful uncertainty articulation, understood as a methodological strategy, is exemplified by the current (...) practice of the Intergovernmental Panel on Climate Change (IPCC). (shrink)

Wo Meinungen aufeinanderprallen, um Verständnis geworben und Überzeugungsarbeit geleistet wird, sind Begründungen nicht weit. Für jede Überzeugung gibt es immer ein, zwei Gründe, die mit Gegengründen konfrontiert und, im Gegenzug, mit weiteren Überlegungen verteidigt werden usw. usf. Schnell sind wir verwirrt und drohen, ohne uns der "Grammatikregeln" vernünftigen Argumentierens zu besinnen, nicht mehr durchzublicken. Die Theorie dialektischer Strukturen leistet einen Beitrag zur Grammatik vernünftigen Argumentierens. Sie stellt Begriffe und Verfahren bereit, um Fragen, die sich angesichts einer komplexen Argumentation stellen können, (...) zu beantworten: Wie beziehen sich die einzelnen Argumente der Debatte aufeinander? Welche Positionen vertreten die verschiedenen Proponenten, und wie lassen sich diese bewerten? Wie gut ist die zentrale These der Kontroverse alles in allem begründet? Ist die und die Argumentationshandlung angesichts des Debattenstandes tatsächlich zweckmäßig und rational? Liegt hier eine zirkuläre - und damit fehlerhafte - Argumentation vor? Die klassische Logik, die sogenannte informal logic und argumentationstheoretische Ansätze der Künstlichen Intelligenz bilden Anknüpfungspunkte der Theorie dialektischer Strukturen. Exemplarisch werden die entwickelten argumentationstheoretischen Methoden zur Analyse umfangreicher philosophischer Kontroversen eingesetzt. (shrink)

We give a construction of the square principle by means of forcing with finite conditions.

Based on a unique data set on US direct microloans, we study the funding determinants of interest-free peer-to-peer crowdlending aimed at borrowers in the US. By performing logistic regressions on funding success and Tobit regressions on the reversed funding time, the existence of a social underwriting by a third-party trustee and information in the description texts fostering the investors’ trust are shown to be the main predictors of successful funding. Regarding social impact, the possibility to empower women and groups of (...) borrowers appeals to the investors, whereas empowerment of the family or community beyond the borrowers themselves appears to remain unappreciated. When examining the vulnerability of the borrowers as a predictor, the results manifest differences amongst the attitudes of the investors towards social impact. In the subsample of non-endorsed loans, the investors appear to prefer to support borrowers with an immigration background. In contrast, this is not the case with endorsed loans. (shrink)

When does a human being begin to exist? Barry Smith and Berit Brogaard have argued that it is possible, through a combination of biological fact and philosophical analysis, to provide a definitive answer to this question. In their view, a human individual begins to exist at gastrulation, i. e. at about sixteen days after fertilization. In this paper we argue that even granting Smith and Brogaard's ontological commitments and biological assumptions, the existence of a human being can be shown to (...) begin much earlier, viz., with fertilization. Their interpretative claim that a zygote divides immediately into two substances and therefore ceases to exist is highly implausible by their own standards, and their factual claim that there is no communication between the blastomeres has to be abandoned in light of recent embryological research. (shrink)

‘Dancing mania’ has often been understood as an expression of purportedly ‘typical medieval’ mass hysteria. Yet evidence suggests that a better interpretation would be to see it as a disease, the idea of which was shaped by patterns tracing back to antique cosmology. During the later Middle Ages, this concept became reality as a form of suffering primarily determined by spiritual forces which typically struck only individuals or small groups in narrowly defined regions. This article closely examines a key shift (...) in the semiotic setting of how this disease was interpreted: During the 15th and early 16th centuries, it became medicalised and desacralized. Evidence of this development can be found in isolated instances of ‘dancing mania’ in towns of the Rhine and Moselle area which at first glance would appear to be of little significance. As a medical concept, ‘dancing mania’ would survive the Reformation, and as a concept of primarily medical understanding it would later be re-integrated into the renewed Catholic culture of the late 16th and 17th centuries. (shrink)

Gregor Betz explores the following questions: Where are the limits of economics, in particular the limits of economic foreknowledge? Are macroeconomic forecasts credible predictions or mere prophecies and what would this imply for the way economic policy decisions are taken? Is rational economic decision making possible without forecasting at all?

In the debate about the moral status of human embryos, it is not always clear which arguments are actually disputed. This book offers students and researchers, but also laypersons interested in the current debate, the opportunity to inform themselves about the current state of discussion and to learn about the most important arguments in a clear and concise form. These arguments are as follows: Since embryos as members of the species homo sapiens sapiens are human beings, they possess dignity (species (...) argument); embryos develop continuously, i.e. without morally relevant incisions, into adult human beings possessing dignity (continuum argument); embryos are identical with adult human beings possessing dignity (identity argument); embryos have the potential to become human beings, and this potential is without restriction worth protecting (potentiality argument). These arguments are each represented by a pro position and a contra position and defended or criticized. In an accompanying contribution by the editors, the four arguments in context are reconstructed, evaluated, and supported by new arguments. (shrink)

Cellular processes are highly dependent on a dynamic proteome that undergoes structural and functional rearrangements to allow swift conversion between different cellular states. By inducing proteasomal degradation of inhibitory or stimulating factors, ubiquitylation is particularly well suited to trigger such transitions. One prominent example is the remodelling of the centrosome upon cell cycle exit, which is required for the formation of primary cilia – antenna‐like structures on the surface of most cells that act as integrative hubs for various extracellular signals. (...) Over the last decade, many reports on ubiquitin‐related events involved in the regulation of ciliogenesis have emerged. Very often, these processes are considered to be initiated ad hoc, that is, directly before its effect on cilia biogenesis becomes evident. While such a temporal restriction may hold true for the majority of events, there is evidence that some of them are initiated earlier during the cell cycle. Here, we provide an overview of ubiquitin‐dependent processes in ciliogenesis and discuss available data that indicate such an early onset of proteolytic regulation within preceding cell cycle stages. (shrink)

InhaltVorwortSiglenverzeichnisDaniel BREAZEALE: »Der Blitz der Einsicht« and »der Akt der Evidenz«. A Theme from Fichte’s Berlin Introductions to PhilosophyJürgen STAHL: Von der Form der Anschauung zur Anschauung der Form. Zu Fichtes Verständnis des Formbegriffs Albert MUES: Die Position der Anschauung im Wissen oder Die Position der Anschauung in der Welt. Der Unsinn der SubjektphilosophieChristoph ASMUTH: Transzendentalphilosophie oder absolute Metaphysik? Grundsätzliche Fragen an Fichtes SpätphilosophieMarek J. SIEMEK: Unendlichkeit und Schranke. Zum Fichteschen Entwurf einer transzendentalen Ontologie des WissensTom ROCKMORE: On Fichte and (...) IdealismSabine AMMON: Realismus oder Idealismus? – Irrealismus!Akira OMINE: Der Begriff des Übersinnlichen in der Philosophie FichtesRoderich BARTH: Wahrheit als Sein von Einheit. Die gewißheitstheoretische Reformulierung des absoluten Wahrheitsbegriffs in Fichtes Phänomenologie von 1804-IIArkadij LUKJANOW: Auf der Suche nach einer neuen Theorie des Absoluten. Die Idee der Synthesis in den späteren Systemen von Fichte und Schelling«Lu De VOS: Der Gedanke des Lebens in den späten Schriften FichtesMichael GERTEN: Geistige Blindheit und der Sinn für Philosophie. Das systematische Problem einer Einleitung in Fichtes WissenschaftslehreKai GREGOR: »Revolution der Gesinnung« und »Vollendung der Freiheit« – Wesen und Möglichkeit höherer Lebensformen bei Kant und FichteVioletta L. WAIBEL: Die bildende Kraft des Wissens vom Wissen in der Spätphilosophie Johann Gottlieb Fichtes Elvira GAREEWA: Wissen als ein freies und selbständiges Leben in den »Thatsachen des Bewußtseyns« Franco GILLI: Die Präsenz der ›Populärphilosophie‹ im Spätwerk FichtesHans Georg von MANZ: Die Funktion der »Tatsachen des Bewußtseins« im Blick auf die Wissenschaftslehre George di GIOVANNI: Sacramentalizing the World: On Fichte’s Wissenschaftslehre of 1810Stamatios D. GEROGIORGAKIS: Der Begriff Schema in Fichtes Spätwerk. Seine Unterschiede zum Schemabegriff in Fichtes Frühwerk und seine Einbettung in der philosophischen Tradition vor KantJacinto Rivera de ROSALES: Die transzendentale Logik . Ihr systematischer Ort und ihre BedeutungAlessandro BERTINETTO: Die transzendentale Argumentation in der Transzendentalen Logik FichtesMarc MAESSCHALCK: Attention et réflexivité dans la Logique de 1812 et la dernière philosophie de Fichte. (shrink)

The paper deals with the question of the structure of knowledge and the precise relationship between propositional "knowledge that" and dispositional "knowledge how." In the first part of my essay, I provide an analysis of the term 'knowing how' and argue that the usual alternatives in the recent epistemological debate – knowing how is either a form of propositional or dispositional knowledge – are misleading. In fact it depends on the semantic and pragmatic context of the usage of this term (...) whether 'knowing how' refers to a type of dispositional knowledge, to propositional knowledge, or to a hybrid form of both. Only in the first case, can one say that dispositional know how cannot be reduced to any form of propositional knowledge. Yet, this case is the most interesting one to consider in the investigation of the nature of knowledge, if one assumes that knowing that p presupposes "having found out that p." Having found something out, however, presupposes certain acts of epistemic inquiry and corresponding epistemic abilities. Examined more carefully, it is shown that the dispositional knowledge-how is a necessary condition for propositional knowledge-that, hence propositional knowledge-that is a species of the dispositional knowledge-how. Accordingly, dispositional knowledge has to be understood as being at the very core of our notion of knowledge, including propositional knowledge. (shrink)

Its author was a Carthusian monk. Offered here is a translation, with annotation and an important introduction, of the four books on natural philosophy, the predecessor of modern science.

This study investigates the ethical aspects of deploying and researching into so-called climate engineering methods, i.e. large-scale technical interventions in the climate system with the objective of offsetting anthropogenic climate change. The moral reasons in favour of and against R&D into and deployment of CE methods are analysed by means of argument maps. These argument maps provide an overview of the CE controversy and help to structure the complex debate.

Menschliches Bewusstein findet sich immer schon als verkörpertes vor. Diese Einsicht steht im Zentrum des kognitionswissenschaftlichen Paradigmas der embodied cognition: Der Geist ist „innig an einen Körper gebunden und innig in seine Welt eingebettet“. Der Geist ist kein in einem vermeintlichen Innenraum verborgenes und von der Welt weitgehend gelöstes neuronales Netzwerk, sondern als eine dynamische Weise des leiblichen In-der-Welt-Seins zu verstehen. Mit der Philosophie der Verkörperung gewinnt die Theologie einen Gesprächspartner, der ihr hilft, ihre eigene Körpervergessenheit zu überwinden und Anschluss (...) an die biblischen Anthropologien zu gewinnen. Denn diese verstehen die menschliche Existenz grundsätzlich als leiblich verfasst. Aktuelle Forschungen an der Schnittstelle von Neurobiologie und Philosophie einerseits und Exegese und Systematik andererseits lassen sich so in einen spannenden Diskurs bringen, an dessen Ende eine neue interdisziplinäre Anthropologie stehen könnte. Der vorliegende Band eröffnet diesen Diskurs mit Beiträgen aus Philosophie, Exegese und Systematischer Theologie. (shrink)

Physicalism is a metaphysical thesis easily presented in slogan form – there is nothing over and above the physical – but notoriously difficult to formulate precisely. "Understanding physicalism" combines insights from contemporary philosophy of mind and metaphysics to present a new account of physical properties and metaphysical dependence and, on this foundation, develop a more rigorous and illuminating formulation of the thesis of physicalism.

Limits of the Conversation about Forms. Types of Knowledge and Necessity of Forms in Plato's "Parmenides". - Forms (ideas) are among the things that Plato is serious about. But about these things he says in his "Seventh Letter": "There neither is nor ever will be a treatise of mine on the subject." (341c, transl. J. Harward). Plato's statement suggests the question, why one does not and never can do justice to the Platonic forms by means of a written text about (...) the forms. Another big question of Plato research is whether the conversations documented in the Platonic dialogues are also affected by this verdict. This paper aims to provide, as far as possible, newly substantiated answers to these two questions. To this end, the systematic limits of the discussion about forms, which are particularly evident in Plato's dialogue "Parmenides", are examined in eight steps: First, two types of knowledge are presented that play an important systematic role in Plato's philosophy with regard to the limits of conversation: knowledge-how (practical knowledge) and knowledge-that (propositional knowledge) (I). Then the Socratic model of these two types of knowledge is interpreted, which is drafted in the tenth book of the "Republic". This model uses the example of bridle, bridlemaker and rider to explain the primacy of practical knowledge and the limits of propositional knowledge (II). Subsequently, it will be shown how the dialogues "Republic" and "Parmenides" are connected with each other in content and form (III). The gradation of the two types of knowledge, which is indicated by the motifs of the bridle and the horse on the image level of the "Parmenides", proves to be the structure that systematically underlies the structure of the entire dialogue (IV). It also makes clear why the conversation about the forms in the first part of the "Parmenides" has to fail (V). The assumption that the two parts of the "Parmenides" express two different types of knowledge in dealing with forms is supported by the results of a logical analysis of the last defence of the acceptance of forms (135b-c). This analysis shows why, for reasons of principle, it is impossible to speak adequately about forms (VI). Forms have the function of being presuppositions of 'talking about something'. Thus forms are always presupposed in conversation when one talks about them, and thus elude appropriate discussion in conversation (VII). That this is not only a methodical insight of the Platonic Parmenides, but can also be attributed to Plato himself, is demonstrated by the concluding reinterpretation of the central sentence of the critique of writing in Plato's "Seventh Letter". It will become apparent that, contrary to the now widespread view of the representatives of the Tübingen school, philosophical and also good philological reasons speak for the fact that Plato related his criticism only to the communicability of forms through treatises, i.e. tract-like writings (VIII). (shrink)

Climate models don’t give us probabilistic forecasts. To interpret their results, alternatively, as serious possibilities seems problematic inasmuch as climate models rely on contrary-to-fact assumptions: why should we consider their implications as possible if their assumptions are known to be false? The paper explores a way to address this possibilistic challenge. It introduces the concepts of a perfect and of an imperfect credible world, and discusses whether climate models can be interpreted as imperfect credible worlds. That would allow one to (...) use models for possibilistic prediction and salvage widespread scientific practice. (shrink)

This article examines the formation-process of the atmospheric sciences in the Federal Republic of Germany (FRG) with a particular focus on the 1970’s, when atmospheric research expanded massively on an institutional, methodological and conceptual level. Up until now this episode is just rudimental studied historically or sociologically, especially for the FRG. The formation of the atmospheric sciences will be illustrated by two case studies: the foundation and development since 1968 of the first department of atmospheric chemistry in the Max Planck (...) Society (Max-Planck-Gesellschaft, MPG) and the collaborative research program “atmospheric tracegases” initiated in 1970 by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG). (shrink)

This article examines the formation-process of the atmospheric sciences in the Federal Republic of Germany (FRG) with a particular focus on the 1970’s, when atmospheric research expanded massively on an institutional, methodological and conceptual level. Up until now this episode is just rudimental studied historically or sociologically, especially for the FRG. The formation of the atmospheric sciences will be illustrated by two case studies: the foundation and development since 1968 of the first department of atmospheric chemistry in the Max Planck (...) Society (Max-Planck-Gesellschaft, MPG) and the collaborative research program “atmospheric tracegases” initiated in 1970 by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG). (shrink)

Name der Zeitschrift: Neue Zeitschrift für Systematische Theologie und Religionsphilosophie Jahrgang: 60 Heft: 2 Seiten: 305-309.

Gregor Moder’s Hegel and Spinoza: Substance and Negativity is a lively entry into current debates concerning Hegel, Spinoza, and their relation. Hegel and Spinoza are two of the most influential philosophers of the modern era, and the traditions of thought they inaugurated have been in continuous dialogue and conflict ever since Hegel first criticized Spinoza. Notably, eighteenth- and nineteenth-century German Idealists aimed to overcome the determinism of Spinoza’s system by securing a place for the freedom of the subject within (...) it, and twentieth-century French materialists such as Althusser and Deleuze rallied behind Spinoza as the ultimate champion of anti-Hegelian materialism. This conflict, or mutual rejection, lives on today in recent discussions about materialism. Contemporary thinkers either make a Hegelian case for the productiveness of concepts of the negative, nothingness, and death, or in a way that is inspired by Spinoza they abolish the concepts of the subject and negation and argue for pure affirmation and the vitalistic production of differences. Hegel and Spinoza traces the historical roots of these alternatives and shows how contemporary discussions between Heideggerians and Althusserians, Lacanians and Deleuzians are a variation of the disagreement between Hegel and Spinoza. Throughout, Moder persuasively demonstrates that the best way to read Hegel and Spinoza is not in opposition or contrast but together: as Hegel and Spinoza. (shrink)

Ordinary language and scientific discourse are filled with linguistic expressions for dispositional properties such as “soluble,” “elastic,” “reliable,” and “humorous.” We characterize objects in all domains – physical objects as well as human persons – with the help of dispositional expressions. Hence, the concept of a disposition has historically and systematically played a central role in different areas of philosophy ranging from metaphysics to ethics. The contributions of this volume analyze the ancient foundations of the discussion about disposition, examine the (...) problem of disposition within the context of the foundation of modern science, and analyze this dispute up to the 20th century. Furthermore, articles explore the contemporary theories of dispositions. (shrink)

With the evidence for anthropogenic climate change piling up, suggesting that climate impacts of GHG emissions might have been underestimated in the past (Allison et al. 2009; WBGU 2009), and mitigation policies apparently lagging behind what many scientists consider as necessary reductions in order to prevent dangerous climate change, the debate about intentional climate change, or “climate engineering”, as we shall say in the following, has gained momentum in the past years. While efforts to technically modify earth’s climate had been (...) the focus of sporadic discussions at least since the White House’s Report “Restoring the Quality of Our Environment” (cf. Keith 2000), Paul Crutzen’s cautious plea for research into the feasibility and side-effects of stratospheric sulphur injections (Crutzen 2006) has incited an inter-disciplinary controversy (with a preliminary culmination in the Royal Society’s assessment (Royal Society 2009)), while increasing public awareness and debate about climate engineering, as well. The controversy, though, does not focus on the question whether climate engineering should be carried out today (which is largely reckoned to be a bad idea, unnecessary, or premature) or at some point in the future (which is considered a decision we don’t have to take now), but on whether to engage in large-scale research into the alternative technological options for carrying out intentional climate change. It is this paper’s purpose to make that controversy more transparent. In order to do so, we analyse what seems to be the major argument in favour of research into climate engineering: the lesser evil-, or, as Stephen Gardiner has called it, the arm the future-argument — in short: the AF-argument (Gardiner 2010). Such an argumentative analysis makes explicit the normative and descriptive assumptions which underlie the reasoning, without ascertaining or denying them, and thus enables one to assess the overall strength of the argument as well as to determine which objections do, and which don’t undermine it. (shrink)

The aim of this paper is to develop and defend an Attentional View of bodily awareness, on which attention is necessary for bodily awareness. The original formulation of the Attentional View is due to Marcel Kinsbourne. First, I will show that the Attentional View of bodily awareness as formulated by Kinsbourne is superior to other accounts in the literature for characterizing the relationship between attention and bodily awareness. Kinsbourne’s account is the only account in the literature so far which can (...) accommodate key neurological diseases such as personal neglect. Second, when I consider Kinsbourne’s view in more detail, I will argue that Kinsbourne’s Attentional View faces problems because it is too reductive. Kinsbourne deviates from the standard taxonomy on which there is a body schema and a body image. Instead he reduces the body image to the neural representation of the body in the somatosensory cortex, the body schema and attentional shifts. I will present two challenges to Kinsbourne’s view which demonstrate that Kinsbourne’s reduction of the body image is unsuccessful. Finally, I will present a revised version of the Attentional View that is both empirically adequate and philosophically satisfactory. (shrink)

How does microbiota research impact our understanding of biological individuality? We summarize the interdisciplinary summer school on "Microbiota, Symbiosis and Individuality: Conceptual and Philosophical Issues" (July 2019), which was supported by a European Research Council starting grant project "Immunity, DEvelopment, and the Microbiota" (IDEM). The summer school centered around interdisciplinary group work on four facets of microbiota research: holobionts, individuality, causation, and human health. The conceptual discussion of cutting-edge empirical research provided new insights into microbiota and highlights the value of (...) incorporating into meetings experts from other disciplines, such as philosophy and history of science. (shrink)

Suppose a fire broke out in a fertility clinic. One had time to save either a young girl, or a tray of ten human embryos. Would it be wrong to save the girl? According to Michael Sandel, the moral intuition is to save the girl; what is more, one ought to do so, and this demonstrates that human embryos do not possess full personhood, and hence deserve only limited respect and may be killed for medical research. We will argue, however, (...) that no relevant ethical implications can be drawn from the thought experiment. It demonstrates neither that one always ought to let the embryos die, nor does it allow for any general conclusion concerning the moral status of human embryos. (shrink)

Neither secular moral theory nor religious ethics have had much place for persons in need of constant physical help and cognitive support, nor for those who provide care for them. Writing as the father of a fourteen-year-old daughter with multiple disabilities, I will explore some of moral issues that arise here, both from the point of view of the disabled child and from that of the child's caretaker(s).