Many of our attitudes are non-culpable: there was nothing that we should have done to avoid holding them. I argue that we can still be blameworthy for non-culpable attitudes: they can impair our relationships in ways that make our full practice of apology and forgiveness intelligible. My argument poses a new challenge to indirect voluntarists, who attempt to reduce all responsibility for attitudes to responsibility for prior actions and omissions. Rationalists, who instead explain attitudinal responsibility by appeal to reasons-responsiveness, can (...) make sense of blameworthiness for non-culpable attitudes. In response, voluntarists could propose a revision of our actual practices. This would lead us into a quite different debate. (shrink)

Departing from the claim that AI needs to be trustworthy, we find that ethical advice from an AI-powered algorithm is trusted even when its users know nothing about its training data and when they learn information about it that warrants distrust. We conducted online experiments where the subjects took the role of decision-makers who received advice from an algorithm on how to deal with an ethical dilemma. We manipulated the information about the algorithm and studied its influence. Our findings suggest (...) that AI is overtrusted rather than distrusted. We suggest digital literacy as a potential remedy to ensure the responsible use of AI. (shrink)

Long presented as a universal policy-recipe for social prosperity and economic growth, the promise of innovation seems to be increasingly in question, giving way to a new vision of progress in which society is advanced as a central enabler of technoeconomic development. Frameworks such as “Responsible” or “Mission-oriented” Innovation, for example, have become commonplace parlance and practice in the governance of the innovation–society nexus. In this paper, we study the dynamics by which this “social fix” to technoscience has gained legitimacy (...) in institutions of global governance by investigating recent projects at two international organizations, the Organization for Economic Cooperation and Development and the European Commission, to mainstream “Responsible Innovation” frameworks and instruments across countries. Our analysis shows how the turn to societal participation in both organizations relies on a new deficit logic—a democratic deficit of innovation—that frames a lack of societal engagement in innovation governance as a major barrier to the uptake and dissemination of new technologies. These deficit politics enable global governance institutions to present “Responsible Innovation” frameworks as the solution and to claim authority over the coproduction of particular forms of democracy and innovation as intertwined pillars of a market-liberal international order. (shrink)

Die analytische Philosophie hat selbst da, wo sie explizit an Kant anschließt, erhebliche Schwierigkeiten mit dessen Idee eines synthetischen Wissens a priori. Damit verliert sie eine ganze Dimension der philosophischen Tradition. Das vorliegende Buch gewinnt diese Idee zurück, indem es gerade den Anschauungsbezug und damit den Zeitbezug des menschlichen Denkens zum Gegenstand einer logischen Untersuchung macht. Nur wenn man die Zeit als inneres und formbildendes Merkmal des menschlichen Aussagens erkennt, versteht man den Begriff empirischer Wahrheit und sinnlich vermittelter Erkenntnis. In (...) diesem Gedanken, so zeigt sich, liegt die Einheit einer philosophischen Tradition, die Aristoteles mit Kant und beide mit dem späten Wittgenstein verbindet. (shrink)

In this paper we present a schema for describing dualities between physical theories, and illustrate it in detail with the example of bosonization: a boson-fermion duality in two-dimensional quantum field theory. The schema develops proposals in De Haro : these proposals include construals of notions related to duality, like representation, model, symmetry and interpretation. The aim of the schema is to give a more precise criterion for duality than has so far been considered. The bosonization example, or boson-fermion duality, has (...) the feature of being simple, yet rich enough, to illustrate the most relevant aspects of our schema, which also apply to more sophisticated dualities. The richness of the example consists, mainly, in its concern with two non-trivial quantum field theories: including massive Thirring-sine-Gordon duality, and non-abelian bosonization. This prompts two comparisons with the recent philosophical literature on dualities:--- Unlike the standard cases of duality in quantum field theory and string theory, where only specific simplifying limits of the theories are explicitly known, the boson-fermion duality is known to hold {\it exactly}. This exactness can be exhibited explicitly. The bosonization example illustrates both the cases of isomorphic and {\it non-isomorphic} models: which we believe the literature on dualities has not so far discussed. (shrink)

The Description for this book, Machiavelli in Hell, will be forthcoming.

Although the ethical aspects of transformational leadership have attracted considerable attention, very little is known about followers’ reactions to the moral and immoral conduct of transformational leaders. Against this background, this study examined whether and how transformational leadership interacts with moral and authoritarian leadership behaviors in predicting followers’ in-role and extra-role efforts. Building on attribution theory, we hypothesized that the positive and negative effects of these leadership behaviors would be particularly pronounced for highly transformational leaders given that this leadership style (...) elicits strong attention and sense-making efforts among followers. We tested our model in a sample of 228 individuals comprising 114 leader–follower dyads from a wide range of organizations and industries. In line with our hypotheses, results revealed that for highly transformational leaders, moral leadership behaviors related positively to employees’ in-role and extra-role efforts whereas authoritarian leadership behaviors related negatively to employees’ in-role and extra-role efforts. In contrast, moral and authoritarian leadership behaviors did not significantly affect followers’ reactions to leaders low in transformational leadership. Taken together, these findings suggest that transformational leadership, contrary to its largely positive perception in the literature, can be a rather mixed blessing. Implications for theory, future research, and managerial practice are discussed. (shrink)

This paper analyzes the concept of a spirituality without religion. I argue that spirituality is best understood as a specific attitude that a subject has towards the totality of existence, characterized by a certain emotional, evaluative and noetic quality. The spiritual attitude typically involves a shift in the way a subject interprets their relation to themselves and to the whole of reality. Understood this way, religious and non-religious spiritualities are varieties of the same core phenomenon. Religious beliefs are compatible with, (...) but not necessary for spiritual attitudes. (shrink)

We argue that dualities offer new possibilities for relating fundamentality, levels, and emergence. Namely, dualities often relate two theories whose hierarchies of levels are inverted relative to each other, and so allow for new fundamentality relations, as well as for epistemic emergence. We find that the direction of emergence typically found in these cases is opposite to the direction of emergence followed in the standard accounts. Namely, the standard emergence direction is that of decreasing fundamentality: there is emergence of less (...) fundamental, high-level entities, out of more fundamental, low-level entities. But in cases of duality, a more fundamental entity can emerge out of a less fundamental one. This possibility can be traced back to the existence of different classical limits in quantum field theories and string theories. (shrink)

Due to the frequent occurrence of ethical transgressions and unethical employee behaviors, there has lately been an increasing interest in the ethical foundations of contemporary organizations. However, large-scale comprehensive analyses of organizational ethics are still comparatively limited. Our study contributes to both management control and business ethics literature by empirically examining potential antecedents as well as resulting effects of ethical work climates on organizational-level outcomes. Based on a cross-sectional survey among 295 large- and medium-sized companies, we find that more informal (...) means of control constitute important elements of a broader organizational control context that are strongly related to the emergence of coherent ethical work climates with an increased awareness of ethical issues. Moreover, our results show that the relationship between ethical work climates and organizational performance can be considered as rather indirect as it is fully mediated by increased mutual trust among employees. Overall, our study thus supports the particular importance of ethical work climates and identifies appropriate means to encourage ethical conduct. (shrink)

Nelson Goodman observed that we use only certain ‘good’ (viz. projectible) predicates during reasoning, with no obvious demarcation criterion in sight to distinguish them from the bad and gruesome ones. This apparent arbitrariness undermines the justifiability of our reasoning practices. Inspired by Quine’s 1969 paper on Natural Kinds, Peter Gärdenfors proposes a cognitive criterion based on his theory of Conceptual Spaces (CS). He argues the good predicates are those referring to natural concepts, and that we can capture naturalness in terms (...) of similarity. In contrast to Quine, he does not primarily rely on logic, but geometry. He frames his account as a descriptive project, however, and it is not obvious how it addresses the normative dimension of Goodman’s Riddle. This paper develops a charitable reconstruction of his argument, based on the idea that the instrumental success of our projectible concepts is grounded in their cognitive-pragmatic naturalness. It then explores three lines of reasoning against the argument: Evolutionarily motivated skepticism, the miracles argument, and the relation between instrumental and pragmatic success. I conclude that in its current form, the CS account fails to provide any justification of reasoning beyond appealing to its instrumental success, and that a metaphysically robust notion of naturalness helps to achieve the desired goal. (shrink)

Wenn wir Peter Singers Konklusion in „Famine, Affluence, and Morality“ (1972) akzeptieren, dann handeln wir im Alltag sehr viel häufiger falsch, als es uns lieb ist. Anstatt über die Natur von Altruismus zu philosophieren, könnten wir auch möglichst effektiv Hungerleidenden helfen. Ist es daher etwa moralisch verwerflich – weil egoistisch – zu philosophieren? In diesem Beitrag beleuchte ich die Gründe, die wir haben, Philosophie in den Mittelpunkt unseres Lebens zu stellen. Ich argumentiere, dass Philosophieren – genauso wie die Beschäftigung mit (...) Kunst und Wissenschaft – nur dann gerechtfertigt sein kann, wenn es praktische Gründe jenseits von Gründen des persönlichen Nutzens und der Moral gibt. Dabei schliesse ich an Susan Wolfs Idee an, dass diese Tätigkeiten ein Leben mit Sinn erfüllen können. Es bleibt jedoch offen, ob in einer Welt voller Ungerechtigkeit die moralischen Gründe gegen das Philosophieren (und für andere Handlungsoptionen) nicht dennoch überwiegen. (shrink)

This paper aims to counter the recent opinion that there is a peculiar epistemology in the reformed Church which made it negative to natural theology. First, it is shown that there was an early and unanimous adoption of natural theology as the culmination of physics and the beginning of metaphysics by the sixteenth and seventeenth century philosophers of good standing in the reformed Church. Second, it is argued that natural theology cannot be based on revelation, should not assume a peculiar (...) analysis of knowledge and must not pass over demonstration. (shrink)

Hume is an avowed critic of contractarianism. He opposes the idea that a legitimate government is based on an ‘original contract’ or on the consent of those who are governed. Most scholars assume, though, that his criticisms apply only to a limited range of contractarian theories, namely to theories according to which actual contractors reach an actual agreement. Theories on which the agreement in question is understood in hypothetical or counterfactual terms, however, are oftentimes seen as being compatible with Hume’s (...) views. Against such interpretations, this paper shows that Hume rejects all contractarian theories, including hypothetical ones. It argues, first, that Hume employs a so far unacknowledged empiricist debunking strategy against contractarianism; if successful, this strategy undermines all variants of contractarianism. Second, it shows that the Humean conception of the state of nature (a topic that has received virtually no scholarly attention) is incompatible with hypothetical contractarianism. Finally, it argues that Hume rejects contractarianism in part because he anticipates a line of criticism which nowadays is often leveled against so-called ideal theory. On Hume’s view, the agreements reached by highly idealized contractors are of little relevance to the non-ideal individuals in the actual world. (shrink)

It is a commonplace to sum up Plato's dialectical method under the formula logon didonai, which means to account for one's belief. The expression along with its genuine meaning seems to have originated at Greek courts of law, and Plato's Socrates, having adopted this formula to describe his philosophical method, seems to be the best advocate of the idea that to know means to be able to render an account. This paper aims to give a critical discussion of these traditional (...) views. First, there is no hint of any offspring of the expression logon didonai at Greek courts of law. Second, in pre-Socratic contexts the expression had not one but several meanings. And third, Plato, through the voice of Socrates, criticizes the unclear meaning of this expression in epistemological contexts. (shrink)

Adrian Moore argues that Kant’s transcendental idealism is incoherent, and that its incoherence gives us an invaluable insight into the fundamental nature of metaphysics, motivating the reconception of metaphysical inquiry with which Moore concludes his story of the development of modern philosophy. My discussion has three parts. First, I focus on the treatment of Kant’s transcendental idealism in Moore’s earlier book, Points of View, and highlight ways in which Moore is, I argue, open to challenge. Second, I suggest that the (...) historical record does not bear out Moore’s criticism of Kant’s transcendental idealism. Third, I compare Moore’s response to the alleged incoherence of transcendental idealism with that of the German Romantics. (shrink)

LANDEMORE, Hélène. Open Democracy. Reinventing Popular Rule for the Twenty-First Century. New Jersey: Princeton University Press, 2020.

Summary Until recently it was believed that Christian Huygens’ earliest publication of his pendulum invention was Horologium of 1658. He published the more famous general treatise, Horologium Oscillatorium, fifteen years later in 1673. Two years ago, an article1 suggesting an unknown collaboration in developing the clock pendulum between Huygens and the Paris clockmaker Isaac Thuret, presented the evidence of Benjamin Martin, an 18th century educationalist and retailer of scientific material. Martin described a Huygens publication of 1657 and reproduced the illustration (...) it contained. This illustration shows a different clock from the one drawn in Horologium and different also from those previously considered as Huygens’ earliest surviving examples. However, the illustration is similar to part of a plate in Horologium Oscillatorium and this similarity caused one historian to cast doubt on the existence of the 1657 publication.2 This article, with information presented for the first time, seeks to prove the existence of that work and thereby establish it in the canon of Huygens’ writings while re-examining the invention in the light that it casts. 1Whitestone, Sebastian, ‘The Identification and Attribution of Christiaan Huygens’ First Pendulum Clock', Antiquarian Horology, December (2008), 201–222. 2Plomp, R., ‘Letter', Antiquarian Horology, December (2009), 714–17. See also author's reply, ibid, 717–19. (shrink)

ABSTRACTWe know from Nietzsche’s posthumously published notebooks and correspondence of his plan in 1868 to compose a doctoral dissertation in philosophy on the subject of teleology in nature and the concept of the organic, with reference to Kant. The bulk of my discussion represents an attempt to extrapolate from Nietzsche’s letters and preparatory notes the view he arrived at. Since the notes do not defend explicitly any single definitive thesis, their interpretation is unavoidably conjectural. I argue that, if Nietzsche’s remarks (...) are considered with close reference to the philosophers who at that point dominated his horizons, namely Kant, Schopenhauer, and Lange, with Goethe also playing a key role, a plausible account can be given of the broad conclusions Nietzsche reached as a result of his early engagement with the problem of teleology. This outlook maintains the necessity and distinctiveness of philosophical reflection, but takes a skeptical view of its basis. In 1868 Nietzsche had no clear idea of how to proceed from this point, but in the end I propose, as others have done, that Nietzsche’s reflections on Kant and teleology helped to lay the ground for The Birth of Tragedy. In conclusion, I hypothesize that Nietzsche’s later philosophy involves no change of metaphilosophical standpoint. (shrink)

This article is a contribution to the history of the Geiger-Müller counter, based on the replication method. Along with a historical analysis of the Geiger-Müller counter I present and discuss my experience with replicas of early counters from 1928. The explicit and tacit knowledge that was gained during my construction und the experimentation process allows a different view of the development process in 1928. Against this background, I discuss Walter Müller’s role in the development and the significance of experimental work (...) in Geiger’s laboratory by illustrating the status of data gained from indirect electrical measurements in the field of early radioactivity research. All things considered it was not the instrument itself, but Geiger’s influence and status that affected its establishment in the scientific community in an authoritative way. (shrink)

Zusammenfassung: Aktuelle Debatten zu gesellschaftspolitischen Folgen der Corona-Pandemie zeigen, dass Intellektuelle wie Giorgio Agamben und Roberto Esposito den Begriff „Biopolitik“ ins Treffen führen, um Regierungsmaßnahmen zur Eindämmung des Virus zu analysieren. Seit Michel Foucaults Überlegungen zur Funktionsweise und Genealogie der Biopolitik birgt der Begriff jedoch eine gewisse Problematik: Aufgrund strukturell bedingter Mechanismen der Inklusion und Exklusion menschlichen Lebens gelingt es den biopolitischen Modellen nach Agamben und Esposito nicht – so die These –, ein zentrales Element des Politischen zu beschreiben. Unberücksichtigt (...) bleibt die Möglichkeit des Widerstands und der Kritik an Regierungsmaßnahmen; eine Möglichkeit, die gerade die Heterogenität politischer Ordnungsstrukturen anzeigt. Im Zuge der Analytik moderner Machttechniken verschiebt Foucault anders als Agamben und Esposito den Fokus von der Biopolitik hin zu einem umfassenderen Paradigma des „Regierens“, der Gouvernementalität. Infolgedessen lässt sich die Biopolitik als Regierungsweise thematisieren, mit der immer schon Formen widerständigen Handelns einhergehen. Um dieser Perspektive Rechnung zu tragen, argumentiert mein Beitrag mit Foucault gegen die primär strukturale Auffassung politischer Ordnungen nach Agamben und Esposito. (shrink)

During the Second World War, through innovations in officer selection and group therapy, the army psychiatrists John Rickman and Wilfred Bion changed our understanding of leadership. They showed how soldiers under stress could develop real authority through their attentiveness to each other. From contrasting experiences 25 years earlier each had seen how people in groups are moved by elemental forces that undermine judgement and thought. This article arose from my experiences as a trainee at the Tavistock Clinic, where the method (...) of reflective work discussion, giving individuals seated in a circle the choice to speak or to remain silent, seemed similar to a Quaker meeting. Many decades later I found that this association had a basis in fact. Among other influences on Bion — a childhood in India, distinguished service in the First World War, and a surgical apprenticeship with Wilfred Trotter — there is a little-acknowledged Quaker source, in John Rickman, for Bion’s radical work in the army that led to new methods of training and organizational consultancy in the postwar Tavistock. (shrink)

We address the considerations of the European Commission Expert Group on the ethics of connected and automated vehicles regarding data provision in the event of collisions. While human drivers’ appropriate post-collision behavior is clearly defined, regulations for automated driving do not provide for collision detection. We agree it is important to systematically incorporate citizens’ intuitions into the discourse on the ethics of automated vehicles. Therefore, we investigate whether people expect automated vehicles to behave like humans after an accident, even if (...) this behavior does not directly affect the consequences of the accident. We find that appropriate post-collision behavior substantially influences people’s evaluation of the underlying crash scenario. Moreover, people clearly think that automated vehicles can and should record the accident, stop at the site, and call the police. They are even willing to pay for technological features that enable post-collision behavior. Our study might begin a research program on post-collision behavior, enriching the empirically informed study of automated driving ethics that so far exclusively focuses on pre-collision behavior. (shrink)

This chapter contains sections titled: Introduction Don't Laugh at “Slow” Sailing: Average Versus Instantaneous Motion Motion Relative to What? – Galilean Relativity But There are No Fixed Reference Frames – Special Relativity General Relativity – Can it Really Matter?

For years as an award-winning war reporter, Sebastian Junger traveled to many front lines and frequently put his life at risk. And yet the closest he ever came to death was the summer of 2020 while spending a quiet afternoon at the New England home he shared with his wife and two young children. Crippled by abdominal pain, Junger was rushed to the hospital by ambulance. Once there, he began slipping away. As blackness encroached, he was visited by his (...) dead father, inviting Junger to join him. "It's okay," his father said. "There's nothing to be scared of. I'll take care of you." That was the last thing Junger remembered until he came to the next day when he was told he had suffered a ruptured aneurysm that he should not have survived. This experience spurred Junger--a confirmed atheist raised by his physicist father to respect the empirical--to undertake a scientific, philosophical, and deeply personal examination of mortality and what happens after we die. How do we begin to process the brutal fact that any of us might perish unexpectedly on what begins as an ordinary day? How do we grapple with phenomena that science may be unable to explain? And what happens to a person, emotionally and spiritually, when forced to reckon with such existential questions? (shrink)

Through a close reading of the two definitions of evil in the Introduction to Responses to Thalassios, this article points out a circular, cognitive-affective-somatic, genetic mechanism that St. Maximos the Confessor considers responsible for the initiation and transmission of the fallness as a human condition and the specific manifestation of it in the form of passions. It elucidates the first definition as mainly phenomenological, by identifying the circular mechanism and its behavioural expressions, and the second definition as more aetiological, by (...) explaining why this mechanism emerges and reemerges with the fallen humanity despite its catastrophic results. CONTRIBUTION: This article highlights a double genetic mechanism that St. Maximos the Confessor grasped within the fallen human condition as a curse solvable only in Christ, a notion largely carved out by previous Maximian scholarship, but fully explained and valuated here. (shrink)

El presente trabajo intenta analizar la naturaleza de la derivatio per modum determinationis. La filosofía escolástica enseña que la determinatio es uno de los modos de derivarse la ley humana desde la ley natural, particularmente el modo en que se deriva el derecho positivo o civil. En este trabajo el autor se detiene a revisar su modalidad, así como algunos criterios para reconocer las determinaciones o normas positivas. O presente trabalho procura analisar a natureza da derivatio per modum determinationis. A (...) filosofia escolástica ensina que a determinatio é um dos modos por meio dos quais se deriva a lei humana a partir da lei natural, particularmente o modo no qual se deriva o direito positivo ou civil. Neste trabalho o autor se detém a revisar sua modalidade, bem como alguns critérios para reconhecer as determinações ou normas positivas. (shrink)

The article talks of an evolution of a Biblical notion of Law. The author shows the way, the meaning of the Hebrew term “Torah” was transformed throughout the Pentateuch, in the prophetic tradition and in the wisdom books. He puts into analysis the relationship between the Judaism as a religious formation and the Law as a code. The Law included basic regulations to the moral, religious and political life of Israel.

El concepto de "inmanencia" ha adquirido una creciente relevancia en el campo filosófico contemporáneo. Dos destacados pensadores franceses, Gilles Deleuze y Franfois Jullien, le han otorgado un lugar fundamental en sus investigaciones. El propósito de este artículo es indagar el diálogo, poco explorado aún, entre ambos autores. Nuestra hipótesis de trabajo propone los siguientes ejes de análisis: primero, comparamos los usos de la expresión "absolutización de la inmanencia", acuñada por el sinólogo a fin de relativizar la trascendencia en el pensamiento (...) chino y luego empleada por Deleuze en el marco de la creencia en este mundo. En segundo lugar, examinamos las críticas que Jullien le dirige a Deleuze respecto a la relación entre la filosofía y la sabiduría. En tercer lugar, confrontamos sus perspectivas divergentes sobre la inmanencia en tanto "plano" (Deleuze) y como "fondo" (Jullien). Finalmente, ponemos de manifiesto la dificultad presente en ambos autores para pensar la idea de inmanencia. The concept of "immanence" has acquired substantial relevance within the contemporary philosophical field. Two influential french thinkers, Gilles Deleuze and Franfois Jullien, have conferred this concept a fundamental standing in their research. The purpose of this work is to explore the dialogue between both authors as this exploration has not been concluded. Our hypothesis puts forward the following axes of analysis. First, we shall compare the usage of the expression "absolutization of immanence" coined by the sinologist in order to put in perspective the idea of transcendence in Chinese thought. This expression was then applied by Deleuze within the frame of the belief in this world. Second, we shall examine Jullien's critique of Deleuze concerning the relationship between Philosophy and Wisdom. Third, we shall confront the divergent perspectives on immanence: as "plane" (Deleuze) and as "buttom" (Jullien). Finally, we shall show the difficulty to ponder the idea of immanence in both authors. (shrink)

It is well known that Sartre describes his form of existentialism as atheistic, and much of the rhetoric of Sartrean existentialism draws off the image of God's absence from the world. There are nevertheless, I argue, deep grounds for thinking that the coherence and well-groundedness of Sartre's thought requires that his phenomenological ontology take finally the form of an onto-theology: Sartre's ontology runs into difficulties concerning the origin of the for-itself and the unity of being; an onto-theology like Schelling's, which (...) avoids the ‘ontological optimism’ that Sartre objects to in Hegel, both releases Sartre's ontology from its difficulties and furthers Sartre's central philosophical purposes. (Published Online July 10 2006). (shrink)

Educational disparities between traditional and non-traditional student groups in higher distance education can potentially be reduced by alleviating social identity threat and strengthening students’ sense of belonging in the academic context. We present a use case of how Learning Analytics and Machine Learning can be applied to develop and implement an algorithm to classify students as at-risk of experiencing social identity threat. These students would be presented with an intervention fostering a sense of belonging. We systematically analyze the intervention’s intended (...) positive consequences to reduce structural discrimination and increase educational equity, as well as potential risks based on privacy, data protection, and algorithmic fairness considerations. Finally, we provide recommendations for Higher Education Institutions to mitigate risk of bias and unintended consequences during algorithm development and implementation from an ethical perspective. (shrink)

Papers presented at the 38th Annual Meeting of the Husserl Circle, Marquette University, Milwaukee, Wis., June 26-29, 2008.

In this review, we present a rigorous construction of an algebraic method for quantum unstable states, also called Gamow states. A traditional picture associates these states to vectors states called Gamow vectors. However, this has some difficulties. In particular, there is no consistent definition of mean values of observables on Gamow vectors. In this work, we present Gamow states as functionals on algebras in a consistent way. We show that Gamow states are not pure states, in spite of their representation (...) as Gamow vectors. We propose a possible way out to the construction of averages of observables on Gamow states. The formalism is intended to be presented with sufficient mathematical rigor. (shrink)