This article is a logical continuation of the Henri Lombardi and Franz-Viktor Kuhlmann article [9]. We address some classical points of the theory of valued fields with an elementary and constructive point of view. We deal with Krull valuations, and not simply discrete valuations. First of all, we show how to construct the Henselization of a valued field; we restrict to fields in which one has at one's disposal algorithmic tools to test the nullity or the valuation ring (...) membership. It is therefore a work that differs as much in spirit as in field of application from that of Mines, Richman and Bridges , who address the framework of Heyting fields and discrete valuation. We show then in a constructive way a batch of classical results in Henselian fields, notably factorization criteria and Krasner's Lemma. We conclude by a construction of the inertia field of a valued field. (shrink)

A suggestion for research on Rosenzweig and Viktor von Weizsacker, Franz Rosenzweig's Philosophical legacy: Levinas or Strauss?

We paraphrase Descartes’ famous dictum in the area of AI ethics where the “I doubt and therefore I am” is suggested as a necessary aspect of morality. Therefore AI, which cannot doubt itself, cannot possess moral agency. Of course, this is not the end of the story. We explore various aspects of the human mind that substantially differ from AI, which includes the sensory grounding of our knowing, the act of understanding, and the significance of being able to doubt ourselves. (...) The foundation of our argument is the discipline of ethics, one of the oldest and largest knowledge projects of human history, yet, we seem only to be beginning to get a grasp of it. After a couple of thousand years of studying the ethics of humans, we (humans) arrived at a point where moral psychology suggests that our moral decisions are intuitive, and all the models from ethics become relevant only when we explain ourselves. This recognition has a major impact on what and how we can do regarding AI ethics. We do not offer a solution, we explore some ideas and leave the problem open, but we hope somewhat better understood than before our study. (shrink)

In einem auf drei Bände angelegten Dokumentationswerk werden Entstehung und Ausbreitung des Paracelsismus in den kontroversen Verflechtungen der Wissenschafts-, Literatur- und Sozialgeschichte des späten 16. Jahrhunderts verankert. Die kritische Edition aufschlußreicher, oft in unbekanntes Terrain führender Texte ist begleitet von umfangreichen Kommentaren sowie von biographischen Darstellungen der Urheber, Adressaten, Gegner bzw. Sympathisanten der paracelsistischen Reform und Protestbewegung. Der zweite Band des »Corpus Paracelsisticum« erschließt das weitläufige Oeuvre von Michael Toxites und Gerhard Dorn, wirkmächtige Gründergestalten des oberrheinischen Paracelsismus. Von da aus (...) fällt der Blick quer über die Konfessionsgrenzen auf andere kulturelle Zentren in Bayern, Sachsen, Schlesien, Böhmen und am Niederrhein. Mit Verfassern wie G. Fedro, M. Ambrosius, L. Span, B. Flöter, G. Etschenreutter, B. Scultetus, P. Perna, Th. Zwinger und J. Albrecht eröffnet sich ein epochaler, äußerst weitläufiger Diskurszusammenhang. In ihm lassen sich doxographische, methodische, hermeneutische, sprachtheoretische und überlieferungsspezifische Auseinandersetzungen ebenso beobachten wie Tendenzen einer theosophischen Spiritualisierung und heterodoxen Aufladung der in Paracelsus' Namen entwickelten Anthropologie und Kosmologie. Direkte Verbindungen ergeben sich unter anderem zu führenden Vertretern der sogenannten Schwenckfelder, damit auch zu Fraktionen aktiver protestantischer Dissidenten. Der Band wird neben dem weiterführenden Kommentar begleitet von einer ausführlichen Einleitung und erschlossen nicht nur durch mehrere Register, sondern auch durch wissenschaftshistorische Zusammenfassungen zu jedem Autorcorpus. (shrink)

Dr. Viktor Dörfler combines his background in developing and implementing AI with scholarly research on knowledge and cultivating talent to address misconceptions about AI. The Element explains what AI can and cannot do, carefully delineating facts from beliefs or wishful thinking. Filled with examples, this practical Element is thought-provoking. The purpose is to help CEOs figure out how to make the best use of AI, suggesting how to extract AI’s greatest value through appropriate task allocation between human experts and (...) AI. The author challenges the attribution of characteristics like understanding, thinking, and creativity to AI, supporting his argument with the ideas of the finest AI philosophers. He also discusses in depth one of the most sensitive AI-related topics: ethics. The readers are encouraged to make up their own minds about AI and draw their own conclusions rather than accepting opinions from people with vested interests or an agenda. (shrink)

Despite a strong sensitization to the corruption problem and a large body of interdisciplinary research, scientists have only rarely investigated which motivational, volitional, emotional, and cognitive components make decision makers in companies act corruptly. Thus, we examined how their interrelation leads to corruption by proposing an action model. We tested the model using a business simulation game with students as participants. Results of the PLS structural equation modeling showed that both an attitude and subjective norm favoring corruption led to a (...) desire to act corruptly. Given high perceived behavioral control, this desire was transformed into an intention that finally resulted in corrupt action. Components related to general private and professional goals did not allow for any prediction. Based on these results, we discuss preventative measures and methods for combating intra- and inter-organizational corruption. (shrink)

We present results from a single case study based on semi-structured interviews with a student (a boy in school year 3) diagnosed with autism spectrum disorder and his school staff after participating in a short and small-scale intervention carried out in a socio-economically disadvantaged Swedish elementary school in 2019. The student participated in a seven week long intervention with a total of 12 philosophical dialogues (ranging from 45 to 60 minutes). Two facilitators, both with years of facilitation experience and teacher (...) degree and at least BA in philosophy, facilitated the majority of the dialogues and mainly followed a ”routine” procedure. The student was interviewed in direct connection to the end of the intervention about his experiences from the dialogues and his perceptions about whether and how the dialogues had influenced him. The student’s two teachers, who had participated in the dialogues as participants, were interviewed as a pair, also in direct connection to the end of the intervention, while the school principal was interviewed two years after the study. These staff interviews concerned the staff’s experiences of the influence of the dialogues on the students within the intervention as well as transfer effects to other contexts in school. The data from the study include detailed elaborations from a student perspective of different effects on the student’s communicative and cognitive development, which are in several respects supported also by staff reports. The results show that the student was able, interested, and willing to participate in philosophical dialogues, and our data point to several positive outcomes for the student in the communicative and cognitive domains. (shrink)

Purpose. Institutionalism is gaining strength as a dominant point of view on the world. Its philosophical basis is the postulate of the uncertainty of the development, which comes to replace the neoclassical certainty characteristic of industrial society. The postulate of uncertainty is closely connected with the idea of subjectivization and individualization of post-industrial society. All these were very important components of the new paradigm, although they do not exhaust the problem. In the heart of postmodernism is a mass identity as (...) a spiritual substance, while the more recently mass of people to realize themselves as natural and social beings. Person has absolute freedom in the acceptance and rejection of culture and civilization; it is pluralistic in their actions and in their consciousness. It is the subject of history and it should be creative, fluent mastering all the achievements of culture. Methodology. The dialogue system of the Postmodern, which is the basis of human communication with another person, human with society is a model of convergent formation of the world community and world economy. The same model of rationalism and adequate industrial society is a monologue, which is easily builds a bridge to violence, even if it is carried out in the name of the man behind him and the pathos of the exaltation of man as the bearer of unlimited creation possibilities. However, it is very important not just to modify rationalism, and to understand the origins of civilization. Scientific novelty. The postmodern era begins is not easy. Modern defending, using all their reserves: public thirst for justice, the priority of rationality, monologist public agencies and politicians in contrast to the dialogic postmodern imperative modality in the spiritual existence of man instead the freedom. Finally, the world of the story is set a trap – the anthropological paradigm of the globalization ideology formation. In this paradigm, people see materialistic rational measure of space and society building, i.e. the natural and social being, not a spiritual person. All this was evident in the course of transformation in Ukraine. Its main weakness is obvious. This narrows the field of mass participation in the market or by the adopted symbolism, the field of subjectivity. The population is invited to wait and endure, i.e. plays the role of the object of political and economic manipulation. Even more unacceptable monopolization of subjectivity government, for which everything is regarded as a subject of state regulation. Conclusions. For civilization of cardinal feature is the treatment of the person as the subject of history. The need for the development of civilization to increase the degree of subjectivity in an economy where people can express themselves freely and responsibly through a system of private property relations: economic entity is the subject of property. Policy enhancing the role of human rights and the development of the principle of subjectivity means deepening the democratic foundations of the state structure. In the social sphere the subjectivity is expressed in the individualization of the social existence of man and the personification of public relations and it is implemented through the mechanisms of liberal institutions. It seems that the civilizational unity of the economy, democratic state and liberal society has the value of a scientific paradigm. Whatever the great cultural peaks of the postmodern, the main processes of a new society formed at its foot: in the area of formation of public consciousness and public preferences with the mass participation of the individual in the economy, in the field of state-building and the formation of social institutions on the principles of Amateur participation. (shrink)

Purpose. Institutionalism is gaining strength as a dominant point of view on the world. Its philosophical basis is the postulate of the uncertainty of the development, which comes to replace the neoclassical certainty characteristic of industrial society. The postulate of uncertainty is closely connected with the idea of subjectivization and individualization of post-industrial society. All these were very important components of the new paradigm, although they do not exhaust the problem. In the heart of postmodernism is a mass identity as (...) a spiritual substance, while the more recently mass of people to realize themselves as natural and social beings. Person has absolute freedom in the acceptance and rejection of culture and civilization; it is pluralistic in their actions and in their consciousness. It is the subject of history and it should be creative, fluent mastering all the achievements of culture. Methodology. The dialogue system of the Postmodern, which is the basis of human communication with another person, human with society is a model of convergent formation of the world community and world economy. The same model of rationalism and adequate industrial society is a monologue, which is easily builds a bridge to violence, even if it is carried out in the name of the man behind him and the pathos of the exaltation of man as the bearer of unlimited creation possibilities. However, it is very important not just to modify rationalism, and to understand the origins of civilization. Scientific novelty. The postmodern era begins is not easy. Modern defending, using all their reserves: public thirst for justice, the priority of rationality, monologist public agencies and politicians in contrast to the dialogic postmodern imperative modality in the spiritual existence of man instead the freedom. Finally, the world of the story is set a trap – the anthropological paradigm of the globalization ideology formation. In this paradigm, people see materialistic rational measure of space and society building, i.e. the natural and social being, not a spiritual person. All this was evident in the course of transformation in Ukraine. Its main weakness is obvious. This narrows the field of mass participation in the market or by the adopted symbolism, the field of subjectivity. The population is invited to wait and endure, i.e. plays the role of the object of political and economic manipulation. Even more unacceptable monopolization of subjectivity government, for which everything is regarded as a subject of state regulation. Conclusions. For civilization of cardinal feature is the treatment of the person as the subject of history. The need for the development of civilization to increase the degree of subjectivity in an economy where people can express themselves freely and responsibly through a system of private property relations: economic entity is the subject of property. Policy enhancing the role of human rights and the development of the principle of subjectivity means deepening the democratic foundations of the state structure. In the social sphere the subjectivity is expressed in the individualization of the social existence of man and the personification of public relations and it is implemented through the mechanisms of liberal institutions. It seems that the civilizational unity of the economy, democratic state and liberal society has the value of a scientific paradigm. Whatever the great cultural peaks of the postmodern, the main processes of a new society formed at its foot: in the area of formation of public consciousness and public preferences with the mass participation of the individual in the economy, in the field of state-building and the formation of social institutions on the principles of Amateur participation. (shrink)

Discoverers of “market failures” as well as advocates of the general efficiency of a “true, unhampered market” sometimes seem to disregard the fundamental fact that there is no such thing as a “market as such.” What we call a market is always a system of social interaction characterized by a specific institutional framework, that is, by a set of rules defining certain restrictions on the behavior of the market participants, whether these rules are informal, enforced by private sanctions, or formal, (...) enforced by a particular agency, the “protective state,” in J. M. Buchanan's terminology. (shrink)

Journal of Philosophy of Education, EarlyView.

In solving judgment aggregation problems, groups often face constraints. Many decision problems can be modelled in terms the acceptance or rejection of certain propositions in a language, and constraints as propositions that the decisions should be consistent with. For example, court judgments in breach-of-contract cases should be consistent with the constraint that action and obligation are necessary and sufficient for liability; judgments on how to rank several options in an order of preference with the constraint of transitivity; and judgments on (...) budget items with budgetary constraints. Often more or less demanding constraints on decisions are imaginable. For instance, in preference ranking problems, the transitivity constraint is often contrasted with the weaker acyclicity constraint. In this paper, we make constraints explicit in judgment aggregation by relativizing the rationality conditions of consistency and deductive closure to a constraint set, whose variation yields more or less strong notions of rationality. We review several general results on judgment aggregation in light of such constraints. (shrink)

Eventually, Kuhlmann proposes a dispositional trope ontology, according to which particularized properties and not things are the most basic entities.

The purpose. Critical social philosophy of education strives to provide a radical critique of existing models of education in the so-called Western models of democracy, creating progressive alternative models. In this context, the proposed integrative metatheory, which is based on classical and modern sources, concepts, aims for a comprehensive understanding and reconstruction of the phenomenon of education. One of the main tasks in the sphere of education’s democratization today, therefore, is to bring to education the results of restructuring and democratization (...) of the society, to reflect changes in conditions of life and thinking, experience and transformation of subjectivity in the context of the technological revolution and globalization. Methodology. The critical social theory, which developed in the framework of contemporary neo-Marxism, indicates the need for a thorough analysis of society, however, unlike other theoretical concepts and research programs in order to analyze not a fixation and a statement of the existing social givens. On the contrary, critical analysis of society involves the identification of existing antagonistic, alienating factors that distort public communication.The subject of social analysis is the whole sphere of human and non-human nature, which interacts a person depend on it, the whole system of relations between society and nature, society and man, which is covered by the historical practice of conscious – "praxis". The representative of "pure science" isn't the learning, research subject. He is a public a person, which is the totality of all social definitions included in society and its constituent individuals. For such a "total subject" Object of interest is not something external; on the contrary, the latter appears as a product of his own activity. The scientific novelty examines trends in educational institutions and models of globalizing society in the context of our particular relationship of education and society, man and the state, and processes. The research and systematic analysis of neoliberal reforms at the level of society in general and education in particular are conducted. It examines substantive, structural and functional characteristics of the concept of «critical social philosophy of education» in the context of institutional tendencies of social life, as well as forms and possibilities of its methodological application. It consider a model of «critical social philosophy of education», as embodied in the programs of social development and learning, which are primarily designed to teach people how to lead an independent and original research themselves, society and knowledge systems. However, it is proved that the models and programs should not be cut off from any individual and the collective system of moral and social values, theoretical and applied training, nor from further use of the acquired values, norms and skills in everyday life, science, or in production, sphere of all social institutions. Conclusions. Critical philosophical, educational, pedagogical-psychological surprisingly theory, its models and concepts seek to redefine public and private and the public mind. Based on these grounds, in the future, it allows philosophy of education to develop a more inclusive philosophical vision of education, to apply directly to the problems of democratization and changes in social relations in the direction of equality and social justice in the field of education. The point of view of socio-philosophical and philosophical-еducational, pedagogical-psychological, normative understanding and social critics also requires the use of active efforts in the reconstruuction of education and society, the social vision of what education and human life can be and what their specific limitations in existing societies. (shrink)

The purpose. Critical social philosophy of education strives to provide a radical critique of existing models of education in the so-called Western models of democracy, creating progressive alternative models. In this context, the proposed integrative metatheory, which is based on classical and modern sources, concepts, aims for a comprehensive understanding and reconstruction of the phenomenon of education. One of the main tasks in the sphere of education’s democratization today, therefore, is to bring to education the results of restructuring and democratization (...) of the society, to reflect changes in conditions of life and thinking, experience and transformation of subjectivity in the context of the technological revolution and globalization. Methodology. The critical social theory, which developed in the framework of contemporary neo-Marxism, indicates the need for a thorough analysis of society, however, unlike other theoretical concepts and research programs in order to analyze not a fixation and a statement of the existing social givens. On the contrary, critical analysis of society involves the identification of existing antagonistic, alienating factors that distort public communication.The subject of social analysis is the whole sphere of human and non-human nature, which interacts a person depend on it, the whole system of relations between society and nature, society and man, which is covered by the historical practice of conscious – "praxis". The representative of "pure science" isn't the learning, research subject. He is a public a person, which is the totality of all social definitions included in society and its constituent individuals. For such a "total subject" Object of interest is not something external; on the contrary, the latter appears as a product of his own activity. The scientific novelty examines trends in educational institutions and models of globalizing society in the context of our particular relationship of education and society, man and the state, and processes. The research and systematic analysis of neoliberal reforms at the level of society in general and education in particular are conducted. It examines substantive, structural and functional characteristics of the concept of «critical social philosophy of education» in the context of institutional tendencies of social life, as well as forms and possibilities of its methodological application. It consider a model of «critical social philosophy of education», as embodied in the programs of social development and learning, which are primarily designed to teach people how to lead an independent and original research themselves, society and knowledge systems. However, it is proved that the models and programs should not be cut off from any individual and the collective system of moral and social values, theoretical and applied training, nor from further use of the acquired values, norms and skills in everyday life, science, or in production, sphere of all social institutions. Conclusions. Critical philosophical, educational, pedagogical-psychological surprisingly theory, its models and concepts seek to redefine public and private and the public mind. Based on these grounds, in the future, it allows philosophy of education to develop a more inclusive philosophical vision of education, to apply directly to the problems of democratization and changes in social relations in the direction of equality and social justice in the field of education. The point of view of socio-philosophical and philosophical-еducational, pedagogical-psychological, normative understanding and social critics also requires the use of active efforts in the reconstruuction of education and society, the social vision of what education and human life can be and what their specific limitations in existing societies. (shrink)

What role, if any, should Confucianism play in the politics of our time? In some of my previous works, I claimed that modern liberal states are not permitted to promote Confucian values on the basis of their intrinsic merits. Yet, drawing insights from Joseph Chan’s moderate state perfectionism and John Rawls’s wide view of public political culture, I proposed the “wide view of moderate perfectionism.” According to this view, in public political discussion, citizens should be allowed to deliberate whether and (...) how Confucianism, among other reasonable moral doctrines, can make positive contributions to their social and political thinking and public policymaking, provided that certain conditions are met. This view has been criticized by some scholars, in particular Zhuoyao Li. Li argues that the practice of the wide view of moderate perfectionism would inevitably harm civility. In this article, I clarify and develop the wide view and respond to Li’s criticisms. (shrink)

In this article, we distinguish between three approaches to ethics in school, each giving an interpretation of the expression ‘ethics in school’: the descriptive facts about ethics approach, roughly consisting of teaching empirical facts about moral matters to students; the moral fostering approach, consisting of mediating a set of given values to students; and the philosophical ethics (PE) approach, consisting of critically discussing and evaluating moral issues with students. Thereafter, three influential arguments for why there ought to be ethics in (...) school are discussed, and each argument is interpreted given each approach to ethics in school, respectively. Thereby, we evaluate which interpretation of ‘ethics in school’ produces the strongest arguments, and thus, which approach is best supported by these arguments. The conclusion is that there ought to be PE in school. (shrink)

Sociological theories of space have so far not provided an in-depth analysis of online spaces. The paper addresses this issue by means of Löw’s relational theory of space. As this theory mainly focuses on material spaces, it is necessary to embrace the phenomenological perspective in order to apply it to the virtual realm. More recent phenomenological research has highlighted the ongoing mediatization or virtualization of the life-world. These theories, and presence research more generally, are useful for examining the layers of (...) virtual presence. This paper focuses on two emblematic types of spaces: multiplayer online role-playing games and Skype video chats. The first represents an online version of a Schutzian finite province of meaning, while Skyping is an example of how the paramount reality of everyday life expands into the virtual realm. Albeit differently, actors in both cases constitute hybrid, virtual-material spaces with various forms and degrees of virtual presence. User experiences in these spaces are in line with contemporary sociological diagnoses indicating the vanishing experience of living in space and the general tendency of late modernity to question previous social forms of modernity. (shrink)

Advocates of the New Mechanicism in philosophy of science argue that scientific explanation often consists in describing mechanisms responsible for natural phenomena. Despite its successes, one might think that this approach does not square with the ontological strictures of quantum mechanics. New Mechanists suppose that mechanisms are composed of objects with definite properties, which are interconnected via local causal interactions. Quantum mechanics calls these suppositions into question. Since mechanisms are hierarchical it appears that even macroscopic mechanisms must supervene on a (...) set of “objects” that behave non-classically. In this paper we argue, in part by appeal to the theory of quantum decoherence, that the universal validity of quantum mechanics does not undermine neo-mechanistic ontological and explanatory claims as they occur within in classical domains. Additionally, we argue that by relaxation of certain classical assumptions, mechanistic explanatory strategies can sometimes be carried over into the quantum domain. (shrink)

Purpose – The purpose of this study is to improve our understanding of bracketing, one of the most central philosophical and theoretical constructs of phenomenology, as a theory of mind. Furthermore, we wanted to showcase how this theoretical construct can be implemented as a methodological tool. -/- Design/methodology/approach – In this study we have adopted an approach similar to a qualitative metasynthesis, comparing the emergent patterns of two empirical projects, seeking synergies and contradictions and looking for additional insights from new (...) emerging patterns. -/- Findings – On a philosophical level, we have found that bracketing, as a theoretical construct, is not about the achievement of objectivity; quite to the contrary, it embraces subjectivity and puts it centre-stage. On a theoretical level, we have achieved a better understanding of Husserl’s phenomenology, as a theory of mind. On a methodological level, we have achieved a powerful way of supplementing and/or clarifying research findings, by using a theoretical construct as a methodological tool. -/- Originality/value – Our paper contributes to the phenomenology literature at a philosophical, theoretical and methodological level, by offering a better understanding and a novel implementation of one of the central theoretical constructs of phenomenology. (shrink)

In this chapter we offer a reflection on the notion of sample representativeness from an interpretivist-qualitative perspective. Specifically we are looking into the idea of learning about a phenomenon through examining extraordinary individuals characterized by that phenomenon; to describe them we use the term ‘extraordinary’ as a noun, thereby building on Howard Gardner’s notion of ‘extraordinary minds’ (Gardner, 1997). We are looking at the ‘extraordinary’ in their professional socio-historical contexts, as the phenomena we are interested in cannot be divorced from (...) the contexts in which they are embedded. In this particular book chapter we are interested in the phenomenon of creativity, and the two research projects on which we base our argument are also concerned with creativity. However, we do not see any reason why similar considerations could not be made in other areas – but we do not suggest that a simple generalizability is possible. -/- The basis of our reflection are two research projects we have done in the past: In the first one, we conducted ‘insider interviews’ (the second-named author used to be a chef in Michelin-starred restaurants) with 18 extraordinary chefs in order to gain a better understanding of how creativity manifests itself socio-culturally in the culinary domain (Cousins, O’Gorman, & Stierand, 2010; Stierand, 2015; Stierand & Dörfler, 2012b, 2016; Stierand, Dörfler, & MacBryde, 2014; Stierand & Lynch, 2008). In the second one, we interviewed 20 extraordinary scientists, including 17 Nobel Laureates in order to gain a better understanding of cognitive complexity and how cognitive complexity is manifested in the socio-cultural acceptance of creative outcomes in the scientific world (Dörfler & Eden, 2014a, 2014b, 2017). -/- We have presented our research at various conferences, and, perhaps as we were so passionate about it, we have received a great deal of interest from others, mainly PhD students and early career researchers, who were keen to undertake similar research projects. But, although we believe that the methodological journey we have taken can be an excellent path to very interesting and meaningful research, we cannot wholeheartedly recommend it to junior colleagues, knowing the difficulties they will face when trying to justify their findings and methodological choices and the uncertain profits in the form of publication of the results (see an excellent overview of the difficulties and profits in Lebuda, 2014). We made our initial methodological choices, i.e. interviewing extraordinary chefs and scientists, purely intuitively that is, we just knew that the insights we could gain from these people would potentially lead to excellent findings. However, this is not an acceptable justification in the academic world. Therefore, we started to develop a framework for conducting this type of research, but we are not quite there yet. This reflection chapter is a midway point for taking stock of the convincing arguments we have developed over time and of the problems we still need to solve. (shrink)

The article has two main goals. 1. To reveal the psychological mechanism of the assimilation of faith and the concept of its relationship with reason in the philosophy of B. Pascal, as well as the role of faith both in knowledge in general and in knowledge of God. 2. To determine the degree of influence of Augustine's theological and philosophical concepts on the formation of Pascal's views. By comparing the concepts of will, understanding, faith and reason, the author comes to (...) the conclusion that Augustine, like Pascal, does not oppose faith to reason, but includes reason in the "mechanism" of acquiring faith. In this way, the reason in the act of faith becomes a direct partner of consciousness and reason. The logic of faith, according to Pascal and Augustine, differs from the logic of understanding in that understanding is based on the material reality of earthly existence, while faith is based on the supernatural reality of divine inspiration. (shrink)

Agent-based models derive the behavior of artificial socio-economic entities computationally from the actions of a large number of agents. One objection is that highly idealized ABMs fail to represent the real world in any reasonable sense. Another objection is that they at best show how observed patterns may have come about, because simulations are easy to produce and there is no evidence that this is really what happens. Moreover, different models may well yield the same result. I will rebut these (...) objections by focusing on an often neglected, but crucial function of ABMs. Building on Gelfert’s account of the exploratory uses of scientific models I show that, in the absence of an accepted underlying theory, successful ABMs lend inductive support to assumptions concerning certain structural feutures of the behavioral rules employed. One core step towards this goal is what I call multiple-model robustness analysis. (shrink)

The geometrical algebra hypothesis was once the received interpretation of Greek mathematics. In recent decades, however, it has become anathema to many. I give a critical review of all arguments against it and offer a consistent rebuttal case against the modern consensus. Consequently, I find that the geometrical algebra interpretation should be reinstated as a viable historical hypothesis.

I present a systematic interpretation of the foundational purpose of constructions in ancient Greek geometry. I argue that Greek geometers were committed to an operationalist foundational program, according to which all of mathematics—including its entire ontology and epistemology—is based entirely on concrete physical constructions. On this reading, key foundational aspects of Greek geometry are analogous to core tenets of 20th-century operationalist/positivist/constructivist/intuitionist philosophy of science and mathematics. Operationalism provides coherent answers to a range of traditional philosophical problems regarding classical mathematics, such (...) as the epistemic warrant and generality of diagrammatic reasoning, superposition, and the relation between constructivism and proof by contradiction. Alleged logical flaws in Euclid can be interpreted as sound operationalist reasoning. Operationalism also provides a compelling philosophical motivation for the otherwise inexplicable Greek obsession with cube duplication, angle trisection, and circle quadrature. Operationalism makes coherent sense of numerous specific choices made in this tradition, and suggests new interpretations of several solutions to these problems. In particular, I argue that: Archytas’s cube duplication was originally a single-motion machine; Diocles’s cissoid was originally traced by a linkage device; Greek conic section theory was thoroughly constructive, based on the conic compass; in a few cases, string-based constructions of conic sections were used instead; pointwise constructions of curves were rejected in foundational contexts by Greek mathematicians, with good reason. Operationalism enables us to view the classical geometrical tradition as a more unified and philosophically aware enterprise than has hitherto been recognised. (shrink)