By the end of his life Plato had rearranged the theory of ideas into his teaching about ideal numbers, but no written records have been left. The Ideal mathematics of Plato is present in all his dialogues. It can be clearly grasped in relation to the effective use of mathematical modelling. Many problems of mathematical modelling were laid in the foundation of the method by cutting the three-level idealism of Plato to the single-level “ideism” of Aristotle. For a long time, (...) the real, ideal numbers of Plato’s Ideal mathematics eliminates many mathematical problems, extends the capabilities of modelling, and improves mathematics. (shrink)

This article examines Aristotle’s use of the term philia. As a basis for the analysis, the author employs the communicative component of this notion. This allows us to consider friendship as a process, distinguishing it from everything else that cannot be identified as such. This “residue” is something that comes from nature, common to all living creatures, and is at the root of all types of positive communication. The goal of this article is to show that the content identified as (...) such can be understood as a separate concept. (shrink)

It is my hope that the book will be widely read and debated."--Axel Leijonhufvud, UCLA and the University of Trento "This is a major and controversial contribution to macroeconomics that cannot fail to make an impact in several areas.

Growing out of a conference on Expectations Formation and Economic Disequilibrium held in New York City in 1981, the papers in this volume provide a complex view of market processes in which individual rationality is no guarantee of convergence to the 'correct' model and the equilibrium coordination of agents' plans. They reject the 'optimality' argument for the rational expectations hypothesis, opening the door to other hypotheses of optimal expectations of agents in the decentralized market economy.

We reconsider the Nagelian theory of reduction and argue that, contrary to a widely held view, it is the right analysis of intertheoretic reduction. The alleged difficulties of the theory either vanish upon closer inspection or turn out to be substantive philosophical questions rather than knock-down arguments.

The aim of this book is to present and analyze philosophical conceptions concerning mathematics and logic as formulated by Polish logicians, mathematicians and philosophers in the 1920s and 1930s. It was a remarkable period in the history of Polish science, in particular in the history of Polish logic and mathematics. Therefore, it is justified to ask whether and to what extent the development of logic and mathematics was accompanied by a philosophical reflection. We try to answer those questions by analyzing (...) both works of Polish logicians and mathematicians who have a philosophical temperament as well as their research practice. Works and philosophical views of the following Polish scientists will be analyzed: Wacław Sierpiński, Zygmunt Janiszewski, Stefan Mazurkiewicz, Stefan Banach Hugo Steinhaus, Eustachy Żylińsk and Leon Chwistek, Jan Łukasiewicz, Zygmunt Zawirski, Stanisław Leśniewski, Tadeusz Kotarbiński, Kazimierz Ajdukiewicz, Alfred Tarski, Andrzej Mostowski and Henryk Mehlberg, Jan Sleszyński, Stanisław Zaremba and Witold Wilkosz. To indicate the background of scientists being active in the 1920s and 1930s we consider in Chapter 1 some predecessors, in particular: Jan Śniadecki, Józef Maria Hoene-Wroński, Samuel Dickstein and Edward Stamm. (shrink)

Transformácia politického systému -- Aktuálne problémy a riešenia -- Alternatívy súčasného kapitalizmu -- Cynizmus ako princíp -- Appendix o školstve.

Between the zone of certainty beyond all doubt and the zone of incomprehensible uncertainty, the sources of which are nothing but chance, we need to use solid results from a vast interdisciplinarity. We wish to give here a sense of the factors in play and the state of the debate and advance in the territory of how interdisciplinarity may help to solve problems which are common in many areas of knowledge. Chaos and complexity certainly put limits on what we can (...) know. High complexity, asymmetry and/or non-linearity are universal types of imprecision. Can hazard have purpose and direction?The idea is that the more effort we put into project design to cover as many details and possible consequences as possible we can grasp in our in-depth analysis aiming to create the project (in art or science or society), the greater the chances that the random occurrence of the unpredictable event will settle on the project's purpose and direction and not on contrary to them. There is no vicious circle here. This kind of method can explain many good results already obtained in such circumstances. Simplicity, beauty, rationalistic optimism, are features of unshakeable scientific results We may call this feature of scientific theory or art _uniqueness. _Uniqueness is strongly correlated with _essentialization. _Science is working in that sense: to simplify a phenomenon to its essence in order to study it easily without losing anything important in the analysis. That is _essentialization. _Why and how complex systems move to the edge of chaos? And what do they do to stay there? They are in constant struggle to create or keep order in complexity. That is the pattern of self-organization, the specific feature of human nature. That is why our action is meant to build resilience to deal better with unpredictable events and prevent the emergence of a critical threshold. Uncertainty, indeterminacy, randomness, and contradictions appear, not as non-essential substances of debate to be eliminated by explanation, but as everlasting ingredients of our conception of reality. There are compelling reasons to believe that it is impossible to make accurate, nontrivial predictions concerning human behavior. Logic and reason are and remain priority, but unpredictability forces us to imagination and creative thinking. Indeed we are confronted with a new human landscape. The anomalies become the new normal. (shrink)

Over the last decade, numerous interventions and techniques that aim to engender, strengthen, and expand compassion have been created, proliferating an evidence base for the benefits of compassion meditation training. However, to date, little research has been conducted to examine individual variation in the learning, beliefs, practices, and subjective experiences of compassion meditation. This mixed-method study examines changes in novice meditators’ knowledge and contemplative experiences before, during, and after taking an intensive course in CBCT®, a contemplative intervention that is increasingly (...) used for both inter- and intrapersonal flourishing. The participants in this study were Christian healthcare chaplains completing a 1-year residency in Clinical Pastoral Education who learned CBCT as part of their professional chaplaincy training curriculum. Prior to and upon completion of training, we surveyed participants to assess their beliefs about the malleability of compassion, types of engagement in compassion meditation, and perceptions of the impact of taking CBCT. We also conducted in-depth interviews with a subset of participants to gain a qualitative understanding of their subjective experiences of learning and practicing compassion meditation, a key component of CBCT. We found that participants reported increases in the extent to which they believed compassion to be malleable after studying CBCT. We also found high levels of variability of individual ways of practicing and considered the implications of this for the study of contemplative learning processes. This multi-methodological approach yielded novel insights into how compassion practice and compassion-related outcomes interrelate, insights that can inform the basic scientific understanding of the experience of learning and enacting compassion meditation as a means of strengthening compassion itself. (shrink)

Il est commun, aujourd'hui, d'associer la démocratie au consensus, et ce d'une double manière : d'une part en admettant qu'elle est le meilleur régime politique possible, d'autre part en considérant que l'accord vaut intrinsèquement mieux que le désaccord, et l'entente que le conflit: La qualité de la démocratie tiendrait à ses débats publics, qui à la fois rendent possible la confrontation des points de vue, tout en y mettant fin par l'obtention de consensus éclairés et légitimés par la règle de (...) la majorité. Et si le conflit, au contraire, dans certaines conditions, devait servir de principe à la vie politique? Il ne suffit pas de vivre en démocratie pour rendre la démocratie vivante. La démocratie n'est pas un régime mais un questionnement. Elle exige des citoyens une interrogation continue sur le bien commun à suivre. Machiavel n'était pas un démocrate. Mais c'est étrangement en actualisant sa pensée, dans le sillage des travaux de Lefort, qu'il est possible d'associer le conflit civil avec l'imaginaire social pour redynamiser la démocratie par la tension conflictuelle entre l'idéologie et l'utopie. Penser la démocratie à partir de ce que donne à penser Machiavel : voilà ce que s'efforce de faire Sébastien Roman, pour proposer dans une perspective républicaine le modèle d'un espace public dissensuel."--Page 4 of cover. (shrink)

The volume contains twenty essays devoted to the philosophy of mathematics and the history of logic. They have been divided into four parts: general philosophical problems of mathematics, Hilbert's program vs. the incompleteness phenomenon, philosophy of mathematics in Poland, mathematical logic in Poland. Among considered problems are: epistemology of mathematics, the meaning of the axiomatic method, existence of mathematical objects, distinction between proof and truth, undefinability of truth, Goedel's theorems and computer science, philosophy of mathematics in Polish mathematical and logical (...) schools, beginnings of mathematical logic in Poland, contribution of Polish logicians to recursion theory. (shrink)

The volume consists of thirteen papers devoted to various problems of the philosophy of logic and mathematics. They can be divided into two groups. The first group contains papers devoted to some general problems of the philosophy of mathematics whereas the second group - papers devoted to the history of logic in Poland and to the work of Polish logicians and math-ematicians in the philosophy of mathematics and logic. Among considered problems are: meaning of reverse mathematics, proof in mathematics, the (...) status of Church's Thesis, phenomenology in the philosophy of mathematics, mathematics vs. theology, the problem of truth, philosophy of logic and mathematics in the interwar Poland. (shrink)

The book is a collection of the author’s selected works in the philosophy and history of logic and mathematics. Papers in Part I include both general surveys of contemporary philosophy of mathematics as well as studies devoted to specialized topics, like Cantor's philosophy of set theory, the Church thesis and its epistemological status, the history of the philosophical background of the concept of number, the structuralist epistemology of mathematics and the phenomenological philosophy of mathematics. Part II contains essays in the (...) history of logic and mathematics. They address such issues as the philosophical background of the development of symbolism in mathematical logic, Giuseppe Peano and his role in the creation of contemporary logical symbolism, Emil L. Post's works in mathematical logic and recursion theory, the formalist school in the foundations of mathematics and the algebra of logic in England in the 19th century. The history of mathematics and logic in Poland is also considered.This volume is of interest to historians and philosophers of science and mathematics as well as to logicians and mathematicians interested in the philosophy and history of their fields. (shrink)

While Hermann Levin Goldschmidt didn’t read Yiddish anarchists, there seems to have been a convergent evolution in their thinking. Goldschmidt’s looking up to Jewish lore as a source of liberating creativity is commonly encountered in Yiddish anarchist texts. His view of action as a constant response to internal and external challenges in the struggle for an open future is developed by Isaac Nachman Steinberg on the basis of nineteenth-century vitalism. Goldschmidt’s theory of anarchist individualism as willed self-limiting solidarity has a (...) compelling parallel in Hillel Solotaroff’s view of history. His use of impressionism and photography to eternalize the immediacy of human actuality is akin to Rudolf Rocker’s championing of decadent literature. In both cases, the goal of anarchism is not a dictatorship of the former downtrodden, but a continuous and contradictory evolution of freedom in ever-changing contexts. (shrink)

The sensitive dependence on initial conditions (SDIC) associated with nonlinear models imposes limitations on the models’ predictive power. We draw attention to an additional limitation than has been underappreciated, namely, structural model error (SME). A model has SME if the model dynamics differ from the dynamics in the target system. If a nonlinear model has only the slightest SME, then its ability to generate decision-relevant predictions is compromised. Given a perfect model, we can take the effects of SDIC into account (...) by substituting probabilistic predictions for point predictions. This route is foreclosed in the case of SME, which puts us in a worse epistemic situation than SDIC. (shrink)

Science provides us with representations of atoms, elementary particles, polymers, populations, genetic trees, economies, rational decisions, aeroplanes, earthquakes, forest fires, irrigation systems, and the world’s climate. It's through these representations that we learn about the world. This entry explores various different accounts of scientific representation, with a particular focus on how scientific models represent their target systems. As philosophers of science are increasingly acknowledging the importance, if not the primacy, of scientific models as representational units of science, it's important to (...) stress that how they represent plays a fundamental role in how we are to answer other questions in the philosophy of science. This entry begins by disentangling ‘the’ problem of scientific representation, before critically evaluating the current options available in the literature. (shrink)

Our reply to Fabian Freyenhagen’s article “Was ist orthodoxe Kritische Theorie?” (DZPhil 65.3 [2017], 456-469) raises the question whether his proposal that Critical Theory only “be adequately and appropriately critical” without a program of justification spares the search for any general criteria. Answering negatively we conversely want to recall, particularly with regard to Horkheimers’s and Adornos’s Dialectic of Enlightment as well as Habermas‘s concept of an emancipatory interest, that such a criterion as a normative foundation of critique is crucial not (...) only for systematical purposes, but also recognised as necessary in this respect by Adorno, who Freyenhagen wants to play off against programs of justification. Critical Theory needs to be clear in this respect. Against this background we are questioning Freyenhagen‘s recourse to an “interest in abolishing social injustice” as the “only criterion for Critical Theory.” Because Freyenhagen ignores the fact that Critical Theory has been understood by its representatives in a twofold manner – as a theoretical program of justification for one and secondly as a cultural diagnosis – his plea for an orthodox Critical Theory is endangered by decisionism. (shrink)

Classical statistical mechanics posits probabilities for various events to occur, and these probabilities seem to be objective chances. This does not seem to sit well with the fact that the theory’s time evolution is deterministic. We argue that the tension between the two is only apparent. We present a theory of Humean objective chance and show that chances thus understood are compatible with underlying determinism and provide an interpretation of the probabilities we find in Boltzmannian statistical mechanics.

Many scientific models are representations. Building on Goodman and Elgin’s notion of representation-as we analyse what this claim involves by providing a general definition of what makes something a scientific model, and formulating a novel account of how they represent. We call the result the DEKI account of representation, which offers a complex kind of representation involving an interplay of, denotation, exemplification, keying up of properties, and imputation. Throughout we focus on material models, and we illustrate our claims with the (...) Phillips-Newlyn machine. In the conclusion we suggest that, mutatis mutandis, the DEKI account can be carried over to other kinds of models, notably fictional and mathematical models. (shrink)

The article is devoted to the analysis of the phenomenon of historical experience in Gadamer's hermeneutics and Ankersmit's philosophical-historical concept. The interest of the philosophy of history in experience was actualized against the background of exhaustion of the heuristic potential of historical narrativism and constructivism, closely related to the so-called "linguistic turn". At first glance, Gadamer and Ankersmit are representing antinomic interpretations of historical experience: as mediated by the effects of involvement in a tradition or heritage and direct, extracontextual encounter (...) with the past. However, the investigation proves that, despite the apparent antinomy of these approaches, the Gadamerian hermeneutic experience as an experience of the prevailing historical reality is not so far from the sublime historical experience of Ankersmit. And, on the contrary, the sublime historical experience, despite its claims to immediacy, turns out to be an experience of the finitude of human existence, that is, it is close to what Gadamer considered the essence of hermeneutic experience. In both cases, historical experience is considered as a condition for the possibility of understanding the past, and therefore, the question of the universal structure of such experience and understanding necessarily arises. The differences in the positions of the two authors stem from fundamentally different ontological prejudices that they share. For Gadamer, this is the reduction of history to a linguistically structured heritage, as a result of which most of the past falls out of hermeneutic experience. For Ankersmit, this is an uncritical understanding of time, as a result of which his concept of the sublime does not receive a reliable methodological foundation. Clarification of the temporality of the sublime historical, as well as rejection of the rigid connection between historical experience and language, open the prospect of removing the abstract antinomy of contextuality and immediacy of historical experience. The temporality of human existence turns out to be a universal prerequisite of historical experience, the two opposite forms of which are heredity and discontinuity. Contrary to the widespread criticism of Ankersmit's theory as far from historiographical practice, the development of the potential of the concept of sublime historical experience reveals its relevance to the dynamic and tragic modern history that Ukraine is currently experiencing. (shrink)

Plagiarism and other transgressions of the norms of academic integrity appear to be a persistent problem among upper secondary students. Numerous surveys have revealed high levels of infringement of what appear to be clearly stated rules. Less attention has been given to students’ understanding of academic integrity, and to the potential misconceptions and false beliefs that may make it difficult for them to comply with existing rules and handle complex real-life situations.In this paper we report findings from a survey of (...) European upper secondary students’ views on issues relating to academic integrity. We relate these findings to the students’ training about academic integrity, self-reported level of questionable behavior and country of study.A total of 1654 students at 51 institutions located in 6 European countries participated in the study. The participants generally believed they had a good understanding of the rules applying to them and knew how to behave in compliance with norms of academic integrity. The results indicate, however, that often, in practice, this belief was mistaken. Many students had an inadequate understanding of core elements of academic integrity. They were uncertain about how to act, and they struggled in the handling of complex situations that require context-sensitive judgement. While some differences between countries were identified, they were modest and exhibited no clear pattern. Our results also suggest that reducing students’ level of uncertainty and, to a lesser degree, improving their level of knowledge could lead them to engage less in certain types of questionable behaviours. Surprisingly, the effect of academic training is modest and ambiguous. The study also confirms that perception of peer behaviour has the strongest association with student engagement in questionable behaviours. Thus, academic integrity at the upper secondary level cannot be explained simply in terms of individual ethics or knowledge. (shrink)

Though it is inter-disciplinary in scope, situated as it is on the borderlines of ontology and logic, philosophy of literature and theory of language, Ingarden's work has a deliberately narrow focus: the literary work, its structure and ...

Commentary on the first Ukrainian translation of Thomasius’ work entitled “Nucleus disputationis de plagio literario maxime theoreticus, thesibus paucis & brevibus comprehensus”, which is one of the Appendices to the famous “Philosophical dissertation on literary plagiarism”.

An important contemporary version of Boltzmannian statistical mechanics explains the approach to equilibrium in terms of typicality. The problem with this approach is that it comes in different versions, which are, however, not recognized as such and not clearly distinguished. This article identifies three different versions of typicality‐based explanations of thermodynamic‐like behavior and evaluates their respective successes. The conclusion is that the first two are unsuccessful because they fail to take the system's dynamics into account. The third, however, is promising. (...) I give a precise formulation of the proposal and present an argument in support of its central contention. †To contact the author, please write to: Department of Philosophy, Logic, and Scientific Method, London School of Economics, Houghton Street, London WC2A 2AE, England; e‐mail: [email protected]. (shrink)

Gases reach equilibrium when left to themselves. Why do they behave in this way? The canonical answer to this question, originally proffered by Boltzmann, is that the systems have to be ergodic. This answer has been criticised on different grounds and is now widely regarded as flawed. In this paper we argue that some of the main arguments against Boltzmann's answer, in particular, arguments based on the KAM-theorem and the Markus-Meyer theorem, are beside the point. We then argue that something (...) close to Boltzmann's original proposal is true for gases: gases behave thermodynamic-like if they are epsilon-ergodic, i.e., ergodic on the entire accessible phase space except for a small region of measure epsilon. This answer is promising because there are good reasons to believe that relevant systems in statistical mechanics are epsilon-ergodic. (shrink)