Alternative set theory was created by the Czech mathematician Petr Vopěnka in 1979 as an alternative to Cantor’s set theory. Vopěnka criticised Cantor’s approach for its loss of correspondence with the real world. Alternative set theory can be partially axiomatised and regarded as a nonstandard theory of natural numbers. However, its intention is much wider. It attempts to retain a correspondence between mathematical notions and phenomena of the natural world. Through infinity, Vopěnka grasps the phenomena of vagueness. Infinite sets (...) are defined as sets containing proper semisets, i.e. vague parts of sets limited by the horizon. The new interpretation extends the field of applicability of mathematics and simultaneously indicates its limits. Compared to strict finitism and other attempts at a reduction of the infinite to the finite Vopěnka’s theory reverses the process: he models the finite in the infinite. (shrink)

V kontextu české filosofie, kde není nouze o vzdělané a chytré lidi, ale kde se to nijak nehemží skutečnými individualitami, představuje Petr Vopěnka zcela zvláštní případ. Je matematik nejenom vzděláním, ale v matematice i leccos dokázal. Jeho knihy o filosofii matematiky, zejména jeho tetralogie Rozprav s geometrií1, jsou velice vyhraněné: Vopěnka v nich předkládá svůj originální obraz a příliš se nestará o to, aby ho konfrontoval s tím, co si o tom myslí jiní. Jak sám připouští, i historické osoby, (...) o kterých ve svých knihách píše, mu slouží spíše jako kompars, na jehož pozadí rozehrává svá barvitá líčení ‚dobrodružství poznání‘. Vopěnka ve svých knihách protestuje proti tomu, že moderní věda do obrazu světa, který buduje, vůbec nevpustila tak zásadní determinanty našeho přirozeného světa, jakými jsou neostrost či existence horizontu, který činní náš obraz světa v jistém smyslu ‘nehomogenní‘. Proti tomu se samozřejmě nabízí námitka, že to je v podstatě věci, že vědecký obraz světa je svou podstatou ostrý a homogenní. Že chtít po něm, aby byl jiný, pramení pouze z nepochopení jeho povahy a hlavně jeho role: neboť svět vykreslovaný vědou má být světem pouze v metaforickém slova smyslu, je jenom jakýmsi ‚orientačním plánkem‘, který nám má pomoci orientovat se ve světě ‚přirozeném‘. (Tím ovšem nechci říci, že by tohle nepochopení nebylo fakticky dosti rozšířené.) Vopěnka však ukazuje, že vědu, zejména matematiku, by bylo možné dělat i jinak, než jak se to považuje za víceméně samozřejmé: že je možné vytvořit matematizovaný obraz světa, ze kterého nejsou neostrost či horizont vymeteny. (I tento obraz si samozřejmě zachovává jistý druh ostrosti a homogenity, která z něj činí něco kvalitativně odlišného od přirozeného světa, avšak k přirozenému světu má blíže než ten standardní.) Tento jeho návrh je velice originální a pozoruhodný a je škoda, že mu není věnována větší pozornost a není předmětem soustavnější diskuse, ve které by se ověřila jeho nosnost. Originalita.. (shrink)

Dave Ripley has recently argued against the plausibility of multiset consequence relations and of contraction-free approaches to paradox. For Ripley, who endorses a nontransitive theory, the best arguments that buttress transitivity also push for contraction—whence it is wiser for the substructural logician to go nontransitive from the start. One of Ripley’s allegations is especially insidious, since it assumes the form of a trivialisation result: it is shown that if a multiset consequence relation can be associated to a closure operator in (...) the expected way, then it necessarily contracts. We counter Ripley’s objection by presenting an approach to multiset consequence that escapes this trap. This approach is multiple-conclusioned in a heterodox way, for multiple succedents are given a conjunctive, rather than a disjunctive reading. Finally, we address a further objection by French and Ripley to the effect that the informational interpretation of sequents in linear logic does not motivate cut. (shrink)

Analyzing different philosophical and theological components of Aquinas’s view regarding the relation between human agency and divine providence, the monograph shows this view to be compatibilist, based on a determinist conception of causation and an aristocratic understanding of goodness.

Studies man in view of what he may become. Describes how a man must work simultaneously on his knowledge and his being to find inner unity.

Can one extend crisp Peano arithmetic PA by a possibly many-valued predicate Tr(x) saying "x is true" and satisfying the "dequotation schema" $\varphi \equiv \text{Tr}(\bar{\varphi})$ for all sentences φ? This problem is investigated in the frame of Lukasiewicz infinitely valued logic.

Can one extend crisp Peano arithmetic PA by a possibly many-valued predicate Tr(x) saying “xis true” and satisfying the “dequotation schema”for all sentences φ? This problem is investigated in the frame of Łukasiewicz infinitely valued logic.

Rational Pavelka logic extends Lukasiewicz infinitely valued logic by adding truth constants r̄ for rationals in [0, 1]. We show that this is a conservative extension. We note that this shows that provability degree can be defined in Lukasiewicz logic. We also give a counterexample to a soundness theorem of Belluce and Chang published in 1963.

Environmental anxiety is often thought of as a psychopathological condition. Our paper aims to challenge this narrow understanding by offering an existential-phenomenological interpretation of environmental anxiety that posits it as an _existential attunement_ with a transformative potential, capable of opening the anxious individual to a hopeful and meaningful outlook on the future. In the first part of the paper, we provide a conceptual analysis of environmental anxiety, drawing on current interdisciplinary taxonomies of environmental emotions as well as on existential-phenomenological definitions (...) of anxiety. We then proceed to define the two key existential characteristics of environmental anxiety, firstly (i) its ability to reframe the aesthetic perception of nature, and secondly (ii) its impact on the subjective constitution of meaning. In the second part of the paper, drawing on the work of Kierkegaard and contemporary ecopsychological and ecotheological thinkers, a distinction is made between a naïve and a radical form of environmental hope. It is argued that while the former type of hope leads to inactivity, the latter is capable of motivating individuals to pro-environmental action. (shrink)

The theological program of Archpriest Georges Florovsky is understood as a conception of the neopatristic synthesis that he developed. From the beginning, its appearance was associated with the participation of its creator in a public discussion about the historical ways of Russia within the framework of the Eurasian movement, then, with his scientific investigations into the history of Russian Orthodoxy and ancient Christian thought and later with his activity in the ecumenical movement. It is noteworthy that the positive content of (...) the program for modern Orthodox theology turned out to be an indirect response to broader challenges of historical and social order. The focus of attention in this case are some peculiarities in the reception of the program in international and Russian contexts, which in turn requires the clarification of the content of its main points, such as a question about a true fatherland or the sense and meaning of Christian Hellenism. The conclusion notes the significant relevance and openness of Florovsky’s ideas for modern Orthodox theology. (shrink)

In the last few decades many formal systems of fuzzy logics have been developed. Since the main differences between fuzzy and classical logics lie at the propositional level, the fuzzy predicate logics have developed more slowly (compared to the propositional ones). In this text we aim to promote interest in fuzzy predicate logics by contributing to the model theory of fuzzy predicate logics. First, we generalize the completeness theorem, then we use it to get results on conservative extensions of theories (...) and on witnessed models. (shrink)

I examine mystical experience through the history of European religious thought, its modern state, and different spiritual practices of the Patristic epoch. The survey gives some definitions: mystical experience is situated in the field of spirituality along with practices of its acquisition -- ascetics; and the fruits of it -- theology and doctrine. The second part of the article is devoted to a wide field of Christian texts as a representative example of the same experience of the crystallization of mystical (...) experience in ancient tradition, providing a few general types. Reading of religious texts is related very closely with the spiritual condition of the reader and supposes that he/she changes radically in the process of reading, being involved in some existential-hermeneutic circle. (shrink)

The paper is devoted to Nikolay Lossky who was one of the leading Russian philosophers of the first half of the twentieth century. We demonstrate the interrelationship between three aspects of Lossky’s philosophy: realism in the theory of knowledge, hierarchical personalism, and supra-naturalistic concept of evolution. We pay attention to the contemporary relevance of Lossky, and we discuss and critique his ideas in light of those of other philosophers. Lossky acknowledges that the subject interacts with being itself and that knowledge (...) is not a shadow or copy of being. His ontology is based on intuitivism and epistemological optimism. Its main categories are God, as the super-systematic principle, and monads. In Lossky’s metaphysics, the idea of abstract ideal principles of being is quite harmoniously combined with personalism. Lossky’s ontology has strong ethical underpinnings. He considers that values are rooted in being and that the evolution of the world is directed by God towards the good. Lossky elaborates a supra-naturalistic concept of evolution. He extrapolates principles of teleological determination, which are fundamental to human existence, on the underlying levels of the world as a whole. Many trends of modern thought are in tune with Lossky’s philosophy, including a return to metaphysics, panpsychism, Platonism, and the desire to unite the religious worldview with new scientific discoveries. (shrink)

Humans are remarkably adaptable, and therefore a successful species. There are many speculative answers to the question of why this is so. One of them represents the cultural intelligence hypothesis, which consid-ers cultural learning skills as the key to human success. This work aims to present the hypothesis of cultural intelligence as a viable alternative to more conventional approaches within the debate about the origin of human intelligence, such as the hypothesis of general and improvisational intelligence. Theirmutual comparison shows that (...) cultural intelligence hypothesis must necessarily work with flexible social learning strategies to describe cultural transmission, thus losing part of its explanatory power. As the theory of metacognitive strategies of social learning by cognitive psychologist Cecilia Heyes shows, there is a way to combine the flexibility of human reasoning with the “stupid” process of cultural selection. (shrink)

Social networks can influence people’s behaviour and therefore it is assumed that central individuals in social networks, also called “opinion leaders”, play a key role in driving change in agricultural and food systems. I analyse the outcomes of an intervention (that encouraged Sulawesi smallholder farmers to take a specific action toward improving the health of their cocoa trees) to assess the impact of engaging opinion leaders in agricultural programs that aim to change farmers’ practices. The intervention has been implemented through (...) (a) 18 opinion leaders identified by interviews and a social network survey of 1885 cocoa farmers; and (b) 18 randomly selected farmers who were not central in local social networks. The obtained social networks and statistical data were quantitatively analysed and the results were interpreted with input from the field staff. Contrary to expectations, the highly socially central opinion leaders were not more effective in promoting the initiative in their communities. On average, randomly selected low-centrality farmers convinced almost twice as many of their peers to take the recommended action as compared to the identified opinion leaders (17.1 versus 8.6) but the variation within the random group was also significantly higher. Importantly, while the identified opinion leaders were mostly senior men, women performed better in influencing others into taking action even when their centrality in local social networks of agricultural advice was lower. I discuss the implications of the conventional selection of perceived opinion leaders as model farmers for achieving sustainable and equitable change at scale in agriculture and propose practical alternatives. (shrink)

Drawing on current debates at the frontiers of economics, psychology, and political philosophy, this book explores the challenges that arise for liberal democracies from a confrontation between modern technologies and the bounds of human rationality. With the ongoing transition of democracy's underlying information economy into the digital space, threats of disinformation and runaway political polarization have been gaining prominence. Employing the economic approach informed by behavioral sciences' findings, the book's chief concern is how these challenges can be addressed while preserving (...) a commitment to democratic values and maximizing the epistemic benefits of democratic decision-making. The book has two key strands: it provides a systematic argument for building a behaviorally informed theory of democracy; and explores how scientific knowledge on quirks and bounds of human rationality can inform the design of resilient democratic institutions. Drawing these together, the book explores the centrality of the rationality assumption in the methodological debates surrounding behavioral sciences as exemplified by the dispute between neoclassical and behavioral economics; the role of rationality in democratic social choice; behaviorally informed paternalism as a response to the challenge of irrationality; and non-paternalistic avenues to increase the resilience of the democratic institutions towards political irrationality This book is invaluable reading for anyone interested in behavioral economics and sciences, political philosophy and the future of democracy. (shrink)

Shows how different forms of skepticism can lead to remarkably different moral and political implications.

Procedural justifications of democracy emphasize inclusiveness and respect and by doing so come into conflict with instrumental justifications that depend on voters’ competence. This conflict raises questions about jury theorems and makes their standing in democratic theory contested. We show that a type of no-regret learning called meta-induction can help to satisfy the competence assumption without excluding voters or diverse opinion leaders on an a priori basis. Meta-induction assigns weights to opinion leaders based on their past predictive performance to determine (...) the level of their inclusion in recommendations for voters. The weighting minimizes the difference between the performance of meta-induction and the best opinion leader in hindsight. The difference represents the regret of meta-induction whose minimization ensures that the recommendations are optimal in supporting voters’ competence. Meta-induction has optimal truth-tracking properties that support voters’ competence even if it is targeted by mis/disinformation and should be considered a tool for supporting democracy in hyper-plurality. (shrink)

The paper begins by emphasizing the fact that, on a historical scale, one can have several views of the relationship that has existed over time between ethics and capitalism, namely: missionary, ‘Nietzschean’, critical, and ‘regulatory’. It is argued that, nowadays, the capitalization of the contributions supplied, over time, by the four views embraces the form of two modern diametrically opposed perspectives, i.e.: on the one hand, there is the interpretation given by the neo-classical school of thought (mainstream economics) and, on (...) the other hand, it comes to the interpretation given by the Austrian praxeological economic school (libertarian economics). The emphasis of the analysis is put on the assertions developed by the last one, libertarian thinking, that insists on the necessity to operate with a well-defined distinction between the legal level of the matter, the ethical level and the moral one. At the core of the libertarian analysis there is the understanding of the capitalist system being naturally impregnated by ethical values. And this intrinsic ethical nature of capitalism is organically bound to the sphere of the ownership-type relationship. In line with the understanding of the economic system, based on the institutions of the free market as representing ethical capitalism per se, the paper argues that the realities of the world today show governmental interventionism as a main factor that supports non-ethical economic behaviour. As a consequence, the more limited government intervention is, the greater the chance of ethical capitalism, that is, voluntary, non-conflictual and non-aggressive economic market relationships. Under such conditions, a ‘minimal state’ institutional arrangement (that is, the legitimate use of power by the state is limited to preventing fraud or the use of force; it does not include the power to tax or to confiscate property) is the basic condition for the existence of an ethical capitalism that works, which is to say that the chance of an economic system based on ethical values stands in people’s willingness to be part of such an evolution in society that aims to minimise the role of the state. Further, the paper argues that any historical analysis on how societies asserted such a willingness outlines the expression of a secular and unshaken option for growing rather than diminishing state involvement in the economy. It is about people’s perennial preference for the state, namely for the organization of society based on state interventionism (respectively, their preference for the coercive order imposed by the state authorities, order based, through its own nature, on the subjugation of private property and the aggression against individual freedom), with a preference for the government intervention over the organization of a society based on free market functioning (which is equivalent, in fact, to their rejection of a voluntarily and spontaneously non-violent order, based on the observance of private property and individual freedom, brought about by the free functioning of markets). In the last part of the paper there are put forward for discussion the possible explanations for this perennial preference for non-ethical capitalism, the analysis focusing on two directions: firstly, on that of social ontology; and then, on that of human psychology. (shrink)

L'auteur a essayé de démontrer le positionnement de Jean-Paul Sartre sous la bannière de l'ontologie dès sa création de jeunesse, sans laquelle il est difficile de comprendre la place du philosophe français dans l'histoire de la phénoménologie. La nouvelle formule créée par Jean-Paul Sartre, à savoir "l'ontologie phénoménologique" est une forme spécifique de l'ontologie moderne de l'humain comprenant également des questions fondamentales caractéristiques de n'importe quelle pensée philosophique. u u.

We prove that Standardization fails in every nontrivial universe definable in the nonstandard set theory BST, and that a natural characterization of the standard universe is both consistent with and independent of BST. As a consequence we obtain a formulation of nonstandard class theory in the ∈-language.

The paper proposes a synthesis between human scientists and artificial representation learning models as a way of augmenting epistemic warrants of realist theories against various anti-realist attempts. Towards this end, the paper fleshes out unconceived alternatives not as a critique of scientific realism but rather a reinforcement, as it rejects the retrospective interpretations of scientific progress, which brought about the problem of alternatives in the first place. By utilising adversarial machine learning, the synthesis explores possibility spaces of available evidence for (...) unconceived alternatives providing modal knowledge of what is possible therein. As a result, the epistemic warrant of synthesised realist theories should emerge bolstered as the underdetermination by available evidence gets reduced. While shifting the realist commitment away from theoretical artefacts towards modalities of the possibility spaces, the synthesis comes out as a kind of perspectival modelling. (shrink)