This article describes two heuristic strategies for problem solving: the use of false assumption strategy and the use of double false assumption strategy. Both of these strategies have their roots deep in history. In this article, we define these two strategies and illustrate their use in a problem developed by Frances Pellos. The article provides an overview of occurrences of these two strategies in various mathematical and educational texts. The texts show clearly that both of these strategies played a significant (...) role in mathematics education in the past. We present some examples from concrete historical documents, which we use later for the preparation of a teaching experiment. We also present the conclusions of an experiment conducted on three lower secondary schools in the Czech Republic, the goal of which was to test the applicability of the use of false assumption strategy as a propaedeutic to solving word problems using equations. (shrink)

This article is the editors’ introduction to the transcript of a lecture that Harold Garfinkel delivered to a seminar in 1993. Garfinkel extensively discusses the relevance of Aron Gurwitsch’s phenomenological treatment of Gestalt theory for ethnomethodology. Garfinkel uses the term “misreading” to signal a respecification of Gurwitsch’s phenomenological investigations, and particularly his conceptions of contextures, functional significations, and phenomenal fields, so that they become compatible with detailed observations and descriptions of social actions and interactions performed in situ. Garfinkel begins with (...) Gurwitsch’s demonstrations with line drawings and other abstract examples, and suggests how they can be used to suggest original procedures for investigating the vicissitudes of embodied practical actions in the lifeworld. This introduction to the lecture aims to provide some background on the scope of Gurwitsch’s phenomenological critique and elaboration of Gestalt theory and Garfinkel’s “misreading” of it in terms of his own conceptions of indexicality and accountability, and ethnomethodological investigations of the production of social order. (shrink)

On the Notion "Type of Language" Petr Sgall It is well known that the high frequency of terminological vagueness and confusion has been a serious obstacle ...

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)

The life, works, and philosophy of rabbi Hasdai Crescas.

This monograph presents a general theory of weakly implicative logics, a family covering a vast number of non-classical logics studied in the literature, concentrating mainly on the abstract study of the relationship between logics and their algebraic semantics. It can also serve as an introduction to algebraic logic, both propositional and first-order, with special attention paid to the role of implication, lattice and residuated connectives, and generalized disjunctions. Based on their recent work, the authors develop a powerful uniform framework for (...) the study of non-classical logics. In a self-contained and didactic style, starting from very elementary notions, they build a general theory with a substantial number of abstract results. The theory is then applied to obtain numerous results for prominent families of logics and their algebraic counterparts, in particular for superintuitionistic, modal, substructural, fuzzy, and relevant logics. The book may be of interest to a wide audience, especially students and scholars in the fields of mathematics, philosophy, computer science, or related areas, looking for an introduction to a general theory of non-classical logics and their algebraic semantics. (shrink)

In lectures and writings in the decades following the publication of Studies in Ethnomethodology [1967], Harold Garfinkel, the founder of ethnomethodology, developed what he called a “misreading” of the phenomenological writings of Aron Gurwitsch, Maurice Merleau-Ponty and others. Garfinkel’s “misreading” included a selective and creative treatment of themes that Gurwitsch drew from Gestalt psychology, such as figure-ground, Gestalt contexture, and the phenomenal field. Rather than identifying these themes with visual perception demonstrated with picture-puzzles (for example, of animals hidden in foliage) (...) and line drawings of reversible figures, Garfinkel used them to demonstrate praxeological and interactional phenomena: organizations of embodied activity that constitute fields of collective action. Phenomenal fields, for Garfinkel, are formed through embodied work performed in concert with the actions of others. Although Harvey Sacks, the founder of Conversation Analysis, did not explicitly mention Gurwitsch, phenomenology or Gestalt psychology in his writings and transcribed lectures, some of his writings on the sequential organization of conversation seem informed, if only indirectly through his relationship with Garfinkel, by Gurwitsch’s treatment of visual and auditory phenomena. Both Garfinkel and Sacks devised innovative ways to transpose Gestalt phenomena from perceptual psychology to social formations. (shrink)

This book collects most of the invited papers presented at the 12th International Congress of Logic, Methodology and Philosophy of Science in Oviedo, August 2003. It contains state of the art accounts of ongoing work by a selection of the most renowned researchers in the field. The papers in the Logic section deal with topics in mathematical logic, as well as philosophical logic, and the area of logic and computation. The section on General Methodology contains articles on models, theories, probability, (...) induction, causation, and other topics. A number of papers discuss Philosophical Issues of Particular Sciences, such as mathematics, physics, linguistics, psychology, biology, and medicine. There is also a section on Ethics of Science, and papers from a special symposium on the Emergence of Scientific Medicine in the 19th-20th Century. (shrink)

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

Uniform infinite bases are defined for the single-conclusion and multiple-conclusion admissible rules of the implication–negation fragments of intuitionistic logic and its consistent axiomatic extensions . A Kripke semantics characterization is given for the structurally complete implication–negation fragments of intermediate logics, and it is shown that the admissible rules of this fragment of form a PSPACE-complete set and have no finite basis.

Objectivity, as one of the key attributes of science, has become an indispensable part of its ethos and a central theme of the philosophy of science. As such, it has been a subject of philosophical reflection by a number of authors. In our project – in which both philosophers of science and scientists participate – we examine the concept of objectivity in the natural sciences with the tools of experimental philosophy. We aim to identify specific operational dimensions of objectivity, those (...) with which current scientist actually work, thus making them accessible for further theoretical analysis and research. In this text, we present results from the first, qualitative phase of our research based on in-depth interviews and focus groups with scientists working in the Czech Republic. Further, we confront this empirical data with theoretical notions of objectivity. We also present other findings from the research and formulate hypotheses for the research’s subsequent phases. (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.

The text which follows was put together from answers given to questions at meetings held by PD Ouspensky in London and New York between 1935 and 1944. ...

This paper is a contribution to Mathematical fuzzy logic, in particular to the algebraic study of t-norm based fuzzy logics. In the general framework of propositional core and Δ-core fuzzy logics we consider three properties of completeness with respect to any semantics of linearly ordered algebras. Useful algebraic characterizations of these completeness properties are obtained and their relations are studied. Moreover, we concentrate on five kinds of distinguished semantics for these logics–namely the class of algebras defined over the real unit (...) interval, the rational unit interval, the hyperreals , the strict hyperreals and finite chains, respectively–and we survey the known completeness methods and results for prominent logics. We also obtain new interesting relations between the real, rational and hyperreal semantics, and good characterizations for the completeness with respect to the semantics of finite chains. Finally, all completeness properties and distinguished semantics are also considered for the first-order versions of the logics where a number of new results are proved. (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)

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)

Substructural logics extending the full Lambek calculus FL have largely benefited from a systematical algebraic approach based on the study of their algebraic counterparts: residuated lattices. Recently, a nonassociative generalization of FL has been studied by Galatos and Ono as the logic of lattice-ordered residuated unital groupoids. This paper is based on an alternative Hilbert-style presentation for SL which is almost MP -based. This presentation is then used to obtain, in a uniform way applicable to most substructural logics, a form (...) of local deduction theorem, description of filter generation, and proper forms of generalized disjunctions. A special stress is put on semilinear substructural logics. Axiomatizations of the weakest semilinear logic over SL and other prominent substructural logics are provided and their completeness with respect to chains defined over the real unit interval is proved. (shrink)

This paper addresses the ontological status of the body in the context of bodily practices in body-oriented disciplines, such as sport training, dance, and physiotherapy. Following Descartes’, Huss...

This article reviews recent findings indicating some common brain processes during dissociative states and dreaming with the aim to outline a perspective that neural chaotic states during dreaming can be closely related to dissociative states that may manifest in dreams scenery. These data are in agreement with various clinical findings that dissociated states can be projected into the “dream scenery” in REM sleep periods and dreams may represent their specific interactions that may uncover unusual psychological potential of creativity in psychotherapy, (...) art and scientific discoveries. (shrink)

Despite their flaws, large language models (LLMs) deserve a fair chance to prove their mettle against human experts, who are often plagued with biases, conflicts of interest, and other frailties. For epistemically unprivileged laypeople struggling to access expert knowledge, the accessibility advantages of LLMs could prove crucial. While complaints about LLMs' inconsistencies and arguments for human superiority are often justified (for now), they distract from the urgent need to prepare for the likely scenario of LLMs' continued ascent. Experimentation with both (...) the capabilities and institutional architecture of LLMs is necessary. Neither tech-bashing nor excessive gatekeeping will suffice. As LLMs are here to stay and they keep improving, it is high time we started thinking about how to navigate the impending wave of their proliferation. (shrink)

Structural completeness properties are investigated for a range of popular t-norm based fuzzy logics—including Łukasiewicz Logic, Gödel Logic, Product Logic, and Hájek's Basic Logic—and their fragments. General methods are defined and used to establish these properties or exhibit their failure, solving a number of open problems.

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)