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 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)

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)

The article conveys fresh details about activities of the well-known German philosopher F.W. J. Schelling as preseding chair of the local Bible society in Erlangen in 1824-27 and reprints the public address “On value and significance of Bible societies” that was given by him in that position. Newly discovered archival material makes it possible not only to identify the exact date and circumstances of the address but also to demonstrate its wider biographical, philosophical, theological and political significance, especially in relation (...) to Schelling's attitude regarding the differences between Catholicism and Protestantism in Germany in the first part of the nineteenth century, as well as how Schelling's philosophy of revelation relates to the confessional debates of his day. (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 ...

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.

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)

An important task for every major philosopher is to offer us an understanding of the nature of mind. The essays in this volume discuss different aspects of the philosophical theories of mind put forward in the century and a half that followed Descartes' Meditations of 1641. These years, often referred to as the 'early-modern' period, are probably unparalleled for originality and diversity in conceiving the mind. The volume not only includes two essays on Descartes' own thinking, but there are also (...) examinations of what Spinoza, Malebranche, Locke, Berkeley, Reid, the Cambridge Platonists, and others, have to say about the nature of mind. The aim of the volume is to represent some of the best contemporary research and reflection on mind in early-modern philosophy. The contributors, who teach at a range of universities in mainland Europe, Great Britain and North America, are Margaret Atherton, Miran BozoviÄ, Petr GlombìÄek, Boris Hennig, James Hill, Nicholas Jolley, Jan Palkoska, G. A. J. Rogers, and Anthony Savile. All the essays appear here for the first time. (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)

We give a brief introduction to the axiomatization of temporal logics. Branching continuations are shortly presented thereafter and the possibility of their clear syntactical axiomatization in a Hilbert-style system is investigated as last. Some basic preliminary observations and suggestions, how such axiomatization could start, are presented.

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.

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)

This article identifies the assumption of responsibility as a basic need of human beings and applies the concept specifically to older people with dementia or Alzheimer's disease. It suggests a two‐level concept of responsibility, based on the approach of discourse ethicist Karl‐Otto Apel, as a promising approach to recognizing human diversity while at the same time respecting people's equal rights to participate in discourse. This concept can serve as a theoretical starting point for the construction of individually adapted types of (...) responsibility. Furthermore, the article describes practical ideas (primarily the practice of doll therapy) that can enable people with dementia or Alzheimer's disease to assume responsibility. Direct communication and a reflective, sensitive consideration of each individual case are identified as important prerequisites for the inclusion of elderly people with dementia. (shrink)

The paper addresses a mainstream contemporary view of the notion of common sense in Thomas Reid’s philosophy, as proposed by Nicholas Wolterstorff who claims that Reid was not clear about the concept of common sense, or about the principles of common sense. In contrast, this paper presents Reid’s conception as a clear and traditional Aristotelian notion of common sense and its principles as presuppositions of particular sense judgments, usually taken for granted. The alleged confusion about principles is resolved by a (...) distinction between principles of common sense and first principles as such. (shrink)

This comment on E. Borisov's text deals with some technical complications that his proposed analysis faces, according to the author's opinion. The author argues that Borisov's definition of the operator O is not clear and his theory might predict nonexistent readings unless the definition is stated clearly. The author criticizes Borisov's proposal for not being compositional and outlines an alternative analysis in terms of the contemporary semantic treatments of comparative constructions and attitude reports.

The one-variable fragment of a first-order logic may be viewed as an “S5-like” modal logic, where the universal and existential quantifiers are replaced by box and diamond modalities, respectively. Axiomatizations of these modal logics have been obtained for special cases—notably, the modal counterparts $\mathrm {S5}$ and $\mathrm {MIPC}$ of the one-variable fragments of first-order classical logic and first-order intuitionistic logic, respectively—but a general approach, extending beyond first-order intermediate logics, has been lacking. To this end, a sufficient criterion is given in (...) this paper for the one-variable fragment of a semantically defined first-order logic—spanning families of intermediate, substructural, many-valued, and modal logics—to admit a certain natural axiomatization. More precisely, an axiomatization is obtained for the one-variable fragment of any first-order logic based on a variety of algebraic structures with a lattice reduct that has the superamalgamation property, using a generalized version of a functional representation theorem for monadic Heyting algebras due to Bezhanishvili and Harding. An alternative proof-theoretic strategy for obtaining such axiomatization results is also developed for first-order substructural logics that have a cut-free sequent calculus and admit a certain interpolation property. (shrink)

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)

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...

In general, there is only one fuzzy logic in which the standard interpretation of the strong conjunction is a strict triangular norm, namely, the product logic. We study several equations which are satisfied by some strict t-norms and their dual t-conorms. Adding an involutive negation, these equations allow us to generate countably many logics based on strict t-norms which are different from the product logic.

The paper deals with the problem of divine causation in relation to created agents in general and human rational agents in particular. Beyond creation and conservation, Aquinas specifies divine contribution to created agents’ operation as application in the role of the first cause and the operation of the principal cause employing an instrumental cause. It is especially the latter which is open to varying interpretation and which might be potentially threatening to human freedom. There are different readings of what it (...) is for the secondary agent to “act through the power of the principal cause”. Either the divine cause causes only the existence of the effect of the secondary cause, or it also causes the cause to operate in the sense that it determines its outcome. The latter seems to contradict human freedom. Both readings of Aquinas were developed in the latter half of the sixteenth century within scholastic philosophy and theology. (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)

We show that the modal prepositional logicILM (interpretability logic with Montagna's principle), which has been shown sound and complete as the interpretability logic of Peano arithmetic PA (by Berarducci and Savrukov), is sound and complete as the logic ofπ 1-conservativity over eachbE 1-sound axiomatized theory containingI⌆ 1 (PA with induction restricted tobE 1-formulas). Furthermore, we extend this result to a systemILMR obtained fromILM by adding witness comparisons in the style of Guaspari's and Solovay's logicR (this will be done in a (...) separate continuation of the present paper). (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)

Gabriel Vásquez discusses two deterministic arguments ascribed to John Wyclif. He appeals to the Anselmian solution based on the distinction between two types of necessity: antecedent and subsequent necessity. Unlike the former, the latter necessity does not destroy future event’s contingency, which is required if it is to result from a free choice. The paper discusses the Aristotelian objection according to which a statement describing some contingent future event is either without truth-value, and thus antecedently contingent but not subsequently necessary (...) at present, or it has a truth-value, but then it is not merely subsequently necessary but also antecedently necessary. The Anselmian temporal ontology is such that no absolute present parameter is to be included in the evaluation of modal tensed statements. This recognition disposes of modal notions tied to the absolute temporal qualification of statements and thus undercuts the objection. (shrink)

A model for kinetics of circular substrate cleavage by restriction endonuclease was formulated. The aim of the analysis of the model was to extract kinetic constants for all target sites from time- dependence of fragment concentration in reaction products. That was proved to be possible for molecules with an odd number of fragments only. A symmetry of the molecules with an even number of fragment is the cause. A solution for molecules with an odd number of fragments was found and (...) methods for dealing with the other molecules were suggested. (shrink)

‘The Russian Orthodox Church’s Basic Teaching on Human Dignity, Freedom and Rights’ has been a constant source of controversy since its release in 2008. While most scholars debated the document for its political implications, little attention has been paid to its anthropological consequences, particularly those deriving from linking a dignified life with the ethical use of freedom. The article highlights that if the sole criteria for living a dignified life is freedom then the most vulnerable categories in society (persons with (...) severe cognitive disabilities or those struggling with addictions) can claim only basic dignity. Engaging constructively with the work of Romanian theologian Dumitru Stăniloae, it will be argued that the source of human dignity is not a specific capacity, but the recapitulation of all human beings in Christ’s death and resurrection. The dignity that belongs to Christ is transferred through recapitulation to all humans irrespective of their abilities or sins. In fact, what changes with the use of freedom is not the dignity of the person, but our ability to perceive that dignity. (shrink)

Práce se zabývá metodologickou stránkou teorie lidského jednání, která vznikla v rámci Weberovy rozumějící sociologie a byla dále transformována ve fenomenologické sociologii Alfreda Schütze. Analýza se zaměřuje především na to, jakým způsobem se oba myslitelé pokusili vyřešit problém interpretace lidského jednání ze strany (vědeckého) pozorovatele a samotného aktéra. Ukazuje se, že Weber stojí i přes snahu zůstat v kontaktu s psychologickou realitou jednání vždy již na pozici vědeckého pozorovatele. Schütz usiluje o důkladnější založení weberiánského postoje a ukazuje, jakým způsobem stanovisko (...) nezaujatého pozorovatele vystupuje z bezprostředně ("naivně") prožívané reality přirozeného světa. Oba myslitelé diskutují otázku racionality jednání a v závěru dospívají k přesvědčení, že racionalita (chápaná jako logická konzistence a empirická efektivita jednání) není ani tak charakteristikou, která by připadala "reálnému" jednání, ale spíše normou vědeckého popisu a vědeckého postupu. Argumentace je rozvinuta v rámci úvahy o chápání racionality v současné ekonomické teorii a roli introspekce. (shrink)