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.

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.

We are thankful to Gerhard Schurz for his response (Schurz 2023) to our paper (Spelda et al. 2023). Spelda et al. (2023) shows how a variant of no-regret learning called meta-induction (Schurz 2008; 2019) can be used for optimal selection from available political alternatives and, as a result, also for increasing voter competence that has come under attack from mis/disinformation. Since our paper takes a first step in applying meta-induction to long-standing issues in Democratic Theory (e.g., the usefulness of jury (...) theorems for justifying democracy), we are grateful to Gerhard Schurz for highlighting some of the conditions that need to be met for the development of practical applications. (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)

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 is the continuation of the paper :417–446, 2010). We continue the abstract study of non-classical logics based on the kind of generalized implication connectives they possess and we focus on semilinear logics, i.e. those that are complete with respect to the class of models where the implication defines a linear order. We obtain general characterizations of semilinearity in terms of the intersection-prime extension property, the syntactical semilinearity metarule and the class of finitely subdirectly irreducible models. Moreover, we consider extensions (...) of the language with lattice connectives and generalized disjunctions, study their interplay with implication and obtain axiomatizations and further descriptions of semilinear logics in terms of disjunctions and the proof by cases property. (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)

This paper is a contribution to the study of the rôle of disjunction inAlgebraic Logic. Several kinds of (generalized) disjunctions, usually defined using a suitable variant of the proof by cases property, were introduced and extensively studied in the literature mainly in the context of finitary logics. The goals of this paper are to extend these results to all logics, to systematize the multitude of notions of disjunction (both those already considered in the literature and those introduced in this paper), (...) and to show several interesting applications allowed by the presence of a suitable disjunction in a given logic. (shrink)

While the assumption that the sociopolitical and economic situation affects adolescents’ well-being, encompassing life satisfaction and a positive sense of self, is plausible, few studies have confirmed such macrosocial influences. The case of the Czech Republic offers an example of a society transitioning from totalitarian government (from 1989) to western democracy. Our study provides statistical description of Czech adolescents’ well-being over the past 30 years in association with the subjective perception of everyday problems. These daily hassles represent experiences and conditions (...) of daily living that have been appraised as salient and harmful or threatening to adolescents’ well-being. We analyzed four samples of adolescents aged 14–17 years surveyed at four time points over the last three decades—1992, 2001, 2011, and 2019, totalN = 4,005 (1992: 255, 2001: 306, 2011: 363, 2019: 3081; 54.6% females). The results show that life satisfaction, self-esteem, and self-reported daily hassles changed only marginally from 1992 to 2019 with small differences related to the post-revolution 1992 cohort. Adolescents reported increasing problems in school, relationships with parents, sports, and leisure time over the study period. A model linking daily hassles and self-esteem to life satisfaction across four cohorts showed that daily hassles strongly predicted life satisfaction except in the post-revolution cohort of 1992 when life satisfaction was also the lowest. The effect was slightly higher in females. Across the cohorts, gender differences in life satisfaction changed from males being more satisfied in 1992 to females being more satisfaction in 2019. Limitations stemming from sampling differences across cohorts are discussed. (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 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)

Fuzzy logic is understood as a logic with a comparative and truth-functional notion of truth. Arithmetical complexity of sets of tautologies and satisfiable sentences as well of sets of provable formulas of the most important systems of fuzzy predicate logic is determined or at least estimated.

In the literature on vagueness one finds two very different kinds of degree theory. The dominant kind of account of gradable adjectives in formal semantics and linguistics is built on an underlying framework involving bivalence and classical logic: its degrees are not degrees of truth. On the other hand, fuzzy logic based theories of vagueness—largely absent from the formal semantics literature but playing a significant role in both the philosophical literature on vagueness and in the contemporary logic literature—are logically nonclassical (...) and give a central role to the idea of degrees of truth. Each kind of degree theory has a strength: the classical kind allows for rich and subtle analyses of the comparative form of gradable adjectives and of various types of gradable precise adjectives, while the fuzzy kind yields a compelling solution to the sorites paradox. This paper argues that the fuzzy kind of theory can match the benefits of the classical kind and hence that the burden is on the latter to match the advantages of the former. In particular, we develop a new version of the fuzzy logic approach that—unlike existing fuzzy theories—yields a compelling analysis of the comparative as well as an adequate account of gradable precise predicates, while still retaining the advantage of genuinely solving the sorites paradox. (shrink)

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)

We generalise the Blok–Jónsson account of structural consequence relations, later developed by Galatos, Tsinakis and other authors, in such a way as to naturally accommodate multiset consequence. While Blok and Jónsson admit, in place of sheer formulas, a wider range of syntactic units to be manipulated in deductions (including sequents or equations), these objects are invariablyaggregatedvia set-theoretical union. Our approach is more general in that nonidempotent forms of premiss and conclusion aggregation, including multiset sum and fuzzy set union, are considered. (...) In their abstract form, thus,deductive relationsare defined as additional compatible preorderings over certain partially ordered monoids. We investigate these relations using categorical methods and provide analogues of the main results obtained in the general theory of consequence relations. Then we focus on the driving example of multiset deductive relations, providing variations of the methods of matrix semantics and Hilbert systems in Abstract Algebraic Logic. (shrink)

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.

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

Formal systems of fuzzy logic are well-established logical systems and respected members of the broad family of the so-called substructural logics closely related to the famous logic BCK. The study of fragments of logical systems is an important issue of research in any class of non-classical logics. Here we study the fragments of nine prominent fuzzy logics to all sublanguages containing implication. However, the results achieved in the paper for those nine logics are usually corollaries of theorems with much wider (...) scope of applicability. In particular, we show how many of these fragments are really distinct and we find axiomatic systems for most of them. In fact, we construct strongly separable axiomatic systems for eight of our nine logics. We also fully answer the question for which of the studied fragments the corresponding class of algebras forms a variety. Finally, we solve the problem how to axiomatize predicate versions of logics without the lattice disjunction. (shrink)

Witnessed models of fuzzy predicate logic are models in which each quantified formula is witnessed, i.e. the truth value of a universally quantified formula is the minimum of the values of its instances and similarly for existential quantification. Systematic theory of known fuzzy logics endowed with this semantics is developed with special attention paid to problems of arithmetical complexity of sets of tautologies and of satisfiable formulas.

The pace of technological change continues to outstrip the evolution of democratic institutions, creating an urgent need for innovative approaches to democratic reform. However, the experimentation bottleneck - characterized by slow speed, high costs, limited scalability, and ethical risks - has long hindered progress in democracy research. This paper proposes a novel solution: employing generative artificial intelligence (GenAI) to create synthetic data through the simulation of digital homunculi, GenAI-powered entities designed to mimic human behavior in social contexts. By enabling rapid, (...) low-risk experimentation with alternative institutional designs, this approach could significantly accelerate democratic innovation. I examine the potential of GenAI-assisted research to mitigate current limitations in democratic experimentation, including the ability to simulate large-scale societal interactions and test complex institutional mechanisms. While acknowledging potential risks such as algorithmic bias, reproducibility challenges, and AI alignment issues, I argue that the benefits of synthetic data are likely to outweigh their drawbacks if implemented with proper caution. To address existing challenges, I propose a range of technical, methodological, and institutional adaptations. The paper concludes with a call for interdisciplinary collaboration in the development and implementation of GenAI-assisted methods in democracy research, highlighting their potential to bridge the gap between democratic theory and practice in an era of rapid technological change. (shrink)

The article is a presentation of the Thomist response to Scotist criticism of analogy; namely, the defense of St. Thomas’ teaching in some leading renaissance and post-renaissance Thomists: Thomas de Vio, better known as Cajetan, Sylvester of Ferrara, John Versor and John of Saint Thomas. The author first explains the general core of the semantic doctrine of analogy and outlines the basic terminology. Then he exposes the way Cajetan and other Thomists knit Aquinas’ dispersed remarks on analogy into a systematic (...) doctrinal whole. (shrink)

Current research suggests that stressful life experiences and situations create a substantive effect in the development of the initial manifestations of psychotic disorders and may influence temporo-limbic epileptic-like activity manifesting as cognitive and affective seizure-like symptoms in non-epileptic conditions. The current study assessed trauma history, hair cortisol levels, epileptic-like manifestations and other psychopathological symptoms in 56 drug naive adult young women experiencing their initial occurrence of psychosis. Hair cortisol levels among patients experiencing their initial episode of psychosis, were significantly correlated (...) with stress symptoms measured by Trauma Symptom Checklist-40, and complex partial seizure-like symptoms measured by the Complex Partial Seizure-Like Symptoms Inventory and LSCL-33. Hair cortisol levels were not found to be significantly correlated with symptoms of anxiety and depression measured by Beck depression Inventory and Zung Anxiety Scale. These findings suggest a significant relationship between epileptic-like symptoms and stress responses demonstrated by patients in their first psychotic episode. These findings may suggest the potential for research to explore usefulness of anticonvulsant treatment in patients who do not respond to usual psychotropic medication. (shrink)

We explored differences in the course of physiological functions and in the subjective evaluations in response to listening to a 7-min recording of the sound of a chainsaw and to the sounds of a forest. A Biofeedback 2000x-pert apparatus was used for continual recording of the following physiological functions in 50 examined persons: abdominal and thoracic respiration and their amplitude and frequency, electrodermal activity, finger skin temperature, heart rate and heart rate variability. The group of 25 subjects listening to the (...) sound of a chainsaw exhibited significantly lower values of blood volume pulse amplitude, lower values in peak alpha frequency HRV and higher values in peak high-frequency HRV. In the time interval from 80 s to 209 s, in which the two groups showed the greatest differences, lower values of blood volume pulse were also recorded while listening to the sound of a chainsaw. Listening to the sound of a chainsaw is associated with a greater feeling of fatigue and higher tension, while listening to the sounds of a forest is even considered to elicit feelings of improved learning abilities. The assumption that listening to the sound of a chainsaw results in higher defense arousal was confirmed. The greater variability which is exhibited by a majority of physiological functions while listening to the forest sounds may also be an innovative finding. It seems that there are two types of arousal following from correlations between physiological functions and subjective assessment. Low values of blood volume pulse amplitude are especially important from the health perspective. They correspond to the amount of vasoconstriction which occurs in the endothelial dysfunction related to increased mortality, incidence of myocardial infarction, leg atherosclerosis and topically to COVID-19. (shrink)

Die 1922 in Der jüdische Student im Berliner Verlag Ferdinand Ostertag publizierte Schrift Die Idee der Zerstreuung und Widersammlung bei den Propheten war die erste Veröffentlichung von Hans Jonas. Zur Zeit der Verfassung des Textes war Jonas Mitglied in der 1906 gegründeten jüdischen Studentenvereinigung Maccabaea, der er vom Herbst 1921 bis Frühjahr 1923 angehörte. Der Staat Israel existierte noch nicht, das heutige Staatsgebiet stand seit dem Zusammenbruch des Osmanischen Reiches 1920 unter britischem Mandat.

In contrast to Anglophone debates on personal identity initially formed by John Locke’s investigation of personal identity in the sense of personal continuity or persistence through time, the Continental tradition focuses on what constitutes ipseity in the sense of individuality or uniqueness of the human being “constituted” by its continuous transformation through changing experience. In this study, I claim that contemporary phenomenological research in France—especially the “phenomenology of the event” as represented by Henri Maldiney and Claude Romano—contributes to this Continental (...) discussion in a significant way: it formulates the conditions of personal uniqueness or distinctiveness with regard to other persons, conditions not to be found in Heidegger’s existential conception of selfhood in Being and Time. More precisely, Maldiney and Romano allow us to answer the principal questions of this study: In what does the personal uniqueness consist? What exactly individualizes the first-person selfhood disclosed in Dasein’s relation to death? In my three-stage analysis, I first deal with Heidegger’s conception of selfhood in Being and Time and its limits with respect to the question of personal uniqueness. Next, I analyse Maldiney’s conception of “eventful selfhood” in which he “completes” Heidegger’s conception of selfhood by describing Dasein’s openness to ontical, and yet fully authentic events. Finally, I develop the argumentation by presenting Romano’s even more radical conception of the “happening subjectivity”, which allows us to return to the second major feature of personal identity: personal persistence. Nonetheless, I conclude that the connection between personal uniqueness and persistence is not sufficiently examined in the phenomenology of the event, which opens the path towards another related inquiry into the following problem: What is the proper subjective dimension or the “underlying thing” in the background of personal persistence which somehow resists events? (shrink)