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.

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)

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.

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)

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)

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.

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)

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)

A very simple many-valued predicate calculus is presented; a completeness theorem is proved and the arithmetical complexity of some notions concerning provability is determined.

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)

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)

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)

Many democratic countries have failed to stand up to the challenge presented by the COVID-19 pandemic. I argue that the collective response to the pandemic has been incapacitated by an ‘epistemic crisis’, (i.e., a breakdown in the social division of epistemic labor) that led to a failure of citizens’ beliefs to converge towards a shared perception of the situation. Neither a paucity of relevant expert knowledge nor democratic citizens’ irrationality is required for the crisis to emerge. In particular, I highlight (...) three obstacles capable of preventing relevant expert testimony from gaining democratic legitimacy necessary for an effective policy response: 1) the proper domain of expertise is uncertain; 2) regular citizens’ meta-expertise – (i.e., ability to discriminate among the putative experts based on their relative epistemic merit) – is not efficacious enough to trigger truth-convergence of the public opinion; 3) the prominent sources of third-party meta-expertise lack credibility due to their conflicts of interest. Since the first two problems appear irresolvable, I propose that the search for a path towards preclusion of future epistemic crises concentrates on upgrading the institutional fundament for meta-expertise provision. Social epistemology plays a vital role in this search, but its close cooperation with other disciplines is a must. (shrink)

The article deals with various modal versions of the ontological argument from N. Malcolm’s to P. Tichý’s interpretation of Anselm’s second proof. Three key presuppositions of the modal proof are pin-pointed and examined. The principal problem with the proof seems to be the notion of necessary existence attributed to God. More precisely, the question is whether this is not too strong an attribute, for then there would not be a situation, i.e. a possible world, consistently thinkable which precludes the existence (...) of God. However, this seems to be wrong. (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)

The paper deals with Aristotle’s argument against determinism and in favor of contingency in nature as interpreted by Thomas Aquinas. The case against determinism is based on the idea that there are properly uncaused accidental events in reality. This means that in case there is some coincidental future event e, one cannot trace an unbroken causal chain leading to e back to the present or the past. For a Christian Aristotelian, such as Aquinas, there arises a difficulty concerning divine foreknowledge (...) and volitional determination of events of this sort. Thomas’s solution is based on the claim that the latter divine acts are not within the scope of modal determination (necessity/contingency). (shrink)

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 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)

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)

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)

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)

Current thinking suggests that dissociation could be a significant comorbid diagnosis in a proportion of schizophrenic patients with a history of trauma. This potentially may explain the term “schizophrenia” in its original definition by Bleuler, as influenced by his clinical experience and personal view. Additionally, recent findings suggest a partial overlap between dissociative symptoms and the positive symptoms of schizophrenia, which could be explained by inhibitory deficits. In this context, the process of dissociation could serve as an important conceptual framework (...) for understanding schizophrenia, which is supported by current neuroimaging studies and research of corollary discharges. These data indicate that the original conception of “split mind” may be relevant in an updated context. Finally, recent data suggest that the phenomenal aspects of dissociation and conscious disintegration could be related to underlying disruptions of connectivity patterns and neural integration. (shrink)

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)

According to Michael Tomasello’s evolutionary anthropological approach, joint attention is one of the essential keys to understanding the difference between human and animal. The present paper discusses a recent phenomenological account of the anthropological difference inspired by Tomasello’s conception. A criticism of this account is put forward, while an alternative view is also introduced that stresses the impact of differential rearing experiences on the socio-cognitive development of human and non-human animals.

While correctly emphasizing that the idea of theological inspiration in phenomenology and vice versa might be very fecund, the current discussion on the theological turn does not always affirm that Janicaud was simply wrong as regards the characterization of new French phenomenology. This is why it is necessary to create a more balanced image of the discussions on the theological turn and contemporary phenomenology. The paper achieves this aim 1) by demonstrating that there was no theological turn in French phenomenology; (...) 2) by analysing the true nature of the turn taking place in phenomenology. It concludes by affirming that contemporary French phenomenology—freed from the label “theological turn”—is a living branch of philosophy capable of contributing to the solution of some of the burning issues of today’s world, such as ecological crisis. (shrink)

The possibility of performing germline modifications on currently living individuals targets future generations’ health and well-being by reducing the diversity of the human gene pool. This can have two negative repercussions: reduction of heterozygosity, the latter being associated with a health or performance advantage; uniformization of the genes involved in reproductive recombination, which may lead to the health risks involved in asexual reproduction. I argue that germline interventions aimed at modifying the genomes of future people cannot be ethically justifiable if (...) there is no possibility of controlling the intervention either by reversing or altering it, whenever need demands it. This argument is challenged on six different grounds: safety, population versus individual focus, spontaneous mutations, exceptionalism, the intentional pursuit of genetic diversity through germline interventions, and harm reduction potential. (shrink)

Later works of C.G. Jung contain comprehensive descriptions of the relationship between psychological and physical research. These considerations described in Jung’s works and in his correspondence with Wolfgang Pauli represent interesting philosophical ideas that are related to interpretation of psychological data. The so-called “collective unconscious” studied by Jung in analysis of dream material, mythology, psychopathological symptoms, and several cultural manifestations led him to postulate complementarity and unity of scientific principles, and to define the psyche as complementary to physical reality. Likewise (...) recent neuroscientific studies and physical analyses on the role of the observer in physical reality led to the study of “quantum consciousness.” This review compares the philosophical postulates by Roger Penrose with Jung’s and Pauli’s studies, and suggests novel links of these concepts to recent findings of chaos theory in the brain. (shrink)

The article deals with various modal versions of the ontological argument from N. Malcolm’s to P. Tichý’s interpretation of Anselm’s second proof. Three key presuppositions of the modal proof are pin-pointed and examined. The principal problem with the proof seems to be the notion of necessary existence attributed to God. More precisely, the question is whether this is not too strong an attribute, for then there would not be a situation, i.e. a possible world, consistently thinkable which precludes the existence (...) of God. However, this seems to be wrong. (shrink)

The well-known Ratio Studiorum of 1599 states that logical instruction should follow F. Toletus or P. Fonseca. The latter authored the famous Institutionum Dialecticarum Libri Octo, the former a similar manual, Introductio in Dialecticam Aristotelis. As is often observed, the contrast between the Aristotelian and present symbolic logics is perhaps most striking in their analysis of relational statements. Both authors recognize the relational logical form as independent from the traditional subject-predicate form and see the need to recognize relational inferential rules. (...) They differ in their specific rules, however, so neither of the authors has captured the system of relational syllogism in its entirety. (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)

Two variants of monadic fuzzy predicate logic are analyzed and compared with the full fuzzy predicate logic with respect to finite model property (properties) and arithmetical complexity of sets of tautologies, satisfiable formulas and of analogous notion restricted to finite models.

In [10] it is claimed that the set of predicate tautologies of all complete BL-chains and the set of all standard tautologies coincide. As noticed in [11], this claim is wrong. In this paper we show that a complete BL-chain B satisfies all standard BL-tautologies iff for any transfinite sequence of elements of B, the condition ∧i ∈ I = 2 holds in B.