We establish a completeness theorem for first-order basic predicate logic BQC, a proper subsystem of intuitionistic predicate logic IQC, using Kripke models with transitive underlying frames. We develop the notion of functional well-formed theory as the right notion of theory over BQC for which strong completeness theorems are possible. We also derive the undecidability of basic arithmetic, the basic logic equivalent of intuitionistic Heyting Arithmetic and classical Peano Arithmetic.

We characterize the first-order formulas with one free variable that are preserved under bisimulation and persistence or strong persistence over the class of Kripke models with transitive frames and unary persistent predicates.

In classical propositional calculus for each proposition A(p) the following holds: $\vdash A(p) \leftrightarrow A^3(p)$ . In this paper we consider what remains of this in the intuitionistic case. It turns out that for each proposition A(p) the following holds: there is an n ∈ N such that $\vdash A^n(p) \leftrightarrow A^{n + 2}(p)$ . As a byproduct of the proof we give some theorems which may be useful elsewhere in propositional calculus.

We generalize the double negation construction of Boolean algebras in Heyting algebras to a double negation construction of the same in Visser algebras. This result allows us to generalize Glivenko’s theorem from intuitionistic propositional logic and Heyting algebras to Visser’s basic propositional logic and Visser algebras.

We present an axiomatization for Basic Propositional Calculus BPC and give a completeness theorem for the class of transitive Kripke structures. We present several refinements, including a completeness theorem for irreflexive trees. The class of intermediate logics includes two maximal nodes, one being Classical Propositional Calculus CPC, the other being E1, a theory axiomatized by T → ⊥. The intersection CPC ∩ E1 is axiomatizable by the Principle of the Excluded Middle A V ∨ ⌝A. If B is a formula (...) such that → B is not derivable, then the lattice of formulas built from one propositional variable p using only the binary connectives, is isomorphically preserved if B is substituted for p. A formula → B is derivable exactly when B is provably equivalent to a formula of the form → A) →. (shrink)

Given a finite lexicon L of relational symbols and equality, one may view the collection of all L-structures on the set of natural numbers ω as a space in several different ways. We consider it as: (i) the space of outcomes of certain infinite two-person games; (ii) a compact metric space; and (iii) a probability measure space. For each of these viewpoints, we can give a notion of relative ubiquity, or largeness, for invariant sets of structures on ω. For example, (...) in every sense of relative ubiquity considered here, the set of dense linear orderings on ω is ubiquitous in the set of linear orderings on ω. (shrink)

A latarre is a lattice with an arrow. Its axiomatization looks natural. Latarres have a nontrivial theory which permits many constructions of latarres. Latarres appear as an end result of a series of generalizations of better known structures. These include Boolean algebras and Heyting algebras. Latarres need not have a distributive lattice.

Let ℒ and ? be propositional languages over Basic Propositional Calculus, and ℳ = ℒ∩?. Weprove two different but interrelated interpolation theorems. First, suppose that Π is a sequent theory over ℒ, and Σ∪ {C⇒C′} is a set of sequents over ?, such that Π,Σ⊢C⇒C′. Then there is a sequent theory Φ over ℳ such that Π⊢Φ and Φ, Σ⊢C⇒C′. Second, let A be a formula over ℒ, and C 1, C 2 be formulas over ?, such that A∧C 1⊢C (...) 2. Then there exists a formula B over ℳ such that A⊢B and B∧C 1⊢C 2. (shrink)

We present axiom systems, and provide soundness and strong completeness theorems, for classes of Kripke models with restricted extension rules among the node structures of the model. As examples we present an axiom system for the class of cofinal extension Kripke models, and an axiom system for the class of end-extension Kripke models. We also show that Heyting arithmetic is strongly complete for its class of end-extension models. Cofinal extension models of HA are models of Peano arithmetic.

Kolmogorov established the principle of the double negation translation by which to embed Classical Predicate Logic |${\operatorname {CQC}}$| into Intuitionistic Predicate Logic |${\operatorname {IQC}}$|⁠. We show that the obvious generalizations to the Basic Predicate Logic of [3] and to |${\operatorname {BQC}}$| of [12], a proper subsystem of |${\operatorname {IQC}}$|⁠, go through as well. The obvious generalizations of Kuroda’s embedding are shown to be equivalent to the Kolmogorov variant. In our proofs novel nontrivial techniques are needed to overcome the absence of (...) full modus ponens in Basic Predicate Logic. In [3] we argued that |${\operatorname {IQC}}$| is not the logic of constructive mathematics. Our doubts were far from new. New was that we put forward an alternative, |${\operatorname {BQC}}$|⁠. One concern is that |${\operatorname {BQC}}$| is too weak for serious mathematics, or even trivial. This paper is one step to alleviate such concerns. (shrink)

We define two notions for intuitionistic predicate logic: that of a submodel of a Kripke model, and that of a universal sentence. We then prove a corresponding preservation theorem. If a Kripke model is viewed as a functor from a small category to the category of all classical models with morphisms between them, then we define a submodel of a Kripke model to be a restriction of the original Kripke model to a subcategory of its domain, where every node in (...) the subcategory is mapped to a classical submodel of the corresponding classical model in the range of the original Kripke model. We call a sentence universal if it is built inductively from atoms using ∧, ∨, ∀, and →, with the restriction that antecedents of → must be atomic. We prove that an intuitionistic theory is axiomatized by universal sentences if and only if it is preserved under Kripke submodels. We also prove the following analogue of a classical model-consistency theorem: The universal fragment of a theory Γ is contained in the universal fragment of a theory Δ if and only if every rooted Kripke model of Δ is strongly equivalent to a submodel of a rooted Kripke model of Γ. Our notions of Kripke submodel and universal sentence are natural in the sense that in the presence of the rule of excluded middle, they collapse to the classical notions of submodel and universal sentence. (shrink)

From classical, Fraïissé-homogeneous, ($\leq \omega$)-categorical theories over finite relational languages, we construct intuitionistic theories that are complete, prove negations of classical tautologies, and admit quantifier elimination. We also determine the intuitionistic universal fragments of these theories.

Inventing Peace' revolves around the question of how we look at the world, but do not see it when there is so much war, injustice, suffering and violence. What are the ethical and moral consequences of looking, but not seeing, and, most of all, what has become of the notion of peace in all this? In the form of a written dialogue, Wim Wenders and Mary Zournazi consider this question as one of the fundamental issues of our times as well (...) as the need to reinvent a visual and moral language for peace. Inspired by various cinematic, philosophical, literary and artistic examples, Wenders and Zournazi reflect on the need for a change of perception in the everyday as well as in the creation of images. In its unique style and method, 'Inventing Peace' demonstrates an approach to peace through sacred, ethical and spiritual means, to provide an alternative to the inhumanity of war and violence. (shrink)

Studies of early modern scholasticism are experiencing a boom today. Legal scholars, philosopher, theologians, and economists are approaching the texts of the “Spanish late scholastics” and “Catholic natural law theorists” from their own perspectives. Both beginners and experts will find the tools in this volume for conducting independent research on the sources and cross-disciplinary insight regarding the state of research.

This textbook not only provides the student with a solid foundation in ethics, but introduces students to the most important themes relevant to business today. Issues such as human rights violation down in the supply chain, the effect business has on nature and the environment, and inclusiveness are each discussed in separate chapters, which discuss their importance, but also their challenges. While there are numerous business ethics textbooks, few take a philosophical approach to business ethics. However, without introducing philosophical ethics, (...) discussions about business ethics are bound to get stuck in fallacies and paradoxes. This textbook therefore fills an important societal gap by providing an introduction to profound philosophical issues in clear language at a philosophically high, but accessible level. (shrink)

An arms race for an artificial general intelligence would be detrimental for and even pose an existential threat to humanity if it results in an unfriendly AGI. In this paper, an all-pay contest model is developed to derive implications for public policy to avoid such an outcome. It is established that, in a winner-takes-all race, where players must invest in R&D, only the most competitive teams will participate. Thus, given the difficulty of AGI, the number of competing teams is unlikely (...) ever to be very large. It is also established that the intention of teams competing in an AGI race, as well as the possibility of an intermediate outcome, is important. The possibility of an intermediate prize will raise the probability of finding the dominant AGI application and, hence, will make public control more urgent. It is recommended that the danger of an unfriendly AGI can be reduced by taxing AI and using public procurement. This would reduce the pay-off of contestants, raise the amount of R&D needed to compete, and coordinate and incentivize co-operation. This will help to alleviate the control and political problems in AI. Future research is needed to elaborate the design of systems of public procurement of AI innovation and for appropriately adjusting the legal frameworks underpinning high-tech innovation, in particular dealing with patenting by AI. (shrink)

This paper provides an early evaluation of Artificial Intelligence against COVID-19. The main areas where AI can contribute to the fight against COVID-19 are discussed. It is concluded that AI has not yet been impactful against COVID-19. Its use is hampered by a lack of data, and by too much data. Overcoming these constraints will require a careful balance between data privacy and public health, and rigorous human-AI interaction. It is unlikely that these will be addressed in time to be (...) of much help during the present pandemic. In the meantime, extensive gathering of diagnostic data on who is infectious will be essential to save lives, train AI, and limit economic damages. (shrink)

In his encyclical 'Aeterni Patris' (1879), Pope Leo XIII expressed the conviction that the renewed study of the philosophical legacy of Saint Thomas Aquinas would help Catholics to engage in a dialogue with secular modernity while maintaining respect for Church doctrine and tradition. As a result, the neo-scholastic framework dominated Catholic intellectual production for nearly a century thereafter. This volume assesses the societal impact of the Thomist revival movement, with particular attention to the juridical dimension of this epistemic community. Contributions (...) from different disciplinary backgrounds offer a multifaceted and in-depth analysis of many different networks and protagonists of the neo-scholastic movement, its institutions and periodicals, and its conceptual frameworks. Although special attention is paid to the Leuven Institute of Philosophy and Faculty of Law, the volume also discloses the neo-Thomist revival in other national and transnational contexts. By highlighting diverse aspects of its societal and legal impact, 'Neo-Thomism in Action' argues that neo-scholasticism was neither a sterile intellectual exercise nor a monolithic movement. The book expands our understanding of how Catholic intellectual discourse communities were constructed and how they pervaded law and society during the late 19th century and the first half of the 20th century. (shrink)

Through a careful analysis of the ethics of Philodemus, this monograph offers the first book-length study of the Epicurean sage. It explores the different aspects of the sage’s way of life and offers a reconstruction of this Epicurean role model.

MartinoEnrico.* * Intuitionistic Proof Versus Classical Truth, The Role of Brouwer’s Creative Subject in Intuitionistic Mathematics. Logic, Methodology and the Unity of Science; 42. Springer, 2018. ISBN: 978-3-319-74356-1 ; 978-3-030-08971-9, 978-3-319-74357-8. Pp. xiii + 170.

This article deals with the question of how self-organization in living organisms is realized. Self-organization may be observed in open systems that are out of equilibrium. Many disequilibria-conversion phenomena exist where free energy conversion occurs by spontaneously formed engines. However, how is self-organization realized in living entities? Living cells turn out to be self-organizing disequilibria-converting systems of a special kind. Disequilibrium conversion is realized in a typical way, through employing information specifying protein complexes acting as nano engines. The genetic code (...) enables processing of information—derived from coding DNA—to produce these molecular machines. Hence, information is at the core of living systems. Two promising approaches to explaining living cells containing sequences carrying information are mentioned. Also discussed is the question of whether a second concept of self-organization—namely, the Kantian concept—applies. (shrink)

BackgroundResearch misconduct and questionable research practices have been the subject of increasing attention in the past few years. But despite the rich body of research available, few empirical works also include the perspectives of non-researcher stakeholders.MethodsWe conducted semi-structured interviews and focus groups with policy makers, funders, institution leaders, editors or publishers, research integrity office members, research integrity community members, laboratory technicians, researchers, research students, and former-researchers who changed career to inquire on the topics of success, integrity, and responsibilities in science. (...) We used the Flemish biomedical landscape as a baseline to be able to grasp the views of interacting and complementary actors in a system setting.ResultsGiven the breadth of our results, we divided our findings in a two-paper series with the current paper focusing on the problems that affect the integrity and research culture. We first found that different actors have different perspectives on the problems that affect the integrity and culture of research. Problems were either linked to personalities and attitudes, or to the climates in which researchers operate. Elements that were described as essential for success were often thought to accentuate the problems of research climates by disrupting research culture and research integrity. Even though all participants agreed that current research climates need to be addressed, participants generally did not feel responsible nor capable of initiating change. Instead, respondents revealed a circle of blame and mistrust between actor groups.ConclusionsOur findings resonate with recent debates, and extrapolate a few action points which might help advance the discussion. First, the research integrity debate must revisit and tackle the way in which researchers are assessed. Second, approaches to promote better science need to address the impact that research climates have on research integrity and research culture rather than to capitalize on individual researchers’ compliance. Finally, inter-actor dialogues and shared decision making must be given priority to ensure that the perspectives of the full research system are captured. Understanding the relations and interdependency between these perspectives is key to be able to address the problems of science.Study registrationhttps://osf.io/33v3m. (shrink)

This paper presents new results from a detailed study of the structure of autocatalytic sets. We show how autocatalytic sets can be decomposed into smaller autocatalytic subsets, and how these subsets can be identified and classified. We then argue how this has important consequences for the evolvability, enablement, and emergence of autocatalytic sets. We end with some speculation on how all this might lead to a generalized theory of autocatalytic sets, which could possibly be applied to entire ecologies or even (...) economies. (shrink)

Budgetary austerity has been implemented by all levels of government in Belgium since 1982. The public attention has focussed on the achievements of the centra[ level. However, also at the local level a remarkable budgetary retrenchment has been realised. This study investigates the various aspects of decremental budgeting of the Belgian municipolities, both at the expenditures and the revenues side.

In this article thinking on corporate social responsibility is compared with the dominant political theory of the market: theneoclassical theory. The comparison shows that thinking on CSR fundamentally collides with that theory. For example, their respectivenormative views on man are incompatible, as are their respective views on the modus operandi of the market. Given that CSR is desirable it follows that a new political theory of the market is needed. This article suggests some initial steps toward developing that new political (...) theory of the market. For example, it defends the proposition that the neoclassical idea of the market as a harmonic sphere must be replaced by the idea of the market as a fragile system. (shrink)

Liberalist thinking argues that moral agents have a right to pursue an ordinary life. It also insists that moral agent can be bystanders. A bystander is involved with morally bad states of affairs in the sense that they are bound by moral duty, but for a non-blameworthy reason. A common view on the morality of commercial life argues that commercial agents cannot and ought not to assume the status of bystander, when confronted with child labor, pollution, or other overwhelmingly big (...) morally bad states of affairs. According to the common view, the agent will get overdemanded. In this paper, the overdemandingness charge is interpreted as a criticism of the liberalist position. According to this charge, bystander status must be given up in the market because otherwise the right to pursue a personal life is crushed. In this paper, we demonstrate that the overdemandingness charge fails. It does not make sense if bystander status is grounded in the duty of beneficence. It would make sense if the status were grounded in the duty of rescue but that duty does not apply in relation to oMBS. The condition of ‘subjective urgency’ is not fulfilled. Hence, liberalist thinking can withstand the charge of overdemandingness and commercial agents cannot assume a right never to acknowledge bystander status. (shrink)

The ongoing COVID-19 pandemic and resulting health and economic crisis has caused major disruptions in the functioning of food systems and revived the discussion on what forms balanced, effective and responsible crisis management. As part of its thought leadership and its social responsibility in times of crisis, WUR is uniquely placed to contribute to the scientific knowledge base and data collection mechanisms required for early recognition and rapid response. In addition, WUR takes on the challenge to generate timely insights into (...) the possible scenarios for the prevention of a crisis and during and after emergencies to enable our clients and stakeholders to make informed decisions. Lastly, WUR can provide a better understanding of the mechanisms of spillover, and tangible and practical tools to help reduce the risk of spillover events from occurring, prevent pathogen spread, or mitigate the impacts of a future pandemic. In its research institutes and university, WUR brings together expertise in human, animal, plant and environmental health, the global agri-food system, economics, social sciences, food safety and security, ethics, and policy. Here, in the knowledge that COVID-19 will not be the last pandemic, we present WUR’s ambition and capabilities towards an integrated global multi-stakeholder approach to the prevention and management of potentially pandemic diseases, across the four phases of crisis management; prevention, preparedness, response, and recovery and learning. (shrink)

Silent gestures consist of complex multi‐articulatory movements but are now primarily studied through categorical coding of the referential gesture content. The relation of categorical linguistic content with continuous kinematics is therefore poorly understood. Here, we reanalyzed the video data from a gestural evolution experiment (Motamedi, Schouwstra, Smith, Culbertson, & Kirby, 2019), which showed increases in the systematicity of gesture content over time. We applied computer vision techniques to quantify the kinematics of the original data. Our kinematic analyses demonstrated that gestures (...) become more efficient and less complex in their kinematics over generations of learners. We further detect the systematicity of gesture form on the level of thegesture kinematic interrelations, which directly scales with the systematicity obtained on semantic coding of the gestures. Thus, from continuous kinematics alone, we can tap into linguistic aspects that were previously only approachable through categorical coding of meaning. Finally, going beyond issues of systematicity, we show how unique gesture kinematic dialects emerged over generations as isolated chains of participants gradually diverged over iterations from other chains. We, thereby, conclude that gestures can come to embody the linguistic system at the level of interrelationships between communicative tokens, which should calibrate our theories about form and linguistic content. (shrink)

Moral purism is a commonly held view on moral worthiness and how to identify it in concrete cases. Moral purists long for a moral world in which (business) people—at least sometimes—act morally worthy, but in concrete cases they systematically discount good deeds as grounded in self-interest. Moral purism evokes moral cynicism. Moral cynicism is a problem, both in society at large and the business world. Moral cynicism can be fought by refuting moral purism. This article takes issue with moral purism. (...) The common strategy to tackle moral purism is to reject the exclusion thesis which states that self-interest and the ‘pure’ moral motive (and thus moral worthiness) exclude each other. We develop a different strategy. We argue that moral purists are mistaken in the way they judge moral worthiness in concrete cases. They employ the wrongprocedureand the wrongcriteria.We develop a proper procedure and proper criteria. We build on Kant, who we argue is unfairly regarded as the champion of moral purism. In order to see how Kant can develop a consistent (non-purist) philosophy, the exclusion thesis must be embedded in Kant’s transcendental philosophy. Properly embedded, Kant turns out to be both anti-purist and anti-cynical. (shrink)

Transparency is a crucial condition to implement a CSR policy based on the reputation mechanism. The central question of this contribution is how a transparency policy ought to be organised in order to enhance the CSR behaviour of companies. Governments endorsing CSR as a new means of governance have different strategies to foster CSR transparency. In this paper we discuss the advantages and disadvantages of two conventional policy strategies: the facilitation policy and the command and control strategy. Using three criteria (...) (efficiency, freedom and virtue) we conclude that both strategies are defective. Most attention is paid to the facilitation strategy since governments nowadays mainly use this. In evaluating this strategy we analyse the Dutch case. As an alternative we introduce a third government policy: the development of a self-regulating sub-system. By construing an analogy with the historical development of corporate financial disclosure, we point out that the vital step in the creation of a self-regulating subsystem is the creation of strong informational intermediate organisations. (shrink)