In this article complexity results for adaptive logics using the minimal abnormality strategy are presented. It is proven here that the consequence set of some recursive premise sets is $\Pi _1^1 - complete$ . So, the complexity results in (Horsten and Welch, Synthese 158:41–60,2007) are mistaken for adaptive logics using the minimal abnormality strategy.

The early calculus is a popular example of an inconsistent but fruitful scientific theory. This paper is concerned with the formalisation of reasoning processes based on this inconsistent theory. First it is shown how a formal reconstruction in terms of a sub-classical negation leads to triviality. This is followed by the evaluation of the chunk and permeate mechanism proposed by Brown and Priest in, 379–388, 2004) to obtain a non-trivial formalisation of the early infinitesimal calculus. Different shortcomings of this application (...) of C&P as an explication of inconsistency tolerant reasoning are pointed out, both conceptual and technical. To remedy these shortcomings, an adaptive logic is proposed that allows for conditional permeations of formulas under the assumption of consistency preservation. First the adaptive logic is defined and explained and thereafter it is demonstrated how this adaptive logic remedies the defects C&P suffered from. (shrink)

In this book we present a collection of papers on the topic of applying paraconsistent logic to solve inconsistency related problems in science, mathematics and computer science. The goal is to develop, compare, and evaluate different ways of applying paraconsistent logic. After more than 60 years of mainly theoretical developments in many independent systems of paraconsistent logic, we believe the time has come to compare and apply the developed systems in order to increase our philosophical understanding of reasoning when faced (...) with inconsistencies. This book wants to be a first step toward an application based, constructive debate to tackle the question which systems are best applied for which kind of problems and which philosophical conclusions can be drawn from such applications. (shrink)

In this paper, we first develop truthmaker semantics for four relevance logics defined as the non-transitive relevant cores [as introduced in Verdée et al. (Aust J Log 16:10–40, 2019)] of the well-known propositional logics CL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textbf {CL}}$$\end{document} (classical logic), LP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textbf {LP}}$$\end{document} (the logic of paradox), K3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textbf {K3}}$$\end{document} (strong Kleene logic), and FDE\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} (...) \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textbf {FDE}}$$\end{document} (first degree entailment). The semantics is similar to Kit Fine’s truthmaker semantics for classical logic, but we define the notion of exact verification similarly to Fine’s notion of loose verification. Dropping Fine’s principle of Downward Closure of the set of consistent states nevertheless warrants the exactness of our verification notion. The semantics of the four non-transitive relevance logics shows that they are in fact straightforward cut-free substructural logics, despite their definition by means of a filtering criterion. We develop the associated sound and complete sequent calculi for these logics. Finally, we argue that the four presented truthmaker semantics are also interesting alternatives to the standard Kit Fine style truthmaker semantics for the original (irrelevant) consequence relations FDE\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textbf {FDE}}$$\end{document}, LP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textbf {LP}}$$\end{document}, K3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textbf {K3}}$$\end{document}, and CL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textbf {CL}}$$\end{document} themselves. The most interesting difference with Fine’s approach is the way in which tautologies are handled: next to their usual verifiers, they are also made true by the empty state. We provide philosophical arguments for the plausibility of such an account. (shrink)

This paper presents eight (previously unpublished) adaptive logics for belief revision, each of which define a belief revision operation in the sense of the AGM framework. All these revision operations are shown to satisfy the six basic AGM postulates for belief revision, and Parikh's axiom of Relevance. Using one of these logics as an example, we show how their proof theory gives a more dynamic flavor to belief revision than existing approaches. It is argued that this turns belief revision (that (...) obeys Relevance) into a more natural undertaking, where analytic steps are performed only as soon as they turn out to be necessary in order to uphold certain beliefs. (shrink)

In this paper, we aim to devise a logic that can deal with both the paradoxes that motivate dialetheism and the paradoxes related to the irrelevance of material implication. We propose the semantics and the sequent calculus of a relevant logic inspired by difference-making accounts of causation and arguably true to Graham Priest’s Logic of Paradox \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {LP}$$\end{document}: a relevant logic that validates those and only those \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} (...) \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {LP}$$\end{document}-consequences that are not irrelevant. The new logic’s relevant implication is then added to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {LP}$$\end{document} to obtain a logic with the logical vocabulary required to cope with the mentioned paradoxes. (shrink)

Reflection Principles are commonly thought to produce only strong axioms of infinity consistent with V = L. It would be desirable to have some notion of strong reflection to remedy this, and we have proposed Global Reflection Principles based on a somewhat Cantorian view of the universe. Such principles justify the kind of cardinals needed for, inter alia , Woodin’s Ω-Logic.

In this paper I propose a new approach to the foundation of mathematics: non-monotonic set theory. I present two completely different methods to develop set theories based on adaptive logics. For both theories there is a finitistic non-triviality proof and both theories contain (a subtle version of) the comprehension axiom schema. The first theory contains only a maximal selection of instances of the comprehension schema that do not lead to inconsistencies. The second allows for all the instances, also the inconsistent (...) ones, but restricts the conclusions one can draw from them in order to avoid triviality. The theories have enough expressive power to form a justification/explication for most of the established results of classical mathematics. They are therefore not limited by Gödel’s incompleteness theorems. This remarkable result is possible because of the non-recursive character of the final proofs of theorems of non-monotonic theories. I shall argue that, precisely because of the computational complexity of these final proofs, we cannot claim that non-monotonic theories are ideal foundations for mathematics. Nevertheless, thanks to their strength, first order language and the recursive dynamic (defeasible) proofs of theorems of the theory, the non-monotonic theories form (what I call) interesting pragmatic foundations. (shrink)

According to an intuitive picture of relevant entailment, an entailment is relevant if all the formulas it contains contribute to its validity. In this paper, we provide a ground-theoretic analysis of this notion of contribution, and as a result of relevant entailment. We build a system of bilateral logical grounding within which we can derive classical entailment and analyze the contribution of premises and conclusions, in terms of a certain type of connection between their respective logical grounds. The resulting framework (...) is shown to have a strong unifying and explanatory power by bringing together the notions of grounding and relevance and explaining the commonalities and differences between alternative contribution-based accounts of relevance. (shrink)

In this paper we first develop a logic independent account of relevant implication. We propose a stipulative denition of what it means for a multiset of premises to relevantly L-imply a multiset of conclusions, where L is a Tarskian consequence relation: the premises relevantly imply the conclusions iff there is an abstraction of the pair such that the abstracted premises L-imply the abstracted conclusions and none of the abstracted premises or the abstracted conclusions can be omitted while still maintaining valid (...) L-consequence. Subsequently we apply this denition to the classical logic consequence relation to obtain NTR-consequence, i.e. the relevant CL-consequence relation in our sense, and develop a sequent calculus that is sound and complete with regard to relevant CL-consequence. We present a sound and complete sequent calculus for NTR. In a next step we add rules for an object language relevant implication to the sequent calculus. The object language implication reflects exactly the NTR-consequence relation. One can see the resulting logic NTR-> as a relevant logic in the traditional sense of the word. By means of a translation to the relevant logic R, we show that the presented logic NTR is very close to relevance logics in the Anderson-Belnap-Dunn-Routley-Meyer tradition. However, unlike usual relevant logics, NTR is decidable for the full language, Disjunctive Syllogism and Adjunction are valid, and neither Modus Ponens nor the Cut rule are admissible. (shrink)

In this article, I present a dynamic logic game for defeasible reasoning. I argue that, as far as defeasible reasoning is concerned, one should distinguish between practical and ideal rationality. Starting from the adaptive logic framework, I formalize both rationality notions by means of logic games. The presented adaptive logic games are based on (i) standard logic games on the one hand and (ii) dynamic proof procedures for adaptive logic on the other hand. The games are similar to standard logic (...) games, but have the extra property that some moves are revisable. This is handled by means of a main control game, which starts different standard logic games. I argue that the adaptive logic games form intuitive reasoning models for rationality in defeasible reasoning contexts. Moreover, I will also demonstrate that the games give a good insight in the computational complexity of defeasible reasoning forms. (shrink)

In this paper, we present a generic format for adaptive vague logics. Logics based on this format are able to (1) identify sentences as vague or non-vague in light of a given set of premises, and to (2) dynamically adjust the possible set of inferences in accordance with these identifications, i.e. sentences that are identified as vague allow only for the application of vague inference rules and sentences that are identified as non-vague also allow for the application of some extra (...) set of classical logic rules. The generic format consists of a set of minimal criteria that must be satisfied by the vague logic in casu in order to be usable as a basis for an adaptive vague logic. The criteria focus on the way in which the logic deals with a special ⊡-operator. Depending on the kind of logic for vagueness that is used as a basis for the adaptive vague logic, this operator can be interpreted as completely true, definitely true, clearly true , etc. It is proven that a wide range of famous logics for vagueness satisfies these criteria when extended with a specific ⊡-operator, e.g. fuzzy basic logic and its well known extensions, cf. [7], super- and subvaluationist logics, cf. [6], [9], and clarity logic, cf. [13]. Also a fuzzy logic is presented that can be used for an adaptive vague logic that can deal with higher-order vagueness. To illustrate the theory, some toy-examples of adaptive vague proofs are provided. (shrink)

In this paper, we present a generic format for adaptive vague logics. Logics based on this format are able to (1) identify sentences as vague or non-vague in light of a given set of premises, and to (2) dynamically adjust the possible set of inferences in accordance with these identifications, i.e. sentences that are identified as vague allow only for the application of vague inference rules and sentences that are identified as non-vague also allow for the application of some extra (...) set of classical logic rules. The generic format consists of a set of minimal criteria that must be satisfied by the vague logic in casu in order to be usable as a basis for an adaptive vague logic. The criteria focus on the way in which the logic deals with a special ⊡-operator. Depending on the kind of logic for vagueness that is used as a basis for the adaptive vague logic, this operator can be interpreted as completely true, definitely true, clearly true, etc. It is proven that a wide range of famous logics for vagueness satisfies these criteria when extended with a specific ⊡-operator, e.g. fuzzy basic logic and its well known extensions, cf. [7], super- and subvaluationist logics, cf. [6], [9], and clarity logic, cf. [13]. Also a fuzzy logic is presented that can be used for an adaptive vague logic that can deal with higher-order vagueness. To illustrate the theory, some toy-examples of adaptive vague proofs are provided. (shrink)

In this paper, we present a generic format for adaptive vague logics. Logics based on this format are able to (1) identify sentences as vague or non-vague in light of a given set of premises, and to (2) dynamically adjust the possible set of inferences in accordance with these identifications, i.e. sentences that are identified as vague allow only for the application of vague inference rules and sentences that are identified as non-vague also allow for the application of some extra (...) set of classical logic rules. The generic format consists of a set of minimal criteria that must be satisfied by the vague logic in casu in order to be usable as a basis for an adaptive vague logic. The criteria focus on the way in which the logic deals with a special ⊡-operator. Depending on the kind of logic for vagueness that is used as a basis for the adaptive vague logic, this operator can be interpreted as completely true, definitely true, clearly true, etc. It is proven that a wide range of famous logics for vagueness satisfies these criteria when extended with a specific ⊡-operator, e.g. fuzzy basic logic and its well known extensions, cf. [7], super- and subvaluationist logics, cf. [6], [9], and clarity logic, cf. [13]. Also a fuzzy logic is presented that can be used for an adaptive vague logic that can deal with higher-order vagueness. To illustrate the theory, some toy-examples of adaptive vague proofs are provided. (shrink)

It is shown that a set of semi-recursive logics, including many fragments of CL, can be embedded within CL in an interesting way. A logic belongs to the set iff it has a certain type of semantics, called nice semantics. The set includes many logics presented in the literature. The embedding reveals structural properties of the embedded logic. The embedding turns finite premise sets into finite premise sets. The partial decision methods for CL that are goal directed with respect to (...) CL are turned into partial decision methods that are goal directed with respect to the embedded logics. (shrink)

This paper is devoted to a consequence relation combining the negation of Classical Logic ) and a paraconsistent negation based on Graham Priest’s Logic of Paradox ). We give a number of natural desiderata for a logic \ that combines both negations. They are motivated by a particular property-theoretic perspective on paraconsistency and are all about warranting that the combining logic has the same characteristics as the combined logics, without giving up on the radically paraconsistent nature of the paraconsistent negation. (...) We devise the logic \ by means of an axiomatization and three equivalent semantical characterizations. By showing that this logic is maximally paraconsistent, we prove that \ is the only logic satisfying all postulated desiderata. Finally we show how the logic’s infinite-valued semantics permits defining different types of entailment relations. (shrink)

Inleidend overzicht van de wijsgerige ethiek.

인간의 이성적 의식과 법의 관계를 밝히고 법의 해석 과 판단에 인간의 의식이 어떻게 작용하는가를 고찰 한 저술. 제1부에서는 법의 형이상학적인 측면에서 법의 실체, 그리스의 법, 데카르트의 법, 로크와 법, 칸트와 법, 헤겔과 법, 아담스미스의 법의 경제, 중국의 도덕과 법사상을 다루었다. 제2부에서는 심리학적 분석으로 헌법의 심리학적 해석, 법의 판결절차, 증거법, 형법과 죄, 청소년과 가족법, 조세법, 플라톤의 법, 칸트의 도덕론의 경험적 확인, 헤겔의 자아와 노동법, 법의 4차원에 대해 다뤘다.

For Tarski logics, there are simple criteria that enable one to conclude that two premise sets are equivalent. We shall show that the very same criteria hold for adaptive logics, which is a major advantage in comparison to other approaches to defeasible reasoning forms. A related property of Tarski logics is that the extensions of equivalent premise sets with the same set of formulas are equivalent premise sets. This does not hold for adaptive logics. However a very similar criterion does. (...) We also shall show that every monotonic logic weaker than an adaptive logic is weaker than the lower limit logic of the adaptive logic or identical to it. This highlights the role of the lower limit for settling the adaptive equivalence of extensions of equivalent premise sets. (shrink)

In this paper we present a logic that determines when implications in a classical logic context express a relevant connection between antecedent and consequent. In contrast with logics in the relevance logic literature, we leave classical negation intact—in the sense that the law of non-contradiction can be used to obtain relevant implications, as long as there is a connection between antecedent and consequent. On the other hand, we give up the requirement that our theory of relevance should be able to (...) define a new standard of deduction. We present and argue for a list of requirements such a logical theory of classical relevance needs to meet and go on to formulate a system that respects each of these requirements. The presented system is a Tarski logic that extends the relevance logic R with a new relevant implication which allows for Disjunctive Syllogism and similar rules. This is achieved by interpreting the logical symbols in the antecedents in a stronger way than the logical symbols in consequents. A proof theory and an algebraic semantics are formulated and interesting metatheorems are proven. Finally we give a philosophical motivation for our non-standard relevant implication and the asymmetric interpretation of antecedents and consequents. (shrink)

George Berkeley is one of the greatest and most influential modern philosophers. In defending the immaterialism for which he is most famous, he redirected modern thinking about the nature of objectivity and the mind's capacity to come to terms with it. Along the way, he made striking and influential proposals concerning the psychology of the senses, the workings of language, the aims of science, and the scope of mathematics. In this Companion volume a team of distinguished authors not only examines (...) Berkeley's achievements but also his neglected contributions to moral and political philosophy, his writings on economics and development, and his defense of religious commitment and religious life. The volume places Berkeley's achievements in the context of the many social and intellectual traditions - philosophical, scientific, ethical, and religious - to which he fashioned a distinctive response. (shrink)

The introduction of novel diagnostic techniques in clinical domains such as genomics and radiology has led to a rich ethical debate on how to handle unsolicited findings that result from these innovations. Yet while unsolicited findings arise in both genomics and radiology, most of the relevant literature to date has tended to focus on only one of these domains. In this article, we synthesize and critically assess similarities and differences between “scanning the body” and “sequencing the genome” from an ethical (...) perspective. After briefly describing the novel diagnostic contexts leading to unsolicited findings, we synthesize and reflect on six core ethical issues that relate to both specialties: terminology; benefits and risks; autonomy; disclosure of unsolicited findings to children; uncertainty; and filters and routine screening. We identify ethical rationales that pertain to both fields and may contribute to more ethically sound policies. Considerations of preserving public trust and ensuring that people perceive healthcare policies as fair also support the need for a combined debate. (shrink)

There has been an increase in recent years in the use of empirical methods in healthcare ethics. Appeals to empirical data cannot answer moral questions, but insights into the knowledge, attitudes, experience, preferences and practice of interested parties can play an important part in the development of healthcare ethics. In particular, while we may establish a general ethical principle to provide explanatory and normative guidance for healthcare professionals, the interpretation and application of such general principles to actual practice still requires (...) interpretation and judgement. And many situations in healthcare practice are complex and may involve a variety of principles, each of which may conflict with the others. Simple surveys or interview studies may not be sufficient if we wish to develop a nuanced approach to ethical practice that can be set out in guidelines, codes or directives. We do not resolve moral questions by plebiscite. In this paper, the authors argue for the use of consensus methods to develop shared understanding of ethical practice, and they argue further for the combination of the Delphi method with the use of vignettes to illustrate the kind of situations that may occur in practice. They develop their argument in part by reference to their experience of using this approach in their recent research. (shrink)

As family physicians, general practitioners play a key role in safeguarding children. Should they suspect child abuse or neglect they may experience a conflict between responding to the needs and interests of the child and those of an adult patient. English law insists on the paramountcy of the interests of the child, but in family practice many other interests may be at stake. The authors argue that uncritical adoption of the paramountcy principle is too simplistic and can lead, paradoxically, to (...) greater harm. They argue for a more subtle and nuanced view of interests and of conflicts of interest in safeguarding children. (shrink)

Together again for the first time, Marx and Durkheim join forces in the pages of Disintegration: Bad Love, Collective Suicide, and the Idols of Imperial Twilight for a dialectical exploration of the moral economy of neoliberalism, animated, as it is not only by the capitalist chase for surplus value, but also by an immortal vortex of sacred powers. Classical sociology and psychoanalysis are reconstituted within Hegelian social ontology and dialectical method that differentiates between the ephemeral and free and the eternal (...) and fixed aspects of modern life. (shrink)

t. 1. Dialog s V. V. Davydovym -- t. 2. Nereshennye problemy razvivai︠u︡shchego obrazovanii︠a︡.

Prospect Theory: For Risk and Ambiguity, provides a comprehensive and accessible textbook treatment of the way decisions are made both when we have the statistical probabilities associated with uncertain future events and when we lack them. The book presents models, primarily prospect theory, that are both tractable and psychologically realistic. A method of presentation is chosen that makes the empirical meaning of each theoretical model completely transparent. Prospect theory has many applications in a wide variety of disciplines. The material in (...) the book has been carefully organized to allow readers to select pathways through the book relevant to their own interests. With numerous exercises and worked examples, the book is ideally suited to the needs of students taking courses in decision theory in economics, mathematics, finance, psychology, management science, health, computer science, Bayesian statistics, and engineering. (shrink)

Doctors’ strikes are legally permissible in the UK, with the situation differing in other countries. But are they morally permissible? Doug McConnell and Darren Mann have systematically attempted to dismiss the arguments for the moral impermissibility of doctors’ strikes and creatively attempted to provide further moral justification for them. Unfortunately for striking doctors, they fail to achieve this. Meanwhile, junior doctors’ strikes have continued in the UK through 2023 and have now extended into 2024. In this response, which focuses on (...) the UK situation and specifically junior doctors’ strikes in the National Health Service (NHS) in England, I will demonstrate a central problem with their arguments—namely that they underplay the harms caused by prolonged doctors’ strikes by ignoring the harms to patients with cancer. This weakens their conclusion that strikes are morally permissible in terms of the conditions and thresholds they set. I then provide a psychological critique of their justification for strikes in terms of the interests of the public. It follows that invoking the controversial concept of supererogatory action is ungrounded but also absurd when you consider time-critical cancer care. If those representing striking doctors wish to maintain a modicum of moral respectability, they should mitigate for patients with cancer and negotiate reasonably and with urgency. (shrink)