Posthumous Fragments: Spring–Autumn 1881 [Excerpts].

This paper develops and defends a new account of B-theoretic endurantism and a new account of the metaphysics of the quantum state, and highlights the parallels between the considerations that motivate them. These new accounts are both fragmentalist, in the sense that they follow Fine (2005) in invoking a symmetric coordination relation between facts, such that facts that are pairwise incompatible (like Hugh's being happy and Hugh's being sad) can both obtain provided that they are not related by this relation. (...) However, while Fine allows that fragments can be logically incoherent— P can obtain in one fragment while not-P obtains in another—the fragmentalist accounts defended here are motivated even if we insist on logical coherence between fragments. (shrink)

The growing interest in fragmentalism is one of the most exciting trends in philosophy of time and is gradually reshaping the contemporary debate. Providing an extensive interpretation of this view, Samuele Iaquinto and Giuliano Torrengo articulate a novel theory of the passage of time and argue that it is the most effective in vindicating the inherent dynamism of reality. Iaquinto and Torrengo offer the first full-range application of fragmentalism to a number of metaphysical topics, including the open future, (...) causation, the A-theoretic interpretation of special relativity and time travel. The resulting picture, they argue, conveys the potential of a radically new understanding of time. (shrink)

It would be good to have a Bayesian decision theory that assesses our decisions and thinking according to everyday standards of rationality — standards that do not require logical omniscience (Garber 1983, Hacking 1967). To that end we develop a “fragmented” decision theory in which a single state of mind is represented by a family of credence functions, each associated with a distinct choice condition (Lewis 1982, Stalnaker 1984). The theory imposes a local coherence assumption guaranteeing that as an agent's (...) attention shifts, successive batches of "obvious" logical information become available to her. A rule of expected utility maximization can then be applied to the decision of what to attend to next during a train of thought. On the resulting theory, rationality requires ordinary agents to be logically competent and to often engage in trains of thought that increase the unification of their states of mind. But rationality does not require ordinary agents to be logically omniscient. (shrink)

In this paper, I will argue that there is a version of possibilism—inspired by the modal analogue of Kit Fine’s fragmentalism—that can be combined with a weakening of actualism. The reasons for analysing this view, which I call Modal Fragmentalism, are twofold. Firstly, it can enrich our understanding of the actualism/possibilism divide, by showing that, at least in principle, the adoption of possibilia does not correspond to an outright rejection of the actualist intuitions. Secondly, and more specifically, it (...) can enrich our understanding of concretism, by proving that, at least in principle, the idea that objects have properties in an absolute manner is compatible with transworld identity. (shrink)

This paper discusses the fragmentation of psychology and proposals for unification hitherto proffered. It is argued that unity will not be achieved until competing ideas regarding morality, ontology, epistemology, and so forth are critically examined and evaluated. Ideas that pass theoretical muster and that cohere with human moral interests will provide a theoretical starting point for unification efforts. 2012 APA, all rights reserved).

In this paper, I consider two curious subsystems ofFrege's Grundgesetze der Arithmetik: Richard Heck's predicative fragment H, consisting of schema V together with predicative second-order comprehension (in a language containing a syntactical abstraction operator), and a theory T in monadic second-order logic, consisting of axiom V and 1 1-comprehension (in a language containing anabstraction function). I provide a consistency proof for the latter theory, thereby refuting a version of a conjecture by Heck. It is shown that both Heck and T (...) prove the existence of infinitely many non-logical objects (T deriving,moreover, the nonexistence of the value-range concept). Some implications concerning the interpretation of Frege's proof of referentiality and the possibility of classifying any of these subsystems as logicist are discussed. Finally, I explore the relation of T toCantor's theorem which is somewhat surprising. (shrink)

In this paper, we articulate a version of non-standard A-theory—which we call Flow Fragmentalism—in relation to its take on the issue of supervenience of truth on being. According to the Truth Supervenes on Being (TSB) Principle, the truth of past- and future-tensed propositions supervenes, respectively, on past and future facts. Since the standard presentist denies the existence of past and future entities and facts concerning them that do not obtain in the present, she seems to lack the resources to (...) accept both past and future-tensed truths and the TSB Principle. Contrariwise, positions in philosophy of time that accept an eternalist ontology (e.g., B-theory, moving spotlight, and Fine’s and Lipman’s versions of fragmentalism) allow for a “direct” supervenience base for past- and future-tensed truths. We argue that Flow Fragmentalism constitutes a middle ground, which retains most of the advantages of both views, and allows us to articulate a novel account of the passage of time. (shrink)

Both communitarianism and casuistry have sought to restore ethics as a practical science—the former by incorporating various traditions into a shared definition of the common good, the latter by considering the circumstances of each situation through critical reasoning. Mark G. Kuczewski analyzes the origins and methods of these two approaches and forges from them a new unified approach. This approach takes the communitarian notion of the person as its starting point but also relies upon the narrative and analogical tools of (...) case-based reasoning. He separates out the rhetoric that is incongruent with the Aristotelian aspirations of each method to show that the two are complementary, and that consensus can emerge from fragmentation. He then applies his resulting method to three major problems in bioethics: the difficulties that the issue of personal identity poses for advance directives, the role of the family in medical decision making, and the refusal of treatment because of religious beliefs. He analyzes the need to assume a communitarian notion of the person as a starting point for the application of casuistic insights. Combining theoretical, practical, and scholarly insights, this book will be of interest to philosophers, political and social scientists, and bioethicists. (shrink)

In order to predict and explain behavior, one cannot specify the mental state of an agent merely by saying what information she possesses. Instead one must specify what information is available to an agent relative to various purposes. Specifying mental states in this way allows us to accommodate cases of imperfect recall, cognitive accomplishments involved in logical deduction, the mental states of confused or fragmented subjects, and the difference between propositional knowledge and know-how .

By a fragment of a natural language we mean a subset of thatlanguage equipped with semantics which translate its sentences intosome formal system such as first-order logic. The familiar conceptsof satisfiability and entailment can be defined for anysuch fragment in a natural way. The question therefore arises, for anygiven fragment of a natural language, as to the computational complexityof determining satisfiability and entailment within that fragment. Wepresent a series of fragments of English for which the satisfiabilityproblem is polynomial, NP-complete, EXPTIME-complete,NEXPTIME-complete (...) and undecidable. Thus, this paper represents a casestudy in how to approach the problem of determining the logicalcomplexity of various natural language constructions. In addition, wedraw some general conclusions about the relationship between naturallanguage and formal logic. (shrink)

Belief storage is often modeled as having the structure of a single, unified web. This model of belief storage is attractive and widely assumed because it appears to provide an explanation of the flexibility of cognition and the complicated dynamics of belief revision. However, when one scrutinizes human cognition, one finds strong evidence against a unified web of belief and for a fragmented model of belief storage. Using the best available evidence from cognitive science, we develop this fragmented model into (...) a nascent theory of the cognitive architecture of belief storage. (shrink)

By a theorem of R. Kaye, J. Paris and C. Dimitracopoulos, the class of the Πn+1-sentences true in the standard model is the only consistent Πn+1-theory which extends the scheme of induction for parameter free Πn+1-formulas. Motivated by this result, we present a systematic study of extensions of bounded quantifier complexity of fragments of first-order Peano Arithmetic. Here, we improve that result and show that this property describes a general phenomenon valid for parameter free schemes. As a consequence, we obtain (...) results on the quantifier complexity, finite axiomatizability and relative strength of schemes for Δn+1-formulas. (shrink)

The idea of fragmentalism has been proposed by Kit Fine as a non-standard view of tense realism. This paper examines a modal version of the view, called modal fragmentalism, which combines genuine realism and realism of modality. Modal fragmentalism has been recently discussed by Iaquinto. But unlike Iaquinto, who primarily focused on possibilities de re, in this paper, we focus on expressions of possibilities de dicto. We argue that the chief idea of modal realism should be that (...) different worlds are distinguished not just in terms of how things are differently with respect to each world, but also in terms of how things could have been differently with respect to each world. This demands a realism-oriented semantics for suppositional contents, and more specifically, for conditionals. By deploying a multidimensional semantics for conditionals, we show that there are good reasons to consider modal fragmentalism as a serious approach in metaphysics, which shares many similarities with the fragmentalism of tense. (shrink)

Fragmentalism allows incompatible facts to constitute reality in an absolute manner, provided that they fail to obtain together. In recent years, the view has been extensively discussed, with a focus on its formalisation in model-theoretic terms. This paper focuses on three formalisations: Lipman’s approach, the subvaluationist interpretation, and a novel view that has been so far overlooked. The aim of the paper is to explore the application of these formalisations to the alethic modal case. This logical exploration will allow (...) us to study (i) cases of metaphysical incompatibility between modal facts and (ii) cases of modal dialetheias. In turn, this will enrich our understanding of the role of impossibility in the fragmentalist framework. (shrink)

According to perspectival realism, reality is (at least partially) constituted by “purely perspectival” facts, that is, facts that appear to describe reality only from a given “perspective”. Fragmentalism is a form of perspectival realism that maintains both that no perspective is privileged and that perspectival facts constitute reality absolutely. Assuming that reality is sufficiently variegated, fragmentalism entails that reality is absolutely constituted by incompatible facts. Given that incompatible facts can never obtain together, reality must be divided into a (...) plurality of “fragments” that never compose a coherent, unitary whole. The main aim of this paper is to provide the first rigorous, detailed map of fragmentalism and its rivals. First, we will argue that fragmentalism is best construed as having two “unitist” (that is, non-fragmentalist) boundaries, which we will call ‘coherent’ and ‘incoherent unitism’. Second, we will present what we take to be the six main viable versions of fragmentalism and show how they can be categorized according to whether they take the logical operations of conjunction and negation to be either “local” or “global”. (shrink)

Online communication is often seen to promote audience fragmentation because it facilitates selective exposure and therefore is likely to divide audiences into sub-publics that hardly share common issues with other sub-publics. This study takes a micro-perspective on fragmentation by focusing on issue diversity in media items users have encountered in a particular week. Diversity was assessed via content analyses based on online diaries of 645 participants who recorded their media use concerning the German debates on climate change and federal elections. (...) Findings show lower degrees of diversity for users of non-journalistic online media than for users of journalistic mass media. (shrink)

The thesis of mental fragmentation has recently attracted increased attention as a way of explaining facts about mind and language. This volume provides an accessible introduction and essays on foundations and applications of fragmentation.

Bayesian confirmation theory is our best formal framework for describing inductive reasoning. The problem of old evidence is a particularly difficult one for confirmation theory, because it suggests that this framework fails to account for central and important cases of inductive reasoning and scientific inference. I show that we can appeal to the fragmentation of doxastic states to solve this problem for confirmation theory. This fragmentation solution is independently well-motivated because of the success of fragmentation in solving other problems. I (...) also argue that the fragmentation solution is preferable to other solutions to the problem of old evidence. These other solutions are already committed to something like fragmentation, but suffer from difficulties due to their additional commitments. If these arguments are successful, Bayesian confirmation theory is saved from the problem of old evidence, and the argument for fragmentation is bolstered by its ability to solve yet another problem. (shrink)

Fragments of Modernity provides a critical introduction to the work of three of the most original German thinkers of the early 20th century. In their different ways, all three illuminated the experience of the modern in urban life, whether in mid-19th-century Paris or in Berlin at the turn of the century or later as the vanguard city of the Weimar Republic. They related the new modes of experiencing the world to the maturation of the money economy (Simmel), the process of (...) rationalization of capital (Kracauer), and the fantasy world of commodity fetishism (Benjamin) - in each case focusing on those fragments of social experience that could best capture the sense of modernity.David Frisby is Reader in Sociology at Glasgow University. Fragments of Modernity is included in the series Studies in Contemporary German Social Thought, edited by Thomas McCarthy. (shrink)

We show that large fragments of MM, e. g. the tree property and stationary reflection, are preserved by strongly -game-closed forcings. PFA can be destroyed by a strongly -game-closed forcing but not by an ω2-closed.

Dealing with and collecting fragments has always been one of the core tasks of scholars of classical antiquity, especially classical philologists. As an examination of the relevant editions and treatises reveals, there is no agreement on what a ‘fragment’ should be. This also has to do with the polysemy of this term, which has gained a new and wider understanding, especially since the Romantic period. In the present contribution it is therefore suggested that the term ‘testimony text’ (‘Zeugnistext’) should be (...) used instead of ‘fragment’. In this way, it is also possible to avoid an editorial pre-determination regarding the authenticity of the testimonies in question. Furthermore, the question of the contextualization of the respective testimony texts will be discussed and suggestions for the practice of their presentation will be made. (shrink)

We study the long-standing open problem of giving$\forall {\rm{\Sigma }}_1^b$separations for fragments of bounded arithmetic in the relativized setting. Rather than considering the usual fragments defined by the amount of induction they allow, we study Jeřábek’s theories for approximate counting and their subtheories. We show that the$\forall {\rm{\Sigma }}_1^b$Herbrandized ordering principle is unprovable in a fragment of bounded arithmetic that includes the injective weak pigeonhole principle for polynomial time functions, and also in a fragment that includes the surjective weak pigeonhole (...) principle for FPNPfunctions. We further give new propositional translations, in terms of random resolution refutations, for the consequences of$T_2^1$augmented with the surjective weak pigeonhole principle for polynomial time functions. (shrink)

Many philosophical debates take for granted that there is such a thing as ‘the’ common-sense conception of the phenomenon of interest. Debates about the nature of perception tend to take for granted that there is a single, coherent common-sense conception of vision, consistent with Direct Realism. This conception is often accorded an epistemic default status. We draw on philosophical and psychological literature on naïve theories and belief fragmentation to motivate the hypothesis that untutored common sense encompasses conflicting Direct Realist and (...) Indirect Realist conceptions: there is no such thing as ‘the’ common-sense conception of vision that could enjoy epistemic default status. To examine this hypothesis, a survey administered an agreement rating task with verbal and pictorial stimuli to lay participants. We found many laypeople simultaneously hold conflicting Direct Realist and Indirect Realist beliefs about vision. Against common assumptions, Direct Realist beliefs are not clearly dominant, and consistent adherence to Direct Realism is not the norm, but the exception. These findings are consistent with recent accounts of belief fragmentation. They forcefully challenge common methodology in philosophical debates about the nature of perception and beyond. (shrink)

Online targeting isolates individual consumers, causing what we call epistemic fragmentation. This phenomenon amplifies the harms of advertising and inflicts structural damage to the public forum. The two natural strategies to tackle the problem of regulating online targeted advertising, increasing consumer awareness and extending proactive monitoring, fail because even sophisticated individual consumers are vulnerable in isolation, and the contextual knowledge needed for effective proactive monitoring remains largely inaccessible to platforms and external regulators. The limitations of both consumer awareness and of (...) proactive monitoring strategies can be attributed to their failure to address epistemic fragmentation. We call attention to a third possibility that we call a civic model of governance for online targeted advertising, which overcomes this problem, and describe four possible pathways to implement this model. (shrink)

In a series of five experiments, we demonstrate that moral judgments and folk intuitions are often predictably fragmented. Drawing on the domains of ethics and action theory, we illustrate ways in which judgment tends to be associated with stable individual differences such as personality traits and reflective cognitive styles. We argue that these individual differences pose several unique challenges as well as provide opportunities for further theoretical development in the emerging field of experimental philosophy. Implications are briefly discussed.

The maqālāt of Abū Qāsim al-Balḫī contain several passages devoted to legal theory. The most important source found there is some extracts of K. al-futyā, a legal treatise by al-Ǧāḥiẓ of which until now only fragments remained, containing the criticisms addressed by al-Naẓẓām to the companions of the Prophet. This article provides a translation of these new extracts preceded by a study of the text and its place in the history of legal theory during this formative period of Islamic thought.

Hermann Diels, professor of classics at Berlin, is chiefly remembered for this collection of quotations from, and reports about, Presocratic philosophers; his system of numbering was later adopted as the scholarly standard. This reissue reproduces the original, single-volume edition of 1903, though the book was revised and expanded three times during Diels' lifetime, and again after his death, and new fragments continue to be discovered. Designed as a reference tool to underpin university classes on the beginnings of Greek philosophy, the (...) book sought to enable students to engage with original evidence. Diels aimed to provide a complete corpus of fragments rather than an arbitrary selection. He intentionally reproduced the texts exactly rather than standardising the language, in order to provide a foundation for future research. While admitting he found the material obscure at times, Diels provided German translations to help make the content more accessible to his readers. (shrink)

Brenda Almond throws down a timely challenge to liberal consensus about personal relationships. She maintains that the traditional family is fragmenting in Western societies, causing serious social problems. She urges that we reconsider our attitudes to sex and reproduction in order to strengthen our most important social institution, the family.

The author deals with the lost works of Empedocles, an often neglected subject, in the frame of the discussion concerning the number of the poems and their main features. He reviews the traces of the Passage of Xerxes, of the Medical Discourse, and of the Proem to Apollo among the fragments and witnesses, taking his cue from textual aspects and dealing with the contents, the significance of each of these writings in Empedocles’ culture and thought and their multifarious relationships with (...) his times. As to the Passage, he tries to reconcile the contrasting interpretations so far proposed (historical or religious poem). Concerning B111, the only relic from the Medical Discourse, he explains why its contents are incompatible with the Physical Poem and the Purifications. He analyzes the Proem to Apollo in several perspectives (text, witnesses, contents also from the epistemological point of view, literary genre). He assigns fragments 131–134 and 142 to the Proem, drawing one of his arguments from the comparison with the third Homeric Hymn to Apollo, and also suggesting a relationship with an intellectual cult of the sun. Formal features help to ascribe each fragment to the relevant poem. Close similarities between fragments do not necessarily mean that they come from the same writing: Empedocles is wont to allude to one poem of his while composing another. The author concludes that the striving for a reductio ad unum of the Acragantine’s output, also evident in the attempt by a number of scholars to make only one poem out of the Περὶ φύσεως and the Καθαρμοί, has often led researchers to take for granted that none of the fragments preserved might belong to the lost works. (shrink)

This paper explores taste fragmentalism, a novel approach to matters of taste and faultless disagreement. The view is inspired by Kit Fine’s fragmentalism about time, according to which the temporal dimension can be constituted—in an absolute manner—by states that are pairwise incompatible, provided that they do not obtain together. In the present paper, we will apply this metaphysical framework to taste states. In our proposal, two incompatible taste states (such as the state of rhubarb’s being tasty and the (...) state of rhubarb’s being distasteful) can both constitute reality in an absolute manner, although no agent can have joint access to both states. We will then develop a formalised version of our view by means of an exact truthmaker semantics for taste assertions. Within this framework—we argue—our linguistic and inferential practices concerning cases of faultless disagreement are elegantly vindicated, thus suggesting that taste fragmentalism is worth of further consideration. (shrink)

Une centaine de fragments inédits attribués au plus célèbre représentant de l'Ecole cynique sommeillait depuis près de 2 500 ans sous le doux soleil d'Orient. La voix de Diogène de Sinope, le philosophe-chien, l'homme au tonneau qui embrasse les statues l'hiver, retraverse les âges. Au terme d'une véritable chasse au trésor remontant jusqu'aux penseurs arabes du Xe siècle, Adeline Baldacchino propose pour la première fois en langue française ces nouveaux fragments. On y retrouve avec délice le Diogène insolent dont les (...) paraboles sont si riches d'enseignements. Maître de l'invective, il témoigne de son amour de la vie, de son intransigeance et de sa résistance au pouvoir. Une occasion unique de redécouvrir l'esprit cynique, sa force critique, sa passion pour la liberté et son invraisemblable modernité. (shrink)

Considerable fragmentation, and awareness of it, have characterized the field of psychology since its inception. It is suggested that over the years, efforts to reduce uncertainty and overcome fragmentation in psychology have clustered around two broad, opposite strategies which might be termed "scientism" and "constructionism." The first wishes to rely on secure methods and controlled experimentation, the second on a postmodern acceptance of radical heterogeneity and "no truth through method." Some of the shortcomings of these strategies are discussed. A hermeneutic (...) approach centering on dialogue and the idea of social inquiry as a kind of ethical practice is outlined which, it is argued, might have success in incorporating some of the virtues and avoiding the pitfalls of other responses to the problem of fragmentation. (shrink)

Frege's Grundgesetze was one of the 19th century forerunners to contemporary set theory which was plagued by the Russell paradox. In recent years, it has been shown that subsystems of the Grundgesetze formed by restricting the comprehension schema are consistent. One aim of this paper is to ascertain how much set theory can be developed within these consistent fragments of the Grundgesetze, and our main theorem shows that there is a model of a fragment of the Grundgesetze which defines a (...) model of all the axioms of Zermelo-Fraenkel set theory with the exception of the power set axiom. The proof of this result appeals to G\"odel's constructible universe of sets, which G\"odel famously used to show the relative consistency of the continuum hypothesis. More specifically, our proofs appeal to Kripke and Platek's idea of the projectum within the constructible universe as well as to a weak version of uniformization (which does not involve knowledge of Jensen's fine structure theory). The axioms of the Grundgesetze are examples of abstraction principles, and the other primary aim of this paper is to articulate a sufficient condition for the consistency of abstraction principles with limited amounts of comprehension. As an application, we resolve an analogue of the joint consistency problem in the predicative setting. (shrink)

Fragmentary utterances such as short answers and subsentential XPs without linguistic antecedents are proposed to have fully sentential syntactic structures, subject to ellipsis. Ellipsis in these cases is preceded by A-movement of the fragment to a clause-peripheral position; the combination of movement and ellipsis accounts for a wide range of connectivity and anti-connectivity effects in these structures. Fragment answers furthermore shed light on the nature of islands, and contrast with sluicing in triggering island effects; this is shown to follow from (...) an articulated syntax and the PF theory of islands. Fragments without linguistic antecedents are argued to be compatible with an ellipsis analysis, and do not support direct interpretation approaches to these phenomena. (shrink)

We consider the problem whether the $\forall \Sigma _{1}^{b}$ theorems of the fragments $T_{2}^{a}$ form a strictly increasing hierarchy. We shall show a link to some results about the lengths of proofs in predicate logic that supports the conjecture that the hierarchy is strictly increasing.

This paper argues that what is currently the most popular version of temporal Fragmentalism—‘unstructured’ temporal Fragmentalism, as I shall call it—faces a problem of Tensed Belief Explosion. Four possible solutions to this problem are reviewed and shown to be wanting; two more promising ones risk fostering scepticism about the existence of tensed facts—hence, about Fragmentalism itself. The tentative moral is that unstructured versions of Fragmentalism are at best unmotivated and at worst seriously flawed.

Frege Arithmetic (FA) is the second-order theory whose sole non-logical axiom is Hume’s Principle, which says that the number of F s is identical to the number of Gs if and only if the F s and the Gs can be one-to-one correlated. According to Frege’s Theorem, FA and some natural definitions imply all of second-order Peano Arithmetic. This paper distinguishes two dimensions of impredicativity involved in FA—one having to do with Hume’s Principle, the other, with the underlying second-order logic—and (...) investigates how much of Frege’s Theorem goes through in various partially predicative fragments of FA. Theorem 1 shows that almost everything goes through, the most important exception being the axiom that every natural number has a successor. Theorem 2 shows that the Successor Axiom cannot be proved in the theories that are predicative in either dimension. (shrink)

We investigate monadic fragments of Intuitionistic Control Logic, which is obtained from Intuitionistic Propositional Logic by extending language of IPL by a constant distinct from intuitionistic constants. In particular we present the complete description of purely negational fragment and show that most of monadic fragments are finite.

This is a review of Kris McDaniel's book, 'The Fragmentation of Being'. In the book McDaniel defends ontological pluralism -- the doctrine that there are multiple 'ways of being' (i.e., multiple modes, or degrees, or orders, or levels, or gradations of existence). In defending ontological pluralism, McDaniel must reject the rival, Quinean position that there is at root just one generic way for a thing to exist: viz., by its falling in the domain of unrestricted quantification. McDaniel argues against Quine (...) by contending that the unrestricted quantifier is really just shorthand for a ‘gruesome’ disjunction of restricted quantifiers. On McDaniel's view, the unrestricted quantifier plays ontological 'second fiddle' to these restricted quantifiers, which are ontologically fundamental, and which each represent one particular mode of being. Against this, I contend that if the disjunction in question was as gruesome as McDaniel makes out then logic would be apt to explode in our faces. If I am right then McDaniel's response to Quine falls flat. (shrink)

Fragments from Dinnaga. H. N. Randle. Motilal Banarsidass, Delhi 1981. xii + 93 pp. Rs. 40.

This is the second of a series of papers that investigate fragments of quasi-Nelson logic (QNL) from an algebraic logic standpoint. QNL, recently introduced as a common generalization of intuitionistic and Nelson’s constructive logic with strong negation, is the axiomatic extension of the substructural logic |$FL_{ew}$| (full Lambek calculus with exchange and weakening) by the Nelson axiom. The algebraic counterpart of QNL (quasi-Nelson algebras) is a class of commutative integral residuated lattices (a.k.a. |$FL_{ew}$|-algebras) that includes both Heyting and Nelson algebras (...) and can be characterized algebraically in several alternative ways. The present paper focuses on the algebraic counterpart (a class we dub quasi-Nelson implication algebras, QNI-algebras) of the implication–negation fragment of QNL, corresponding to the connectives that witness the algebraizability of QNL. We recall the main known results on QNI-algebras and establish a number of new ones. Among these, we show that QNI-algebras form a congruence-distributive variety (Cor. 3.15) that enjoys equationally definable principal congruences and the strong congruence extension property (Prop. 3.16); we also characterize the subdirectly irreducible QNI-algebras in terms of the underlying poset structure (Thm. 4.23). Most of these results are obtained thanks to twist representations for QNI-algebras, which generalize the known ones for Nelson and quasi-Nelson algebras; we further introduce a Hilbert-style calculus that is algebraizable and has the variety of QNI-algebras as its equivalent algebraic semantics. (shrink)

The current system of international law is experiencing profound transformations. Indeed, the simultaneous processes of globalization combined with the disintegration of international systems of governance and law-making pose complex challenges for legal scholarship. The doctrinal response to these challenges has been theorized within two seemingly contradictory discourses in international law: fragmentation and constitutionalisation. This book takes an innovative approach to international law, viewing the processes of the fragmentation and constitutionalisation as being profoundly interconnected and reflective of each other. It brings (...) together a select group of contributors, including both established and emerging scholars and practitioners, in order to explore the ways in which the problems of fragmentation and constitutionalisation are viscerally linked one to the other and thus mutually conditioning and stimulating. The book considers the theory and practice of international law looking at the two phenomena in relation to the various fields of international law such as international criminal law, cultural heritage law and international environmental law. (shrink)