The central aim of this paper is to present a Boolean algebraic approach to the classical Aristotelian Relations of Opposition, namely Contradiction and (Sub)contrariety, and to provide a 3D visualisation of those relations based on the geometrical properties of Platonic and Archimedean solids. In the first part we start from the standard Generalized Quantifier analysis of expressions for comparative quantification to build the Comparative Quantifier Algebra CQA. The underlying scalar structure allows us to define the Aristotelian relations in Boolean terms (...) and to propose a 3D visualisation by transforming a cube into an octahedron. In part two, the architecture of the CQA is shown to carry over, both to the classical quantifiers of Predicate Calculus and to the modal operators—which are given a Generalized Quantifier style re-interpretation. In this way we provide an algebraic foundation for Blanché’s Aristotelian hexagon as well as a 3D alternative to his 2D star-like visualisation. In a final part, a richer scalar structure is argued to underly the realm of Modality, thus generalizing the 3D algebra with eight (2 3 ) operators to a 4D algebra with sixteen (2 4 ) operators. The visual representation of the latter structure involves a transformation of the hypercube to a rhombic dodecahedron. The resulting 3D visualisation allows a straightforward embedding, not only of the classical Blanché star of Aristotelian relations or the paracomplete and paraconsistent stars of Béziau (Log Investig 10, 218–232, 2003) but also of three additional isomorphic Aristotelian constellations. (shrink)

Peters and Westerståhl (Quantifiers in Language and Logic, 2006), and Westerståhl (New Perspectives on the Square of Opposition, 2011) draw a crucial distinction between the “classical” Aristotelian squares of opposition and the “modern” Duality squares of opposition. The classical square involves four opposition relations, whereas the modern one only involves three of them: the two horizontal connections are fundamentally distinct in the Aristotelian case (contrariety, CR vs. subcontrariety, SCR) but express the same Duality relation of internal negation (SNEG). Furthermore, the (...) vertical relations in the classical square are unidirectional, whereas in the modern square they are bidirectional. The present paper argues that these differences become even bigger when two more operators are added, namely the U ( ${{\equiv} {\rm A}\,{\vee} \,{\rm E} }$ , all or no) and Y ( ${\equiv{\rm I} \,{\wedge} \,{\rm O}}$ , some but not all) of Blanché (Structures Intellectuelles, 1969). In the resulting Aristotelian hexagon the two extra nodes are perfectly integrated, yielding two interlocking triangles of CR and SCR. In the duality hexagon by contrast, they do not enter into any relation with the original square, but constitute a independent pair of their own, since they are their own SNEGs. Hence, they not only stand in a relation of external NEG, but also in one of duality. This reflexive nature of the SNEG will be shown to result in defective monotonicity configurations for the pair, namely the absence of right-monotonicity (on the predicate argument). In the second half of the paper, we present an overview of those hexagonal structures which are both Aristotelian and Duality configurations, and those which are only Aristotelian. (shrink)

In this paper we provide an analysis of the logical relations within the conceptual or lexical field of angles in 2D geometry. The basic tripartition into acute/right/obtuse angles is extended in two steps: first zero and straight angles are added, and secondly reflex and full angles are added, in both cases extending the logical space of angles. Within the framework of logical geometry, the resulting partitions of these logical spaces yield bitstring semantics of increasing complexity. These bitstring analyses allow a (...) straightforward account of the Aristotelian relations between angular concepts. In addition, also relational concepts such as complementary and supplementary angles receive a natural bitstring analysis. (shrink)

This paper presents a generalization of the standard notions of left monotonicity (on the nominal argument of a determiner) and right monotonicity (on the VP argument of a determiner). Determiners such as “more than/at least as many as” or “fewer than/at most as many as”, which occur in so-called propositional comparison, are shown to be monotone with respect to two nominal arguments and two VP-arguments. In addition, it is argued that the standard Generalized Quantifier analysis of numerical determiners such as (...) “more than three/at least three” is a simplification which ignores the fundamental parallellism with the propositional comparatives. Furthermore, the symmetric monotonicity configurations of the existential “some” and “no” are shown to be straightforwardly related to those of numerical comparatives with the limit numeral zero, whereas the asymmetric configurations of universal “all” and “not all” involve the extra complicating mechanism of polarity reversal, which is related to Keenan's notion of co-intersectivity (as opposed to intersectivity). A second aim of the paper is to investigate some of the factors reducing the inferential potential of determiners. Different types of comparative determiners and their modification will be considered in detail. In addition, a systematic interaction will be revealed between the monotonicity properties of the determiners in propositional comparatives and the differ ent types of ellipsis in the “than”-complement. Different degrees of ellipsis are defined in terms of informational dependencies between the “than”-complement and the main clause. A general balancing mechanism is observed by virtue of which an increase in informational dependency is compensated by a reduction of the inferential potential of the comparative determiner. The structure of the paper is as follows. Part two deals with propositional comparison and introduces the two basic monotonicity configurations. Part three distinguishes three types of informational dependencies or ellipsis between the “than”-complement and the main clause. In Section 3.1 the “than”-complement only contains a VP constituent, whereas in Section 3.2. it only consists of a nominal constituent. Section 3.3 considers more complex instances of multiple dependencies. Section 3.4 then looks at the interaction of these three types with the modifier “proportionally”. Part four presents the two basic monotonicity configurations for numerical comparison, whereas part five deals with more complex numerical determiners. Bounding determiners, such as “between five and ten”, and other boolean combinations are discussed in Section 5.1, whereas Section 5.2 goes into approximative determiners involving modifiers such as “only” or “almost”. Section 5.3. is devoted to proportional determiners such as “more than two out of three”. Part six then considers the standard existential and universal quantifiers. Section 6.1 reformulates the standard Generalized Quantifier analysis in comparative terms, whereas Section 6.2 deals with exception determiners of the form “all but five”. (shrink)

Duality in Logic and Language [draft--do not cite this article] Duality phenomena occur in nearly all mathematically formalized disciplines, such as algebra, geometry, logic and natural language semantics. However, many of these disciplines use the term ‘duality’ in vastly different senses, and while some of these senses are intimately connected to each other, others seem to be entirely … Continue reading Duality in Logic and Language →.

Validity of dynamic temporal reasoning is semantically characterized for English and Dutch aspectual adverbs in Discourse Representation Theory. This dynamic perspective determines how the content needs to be revised and what information is preserved across updates, when the order of premises is considered relevant. Resetting contextual parameters relies on modelling the basic aspectual polarity transitions and temporal reasoning extensionally. For intensional aspectual adverbials the speaker’s attitudes regarding past alternatives to and possible continuations of the current state come into play. Additional (...) considerations are offered for generalizing this system to the full logical space for linguistic universals, lexicalized quite differently in Dutch and English. (shrink)

In recent years, a number of authors have started studying Aristotelian diagrams containing metalogical notions, such as tautology, contradiction, satisfiability, contingency, strong and weak interpretations of contrariety, etc. The present paper is a contribution to this line of research, and its main aims are both to extend and to deepen our understanding of metalogical diagrams. As for extensions, we not only study several metalogical decorations of larger and less widely known Aristotelian diagrams, but also consider metalogical decorations of another type (...) of logical diagrams, viz. duality diagrams. At a more fundamental level, we present a unifying perspective which sheds new light on the connections between new and existing metalogical diagrams, as well as between object- and metalogical diagrams. Overall, the paper studies two types of logical diagrams and four kinds of metalogical decorations. (shrink)

Inferential or epistemic conditional sentences represent a blueprint of someone’s reasoning process from premise to conclusion. Declerck and Reed (2001) make a distinction between a direct and an indirect type. In the latter type the direction of reasoning goes backwards, from the blatant falsehood of the consequent to the falsehood of the antecedent. We first present a modal reinterpretation in terms of Argumentation Schemes of indirect inferential conditionals (IIC’s) in Declerck and Reed (2001). We furthermore argue for a distinction between (...) epistemic-modal strong and deontic-modal weak IIC’s. In addition, we extend the category of the indirect inferential conditionals in order to include several other deontic-modal subtypes. On the basis of the undesirability of the consequent the hearer in these cases infers that the antecedent is also undesirable. In this way the rhetoric-argumentative strategy of Reductio ad Absurdum is extended from the realm of deductive reasoning to that of practical reasoning. (shrink)

The Aristotelian square of oppositions is a well-known diagram in logic and linguistics. In recent years, several extensions of the square have been discovered. However, these extensions have failed to become as widely known as the square. In this paper we argue that there is indeed a fundamental difference between the square and its extensions, viz., a difference in informativity. To do this, we distinguish between concrete Aristotelian diagrams and, on a more abstract level, the Aristotelian geometry. We then introduce (...) two new logical geometries, and develop a formal, well-motivated account of their informativity. This enables us to show that the square is strictly more informative than many of the more complex diagrams. (shrink)

This paper decentres the predominance of statism and deliberation in ecological democracy scholarship. We use insights from eco-anarchism and cosmopolitics to identify democratic configurations beyond capitalism and its entanglement with the nation-state. These configurations are premised on the idea that sustainability transformation not only implies a move beyond capitalism and the nation-state, but might comprise their dismantling. We propose and apply an analytical framework encompassing the dimensions actors, praxis and processes and institution(s) to contrast these three political theories and bring (...) forward a diversity of democratic praxes that revolve around the generation of autonomy and the building of multispecies political communities. Finally, we discuss transformation possibilities from within the capitalist nation-state and propose research directions for post-statist, autonomous and diverse ecological democracies. (shrink)

This book presents an innovative reading of Daoist philosophy that highlights the critical and therapeutic functions of satire and humor. Moeller and D'Ambrosio show how the Zhuangzi expounds the Daoist art of "genuine pretending" the paradoxical skill of enacting social roles without submitting to them or letting them define one's identity.

This paper compares two 3D logical diagrams for the Boolean algebra B4, viz. the rhombic dodecahedron and the nested tetrahedron. Geometric properties such as collinearity and central symmetry are examined from a cognitive perspective, focussing on diagram design principles such as congruence/isomorphism and apprehension.

Logical geometry systematically studies Aristotelian diagrams, such as the classical square of oppositions and its extensions. These investigations rely heavily on the use of bitstrings, which are compact combinatorial representations of formulas that allow us to quickly determine their Aristotelian relations. However, because of their general nature, bitstrings can be applied to a wide variety of topics in philosophical logic beyond those of logical geometry. Hence, the main aim of this paper is to present a systematic technique for assigning bitstrings (...) to arbitrary finite fragments of formulas in arbitrary logical systems, and to study the logical and combinatorial properties of this technique. It is based on the partition of logical space that is induced by a given fragment, and sheds new light on a number of interesting issues, such as the logic-dependence of the Aristotelian relations and the subtle interplay between the Aristotelian and Boolean structure of logical fragments. Finally, the bitstring technique also allows us to systematically analyze fragments from contemporary logical systems, such as public announcement logic, which could not be done before. (shrink)

© Springer International Publishing AG, part of Springer Nature 2018. The aim of this paper is to lay out the foundations of a typology of diagrams in linguistics. We draw a distinction between linguistic parameters — concerning what information is being represented — and diagrammatic parameters — concerning how it is represented. The six binary linguistic parameters of the typology are: mono- versus multilingual, static versus dynamic, mono- versus multimodular, object-level versus meta-level, qualitative versus quantitative, and mono- versus interdisciplinary. The (...) two diagrammatic parameters are iconic/concrete versus symbolic/abstract representation and static versus dynamic representation. We briefly illustrate how different types of linguistic diagrams can be analysed in terms of the interaction between the linguistic and the diagrammatic parameters. (shrink)

I LAW AND NATURE i. The "Pure" Theory The Pure Theory of Law is a theory of positive law. It is a theory of positive law in general, not of a specific legal ...

erster Teilband. Grundlegung -- zweiter Teilband. Tragweite und Aktualität einer Zukunftsethik.

© Springer International Publishing AG, part of Springer Nature 2018. Nearly all squares of opposition found in the literature represent both the Aristotelian relations and the duality relations, and exhibit a very close correspondence between both types of logical relations. This paper investigates the interplay between Aristotelian and duality relations in diagrams beyond the square. In particular, we study a Buridan octagon, a Lenzen octagon, a Keynes-Johnson octagon and a Moretti octagon. Each of these octagons is a natural extension of (...) the square, both from an Aristotelian perspective and from a duality perspective. The results of our comparative analysis turn out to be highly nuanced. (shrink)

© Springer International Publishing Switzerland 2016. We develop a systematic approach for dealing with informationally equivalent Aristotelian diagrams, based on the interaction between the logical properties of the visualized information and the geometrical properties of the concrete polygon/polyhedron. To illustrate the account’s fruitfulness, we apply it to all Aristotelian families of 4-formula fragments that are closed under negation and to all Aristotelian families of 6-formula fragments that are closed under negation.

"Social ontology, conventionally defined, is not primarily about us. Rather, it is about the social world (or worlds), about social reality (or realities), or about the domain(s) of social facts. Social ontology aims at providing an inventory of the basic kinds of entities that make up the social world(s) - items such as norms, institutions, social practices, status positions, power structures, and artifacts. It is the study of the basic kinds of properties of these entities, and of how the social (...) world exists, how it is constituted, or constructed"--. (shrink)

1947 legt Hans Blumenberg aus Bargteheide in Holstein an der Christian-Albrechts-Universität zu Kiel seine unter schwierigsten persönlichen Umständen entstandene Dissertation 'Beiträge zum Problem der Ursprünglichkeit der mittelalterlich-scholastischen Ontologie" vor. Hinter diesem Titel verbirgt sich eine mit ständigem Bezug auf die Philosophie Heideggers und seine "Fundamentalontologie' geführte Auseinandersetzung mit dem Denken des christlichen Mittelalters, in dem die Frage nach dem Grund des Seins eine so krisenhafte wie produktive Zuspitzung erfahren hatte. Die Dissertation wird von den Gutachtern Ludwig Landgrebe und Rudolf (...) Schneider mit "ausgezeichnet" bewertet, aber sämtliche Bemühungen, zeitnah einen Verlag für die Arbeit zu finden, scheitern. Blumenbergs brillantes Erstlingswerk blieb mehr als 70 Jahre ungedruckt. Nun wird es erstmals publiziert in einer leserorientierten Edition, die unter anderem Übersetzungen der zahlreichen altsprachlichen Zitate wie auch ein "Verzeichnis der Referenzliteratur" bietet, das die Lücke des im Original fehlenden Literaturverzeichnisses schliesst und dieses darüber hinaus durch heute zugängliche Ausgaben ergänzt. In ihrem Nachwort beleuchten die Herausgeber den Entstehungskontext dieses Werks, das überraschende Perspektiven auf Blumenbergs Biographie und Denkentwicklung eröffnet. (shrink)

© 2017 by the authors. Aristotelian diagrams visualize the logical relations among a finite set of objects. These diagrams originated in philosophy, but recently, they have also been used extensively in artificial intelligence, in order to study various knowledge representation formalisms. In this paper, we develop the idea that Aristotelian diagrams can be fruitfully studied as geometrical entities. In particular, we focus on four polyhedral Aristotelian diagrams for the Boolean algebra B4, viz. the rhombic dodecahedron, the tetrakis hexahedron, the tetraicosahedron (...) and the nested tetrahedron. After an in-depth investigation of the geometrical properties and interrelationships of these polyhedral diagrams, we analyze the correlation between logical and geometrical distance in each of these diagrams. The outcome of this analysis is that the Aristotelian rhombic dodecahedron and tetrakis hexahedron exhibit the strongest degree of correlation between logical and geometrical distance; the tetraicosahedron performs worse; and the nested tetrahedron has the lowest degree of correlation. Finally, these results are used to shed new light on the relative strengths and weaknesses of these polyhedral Aristotelian diagrams, by appealing to the congruence principle from cognitive research on diagram design. (shrink)

This volume provides the first English translation of Hans Kelsen's and Carl Schmitt's influential Weimar-era debate on constitutional guardianship and the legitimacy of constitutional review. It includes Kelsen's seminal piece, 'The Nature and Development of Constitutional Adjudication', as well as key extracts from the 'Guardian of the Constitution' which present Schmitt's argument against constitutional review. Also included are Kelsen's review of Schmitt's 'Guardian of the Constitution', as well as some further material by Kelsen and Schmitt on presidential dictatorship under (...) Article 48 of the Weimar Constitution. These texts show Kelsen and Schmitt responding to one another, in the context of a debate focused on a concrete constitutional crisis, thus allowing the reader to assess the plausibility of Kelsen's and Schmitt's legal and constitutional theories. (shrink)

Das Buch gibt einen Überblick über die Arbeiten von Hans Albert und behandelt ausgewählte Konsequenzen seines Werks für die Philosophie des Kritischen Rationalismus und ihre Anwendungen in Gebieten der Soziologie, Wirtschaftswissenschaften, Rechtswissenschaften und weiteren Wissenschaften.

© 2018, Springer International Publishing AG, part of Springer Nature. Aristotelian diagrams are used extensively in contemporary research in artificial intelligence. The present paper investigates the geometric and cognitive differences between two types of Aristotelian diagrams for the Boolean algebra B4. Within the class of 3D visualizations, the main geometric distinction is that between the cube-based diagrams and the tetrahedron-based diagrams. Geometric properties such as collinearity, central symmetry and distance are examined from a cognitive perspective, focusing on diagram design principles (...) such as congruence/isomorphism and apprehension. The cognitive effectiveness of the different visualizations is compared for the representation of implication versus opposition relations, and for subdiagram embeddings. (shrink)

The smooth -- The smooth body -- The aesthetics of the smooth -- Digital beauty -- The aesthetics of veiling -- The aesthetics of injury -- The aesthetics of disaster -- The ideal of beauty -- Beauty as truth -- The politics of beauty -- Pornographic theatre -- Lingering on beauty -- Beauty as reminiscence -- Giving birth in beauty.

The ever-increasing dominance of English within analytic philosophy is an aspect of linguistic globalisation. To assess it, I first address fundamental issues in the philosophy of language. Steering a middle course between linguistic universalism and linguistic relativism, I deny that some languages might be philosophically superior to others, notably by capturing the essential categories of reality. On this background I next consider both the pros and cons of the Anglicisation of philosophy. I shall defend the value of English as a (...) lingua franca, while denying both the feasibility and the desirability of English as the sole universal language of philosophy. Finally I turn to the linguistic inequality in contemporary analytic philosophy. While it does not per se amount to an injustice, there is a need to level the playing field. But the remedy does not lie in linguistic academic sectarianism. Instead, what might be called for are piecemeal measures to reduce explicit and implicit biases against analytic philosophers on the geographic fringes, biases that are only partly connected to the predominance of English. (shrink)

This book proposes a new Ethics of Political Commemoration adapted from the Just War tradition, reflecting that remembrance is often conducted with political – and even coercive – intent. With its Ius ad Memoriam (what to commemorate) and Ius in Memoria (how to commemorate) criteria, the framework looks to guide debates that are currently inchoate so that remembrance of the past can transform relationships in the present and build a shared future. Offering a moral argument with memorable illustrations, Gutbrod and (...) Wood draw on experiences from Armenia, Georgia, Ireland, Lebanon, and Libya, while connecting to mainstream debates in Western Europe and the United States. Bringing together an ethical tradition with the practice of conflict transformation, the framework fuses two perspectives that enrich each other. The book, in providing a first systematic presentation of the ethics, seeks to engage citizens and scholars, and help those who work to transform conflicts. (shrink)

More and more, we present ourselves and encounter others through profiles. A profile shows us not as we are seen directly but how we are perceived by a broader public. As we observe how others observe us, we calibrate our self-presentation accordingly. Profile-based identity is evident everywhere from pop culture to politics, marketing to morality. But all too often critics simply denounce this alleged superficiality in defense of some supposedly pure ideal of authentic or sincere expression. This book argues that (...) the profile marks an epochal shift in our concept of identity and demonstrates why that matters. You and Your Profile blends social theory, philosophy, and cultural critique to unfold an exploration of the way we have come to experience the world. Instead of polemicizing against the profile, Hans-Georg Moeller and Paul J. D’Ambrosio outline how it works, how we readily apply it in our daily lives, and how it shapes our values—personally, economically, and ethically. They develop a practical vocabulary of life in the digital age. Informed by the Daoist tradition, they suggest strategies for handling the pressure of social media by distancing oneself from one’s public face. A deft and wide-ranging consideration of our era’s identity crisis, this book provides vital clues on how to stay sane in a time of proliferating profiles. (shrink)

An in-depth account of how critique and subversion have been integral parts of the history and development of Chinese philosophy from the classical period to the present.

This volume outlines a model of language that can be characterized as functionalist, usage-based, dynamic, and complex-adaptive. The core idea is that linguistic structure is not stable and uniform, but continually refreshed by the interaction between three components: usage, the communicative activities of speakers; conventionalization, the social processes triggered by these activities and feeding back into them; and entrenchment, the individual cognitive processes that are also linked to these activities in a feedback loop. Hans-Joerg Schmid explains how this multiple (...) feedback system works by extending his Entrenchment-and-Conventionalization Model, showing how the linguistic system is created, sustained, and continually adapted by the ongoing interaction between usage, conventionalization, and entrenchment. Fulfilling the promise of usage-based accounts, the model explains how exactly usage is transformed into collective and individual grammar and how these two grammars in turn feed back into usage.0The book is exceptionally broad in scope, with insights from a wide range of linguistic subdisciplines. It provides a coherent account of the role of multiple factors that influence language structure, variation, and change, including frequency, economy, identity, multilingualism, and language contact. (shrink)

This article compares situated cognition to contemporary Neo-Aristotelian approaches to the mind. The article distinguishes two components in this paradigm: an Aristotelian essentialism which is alien to situated cognition and a Wittgensteinian “capacity approach” to the mind which is not just congenial to it but provides important conceptual and argumentative resources in defending social cognition against orthodox cognitive science. It focuses on a central tenet of that orthodoxy. According to what I call “encephalocentrism,” cognition is primarily or even exclusively a (...) computational process occurring inside the brain. Neo-Aristotelians accuse this claim of committing a “homuncular” or “mereological fallacy”. The article explains why the label “fallacy” is misleading, reconstructs the argument to the effect that encephalocentric applications of psychological predicates to the brain and its parts amount to a category mistake, and defends this argument against objections by Dennett, Searle, and Figdor. At the same time it criticizes the Neo-Aristotelian denial that the brain is the organ of cognition. It ends by suggesting ways in which the capacity approach and situated cognition might be combined to provide a realistic and ecologically sound picture of cognition as a suite of powers that flesh-and-blood animals exercise within their physical and social environments. (shrink)

Technik bestimmt auf die mannigfaltigste Weise unser Leben und Zusammenleben. Obgleich sie von Platon und Aristoteles bis in das zwanzigste Jahrhundert in Einzelaspekten betrachtet worden ist, wurde sie erst in den letzten Jahrzehnten zu einem eigenständigen Gegenstand der Philosophie. Dennoch werden ihre philosophischen Probleme immer noch eher beiläufig behandelt. So geht es um die Klärung ganz zentraler und herausfordernder Aufgaben – von der menschlichen Schöpferkraft über eine Klärung, was ein technisches Artefakt ist, zum technischen Wissen, in all diesen Elementen verknüpft (...) mit dem Verantwortungsproblem. Das Ziel ist eine Darstellung dieser faszinierenden philosophischen Fragen vor dem Hintergrund der Tradition. (shrink)

Tracing the thread of “decreation” in Chinese thought, from constantly changing classical masterpieces to fake cell phones that are better than the original. Shanzhai is a Chinese neologism that means “fake,” originally coined to describe knock-off cell phones marketed under such names as Nokir and Samsing. These cell phones were not crude forgeries but multifunctional, stylish, and as good as or better than the originals. Shanzhai has since spread into other parts of Chinese life, with shanzhai books, shanzhai politicians, shanzhai (...) stars. There is a shanzhai Harry Potter: Harry Potter and the Porcelain Doll, in which Harry takes on his nemesis Yandomort. In the West, this would be seen as piracy, or even desecration, but in Chinese culture, originals are continually transformed—deconstructed. In this volume in the Untimely Meditations series, Byung-Chul Han traces the thread of deconstruction, or “decreation,” in Chinese thought, from ancient masterpieces that invite inscription and transcription to Maoism—“a kind a shanzhai Marxism,” Han writes. Han discusses the Chinese concepts of quan, or law, which literally means the weight that slides back and forth on a scale, radically different from Western notions of absoluteness; zhen ji, or original, determined not by an act of creation but by unending process; xian zhan, or seals of leisure, affixed by collectors and part of the picture's composition; fuzhi, or copy, a replica of equal value to the original; and shanzhai. The Far East, Han writes, is not familiar with such “pre-deconstructive” factors as original or identity. Far Eastern thought begins with deconstruction. (shrink)