Values are widely recognized as playing a central role in the formation of our identities, perspectives, and affects. If you want to know who I am, how I see the world, and what has emotional significance for me, you will need to know something about my values. However, I argue that the relationship between value and subjectivity—understood as encompassing a person’s identity, perspective, and affective life—is more complex than it initially appears. Even when two individuals share the same values, their (...) engagement with those values can diverge significantly: it can be manifest either in a positive, affirmative manner or in an oppositional, antagonistic manner. With this distinction at hand, I examine a pervasive but undertheorized phenomenon: the emergence of subjectivities that are fundamentally structured around opposition rather than pursuit of positive ideals. Drawing on examples from contemporary politics and social movements, I distinguish between contingently negative orientations, which dissolve once specific threats disappear, and constitutively negative orientations, which perpetuate themselves through a continual search for new opponents. I argue that these negative orientations are not determined by the contents of evaluative judgments, but by the particular form of valuing that individuals or groups exhibit. Certain valuings are grounded in affects such as hatred, fear, and resentment; when these affects become self-sustaining and detached from stable targets, they generate constitutively negative orientations. (shrink)

A formal theory of oppositions and opposites is proposed on the basis of a non- Fregean semantics, where opposites are negation-forming operators that shed some new light on the connection between opposition and negation. The paper proceeds as follows. After recalling the historical background, oppositions and opposites are compared from a mathematical perspective: the first occurs as a relation, the second as a function. Then the main point of the paper appears with a calculus of oppositions, by means of (...) a non-Fregean semantics that redefines the logical values of various sorts of sentences. A num- ber of topics are then addressed in the light of this algebraic semantics, namely: how to construct value-functional operators for any logical opposition, beyond the classical case of contradiction; Blanché's "closure problem", i.e., how to find a complete structure connecting the sixteen binary sentences with one another. All of this is meant to devise an abstract theory of opposition: it encompasses the relation of consequence as subalternation, while relying upon the use of a primary "proto- negation" that turns any relatum into an opposite. This results in sentential negations that proceed as intensional operators, while negation is broadly viewed as a difference-forming operator without special constraints on it. (shrink)

This paper discusses knowledge of opposites. In particular, attention is given to the linguistic notion of antonymy and how it represents oppositional relations that are commonly found in perception. The paper draws upon the long history of work on the formalisation of antonymy in linguistics and formal semantics, and also upon work on the perception of opposites in psychology, and an assessment is made of the main approaches. Treatments of these phenomena in linguistics and psychology posit that the principles of (...) minimal difference and invariance are centrally important. It will be suggested that the standard approach employing meaning postulates fails to capture the relevant notion of antonymy, in part because it is not informed by these principles, and in part due to a number of other problems with this kind of approach, many of which may be overcome by building in the central principles from the beginning. The paper also discusses the issue of whether we can know that opposites necessarily exclude each other and, if so, how. This issue is intertwined with what is known as the colour incompatibility problem that Wittgenstein wrangled with at various times during his life. The paper assesses various solutions to these problems including an approach that was first put forward by Jerrold J. Katz. The relation between this approach and the theory of determinables and determinates is also examined. A further development upon this approach is proposed and then applied to the case of the formalisation of antonymy. It is argued that this approach avoids the problems suffered by the main approaches discussed earlier in the paper. (shrink)

The earliest recorded philosophical use of the term "phusis" occurs in the fragments of Heraclitus (most notably at B1 and B123). Phusis, in the non-philosophical writings relevant to Heraclitus’s time (e.g. from Homer to Aeschylus and Pindar), was generally used to characterize the external physical appearance of something. Heraclitus, on the other hand, seems to have used the term in the completely opposite manner: an object’s phusis is hidden (kruptesthai) and greater (kreissōn) than the external appearance (B123 and B54). Despite (...) this difference, Heraclitus’s use has an affinity with the common use in his time: phusis is used to characterize things. In B1, for example, Heraclitus makes it clear that he is interested in explaining the nature of each thing as opposed to some cosmic principle of Nature. By examining various fragments, I make the case that the phusis of a thing, for Heraclitus, can be defined as the set of opposites necessarily inherent in an object upon which all objects of that kind depend for their existence. The interesting result is that Heraclitus’s novel use of phusis happens to be the foundation for one of the ways in which opposites form a unity. This particular thesis states that there are essential properties inherent in objects which are pairs of opposites sufficient to determine the unity of the object in question. If this is right, then we can read some fragments which contain descriptions of worldly objects (e.g. bows, lyres, rivers, barley drinks etc.) in a new light. These descriptions of worldly objects might not be meant to stand as metaphoric symbols for cosmic principles, as is often thought; rather, they can be read as instances of Heraclitus attempting to do a metaphysics of objects. (shrink)

Opposition and particularity -- Opposition and intersubjectivity -- Opposition and temporality.

The paper presents the diagrammatic calculus CL, which combines features of tree, Euler-type, Venn-type diagrams and squares of opposition. In its basic form, `CL' (= Cubus Logicus) organizes terms in the form of a square or cube. By applying the arrows of the square of opposition to CL, judgments and inferences can be displayed. Thus CL offers on the one hand an intuitive method to display ontologies and on the other hand a diagrammatic tool to check inferences. The (...) paper focuses mainly on the adaptation of the square of opposition in CL and offers an algebraic notation, which corresponds to the diagrammatic representation. (shrink)

What modal relation must a fact bear to a belief in order for this belief to constitute knowledge of that fact? Externalists have proposed various answers, including some that combine externalism with contextualism. We shall find that various forms of externalism share a modal conception of “sensitivity” open to serious objections. Fortunately, the undeniable intuitive attractiveness of this conception can be explained through an easily confused but far preferable notion of “safety.” The denouement of our reflections, finally, will be to (...) show how replacing sensitivity with safety makes it possible to defend plain Moorean common sense against the spurious advantages over it claimed by skeptical, tracking, relevant-alternative, and contextualist accounts. (shrink)

. The truth conditions that Aristotle attributes to the propositions making up the traditional square of opposition have as a consequence that a particular affirmative proposition such as ‘Some A is not B’ is true if there are no Bs. Although a different convention than the modern one, this assumption remained part of centuries of work in logic that was coherent and logically fruitful.

A logical theory of oppositions deals with the relation between propositions and their truth values. On the basis of a formal semantics that proceeds by means of questions-answers, three theses are claimed in the following: (1) the concept of opposition usually refers to incompatibility, but our logical analysis focusses upon a broader relation of difference; (2) more generally, opposition has to do with negativity; our semantics accounts for it through opposite-forming operators; (3) subalternation is a particular case of (...) non-contradiction expressing an “opposition of an opposition”; it is not a proper opposition, accordingly, but its very meaning depends upon the latter. There is not only one but rather a number of expressions for negativity and the paper presents a detailed analysis of these "floating" expressions in a twofold sense of the word: floating quantification is closely related to the logical operations of sentential negation and denial; to what extent natural languages do not clearly express the meaning of a negative thought will be exemplified. L'objectif du texte qui suit est double : non seulement proposer une analyse logique du concept d'opposition, susceptible d'apporter de la précision à cette notion tout aussi vague que courante ; mais aussi, proposer une explication des différentes façons dont la négation se manifeste dans les langues naturelles, en particulier dans notre modèle local de la langue française. Tandis que la communauté des linguistes propose couramment une distinction entre une négation logique et une négation linguistique, l'article qui suit a la prétention d'une explication unifiée de la négation, c'est-à-dire un cadre théorique commun dans lequel ces deux aspects de l'opérateur de négation apparaissent comme des cas particuliers aux significations distinctes. Il n'y aurait donc pas une négation logique, d'un côté, et une négation linguistique ou "métalinguistique", de l'autre. Une approche structurelle des expressions négatives devrait apporter un éclairage sur ce point, par le biais d'une analyse algébrique de la signification en termes de questions-réponses. Mais revenons pour commencer sur l'origine philosophique du concept d'opposition, avant d'en exposer les propriétés logiques par la suite et les expressions linguistiques pour conclure. (shrink)

Axel Honneth reconstructs Hegel’s social and political philosophy on the basis of the concept of recognition. For Honneth, recognition is a constitutive relation between individuals that is in principle symmetrical. By conceiving recognition through symmetry, Honneth effectively bans the inclusion of power within recognitive relation. He thus regards the relations of power as cases of non-recognition or misrecognition. In this paper, I develop an alternative theory of the constitutive relation between individuals for Hegel, one that is based on the asymmetrical (...) relation of power. To this aim, I focus on the chapter of “determinations of reflection” in the Science of Logic. Through a close analysis of Hegel’s Logic, I argue that the most fundamental form of relation between individuals is the relation of opposition, that individuals are solely constituted in and through the relation of opposition, and that the relation of opposition is essentially asymmetrical. Together, these claims establish... (shrink)

This paper offers a new interpretation of Heraclitus’ use of opposites and how they feature in his explanation of the cosmos. It argues that the so-called “unity of opposites’ thesis does not exhaust Heraclitus’ interest in opposites. It contrasts Heraclitus with his Ionian predecessors, Anaximander and Anaximenes, who treated opposites as fundamental explanantia for the cosmos. Viewed from this perspective, Heraclitus’ opposites appear to be explananda—things to be explained. The paper argues that this analysis of Heraclitus’ use of opposites reveals (...) some features of his theory of explanation. Heraclitus rejects explanatory fundamentality but promotes the idea of a cosmos whose various parts explain its other parts. Opposites are both explananda and (non-fundamental) explanantia along with all the parts of the cosmos. Interestingly, Heraclitus’ cosmos itself appears to be both an explanandum and an explanans. (shrink)

Saba Mahmood’s anthropological work studies the gain in skills, agency and capacity building by the women’s dawa movement in Egypt. These women increase their virtue toward the goal of piety by following dominant, often patriarchal norms. Mahmood argues that “teleological feminism” ignores this gain in agency because this kind of feminism only focuses on opposition or resistance to these norms. In this paper I defend Mahmood’s “anti-teleological” feminist work from criticisms that her project valorizes oppression and has no vision (...) for a nonoppressive feminist future. I argue the future envisioned by teleological feminists gets caught in “the Hegelian” trap of replicating past oppression in their feminist future. I find in Mahmood’s work the tools to escape this trap. I argue, rather than a movement of overcoming oppression, Mahmood’s work suggests an immanent and creative movement that emphasizes difference for a truly new future. I turn to a Bergsonian metaphor and argue that this movement can be seen as akin to the movement of biological evolution. I conclude using the work of Eve Sedgwick that the Egyptian women that Mahmood studies are being read in a “paranoid” fashion and demonstrate using Leila Ahmed a better “reparative” reading of these women. (shrink)

Rule is commonly conceptualized with reference to the compliance it invokes. In this article, we propose a conception of rule via the practice of resistance instead. In contrast to liberal approaches, we stress the possibility of illegitimate rule, and, as opposed to critical approaches, the possibility of legitimate authority. In the international realm, forms of rule and the changes they undergo can thus be reconstructed in terms of the resistance they provoke. To this end, we distinguish between two types of (...) resistance—opposition and dissidence—in order to demonstrate how resistance and rule imply each other. We draw on two case studies of resistance in and to international institutions to illustrate the relationship between rule and resistance and close with a discussion of the normative implications of such a conceptualization. (shrink)

Our daily lives unfold continuously, yet our memories are organised into distinct events, situated in a specific context of space and time, and chunked when this context changes (at event boundaries). Previous research showed that this process, termed event segmentation, enhances object-context binding but impairs temporal order memory. Physiologically, peaks in pupil dilation index event segmentation, similar to emotion-induced bursts of autonomic arousal. Emotional arousal also modulates object-context binding and temporal order memory. Yet, these two critical factors have not been (...) systematically studied together. To address this gap, we ran a behavioural experiment using a paradigm validated to study event segmentation and extended it with emotion manipulation. During encoding, we sequentially presented greyscale objects embedded in coloured frames (colour changes defining events), with a neutral or aversive sound. During retrieval, we tested participants’ memory of temporal order memory and object-colour binding. We found opposite effects of emotion and event segmentation on episodic memory. While event segmentation enhanced object-context binding, emotion impaired it. On the contrary, event segmentation impaired temporal order memory, but emotion enhanced it. These findings increase our understanding of episodic memory organisation in laboratory settings, and potentially in real life with perceptual changes and emotion fluctuations constantly interacting. (shrink)

The square of opposition is a diagram related to a theory of oppositions that goes back to Aristotle. Both the diagram and the theory have been discussed throughout the history of logic. Initially, the diagram was employed to present the Aristotelian theory of quantification, but extensions and criticisms of this theory have resulted in various other diagrams. The strength of the theory is that it is at the same time fairly simple and quite rich. The theory of oppositions has (...) recently become a topic of intense interest due to the development of a general geometry of opposition (polygons and polyhedra) with many applications. A congress on the square with an interdisciplinary character has been organized on a regular basis (Montreux 2007, Corsica 2010, Beirut 2012, Vatican 2014, Rapa Nui 2016). The volume at hand is a sequel to two successful books: The Square of Opposition - A General Framework of Cognition, ed. by J.-Y. Béziau & G. Payette, as well as Around and beyond the Square of Opposition, ed. by J.-Y. Béziau & D. Jacquette, and, like those, a collection of selected peer-reviewed papers. The idea of this new volume is to maintain a good equilibrium between history, technical developments and applications. The volume is likely to attract a wide spectrum of readers, mathematicians, philosophers, linguists, psychologists and computer scientists, who may range from undergraduate students to advanced researchers. (shrink)

How do social institutions exist? How do they direct our conduct? The Opposite Mirrors defends the thesis that the existence of institutions is a conventional matter. Ultimately they exist because we believe in their existence, and because they play a role in our practical reasoning. Human action necessarily has an unpredictable aspect; human institutions perform an important task by reducing uncertainty in our interactions. The author applies this thesis to the most important institutions: the law and the monetary system. In (...) his analysis he connects many traditional topics of the philosophy of law, social philosophy and the philosophy of social sciences in a new way. He discusses the nature of rules, authority, and power and analyzes the Hobbesian presuppositions which have been dominant in legal theory and in the economic analyses of the state. The book is written for legal theorists as well as for political and social philosophers, and theoretically oriented social scientists. (shrink)

Jean-Yves Béziau Abstract In this paper I relate the story about the new rising of the square of opposition: how I got in touch with it and started to develop new ideas and to organize world congresses on the topic with subsequent publications.

The square of opposition (as part of a lattice) is used as a natural way to represent different and opposite ways of who makes decisions, and in what way, in/for a group or a society. Majority logic is characterized by multiple logical squares (one for each possible majority), with the “discursive dilemma” as a consequence. Three-valued logics of majority decisions with discursive dilemma undecided, of veto, consensus, and sequential voting are analyzed from the semantic point of view. For instance, (...) the paraconsistent and paracomplete logics M3, M3veto and C3 are described. The distinction of designated and non-designated values is not used, and instead, the consequence relation is defined as a preservation of the minimum truth-value of the implying set of sentences. The consequence and opposition relations of the logics described are compared, and an ordering of the logics with respect to their opposition relations is established. (shrink)

Our aim is to show that translating the modal graphs of Moretti’s “n-opposition theory” (2004) into set theory by a suited device, through identifying logical modal formulas with appropriate subsets of a characteristic set, one can, in a constructive and exhaustive way, by means of a simple recurring combinatory, exhibit all so-called “logical bi-simplexes of dimension n” (or n-oppositional figures, that is the logical squares, logical hexagons, logical cubes, etc.) contained in the logic produced by any given modal graph (...) (an exhaustiveness which was not possible before). In this paper we shall handle explicitly the classical case of the so-called 3(3)-modal graph (which is, among others, the one of S5), getting to a very elegant tetraicosahedronal geometrisation of this logic. (shrink)

Since antiquity, opposed concepts such as the One and the Many, the Finite and the Infinite, and the Absolute and the Relative, have been a driving force in philosophical, scientific, and mathematical thought. Yet they have also given rise to perplexing problems and conceptual paradoxes which continue to haunt scientists and philosophers. In Oppositions and Paradoxes, John L. Bell explains and investigates the paradoxes and puzzles that arise out of conceptual oppositions in physics and mathematics. In the process, Bell not (...) only motivates abstract conceptual thinking about the paradoxes at issue, he also offers a compelling introduction to central ideas in such otherwise-difficult topics as non-Euclidean geometry, relativity, and quantum physics. These paradoxes are often as fun as they are flabbergasting. Consider, for example, the famous Tristram Shandy paradox: an immortal man composing an autobiography so slowly as to require a year of writing to describe each day of his life and he would, if he had infinite time, presumably never complete the work, although no individual part of it would remain unwritten. Or imagine an English professor who time-travels back to 1599 to offer a printing of Hamlet to Shakespeare, so as to help the Bard overcome writer's block and author the play which will centuries later inspire an English professor to travel back in time. These and many other paradoxes straddle the boundary between physics and metaphysics, and demonstrate the hidden difficulty in many of our most basic concepts. (shrink)

The theory of opposition has always been viewed as the founding principle of structuralism within contemporary linguistics and semiotics. As an analytical technique, it has remained a staple within these disciplines, where it continues to be used as a means for identifying meaningful cues in the physical form ofsigns. However, as a theory of conceptual structure it was largely abandoned under the weight of post-structuralism starting in the 1960s — the exception tothis counter trend being the work of the (...) Tartu School of semiotics. This essay revisits opposition theory not only as a viable theory for understanding conceptual structure, but also as a powerful technique for establishing the interconnectedness of language, culture, and cognition. (shrink)

Various semantics for studying the square of opposition and the hexagon of opposition have been proposed recently. We interpret sentences by imprecise (set-valued) probability assessments on a finite sequence of conditional events. We introduce the acceptability of a sentence within coherence-based probability theory. We analyze the relations of the square and of the hexagon in terms of acceptability. Then, we show how to construct probabilistic versions of the square and of the hexagon of opposition by forming suitable (...) tripartitions of the set of all coherent assessments. Finally, as an application, we present new versions of the square and of the hexagon involving generalized quantifiers. (shrink)

Nous proposons dans cet article des éléments nouveaux pour l’interprétation de la doctrine d’Héraclite, concernant en particulier le rôle de l’opposition des contraires en tant que générateur d’harmonie, mentionné dans les Fragments 8 et 51. Cette interprétation est basée sur l’outil conceptuel que constituent les matrices de concepts. Après avoir décrit les éléments fondamentaux qui régissent ces dernières, nous nous attachons à définir dans ce cadre conceptuel les notions d’opposition et de contraire, ainsi que d’harmonie. Cela permet de (...) fournir une interprétation ainsi qu’une justification pour la doctrine spécifique d’Héraclite, selon laquelle l’opposition des contraires est génératrice d’harmonie. (shrink)

In discussing Socrates's argument for Plato's principle of change in the Phaedo, Syrianus asks, To what kind of opposites is Socrates referring? I offer a new answer to Syrianus's question. I start from David Sedley's view that the opposites in question are converse contraries, which behave as converses in comparative contexts. I show that the quantitative pairs that Socrates cites fit Sedley's view because they are implicit comparatives. Nonetheless, I argue that Socrates's evaluative pairs are better understood as asymmetrical opposites (...) because the Phaedo and the Republic reveal that these pairs have independent, not relational, meanings. So my answer to Syrianus's question is that implicit comparatives and asymmetrical opposites are the kinds of opposites to which Socrates is referring. (shrink)

Most opposition to induced abortion turns on the belief that human fetuses are persons from conception. On this view, the moral status of the fetus alone requires those in a position to provide aid—gestational mothers—to make tremendous sacrifices to benefit the fetus. Recently, critics have argued that this pro-life position requires more than opposition to induced abortion. Pro-life theorists are relatively silent on the issues of spontaneous abortion, surplus in vitro fertilisation human embryos, and the suffering and death (...) of born persons due to lack of access to food, shelter and medical care. Colgrove et al call such arguments inconsistency arguments, arguing they ‘do not matter’ and mischaracterise them as ad hominem attacks. Here, I argue these are better understood as moral dilemmas. While some critics argue pro-life inaction is evidence that they do not really believe human fetuses are persons, I contend this inaction is likely the result of resolvable confusion rather than moral negligence. (shrink)

Quantum complementarity is interpreted in terms of duality and opposition. Any two conjugates are considered both as dual and opposite. Thus quantum mechanics introduces a mathematical model of them in an exact and experimental science. It is based on the complex Hilbert space, which coincides with the dual one. The two dual Hilbert spaces model both duality and opposition to resolve unifying the quantum and smooth motions. The model involves necessarily infinity even in any finitely dimensional subspace of (...) the complex Hilbert space being due to the complex basis. Furthermore, infinity is what unifies duality and opposition, universality and openness, completeness and incompleteness in it. The deduced core of quantum complementarity in terms of infinity, duality and opposition allows of resolving a series of various problems in different branches of philosophy: the common structure of incompleteness in Gödel’s (1931) theorems and Enstein, Podolsky, and Rosen’s argument (1935); infinity as both complete and incomplete; grounding and self-grounding, metaphor and representation between language and reality, choice and information, the totality and an observer, the basic idea of philosophical phenomenology. The main conclusion is: Quantum complementarity unifies duality and opposition in a consistent way underlying the physical world. (shrink)

The doctrine of unity of opposites lays in the centre of the debate on Heraclitus’ philosophy. The present article proposes a critical analysis of the mainstream interpretation of geometrical oppositions (fragments DK 22 B 59, B 60 and B 103) as mere examples of different points of view. Instead, we suggest that these fragments are fundamental pieces in Heraclitus cosmology and that they are traces of a circular and archaic paradigm. Indeed, cyclical formulations are spread throughout the fragments and, read (...) in connection with geometrical oppositions, perform a useful model to describe how permanence and change can be complementary events. In this context, circularity can be a key to the comprehension of unity of opposites as a result of interchangeable processes – as day and night, life and death, beginning and end – so that opposites are part of a concrete and vital unity. (shrink)

A general theory of logical oppositions is proposed by abstracting these from the Aristotelian background of quantified sentences. Opposition is a relation that goes beyond incompatibility (not being true together), and a question-answer semantics is devised to investigate the features of oppositions and opposites within a functional calculus. Finally, several theoretical problems about its applicability are considered.

This essay explores the validity of Gregory Boyd’s open theistic account of the nature of the future. In particular, it is an investigation into whether Boyd’s logical square of opposition for future contingents provides a model of reality for free will theists that can preserve both bivalence and a classical conception of omniscience. In what follows, I argue that it can.

The theory of the square of opposition has been studied for over 2,000 years and has seen a resurgence in new theories and research since the second half of the twentieth century. This volume collects papers presented at the Sixth World Congress on the Square of Opposition, held in Crete in 2018, developing an interdisciplinary exploration of the theory. Chapter authors explore subjects such as Aristotle’s ontological square, logical oppositions in Avicenna’s hypothetical logic, and the power of the (...) square of opposition to solve theological problems regarding predestination and theodicy. Other topics covered include: Hegel’s opposition to diagrams De Morgan’s unpublished octagon of opposition turnstile figures of opposition institutional model-theoretic treatment of oppositions Lacan’s four formulas of sexuation the theory of oppositional poly-simplexes The Exoteric Square of Opposition will appeal to pure logicians, historians of logic, semioticians, philosophers, theologians, mathematicians, and psychoanalysts. (shrink)

We argue that while the new opposition in Azerbaijan between 2005 and 2013 did not realize all the goals set, it influenced a new generation of young activists who became the loudest supporters of democratic and secular values in Azerbaijan. This grassroots activation of the youth brought noticeable changes to some parts of Azerbaijani society by questioning the authority of traditional values. Many young people, especially students found a platform to discuss their problems concerning everyday basic issues such as (...) intimate relationships as well as their freedom to live in accordance with their personal choices and desires without the family interference in the light of theoretical questions such as the importance of liberal democratic values, individual liberties, and the rule of law. The successfully established connections between material problems and transcendental ideals encouraged some young people to participate in the open discussions and seminars organized by the new opposition. Because of the emergence of this new generation of active youth, the government was forced to incorporate some elements of this new discourse at least by making some cosmetic changes within its structures. The government became successful in its attempts of weakening the new opposition by hijacking its ideas and creating similar but pro-government organizations; neutralizing or buying some well-known opposition figures such as writers and journalists; and finally, persecuting the leading members of the youth organizations. (shrink)

An arithmetic theory of oppositions is devised by comparing expressions, Boolean bitstrings, and integers. This leads to a set of correspondences between three domains of investigation, namely: logic, geometry, and arithmetic. The structural properties of each area are investigated in turn, before justifying the procedure as a whole. Io finish, I show how this helps to improve the logical calculus of oppositions, through the consideration of corresponding operations between integers.

In this paper, we provide an overview of some of the results obtained in the mathematical theory of intermediate quantifiers that is part of fuzzy natural logic. We briefly introduce the mathematical formal system used, the general definition of intermediate quantifiers and define three specific ones, namely, “Almost all”, “Most” and “Many”. Using tools developed in FNL, we present a list of valid intermediate syllogisms and analyze a generalized 5-square of opposition.

. Each predicate of the Aristotelian square of opposition includes the word “is”. Through a twofold interpretation of this word the square includes both classical logic and non-classical logic. All theses embodied by the square of opposition are preserved by the new interpretation, except for contradictories, which are substituted by incommensurabilities. Indeed, the new interpretation of the square of opposition concerns the relationships among entire theories, each represented by means of a characteristic predicate. A generalization of the (...) square of opposition is achieved by not adjoining, according to two Leibniz’ suggestions about human mind, one more choice about the kind of infinity; i.e., a choice which was unknown by Greek’s culture, but which played a decisive role for the birth and then the development of modern science. This essential innovation of modern scientific culture explains why in modern times the Aristotelian square of opposition was disregarded. (shrink)

We present a quantum model for the motion of N point particles, implying nonlocal (i.e., superluminal) influences of external fields on the trajectories, that is nonetheless fully relativistic. In contrast to other models that have been proposed, this one involves no additional space-time structure as would be provided by a (possibly dynamical) foliation of space-time. This is achieved through the interplay of opposite microcausal and macrocausal (i.e., thermodynamic) arrows of time. PACS numbers 03.65.Ud; 03.65.Ta; 03.30.+p..

In recent decades, research in the square of opposition has increased. New interpretations, extensions, and generalizations have been suggested, both Aristotelian and non-Aristotelian ones. The paper attempts to compare different versions of the square of opposition. For this reason, we appeal to the wider categorical model-theoretic framework of the theory of institutions.

Opposition theory suggests that binary oppositions (e.g., high vs. low) underlie basic cognitive and linguistic processes. However, opposition theory has never been implemented in a computational cognitive-semiotics model. In this paper, we present a simple model of metaphor identification that relies on opposition theory. An algorithm instantiating the model has been tested on a data set of 100 phrases comprising adjective-noun pairs in which approximately a half represent metaphorical language-use (e.g., dark thoughts) and the rest literal language-use (...) (e.g., dark hair). The algorithm achieved 89% accuracy in metaphor identification and illustrates the relevance of opposition theory for modelling metaphor processing. (shrink)

A general characterization of logical opposition is given in the present paper, where oppositions are defined by specific answers in an algebraic question-answer game. It is shown that opposition is essentially a semantic relation of truth values between syntactic opposites, before generalizing the theory of opposition from the initial Apuleian square to a variety of alter- native geometrical representations. In the light of this generalization, the famous problem of existential import is traced back to an ambiguous interpretation (...) of assertoric sentences in Aristotle's traditional logic. Following Abelard’s distinction between two alternative readings of the O-vertex: Non omnis and Quidam non, a logical difference is made between negation and denial by means of a more fine- grained modal analysis. A consistent treatment of assertoric oppositions is thus made possible by an underlying abstract theory of logical opposition, where the central concept is negation. A parallel is finally drawn between opposition and consequence, laying the ground for future works on an abstract operator of opposition that would characterize logical negation just as does Tarski’s operator of consequence for logical truth. (shrink)

In the recent debate on future contingents and the nature of the future, authors such as G. A. Boyd, W. L. Craig, and E. Hess have made use of various logical notions, such as the Aristotelian relations of contradiction and contrariety, and the ‘open future square of opposition.’ My aim in this paper is not to enter into this philosophical debate itself, but rather to highlight, at a more abstract methodological level, the important role that Aristotelian diagrams can play (...) in organizing and clarifying the debate. After providing a brief survey of the specific ways in which Boyd and Hess make use of Aristotelian relations and diagrams in the debate on the nature of the future, I argue that the position of open theism is best represented by means of a hexagon of opposition. Next, I show that on the classical theist account, this hexagon of opposition ‘collapses’ into a single pair of contradictory statements. This collapse from a hexagon into a pair has several aspects, which can all be seen as different manifestations of a single underlying change. (shrink)

Opposition theory is one of the main outcomes of structural linguistics of the last century. While it is still valid and used in the field of phonology, it has not had the same fortune in other linguistic disciplines and has been replaced by other theoretical concepts. The present paper aims to revisit the opposition theory, particularly Louis Hjelmslev’s theory of participative opposition. Participative oppo si tion seems to have a high application potential not only in linguistics but (...) also in other scientific fields. The first part of the paper outlines a brief history of the binary opposition theory within structural linguistics, while the second part introduces the somewhat forgotten concept of participative opposition, shows its explanatory power and, finally, its possible applicability in biology. (shrink)

This paper investigates some classical oppositional categories, like synthetic versus analytic, posterior versus prior, imagination versus grammar, metaphor versus hermeneutics, metaphysics versus observation, innovation versus routine, and image versus sound, and the role they play in epistemology and philosophy of science. The epistemological framework of _objective cognitive constructivism_ is of special interest in these investigations. Oppositional relations are formally represented using algebraic lattice structures like the cube and the hexagon of opposition, with applications in the contexts of modern color (...) theory, Kantian philosophy, Jungian psychology, and linguistics. (shrink)

The aim of this paper is to analyse categorical propositions and their oppositional relations in Avicenna’s frame. For Avicenna’s expression and conception of categorical propositions is different from those of the authors who preceded him, due to the various conditions he adds to these categorical propositions. These additions make the oppositional relations richer and give rise to many more figures than a simple square. Our analysis exhibits some of these figures by relating all kinds of quantified propositions in various ways. (...) We thus find many squares of oppositions, several octagons, two hexagons and many complex figures which are different from each other and have specific and original structures, due to the propositions they contain. The hexagons are of Blanché’s kind, but one of them is asymmetric. Some octagons are of Buridan’s kind, but one of them is very unusual and seems to be a reversal of Buridan’s octagon. These octagons can also be replaced by cubes, which are three dimensional figures having the same number of vertices. (shrink)

An unconventional formalization of the canonical square of opposition in the notation of classical symbolic logic secures all but one of the canonical square’s grid of logical interrelations between four A-E-I-O categorical sentence types. The canonical square is first formalized in the functional calculus in Frege’s Begriffsschrift, from which it can be directly transcribed into the syntax of contemporary symbolic logic. Difficulties in received formalizations of the canonical square motivate translating I categoricals, ‘Some S is P’, into symbolic logical (...) notation, not conjunctively as \, but unconventionally instead in an ontically neutral conditional logical symbolization, as \. The virtues and drawbacks of the proposal are compared at length on twelve grounds with the explicit existence expansion of A and E categoricals as the default strategy for symbolizing the canonical square preserving all original logical interrelations. (shrink)

At On Generation and Corruption I.7.323b1–324a5, Aristotle claims that his new method of analysis for fundamental bodies and properties resolves a traditional apparent incompatibility between opposed principles applied by different philosophical authorities to the problem of affecting and being affected (poiein and paschein): that the like interacts with the unlike, and that the like interacts with the like. Twice in this passage, Aristotle uses a form of the term hupenantion (etymologically, ‘sub-oppositional’) in an extended discussion that includes his declaration of (...) the critical insight for solving the problem and illuminates the partial truth of each of the apparently antithetical universal principles. Because Aristotle uses the uncommon term twice in close context, and because he also explains in the context how he understands the apparent incompatibility—characterized both as a verbal opposition or enantiologia and also as a partial articulation of what should be theorized as a whole—it seems (and has seemed) plausible that this augmented form of the frequently used term enantion (‘opposite’ or ‘contrary’) carries methodological weight for indicating a kind of apparent incompatibility that can be resolved through supplementation to both of the opposed statements rather than elimination of or even favor for one or the other. Although the sense of hupenantion in On Generation and Corruption 1.7 is not continuous with the concept of the ‘subcontrary’ developed by ancient commentators on Aristotle’s Interpretations and early modern logicians, a full survey of the use of this term in Aristotle’s writings shows that Aristotle did recognize and lexically mark a special kind of opposition, one productive of intellectual progress rather than indicative of total error on one side of the debate. (shrink)

In Opposition to Philosophy in Safavid Iran Ata Anzali and S.M. Hadi Gerami offer a critical edition of what is arguably the most erudite and extensive critique of philosophy from the Safavid period. The editors' extensive introduction offers an in-depth analysis that places the work within the broader framework of Safavid intellectual and social history.

In this paper we deal with two applications of the square of opposition to controversial issues in the philosophy of quantum mechanics. The first one concerns the kind of opposition represented by states in superposition. A superposition of “spin up” and “spin down” for a given spatial direction, for instance, is sometimes said to originate particular kinds of opposition such as contradictoriness. The second application concerns the problem of identical particles. Identity and indiscernibility are entangled in discussions (...) of this problem in such a way that a proper conceptual treatment of those issues through the square seems profitable. (shrink)