A case has been made by various authors that the normative and processual notion of personhood found in African philosophy is discriminatory: it has been labelled as sexist, ableist and anti-queer. Within the anti-queer critique, one area that has not been specifically addressed in the literature is whether this notion of personhood is biased against people who identify as non-binary with respect to gender. This includes people who are gender fluid and gender neutral, among others. In this article, we (...) argue that the binary conception of gender is deeply connected to a colonial agenda, and does not accurately fit extra-colonial gender conceptions. Through an analysis of extra-colonial language and logic, read together with the flexibility inherent in the processual notion of personhood (on our reading), we argue that binaries do not sit comfortably with extra-colonial African thinking, and as such, processual and normative personhood can be understood in a way that embraces non-binary individuals. Further, the standards for achieving personhood are set by and achieved within the community, so a community which recognises and celebrates non-binary individuals can set up a framework for them to achieve personhood. Accordingly, normative personhood in African thought is found not to exclude those of non-binary gender. This reading saves the normative approach from some of the critiques levelled against it, as well as: i) enhancing consistency in an African world view; ii) strengthening the decolonial agenda; and iii) showing normative personhood to be fairer and more inclusive. (shrink)

Hybrid Documentary and Non-Binary Cinema offers an expansive exploration of the contemporary documentary cinema form, aesthetics, and ethics. Beginning with a brief history of early seminal examples of magical realism, and constructed realities in documentary and ethnographic film the book will focus on recent and present-day examples of work that blur the lines between fiction and non-fiction. The book will also take a series of case studies to question the vision and motives of filmmakers working between documentary and fictional (...) film. It will consider the aesthetic and ethical challenges of these works and look toward the future of non-fiction filmmaking after the internet, and in the realm of the metaverse. The book will offer both an entry point to discover new tendencies and a deeper understanding for those readers who are more familiar with the field. Given its interdisciplinary subject nature, the book will appeal to audiences across a spectrum of interests such as film, fine art, anthropology, documentary, sociology and Drama. (shrink)

Robin Dembroff (Real Talk about the Metaphysics of Gender, 2018) believes that ‘non-binary’ is a social kind. I have my doubts about this, but if it is a social kind, then it is a very special one. The membership conditions of the social kind ‘non-binary’ are only accessible to non-binary persons. They establish and police their own membership conditions (Dembroff 2018: 36f.): ‘Individuals are granted authority over their gender kind membership.’ So, if this is indeed a ‘social (...) kind’, then it is a highly unusual one. (shrink)

How do institutions respond to expert contests over epistemologies of sex and gender? In this article, I consider how epistemological ascendancy in debates over the regulation of women athletes with high testosterone is established within a legal setting. Approaching regulation as an institutional act that defines forms of embodied difference, the legitimacy of which may be called into question, I show how sexed bodies are enacted through and as part of determinations of expertise. I focus on proceedings from 2015 when (...) the Court of Arbitration for Sport was asked to decide whether an Indian sprinter, Dutee Chand, could compete as a female athlete. Despite acknowledging that sexed bodies are unruly, the court ultimately endorsed the use of testosterone as seemingly essential to women’s athletic performance, thereby reasserting a two-category model of biological difference. The legitimacy of these regulatory efforts was established through the concurrent narrowing of expertise and the body, a process that is also revealed to be gendered. (shrink)

This article considers the model of recognition in the Gender Recognition Act 2004 (GRA) and, through a critique of the value of stability pursued through this legislation, argues that recognition as a model is incompatible with the variety of experiences of non-binary trans-identified individuals. The article then moves on to analyse self-declaration, part of the proposed reform recently dismissed by the Government. While self-declaration contains provisions that would minimise the length of the process of recognition as well as the (...) level of intrusiveness and stigma associated with it, this analysis highlights some fundamental theoretical concerns with its over-reliance on the strict dialectical logics on recognition and its structural inability to account for and respond to the challenges posed by non-binary trans individuals. (shrink)

The article deals with linguistic relativism in the decisions of the Austrian Verfassungsgerichtshof and the Czech Constitutional Court. It focuses on the Courts argumentation in which the state of language and its limiting perception of the word gender about non-binary and intersex people were used. The article conducts an in-depth analysis of two judgments. The first is the ruling of the Constitutional Court of the Czech Republic Case No. Pl. ÚS 2/20, in which the Court argued the absence of (...) gender-neutral names in Czech as one of the reasons for rejecting the constitutional complaint. The second is the judgment of the Austrian Verfassungsgerichtshof Case No. G 77/2018-9, in which the Court concluded as part of the constitutional review that the language can be adapted to the societal situation. The paper analyses selected parts of both decisions, interpreted using fundamental theses of linguistic relativism (and determinism). I argue that the Czech Constitutional Court has adopted a conservative approach without considering the current societal situation. This opened space for the unequal status of people with an alternative gender identity in society based on ignoring inclusive language, which is the exact opposite of the position of the Austrian Verfassungsgerichtshof. (shrink)

Notini et al 1 offer a timely addition in the wake of a significant increase in young people identifying as transgender and gender diverse. The authors focus specifically on the case of 18-year-old Phoenix’s request for ongoing puberty suppression to affirm a non-binary gender identity. A central issue raised by Phoenix’s predicament, and that I suggest we can extend to ethical consideration of requests for other types of medical intervention by binary and non-binary TGD individuals, is whether (...) we should ‘affirm’ the claims made by TGD young people about what promotes their well-being. As a clinician working with TGD young people who have undergone a range of medical interventions to align their bodies with their gender identity, my starting presumption is that it is important to respect what people think will help them: there are some TGD young people for whom, all things considered, medical interventions to affirm gender identity promote their well-being. Well-being has become an important conceptual currency in ethical debates and lies at the core of the authors’ analysis of Phoenix’s case. While the authors do not ground their argument in favour of OPS in a specific theory of well-being, welfarist considerations 2 appear to underpin …. (shrink)

In this article, we analyse the novel case of Phoenix, a non-binary adult requesting ongoing puberty suppression to permanently prevent the development of secondary sex characteristics, as a way of affirming their gender identity. We argue that the aim of OPS is consistent with the proper goals of medicine to promote well-being, and therefore could ethically be offered to non-binary adults in principle; there are additional equity-based reasons to offer OPS to non-binary adults as a group; and (...) the ethical defensibility of facilitating individual requests for OPS from non-binary adults also depends on other relevant considerations, including the balance of potential benefits over harms for that specific patient, and whether the patient’s request is substantially autonomous. Although the broadly principlist ethical approach we take can be used to analyse other cases of non-binary adults requesting OPS apart from the case we evaluate, we highlight that the outcome will necessarily depend on the individual’s context and values. However, such clinical provision of OPS should ideally be within the context of a properly designed research study with long-term follow-up and open publication of results. (shrink)

We thank the commentators for their thoughtful responses to our article.1 Due to space constraints, we will confine our discussion to just three key issues. The first issue relates to the central ethical conundrum for clinicians working with young people like Phoenix: namely, how to respect, value and defer to a person’s own account of their identity and what is needed for their well-being, while staying open to the possibility that such an account may reflect a work in progress. This (...) conundrum thus relates both to what will be beneficial for that person and what constitutes respecting their autonomy, and clinicians must dwell on these questions when deciding what forms of medical intervention to offer. D’Angelo,2 Lemma3 and Wren4 highlight the importance of considering Phoenix (or, indeed, any person pursuing gender-affirming interventions) as a ‘whole person in context’ (p5)2 prior to initiating treatment or care. In this way, they advocate for a process of ‘therapeutic exploration’ (p1),4 which includes taking sufficient time to explore Phoenix’s personhood with them so as to support them in achieving an ‘authentic self-discovery’ (p5).2 We agree with these authors that identity (including gender identity) development is a complex, life-long process that is influenced by biological, psychosocial and relational aspects, all of which may contribute to an individual’s desire to pursue gender-affirming interventions. To explore the various factors—both conscious and unconscious—that might be motivating Phoenix’s decision to pursue ongoing puberty suppression (OPS), D’Angelo,2 Lemma3 and Wren4 describe a comprehensive psychological approach to working with transgender (trans) and gender diverse (TGD) individuals and propose questions to guide such discussions. Consistent with this approach, we stipulated that Phoenix had undergone regular psychological counselling and that the psychologist had judged that ‘Phoenix’s distress is significant and enduring…not a symptom …. (shrink)

Abstract:In this work, we consider the essence of human freedom as a living link among the forces of the individuation process thought aesthetically; that is, because human understanding is synthetic, imagination can elaborate a whole world that is not linked to conceptual knowledge. Precisely because of that, we can find a way of relationship between ourselves and the environment that is not binary, such as when we ask ourselves whether the emission of carbon gas resulting from our human intervention (...) is harmful to the environment or not. To do so, we will initially outline the meaning of the symbolic (Sinnbild) in Schelling. Then, we will see how Schelling reaches the material conditions of objectification for an extra-theoretical synthesis by which, in a single move, the universe is immediately given. Finally, we turn to the specificity of human freedom and the dual nature of the I, which allows us to understand that the possibility of our human freedom does not consist in being able to choose between good and evil; rather, its possibility consists in a capacity (Vermögen) for good and evil. (shrink)

The concept of non-discrimination has been central in the feminist challenge to gendered violence within international human rights law. This article critically explores non-discrimination and the challenge it seeks to pose to gendered violence through the work of Judith Butler. Drawing upon Butler’s critique of heteronormative sex/gender, the article utilises an understanding of gendered violence as effected by the restrictive scripts of sex/gender within heteronormativity to illustrate how the development of non-discrimination within international human rights law renders it ineffective to (...) challenge gendered violence due to its own commitments to binarised and asymmetrical sex/gender. However, the article also seeks to encourage a reworking of non-discrimination beyond the heteronormative sex binary through employing Butler’s concept of cultural translation. Analysis via the lens of cultural translation reveals the fluidity of non-discrimination as a universal concept and offers new possibilities for feminist engagement with universal human rights. (shrink)

In my paper, I attempt a phenomenological analysis of the lived experience of intersexuality, which I view from the perspective of the problem of indeterminacy concerning the horizon of the givenness of homeworld founded on the broader basis of the pre-givenness of lifeworld. These horizons define the structure of the sedimentation of subjective experience, as well as the layers of cultural meanings sedimented in the lifeworld. The sedimented layers of self-experience and of the shared lifeworld function as a sphere of (...) indeterminacy, that is the horizons of constituted phenomena. In this sense all intentional acts have the nature of horizontal indeterminacy, the layers of which are revealed in the genetic question (Rückfrage) directed toward them. Horizontal indeterminacy also accounts for the distinction between homeworld and alienworld, which appears as something unobvious and unexpected against the obviousness of the homeworld, at the same time thematizing the latter. One of the elements of the sedimented conceptual system, functioning as the horizon of indeterminacy of both self-experience and the pre-reflective life-world, is the notion of human corporeality as given in the binary sexuality/gender. A unique opportunity for phenomenological insight into the constitution of the phenomenon of sex/gender is provided by Hida Viloria's lived experience of intersexuality. Her lived body, originally experienced pre-reflectively as a transparent medium and a perfectly handy tool of undisturbed intentionality, unproblematized also in the sexual activities, gradually undergoes alienation under the objectifying gaze determined by the binary pattern of sexuality. Becoming an alienated object, her body loses its transparency. Viloria begins to experience her corporeality and identity in a way determined by the sedimented "ideology" of sex and gender, trying on the "constructs" of masculine and feminine identities, eventually overcoming alienation and, in a process of secondary self-identification, reclaiming her lived body in its intersexuality and her identity in its non-binary gender fluidity. (shrink)

The scholarship on Frantz Fanon’s theorization of violence is crowded with interpretations that follow the Arendtian paradigm of violence. These interpretations often discuss whether violence is instrumental or non-instrumental in Fanon’s work. This reading, I believe, is the result of approaching Fanon through Hannah Arendt’s framing of violence, i.e. through a binary paradigm of instrumental versus non-instrumental violence. Even some Fanon scholars who question Arendt’s reading of Fanon, do so by employing a similar binary logic, hence repeating the (...) same either/or paradigm of instrumental versus non-instrumental violence. I aim to challenge such interpretations of Fanon by demonstrating that in the context of anticolonial armed struggle in which Fanon writes, the either/or framework of the instrumental/non-instrumental binary of violence cannot fully capture his perspective. Violence can indeed be conceived as having both constructive and instrumental aspects. My argument is supported by Fanon’s corpus, including his 1960 Accra speech, “Why We Use Violence” in Alienation and Freedom. This piece, I suggest, together with Fanon’s other writings, poses a direct challenge to the Arendtian binary of violence. My analysis resists positioning the difference between Arendt and Fanon through the instrumental/non-instrumental binary. By using Judith Butler’s notion of “frame” I complicate their difference and argue Arendt’s framing of violence prevents her from apprehending Fanon and – more importantly – interpretations of Fanon based on this Arendtian frame of violence inevitably lead to misinterpretations. (shrink)

This perspective asserts the existence of only two sexes/genders, male and female, based on not only biological and reproductive processes but also from claims of non-binary or transgender identities as defined through negation which rely on the binary concept of sex/gender. Thus, individuals claiming identities on the "gender/sex spectrum" are again defining themselves through negation (definiens per negationem). This perspective suggests that the diversity of gender experiences, (the sex or gender spectrum) is defined by what individuals are not (...) rather than what they are. While the validity of non-binary and transgender identities definiens per negationem is noted, it is important to accept the reality of the binary nature of sex or gender as a scientific fact, and that all human beings are on a developmental pathway leading to either male or female. Without the reality of binary sex or gender, the gender identity spectrum does not exist as there is nothing to negate from. (shrink)

Sex is often thought of as a straightforwardly binary categorical variable. Yet there is considerable variation in would-be sex traits; from genitals and hormones to morphology, neurology and behaviour, there is rarely if ever a categorical binary. We introduce a strategy that researchers use to deal with this variation: Individualising Variation (IV). IV involves treating non-binary and gradual variation as idiosyncratic, as individual differences rather than sex-based differences. Using the contrasting cases of sex identification in field ornithology (...) and the debate about sex differences in neuroscience, we illustrate IV and investigate its epistemic and conceptual consequences. We argue that IV stabilises the ontological picture of sex as categorical and binary. While IV can be an epistemically benign research strategy in some cases, we argue that it can also be epistemically detrimental. This is because of its ability to mask evidence that would otherwise challenge related assumptions about the phenomenon of interest, such as what sexes are and what they look like. We also identify an alternative strategy, De- individualising Variation, which works against IV and helps life scientists recognise variation beyond categorical binaries. (shrink)

ABSTRACT It is fruitless to interpret Constant's modern liberty from the binary perspective of either the negative/positive freedom opposition or the liberal/republican freedom opposition. Both oppositional perspectives reduce the relationally complex nature of modern liberty to one or another component of the relation. Such reduction inevitably results in an incomplete and, therefore, inadequate interpretation of Constant's modern liberty. Consequently, either of these binary frames of interpretation obscures rather than illuminates the full nature of Constant's modern liberty. Boxed into (...) their irreconcilably opposed alternatives, both binary perspectives fail to appreciate that Constant's conception of modern liberty is a complex achievement irreducible without loss to either liberal negative liberty as non-interference or republican freedom as non-domination. Nor does combining liberal negative freedom and positive freedom (in the sense of ancient liberty), as Holmes well establishes, adequately tells the whole story of Constant's modern liberty. As a complex achievement, Constant's conception of modern liberty, I shall argue, blends negative freedom as associated with neo-Roman republican freedom as non-subjection to arbitrary power, negative freedom as non-interference, associated with the liberal tradition, positive freedom in the sense of inner self-development, and positive freedom as collective self-government or civic republican freedom. (shrink)

This paper provides a constructive topological semantics for non-deducibility of a first order intuitionistic formula. Formal topology theory, in particular the recently introduced notion of a binary positivity predicate, and co-induction are two needful tools.

The paper’s novelty is in combining two comparatively new fields of research: non-transitive logic and the proof method of correspondence analysis. To be more detailed, in this paper the latter is adapted to Weir’s non-transitive trivalent logic \({\mathbf{NC}}_{\mathbf{3}}\). As a result, for each binary extension of \({\mathbf{NC}}_{\mathbf{3}}\), we present a sound and complete Lemmon-style natural deduction system. Last, but not least, we stress the fact that Avron and his co-authors’ general method of obtaining _n_-sequent proof systems for any _n_-valent (...) logic with deterministic or non-deterministic matrices is not applicable to \({\mathbf{NC}}_{\mathbf{3}}\) and its binary extensions. (shrink)

Biomedical and social scientists are increasingly calling the biological sex into question, arguing that sex is a graded spectrum rather than a binary trait. Leading science journals have been adopting this relativist view, thereby opposing fundamental biological facts. While we fully endorse efforts to create a more inclusive environment for gender‐diverse people, this does not require denying biological sex. On the contrary, the rejection of biological sex seems to be based on a lack of knowledge about evolution and it (...) champions species chauvinism, inasmuch as it imposes human identity notions on millions of other species. We argue that the biological definition of the sexes remains central to recognising the diversity of life. Humans with their unique combination of biological sex and gender are different from non‐human animals and plants in this respect. Denying the concept of biological sex, for whatever cause, ultimately erodes scientific progress and may open the flood gates to “alternative truths.”. (shrink)

In this paper, we explore the relation between an agent’s doxastic attitude and her arguments in support of a given claim. Our main contribution is the design of a logical setting that allows us reason about binary arguments which are either in favour or against a certain claim. This is a setting in which arguments and propositions are the basic building blocks so that the concept of argument-based belief emerges in a straightforward way. We work against the background of (...) Dung’s abstract argumentation framework, extending it to a new setting in which we can study the formal properties of binary arguments as well as the larger structures they establish. This paper introduces a formal ‘two-dimensional’ language to talk about propositions and arguments, for which a sound and complete axiom system is provided. (shrink)

Dynamic Topological Logic () is a combination of , under its topological interpretation, and the temporal logic interpreted over the natural numbers. is used to reason about properties of dynamical systems based on topological spaces. Semantics are given by dynamic topological models, which are tuples , where is a topological space, f a function on X and V a truth valuation assigning subsets of X to propositional variables. Our main result is that the set of valid formulas of over spaces (...) with continuous functions is recursively enumerable. We show this by defining alternative semantics for . Under standard semantics, is not complete for Kripke frames. However, we introduce the notion of a non-deterministic quasimodel, where the function f is replaced by a binary relation g assigning to each world multiple temporal successors. We place restrictions on the successors so that the logic remains unchanged; under these alternative semantics, becomes Kripke-complete. We then apply model-search techniques to enumerate the set of all valid formulas. (shrink)

This commentary on Marilyn Strathern's article, “Binary License,” discusses certain implications of her assertion that intertribal relationships among urban migrants in Papua New Guinea are not “ethnic.” For if such social encounters do not involve a conventional politics of identity, what then might its politics be? By comparing Strathern's Melanesian case with ethnographic examples in Corsica and Mongolia, a novel relational modality of “intensive ethnicity” may be identified, one that differs qualitatively from the “extensive ethnicity” with which anthropologists have (...) usually been concerned. The two forms of ethnicity are equally relative, in that a given group's self-understanding and self-designation are in both cases the result of its relations with other groups. However, ethnically extensive relations of the standard anthropological variety involve symbolic processes of boundary making and boundary maintenance whereby contrasting cultural traits or contents are arbitrarily assigned to and distributed among preexisting social forms and social scales (whether individuals, communities, or nations). Conversely, the more intensive intertribal engagements described by Strathern and certain other anthropologists are relational all the way down, given that everything about the terms of these relations (including their form, scale, and dimensioning) is defined by the particular quality in question. Thus a contrast may be established between the politics of identity and what might be called non-identity politics. If the former amounts to an ethnic economy in which subjectivities are exchanged in a commodity-like, alienable way, then, in the latter, stereotypical naming and other seeming “ethnic” practices amount to gift-like, non-alienable insertions of selves into others. (shrink)

Quasi-set theory by S. French and D. Krause has been so far the most promising attempt of a formal theory of non-individuals. However, due to its sharp bivalent truth valuations, maximally fine-grained binary relations are readily found, in which members of equivalence classes are substitutable for each other in formulas salva veritate. Hence its mentioning and non-mentioning of individuals differs from existing set theory with defined identity merely by the range of nominal definitions. On a semantic level, quasi-set theory (...) does not provide an interpretation with explanatory power of its language terms as non-individuals, and it is not easy to see how such an interpretation can be set up. (shrink)

It has been argued that most countries that had been exposed to European colonialism have inherited a Western Christianity thanks to the mission societies from Europe and North America. In such colonial and post-colonial (countries where the political administration is no longer in European hands, but the effects of colonialism are still in place) contexts, together with Western contexts facing the ever-growing impact of migrants coming from the previous colonies, there is a need to reflect on the possibility of what (...) a non-colonial liturgy, rather than a decolonial or postcolonial liturgy, would look like. For many, postcolonial or decolonial liturgies are those that specifically create spaces for the voice of a particular identified other. The other is identified and categorised as a particular voice from the margins, or a specific voice from the borders, or the voices of particular identified previously silenced voices from, for example, the indigenous backyards. A question that this context raises is as follows: Is consciously creating such social justice spaces – that is determined spaces by identifying particular voices that someone or a specific group decides to need to be heard and even making these particular voiceless (previously voiceless) voices central to any worship experience – really that different to the colonial liturgies of the past? To give voice to another voice, is maybe only a change of voice, which certainly has tremendous historical value, but is it truly a transformation? Such a determined ethical space is certainly a step towards greater multiculturalism and can therefore be interpreted as a celebration of greater diversity and inclusivity in the dominant ontology. Yet, this ontology remains policed, either by the state-maintaining police or by the moral (social justice) police. Contribution: In this article, a non-colonial liturgy will be sought that goes beyond the binary of the dominant voice and the voice of the other, as the voice of the other too often becomes the voice of a particular identified and thus determined victim – in other words, beyond the binary of master and slave, perpetrator and victim, good and evil, and justice and injustice, as these binaries hardly ever bring about transformation, but only a change in the face of master and the face of the slave, yet remaining in the same policed ontology. (shrink)

This book explores some of the most pressing existential problems of our times, from climate change and social injustice, to the challenges of balancing personal needs against the needs of others. Pushing back against the tendency to think of dilemmas as clear-cut binary choices, anthropologist Michael Jackson shows us the ingenious ways dilemmas are addressed in non-Western traditions, as well as how they are reimagined and circumvented in a variety of contemporary settings. Each chapter examines a particular dilemma--from the (...) apparent contradictions between history and myth, fact and fiction, science and religion, to the land rights struggles of Indigenous peoples, to migrants from the Global South trying to sustain ties with their homelands while improving their lives abroad. Combining personal reflections with insights from a vast array of interlocutors, Jackson argues that the ways in which people endure dilemmas are as meaningful as the ways they attempt to resolve them"--Publisher's description. (shrink)

Recent controversies surrounding Michel Foucault suggest tensions and unresolved issues in his unfinished work. Here we interrogate Foucault’s legacy in relation to his claim that the welfare-state is a secularization of the Christian pastorate. We challenge Foucault’s binary narrative of the Christian flock versus the Graeco-Roman citizen and expand the focus to other ‘technologies of power’ in medieval Islam. Rather than an outburst of governmentality in modernity, we suggest a transregional and longue durée history of which the Christian pastorate (...) was merely one facet. This non-binary framework indicates that Foucault’s claim of a ‘demonic’ fusion of sovereign and pastoral power in modern politics requires significant revisitation. Finally, we claim that Foucault’s much-discussed fascination with neoliberalism may have roots in this one-sided narrative regarding the birth of the welfare-state. (shrink)

The Gibbs states of binary lattice systems can be characterized by their stability with respect to certain microscopic transitions which have a simple physical interpretation. A detailed analysis is provided for the case of a one-dimensional lattice gas with nearest-neighbor interactions.

We present a method for relevance sensitive non-monotonic inference from belief sequences which incorporates insights pertaining to prioritized inference and relevance sensitive, inconsistency tolerant belief revision. Our model uses a finite, logically open sequence of propositional formulas as a representation for beliefs and defines a notion of inference from maxiconsistent subsets of formulas guided by two orderings: a temporal sequencing and an ordering based on relevance relations between the putative conclusion and formulas in the sequence. The relevance relations are ternary (...) (using context as a parameter) as opposed to standard binary axiomatizations. The inference operation thus defined easily handles iterated revision by maintaining a revision history, blocks the derivation of inconsistent answers from a possibly inconsistent sequence and maintains the distinction between explicit and implicit beliefs. In doing so, it provides a finitely presented formalism and a plausible model of reasoning for automated agents. (shrink)

The rationalization of a choice function, in terms of assumptions that involve expansion or contraction properties of the feasible set, over non-finite sets is analyzed. Schwartz's results, stated in the finite case, are extended to this more general framework. Moreover, a characterization result when continuity conditions are imposed on the choice function, as well as on the binary relation that rationalizes it, is presented.

Agents are often assumed to have degrees of belief (“credences”) and also binary beliefs (“beliefs simpliciter”). How are these related to each other? A much-discussed answer asserts that it is rational to believe a proposition if and only if one has a high enough degree of belief in it. But this answer runs into the “lottery paradox”: the set of believed propositions may violate the key rationality conditions of consistency and deductive closure. In earlier work, we showed that this (...) problem generalizes: there exists no local function from degrees of belief to binary beliefs that satisfies some minimal conditions of rationality and non-triviality. “Locality” means that the binary belief in each proposition depends only on the degree of belief in that proposition, not on the degrees of belief in others. One might think that the impossibility can be avoided by dropping the assumption that binary beliefs are a function of degrees of belief. We prove that, even if we drop the “functionality” restriction, there still exists no local relation between degrees of belief and binary beliefs that satisfies some minimal conditions. Thus functionality is not the source of the impossibility; its source is the condition of locality. If there is any non-trivial relation between degrees of belief and binary beliefs at all, it must be a “holistic” one. We explore several concrete forms this “holistic” relation could take. (shrink)

The binary between the figure of the child and the fully human being is invoked with regularity in analyses of race, yet its centrality to the conception of race has never been fully explored. For most commentators, the figure of the child operates as a metaphoric or rhetorical trope, a non-essential strategic tool in the perpetuation of White supremacy. As I show in the following, the child/human binary does not present a contingent or merely rhetorical construction but, rather, (...) a central feature of racialization. Where Black peoples are situated as objects of violence it is often precisely because Blackness has been identified with childhood and childhood is historically identified as the archetypal site of naturalized violence and servitude. I proceed by offering a historical account of how Black peoples came to inherit the subordination and dehumanization of European childhood and how White youth were subsequently spared through their partial categorization as adults. (shrink)

In 1941, Tarski published an abstract, finitely axiomatized version of the theory of binary relations, called the theory of relation algebras, He asked whether every model of his abstract theory could be represented as a concrete algebra of binary relations. He and Jonsson obtained some initial, positive results for special classes of abstract relation algebras. But Lyndon showed, in 1950, that in general the answer to Tarski's question is negative. Monk proved later that the answer remains negative even (...) if one adjoins finitely many new axioms to Tarski's system. In this paper we describe a far-reaching generalization of the positive results of Jonsson and Tarski, as well as of some later, related results of Maddux. We construct a class of concrete models of Tarski's axioms-called coset relation algebras-that are very close in spirit to algebras of binary relations, but are built using systems of groups and cosets instead of elements of a base set. The models include all algebras of binary relations, and many non-representable relation algebras as well, We prove that every atomic relation algebra satisfying a certain measurability condition-a condition generalizing the conditions imposed by Jonsson and Tarski-is essentially isomorphic to a coset relation algebra. The theorem raises the possibility of providing a positive solution to Tarski's problem by using coset relation algebras instead of the standard algebras of binary relations. (shrink)

This article and associated short film, entitled Threshold, explores the phenomenon of house as a Cartesian construct of rational cultural detachment, set in binary opposition to the indigenous understanding of nature as connected and sacred. Threshold focuses on the liminal in-between zones of a house – its doors and windows – which both separate and join the inside/outside domains – without belonging to either of them. The film explores the liminal act of crossing this ontological threshold – representing it (...) cinematically as a vibrational, ocular/aural wavering between two ‘worlds’. The intention is to destabilize this duality on an emotional level – in order to interrogate its validity. This strategy references anthropological theory, which asserts that the liminal act stimulates the limbic system containing ancestral, instinctual deposits. The function of the limbic system (part of the triune brain model) accords with Jung’s theory of the collective unconscious – which views the house as an archetypal symbol, central to the meaning of dreams – in representing the psyche of the dreamer. Threshold attempts to invoke this and other archaic symbols as the camera journeys through its interior spaces, discovering its material culture artefacts, which reflect the psychic state of its inhabitants. The paper explores the indigenous belief that there is a mystical (unitive, transformative) relationship existing between space and acoustics that can only be fully appreciated through an emotional experience with it. The adoption of an arts interventionist approach, can, the article will argue, provide an important contribution towards our expanded understanding of Space and Place as an embodied, emotional-cognitive act. (shrink)

B. Kooi and A. Tamminga present a correspondence analysis for extensions of G. Priest’s logic of paradox. Each unary or binary extension is characterizable by a special operator and analyzable via a sound and complete natural deduction system. The present paper develops a sound and complete proof searching technique for the binary extensions of the logic of paradox.