In their interesting and informative paper ‘From Szasz to Foucault: On the Role of Critical Psychiatry,’ Pat Bracken and Phil Thomas contrast, in a clear and helpful way, some central themes in the works of Thomas Szasz and Michel Foucault. They go on to endorse a form of critical psychiatry inspired by the latter. Szasz’s critique of psychiatry, they explain, is premised on binary oppositions, principally that between ‘mental’ and ‘bodily.’ Szasz begins by assuming the legitimacy of the distinction and (...) proceeds to argue that the term ‘illness’ can only be legitimately applied to what is ‘bodily.’ According to Szasz, there are medical pathologies, which are to be understood in naturalistic, biological terms, and .. (shrink)

We describe a deep generative model in which the lowest layer represents the word-count vector of a document and the top layer represents a learned binary code for that document. The top two layers of the generative model form an undirected associative memory and the remaining layers form a belief net with directed, top-down connections. We present efficient learning and inference procedures for this type of generative model and show that it allows more accurate and much faster retrieval than latent (...) semantic analysis. By using our method as a filter for a much slower method called TF-IDF we achieve higher accuracy than TF-IDF alone and save several orders of magnitude in retrieval time. By using short binary codes as addresses, we can perform retrieval on very large document sets in a time that is independent of the size of the document set using only one word of memory to describe each document. (shrink)

Recently, a concern has been raised about a particular kind of behaviour that is adversely affecting the quality of nursing theoretical discourse. With the behaviour being attributed to nurses’ tendency to think in binary terms, it has been proposed that nurses replace their binary way of thinking with thinking that is inclusive and expansive and is based on an epistemology of contradiction. While agreeing that the behaviour of concern is indeed unscholarly, I disagree that the culprit is the binary. In (...) this commentary, I argue that the culprit is sophistical argumentation involving a binary (real or not) and that, by not making room for legitimate binaries, we run the danger of ‘throwing out the baby with the bathwater’. Further, I argue that the proffered solution is illusory. Its epistemological basis prohibits the deliverance of that which is promised. (shrink)

This article exploits the “binary license” offered by the title of the symposium in which it appears (“Comparative Relativism”) as a kind of promise of connection. The author suggests, however tentatively, that in the challenge of heterogeneity, fractality, perspective/-alism, and multiplicities lies the power of the forking pathway: the moment a relation is created through divergence. If we are invited—in the same breath—to consider forms of comparison and forms of relativism (dropping difference and similarity), we are also offered two paths, (...) one based on a world of singularities and multiplicities, and the other on a world of not-quite repetitions. The article asks if the binary is not essential to the epistemic work that Western (Euro-American) scholars might want to do, since we forever reinvent the divide between the modern and the post-/pre-modern. Strathern assumes the anthropologist's license to talk about concepts through persons, and begins by asking how Papua New Guineans who come together in a city compare themselves, and in contrast to ethnic comparisons elsewhere (e.g., contra Sarah Green's Balkan interactions). In talking about persons through concepts, it is worth asking what is entailed in relativizing one scholar's work through that of another. The author says that her “hunch” is that in both cases the analyst might wish to have the liberty of discerning—in the same breath—the multiplicities of what John Law and Annemarie Mol call perspectivalism (their very general alternative to comparison) and Eduardo Viveiros de Castro's radically divergent perspectivism (a self-contained, recursive and above all socially specific relativism). (shrink)

We investigate the formal theory of binary quantifiers, that is, quantifiers that take seriously the surface structure of natural language quantifier phrases. We show how to develop a natural deduction system for logics of this sort and demonstrate soundness and completeness results.

Pylyshyn makes a convincing case that early visual processing is cognitively impenetrable, and although I question the utility of binary oppositions such as penetrable/impenetrable, for the most part I am in agreement. The author does not provide explicit designations or denotations for the terms penetrable and impenetrable, which appear quite arbitrary. Furthermore, the use of focal attention smacks of an homunculus, and the account appears to slip too easily between the perceptual, the cognitive, and the neurophysiological.

Everyday thinking and scientific theorizing about human action control are equally driven by the apparently obvious contrast between will and habit or, in their more modern disguise: intentional and automatic processes, and model-based and model-free action planning. And yet, no comprehensive category system to systematically tell truly willed from merely habitual actions is available. As I argue, this is because the contrast is ill-conceived, because almost every single action is both willed and habitual, intentional and automatic, and model-based and model-free, (...) simply because will and habit (and their successors) do not refer to alternative modes or pathways of action control but rather to different phases of action planning. I further discuss three basic misconceptions about action control that binary theorizing relies on: the assumption that intentional processes compete with automatic processes (rather than the former setting the stage for the latter), the assumption that action control is targeting processes (rather than representations of action outcomes), and the assumption that people follow only one goal at a time (rather than multiple goals). I conclude that (at least the present style of) binary theorizing fails to account for action control and should thus be replaced by a more integrative view. (shrink)

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)

We compute the domination monoid in the theory of dense meet‐trees. In order to show that this monoid is well‐defined, we prove weak binarity of and, more generally, of certain expansions of it by binary relations on sets of open cones, a special case being the theory from [7]. We then describe the domination monoids of such expansions in terms of those of the expanding relations.

This paper addresses some problems arising with respect to the male/female binary division that has traditionally been central to most sports. One strategy for dealing with this problem is to remov...

Black-white, male-female — these and other markers, applied maliciously or not, enable the social dominance of one group.

A type quantifier F is symmetric iff F ( X, X )( Y ) = F ( Y, Y )( X ). It is shown that quantifiers denoted by irreducible binary determiners in natural languages are both conservative and symmetric and not only conservative.

Chinese translation courtesy of Zhuanxu Xu. We want to know what gender is. But metaphysical approaches to this question solely have focused on the binary gender kinds men and women. By overlooking those who identify outside of the binary–the group I call ‘genderqueer’–we are left without tools for understanding these new and quickly growing gender identifications. This metaphysical gap in turn creates a conceptual lacuna that contributes to systematic misunderstanding of genderqueer persons. In this paper, I argue that to better (...) understand genderqueer identities, we must recognize a new type of gender kind: critical gender kinds, or kinds whose members collectively resist dominant gender ideology. After developing a model of critical gender kinds, I suggest that genderqueer is best modeled as a critical gender kind that stands in opposition to `the binary assumption', or the prevalent assumption that the only possible genders are the binary, discrete, exclusive, and exhaustive kinds men and women. (shrink)

We introduce the notion of a convex tree. We show that the binary expansion for real numbers in the unit interval ) is equivalent to weak König lemma ) for trees having at most two nodes at each level, and we prove that the intermediate value theorem is equivalent to \ for convex trees, in the framework of constructive reverse mathematics.

In this article we establish the undecidability of representability and of finite representability as algebras of binary relations in a wide range of signatures. In particular, representability and finite representability are undecidable for Boolean monoids and lattice ordered monoids, while representability is undecidable for Jónsson's relation algebra. We also establish a number of undecidability results for representability as algebras of injective functions.

Working in the weakening of constructive Zermelo-Fraenkel set theory in which the subset collection scheme is omitted, we show that the binary refinement principle implies all the instances of the exponentiation axiom in which the basis is a discrete set. In particular binary refinement implies that the class of detachable subsets of a set form a set. Binary refinement was originally extracted from the fullness axiom, an equivalent of subset collection, as a principle that was sufficient to prove that the (...) Dedekind reals form a set. Here we show that the Cauchy reals also form a set. More generally, binary refinement ensures that one remains in the realm of sets when one starts from discrete sets and one applies the operations of exponentiation and binary product a finite number of times. (shrink)

Social care responses to extra-familial harm require social workers to work across the binaries of welfare and justice, victim and perpetrator, parent and professional, risk and protection. This paper examines the ethical consequences of working in this manner, through qualitative data (focus groups, interviews, observations, case file analysis and documentary review) from three children's social care organisations in England who trialled new child protection pathways for significant harm outside of family homes/relationships. The extent to which these pathways created five conditions (...) for a welfare response to extra-familial harm are considered, before these results are brought into conversation with Bourdieu’s meta theory of capital, habitus and doxa, and Fenton's practice theory of ethical stress. The challenges identified evidence of the importance foregrounding social work values in the pursuit of welfare-based response to extra-familial harm. They also offer a rationale for studying theories of care ethics in social work in the context of interagency practice. (shrink)

We shall prove here that any binary relation on a base E with cardinality n > 6 is reconstructible from its restrictions of cardinality 2, 3, 4 and . This proof needs results of part I of this paper where we characterize any pair of relations R, R' which are 2-, 3- and 4-hypomorphic. As a corollary we obtain that any binary relation is -reconstructible.

Orthogonality of all families of pairwise weakly orthogonal 1-types for ℵ0-categorical weakly o-minimal theories of finite convexity rank has been proved in 6. Here we prove orthogonality of all such families for binary 1-types in an arbitrary ℵ0-categorical weakly o-minimal theory and give an extended criterion for binarity of ℵ0-categorical weakly o-minimal theories . © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Standard unary modal logic and binary modal logic, i.e. modal logic with one binary operator, are shown to be definitional extensions of one another when an additional axiom |$U$| is added to the basic axiomatization of the binary side. This is a strengthening of our previous results. It follows that all unary modal logics extending Classical Modal Logic, in other words all unary modal logics with a neighborhood semantics, can equivalently be seen as binary modal logics. This in particular applies (...) to standard modal logics, which can be given simple natural axiomatizations in binary form. We illustrate this in the logic K. We call such logics binary expansions of the unary modal logics. There are many more such binary expansions than the ones given by the axiom |$U$|⁠. We initiate an investigation of the properties of these expansions and in particular of the maximal binary expansions of a logic. Our results directly imply that all sub- and superintuitionistic logics with a standard modal companion also have binary modal companions. The latter also applies to the weak subintuitionistic logic WF of our previous papers. This logic doesn’t seem to have a unary modal companion. (shrink)

Contrastivism is the claim that the knowledge relation is ternary, it relates three relata: a subject, a proposition, and a class of contrastive propositions. The present paper is a discussion of Jonathan Schaffer’s arguments in favour of contrastivism. The case is made that these are unconvincing: the traditional binary account of knowledge can handle the phenomena that ternarity is claimed to handle in a superior way.

This paper presents a way of formalising definite descriptions with a binary quantifier ι, where ιx[F, G] is read as ‘The F is G’. Introduction and elimination rules for ι in a system of intuitionist negative free logic are formulated. Procedures for removing maximal formulas of the form ιx[F, G] are given, and it is shown that deductions in the system can be brought into normal form.

This paper aims to propose an improved learning algorithm for feature selection, termed as binary superior tracking artificial bee colony with dynamic Cauchy mutation. To enhance exploitation capacity, a binary learning strategy is proposed to enable each bee to learn from the superior individuals in each dimension. A dynamic Cauchy mutation is introduced to diversify the population distribution. Ten datasets from UCI repository are adopted as test problems, and the average results of cross-validation of BSTABC-DCM are compared with other seven (...) popular swarm intelligence metaheuristics. Experimental results demonstrate that BSTABC-DCM could obtain the optimal classification accuracy and select the best representative features for the UCI problems. (shrink)

This study explores the relationship between the scoring structure and the win or loss of a badminton match, while providing quantitative analytic data using binary entropy to determine the uncertainty of said win or loss. Scoring structure data were collected from the official match records of the top 16 events of the World Badminton Championships from 2006 to 2020 as collection objects and were analyzed by means of notational analysis. Our entropy analysis showed that the main factor affecting the certainty (...) of win or loss in men’s singles, men’s doubles and mixed doubles comes from the number of leading points, and in women’s singles and women’s doubles from whether the current point is closer to the match point. Our binary-entropy analysis based on scoring structure showed that, to maintain high uncertainty so that players stay competitive, the scoring points of two sides should differ in less than 5; in addition, the decisive factors for victory strongly depend on gender, also justifying research results of previous studies. (shrink)

This commentary responds to Moti Gorin's article “What Is the Aim of Pediatric ‘Gender‐Affirming’ Care?” We argue that Gorin's case against pediatric gender‐affirming care rests upon numerous false conceptual binaries: female/male, public/private, objective/subjective, and medically necessary/elective. Drawing on feminist bioethics, we show how such dichotomous thinking is both inaccurate and marginalizing of gender minorities.

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)

Let ( * X, * T) be the nonstandard extension of a Hausdorff space (X, T). After Wattenberg [6], the monad m(x) of a near-standard point x in * X is defined as m(x) = μ T (st(x)). Consider the relation $R_{\mathrm{ns}} = \{\langle x, y \rangle \mid x, y \in \mathrm{ns} (^\ast X) \text{and} y \in m(x)\}.$ Frank Wattenberg in [6] and [7] investigated the possibilities of extending the domain of R ns to the whole of * X. Wattenberg's (...) extensions of R ns were required to be equivalence relations, among other things. Because the nontrivial ways of constructing such extensions usually produce monadic relations, the said condition practically limits (to completely regular spaces) the class of spaces for which such extensions are possible. Since symmetry and transitivity are not, after all, characteristics of the kind of nearness that is obtained in a general topological space, it may be expected that if these two requirements are relaxed, then a monadic extension of R ns to * X should be possible in any topological space. A study of such extensions of R ns is the purpose of the present paper. We call a binary relation $W \subseteq ^\ast X \times ^\ast X$ an infinitesimal on * X if it is monadic and reflexive on * X. We prove, among other things, that the existence of an infinitesimal on * X that extends R ns is equivalent to the condition that the space (X, T) be regular. (shrink)

A characterization of a property of binary relations is of finite type if it is stated in terms of ordered T-tuples of alternatives for some positive integer T. The concept was introduced informally by Knoblauch (2005). We give a clear, complete definition below. We prove that a characterization of finite type can be used to determine in polynomial time whether a binary relation over a finite set has the property characterized. We also prove a simple but useful nonexistence theorem and (...) apply it to three examples. (shrink)

Gender-inclusive language, such as the Swedish pronoun hen, may aid in breaking a binary notion of gender and avoid sexism. The present study followed the implementation of a gender-inclusive third-person pronoun singular in Swedish in two surveys with representative samples in 2015 and in 2018. The surveys comprised measures of attitudes toward, and use of, hen as well as possible predictors such as area of residence, age, preferred pronoun, political orientation, and interest in gender issues. Results showed that attitudes toward (...) hen became more positive and that use of hen increased between 2015 and 2018. About half of the population used hen in their communication in 2018, which is a 14-percentage-point increase from 2015. Younger age, she or hen as preferred pronoun, political left-wing orientation, and interest in gender issues predicted a more positive attitude and a more frequent use. Furthermore, the positive change between 2015 and 2018 was larger among younger people, indicating that hen will remain in the Swedish language. The present research is unique in that it follows a gender-fair language initiative during its implementation in representative samples, thereby providing insights for social movements aiming for gender-fair language. We also discuss the theoretical implications of a gender-inclusive pronoun in comparison with past studies on gender-fair language. (shrink)

In the moral realm, our deontic judgments are usually (always?) binary. An act (or omission) is either morally forbidden or morally permissible. 1 Yet the determination of an act's deontic status frequently turns on the existence of properties that are matters of degree. In what follows I shall give several examples of binary moral judgments that turn on scalar properties, and I shall claim that these examples should puzzle us. How can the existence of a property to a specific degree (...) demarcate a boundary between an act's being morally forbidden and its not being morally forbidden? Why aren't our moral judgments of acts scalar in the way that the properties on which those judgments are based are scalar, so that acts, like states of affairs, can be morally better or worse rather than right or wrong? I conceive of this inquiry as operating primarily within the realm of normative theory. Presumably it will give aid and comfort to consequentialists, who have no trouble mapping their binary categories onto scalar properties. For example, a straightforward act utilitarian, for whom one act out of all possible acts is morally required (and hence permissible) and all others morally forbidden, can, in theory at least, provide an answer to every one of the puzzles I raise. And, in theory, so can all other types of act and rule consequentialists. They will find nothing of interest here beyond embarrassment for their deontological adversaries. The deontologists, however, must meet the challenges of these puzzles. And for them, the puzzles may raise not just normative questions, but questions of moral epistemology and moral ontology. Just how do we know that the act consequentialist's way of, say, trading off lives against lives is wrong? For example, do we merely intuit that taking one innocent, uninvolved person's life to save two others is wrong? Can our method of reflective equilibrium work if we have no theory by which to rationalize our intuitions? And what things in the world make it true, if it is true, that one may not make the act consequentialist's tradeoff? I do not provide any answers to these questions any more than I provide answers to the normative ones. But they surely lurk in the background. (shrink)

The article considers regional issues of the Kazakh transtoposystem. There are a number of problematic issues related to cross-border Kazakh toponymy. The article analyzes only one aspect – the status of binary names in the cross-border toposystem. The goal is to study how obvious the binary opposition is there, considering the etymology of toponyms based on semantic opposition. The toposystem of the Northern and Western regions bordering Russia was used as the empirical material for the study. According to the border (...) administrative-regional division, a number of districts of such regions of the country as North Kazakhstan, Pavlodar, Kostanay, Western Kazakhstan, Aktobe, and Atyrau border with Russia. In the article, a series of binary names along the toponyms of this cross-border zone is formed. In particular, Úlken-Kіshі (Big-Small), Aq-Qara (Black-White), Qara-Sary (Black-Yellow), Jaqsy-Jaman (Good-Bad), Jyly-Sýyq (Warm-Cold), and Ashy-Tushy (Bitter-Fresh) are analyzed. The difference between toponymic binary names and lexical antonyms is considered. We discuss the fact that the contradiction in lexical antonyms is clearly expressed, but in binary opposition along toponyms, the contradiction may not be complete. It is reported that the contradiction of toponyms is recognized only in the toponymic context, and sometimes it is even possible to form a related pair, rather than a semantic contradiction. (shrink)

The Yijing/Binary System Episode involved Leibniz' discovery of a de facto representation of the binary number system in the sixty-four-hexagram Fu Xi "Yijing." Scholars have left the match unexplained, since they have found no evidence of a forgotten binary number system in ancient China. The interesting similarities and differences are discussed between the thought of Leibniz and that of Shao Yong, both of whom, it is argued, understood and recognized the importance of the double geometric progression in the diagram.

According to Act Consequentialism, an act is right if and only if its outcome is not worse than the outcome of any alternative to that act. This view, however, leads to deontic paradoxes if the alternatives to an act are all other acts that can be done in the situation. A typical response is to only apply this rightness criterion to maximally specific acts and to take the alternatives to a maximally specific act to be the other maximally specific acts (...) that can be done in the situation. (This view can then be supplanted by a separate account for the rightness of acts that are not maximally specific.) This paper defends a rival view, Binary Act Consequentialism, where, for any voluntary act, that act is right if and only if its outcome is not worse than the outcome of not doing that act. Binary Act Consequentialism, which dates back to Jeremy Bentham, has few supporters. A number of seemingly powerful objections have been considered fatal. In this paper, I rebut these objections and put forward a positive argument for the view. (shrink)