“Basic equality” is the thesis that all (or nearly all) human beings are equal in moral status. Widespread interpersonal differences among humans make the task of justifying basic equality notoriously difficult. One strategy for circumventing this difficulty is to identify some morally significant binary (“all-or-nothing”) property that all humans have. This strategy seems promising: if the basis of equality is binary, then those who have it have it equally. However, skeptics have argued against this strategy on the grounds (...) that a proper defense of basic equality requires that we identify a morally significant property that can vary among humans but does not in fact vary. This paper examines various ways in which this skeptical argument can be motivated and concludes that they all fail. (shrink)

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 destabilize one or more pieces of dominant gender ideology. After developing a model of critical gender kinds, I suggest that genderqueer is best modeled as a critical gender kind that destabilizes the ‘binary axis’, or the piece of dominant gender ideology that says that the only possible genders are the binary, discrete, exclusive, and exhaustive kinds men and women. (shrink)

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)

The remarks which follow arise from the daily and simultaneous consulting of two literatures and, in a larger sense, of two cultures, Portuguese and Brazilian, both expressed in the same language, Portuguese. They also arise from an attempt to describe and define by categories which are “internal” to literature the differences which exist between the two bodies of writing under discussion. But they are equally inspired by a desire to isolate in the corpus of the texts which conventionally constitute a (...) national literature those thematic and stylistic recurrences which may serve as starting points for an attempt at formalization. (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)

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.

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. (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.

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)

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)

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)

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.

The feature selection (FS) process has an essential effect in solving many problems such as prediction, regression, and classification to get the optimal solution. For solving classification problems, selecting the most relevant features of a dataset leads to better classification accuracy with low training time. In this work, a hybrid binary crow search algorithm (BCSA) based quasi-oppositional (QO) method is proposed as an FS method based on wrapper mode to solve a classification problem. The QO method was employed in (...) tuning the value of flight length in the BCSA which is controlling the ability of the crows to find the optimal solution. To evaluate the performance of the proposed method, four benchmark datasets have been used which are human intestinal absorption, HDAC8 inhibitory activity (IC50), P-glycoproteins, and antimicrobial. Accordingly, the experimental results are discussed and compared against other standard algorithms based on the accuracy rate, the average number of selected features, and running time. The results have proven the robustness of the proposed method relied on the high obtained value of accuracy (84.93–95.92%), G-mean (0.853–0.971%), and average selected features (4.36–11.8) with a relatively low computational time. Moreover, to investigate the effectiveness of the proposed method, Friedman test was used which declared that the performance supremacy of the proposed BCSA-QO with four datasets was very evident against BCSA and CSA by selecting the minimum relevant features and producing the highest accuracy classification rate. The obtained results verify the usefulness of the proposed method (BCSA-QO) in the FS with classification in terms of high classification accuracy, a small number of selected features, and low computational time. (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)

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 presents rules in sequent calculus for a binary quantifier I to formalise definite descriptions: Ix[F, G] means ‘The F is G’. The rules are suitable to be added to a system of positive free logic. The paper extends the proof of a cut elimination theorem for this system by Indrzejczak by proving the cases for the rules of I. There are also brief comparisons of the present approach to the more common one that formalises definite descriptions with (...) a term forming operator. In the final section rules for I for negative free and classical logic are also mentioned. (shrink)

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)

Philosophical and ethical discussions of warfare are often tied to emerging technologies and techniques. Today we are presented with what many believe is a radical shift in the nature of war-the realization of conflict in the cyber-realm, the so-called.

This paper provides a background to, detailed exploration, and then critique of, the influential notion of economic performativity. It begins with a broad sweep of the theoretical developments in economic sociology in the years before the advance of the performativity program. In doing so it outlines the theoretical quandary that performativity sought to move beyond. Having set the scene, it then looks at the performativity thesis in detail, explaining how it seeks to do away with modern ontological binaries like the (...) object/subject dichotomy. Once the performativity thesis has been unpacked, it is critiqued. Leading to the conclusion, that while there have been some benefits to the performative approach, especially in research looking at finance, the performativity thesis ultimately fails in its attempt to move beyond the ontology of “the moderns”, and does little to shift the debates in economic sociology that predated its popularity. (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)

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)

ArgumentThis essay seeks to identify the cultural significance of Goethe's scientific writings. He reformulates, in the light of his own concrete experience, “crucial turning-points” in the history of science – key ideas, the historical understanding of which is vital to present understanding – thus situating his own scientific work at the bi-polar center of the Western scientific tradition, conceived as the dramatic interplay over centuries of two opposing modes of thought. For in his experimentation he recaptures the glimpse of living (...) form gained in aesthetic perception, from which such inherited theoretical positions are ultimately derived. At each stage of this process, imagination, in its aesthetic modality, is essential, for it alone reveals the world as it truly is. The literary quality of his writings on nature, as on culture, reveals Goethe's stylistic achievement in devising a medium in which the insights gained in contemplation may be so transmitted as to make a similar, imaginative, appeal to his reader – re-enacting the abstract-concrete equilibrium characterizing all aesthetic experience. Matching his style to the subtle, delicate, connectedness of Nature, Goethe recreates the delights of participating in natural creativity. His Janus-faced, scientific-literary, style illustrates “binary synthesis,” the principle that unites Goethe's science with his art.Beauty is the normal state.There can be no such thing as an eclectic philosophy, but there can be eclectic philosophers. But an eclectic is anyone who, from whatever exists and is happening round about, appropriates the things he or she finds congenial to her or his nature; and this context validly includes all that can be called culture and progress in a theoretical and practical sense. It follows that two eclectic philosophers could turn into the greatest opponents if they are antagonistic to one another, each picking out whatever suits him or her in every traditional system of philosophy. (shrink)

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.

Hypatia and Synesius lived in a highly divisive time with religious extremism on the rise and the meaning and role of Classical cultural fixtures like paideia, philosophia and manteia being questioned and redefined. I examine Synesius’ Letters, Dion, and De Insomniis to tease out the universalizing and harmonizing tendencies between pagan and Christian, theoria and paideia, philosophia and manteia that Synesius’ writings, life and career embody. I look at Synesius’ synthesis of Iamblichean and Plotinian tendencies, a binary found in (...) modern scholarship, to show that theurgy was likely part of Hypatia’s teaching within a well-rounded curriculum that included classical paideia and philosophical theoria. Synesius advocates for the importance of paideia, including rhetoric and philosophia as aids in the step-by-step approach to the spiritual ascent, while also acknowledging the value and universal accessibility of theoria reached by desert monks and the dream-divination that everyone can experience in sleep. Paideia makes the fall from the heights of theoria more pleasant, while philosophia is essential for purifying the pneuma and making it receptive to divinely inspired dreams. I propose that it was in Hypatia’s school that Synesius internalized a quote that reconciles the two approaches to the ascent. While society at large was obsessed with ever widening opposites and binaries, Hypatia’s Synesius both overtly and covertly emphasized harmonization and unity that are at the heart of philosophia. (shrink)

The first collection of Leibniz's key writings on the binary system, newly translated, with many previously unpublished in any language. -/- The polymath Gottfried Wilhelm Leibniz (1646–1716) is known for his independent invention of the calculus in 1675. Another major—although less studied—mathematical contribution by Leibniz is his invention of binary arithmetic, the representational basis for today's digital computing. This book offers the first collection of Leibniz's most important writings on the binary system, all newly translated by the (...) authors with many previously unpublished in any language. Taken together, these thirty-two texts tell the story of binary as Leibniz conceived it, from his first youthful writings on the subject to the mature development and publication of the binary system. -/- As befits a scholarly edition, Strickland and Lewis have not only returned to Leibniz's original manuscripts in preparing their translations, but also provided full critical apparatus. In addition to extensive annotations, each text is accompanied by a detailed introductory “headnote” that explains the context and content. Additional mathematical commentaries offer readers deep dives into Leibniz's mathematical thinking. The texts are prefaced by a lengthy and detailed introductory essay, in which Strickland and Lewis trace Leibniz's development of binary, place it in its historical context, and chart its posthumous influence, most notably on shaping our own computer age. (shrink)

How are sex and gender related? Are they the same thing? What exactly is gender? How many genders are there? What is the science on all of this? Is gender a product of nature, nurture, or both? This book introduces readers to fundamental questions about sex and gender categories as they’ve been considered across the centuries and through a wide array of disciplines and perspectives. From the Bible to Darwin, from Enlightenment thinkers to contemporary trans philosophers, _Beyond the Binary_ offers (...) an accessible survey of the wide range of views about sex and gender. This revised and expanded edition uses updated terminology and diagnostic criteria and offers new material with a greater focus on trans, Indigenous, racialized, and subaltern thinkers. It includes useful discussion questions and further reading recommendations at the end of each chapter, as well as an extensive glossary of terms. (shrink)

Examines traditional sites of binary thinking in ancient Greek texts and culture to demonstrate surprising ambiguity, especially with regard to sexual difference.

Postgenderism is an extrapolation of ways that technology is eroding the biological, psychological and social role of gender, and an argument for why the erosion of binary gender will be liberatory. Postgenderists argue that gender is an arbitrary and unnecessary limitation on human potential, and foresee the elimination of involuntary biological and psychological gendering in the human species through the application of neurotechnology, biotechnology and reproductive technologies. Postgenderists contend that dyadic gender roles and sexual dimorphisms are generally to the (...) detriment of individuals and society. Assisted reproduction will make it possible for individuals of any sex to reproduce in any combinations they choose, with or without "mothers" and "fathers," and artificial wombs will make biological wombs unnecessary for reproduction. Greater biological fluidity and psychological androgyny will allow future persons to explore both masculine and feminine aspects of personality. Postgenderists do not call for the end of all gender traits, or universal androgyny, but rather that those traits become a matter of choice. Bodies and personalities in our postgender future will no longer be constrained and circumscribed by gendered traits, but enriched by their use in the palette of diverse self-expression. (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.

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)

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.

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)

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.

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...

Causation is a topic of perennial philosophical concern. As well as being of intrinsic interest, almost all philosophical concepts — such as knowledge, beauty, and moral responsibility — involve a causal dimension. Nonetheless, attempts to provide a satisfactory account of the nature of causation have typically led to barrages of counterexamples. I hope to show that a number of the difficulties plaguing theories of causation have a common source.Most philosophical theories of causation describe a binary relation between cause and (...) effect, or at any rate, a relation that reduces to such a binary relation when certain background information is held fixed. Indeed, most theories provide the same general account of when this relation holds: in order to evaluate whether C causes E, we must make a comparison between two cases, which we may neutrally label as C and ∼C. Where theories of causation differ, of course, is in precisely what is being so compared. Regularity theories of causation require a comparison between what actually happens whenever C occurs, and what actually happens, elsewhere and elsewhen, when C does not occur. (shrink)

Response to Anne Fausto-Sterling's New York Times Op-Ed, in which she purports to explain why sex isn't binary.

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)