We prove that algebras of binary relations whose similarity type includes intersection, union, and one of the residuals of relation composition form a nonfinitely axiomatizable quasivariety and that the equational theory is not finitely based. We apply this result to the problem of the completeness of the positive fragment of relevance logic with respect to binary relations.

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)

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)

Recent ideological positioning on the world stage has born a startling resemblance to a form of positioning within nursing theory – that of taking complex ideas, reducing them to a simplistic binary form, and uncritically adopting one half of that form. In some cases, this adoption of a binary position has led to a passionately held form of ‘othering’ that prohibits a healthy and critical engagement with ideas. As alluring as settling for the binary form may be (...) – we argue for holding binaries in tension as a catalyst for stimulating dialogue – reasoning and exploration of new ways of wrestling with the social and moral complexity of nursing. (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)

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)

Interviews with 41 nonbinary individuals reveal a considerable amount of ambivalence among nonbinary people regarding transgender identification. There is also disagreement about which model of transgender legitimacy determines group membership: the binary and medicalized model or the umbrella model. Those who do not identify as transgender either do not consider themselves to be “trans enough” to claim group membership alongside trans men and trans women or otherwise consider their gender experience to be qualitatively different from the transgender experience. Meanwhile, (...) those who do identify as transgender credit the umbrella model as authoritative while acknowledging that their claims to group membership are often resisted by those who uphold the binary transgender model. Finally, those who defy an easy yes/no transgender categorization schema qualify their transgender identification with admissions of doubt that they are really “trans enough” to claim the label or through linguistic practices that position themselves as tangentially transgender or as distinctly nonbinary transgender. This range of responses illuminates the diverse gender identities that coexist among nonbinary people that cannot be neatly sorted into a man/woman or cisgender/transgender binary. Research on the sociology of gender must expand beyond both of these binary frameworks to reflect the reality of gender diversity. (shrink)

Leibniz’s binary numeral system is generally studied for its arithmetical relevance, but the analysis of several unpublished manuscripts shows that from the very beginning Leibniz also envisaged a new form of algebra in the context of dyadics based on the idea that its letters can only express numbers that are either 1 or 0. In this paper, I shall present the most notable results of this binary algebra: the determination of the algorithm for the expansion of squares and (...) the development of the positional notation used to express any possible number. These achievements explain the priority of dyadics over any other numeral system in Leibniz’s mind and his impressive work on the classification of numbers which was facilitated by tools and notions which were only accessible to him at that time. (shrink)

Leibniz’s binary numeral system is generally studied for its arithmetical relevance, but the analysis of several unpublished manuscripts shows that from the very beginning Leibniz also envisaged a new form of algebra in the context of dyadics based on the idea that its letters can only express numbers that are either 1 or 0. In this paper, I shall present the most notable results of this binary algebra: the determination of the algorithm for the expansion of squares and (...) the development of the positional notation used to express any possible number. These achievements explain the priority of dyadics over any other numeral system in Leibniz’s mind and his impressive work on the classification of numbers which was facilitated by tools and notions which were only accessible to him at that time. (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)

We provide a complete binary implicational axiomatization of the positive fragment of propositional dynamic logic. The intended application of this result are completeness proofs for non-classical extensions of positive PDL. Two examples are discussed in this article, namely, a paraconsistent extension with modal De Morgan negation and a substructural extension with the residuated operators of the non-associative Lambek calculus. Informal interpretations of these two extensions are outlined.

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 paper explores issues of abstraction and space in Sande Zeig's movie The Girl (2001), based on a novella by Monique Wittig, who also co-wrote the script. It argues that, with this movie, Zeig and Wittig strive to re-materialize the lesbian body abstracted by the ‘Straight Mind’ as defined by Wittig in her 1980 essay. The plot revolves around the love affair of two women, the narrator and the Girl (a lesbian painter and a straight B-grade jazz singer), under the (...) oppressive scrutiny of the Man (the Girl's boss). Each part of this paper corresponds to one space where the characters interact: first, it shows how the nightclub stands as a space of transgression for the lesbian subject and how it opens a reflection on temporality as represented by space; then the analysis of the hotel room where the Girl lives and meets the narrator demonstrates how, notably through the use of close-ups in erotic scenes, Zeig redefines abstraction as a new way to envisage the materiality of the lesbian body; finally, in the third part, the discussion on abstraction moves on to the narrator's studio where, through her work as a painter, she also explores abstract representations of the female body. This approach reconciles Wittigian theory with post-modern queer theory, and confirms that the former still offers paths to positive reformulations of modes of relationality through the de-spatialization of gender – de-genderization; the rematerialization of the body outside of heteronormative conventions; and a reconfiguration of human relationships that refuses the inevitability of social and amorous hierarchy, and that shifts the representation of the erotic from possessiveness to disinterested reciprocity. (shrink)

What does feminist disability studies contribute to feminist methods? Feminist disability scholars interweave life-writing about their experiences of disability or caring for a disabled person to challenge ableist stereotypes. As such, they foreground their own vulnerability to build disability identity and community. This style of life-writing, while essential, tends to calcify the dichotomy between the disabled and abled—a binary that the field of feminist disability studies aims to destabilise. Building on new work in feminist disability studies, I show how (...) some scholars use life-writing to cultivate an estranging sensitivity. This new sensitivity builds on prior feminist disability studies scholarship to estrange us from 1) the idea that disability is a cohesive identity and community, 2) that disability is always a socially desirable position, and 3) that allegiance to disability rights insulates us from ableist anxiety. By embracing the tension between solidifying and destabilising the meaning of disability, feminist disability scholars can leverage life-writing as a tool of resistance and thereby lessen the threat of conformity that life narratives tend to produce. (shrink)

Traditionally the study of chemical elements has been limited to well-known concepts like the periodic properties and chemical families. However, current information shows a new and rich language that allows us to observe relations in the elements that are not limited to their positions in the table. These relations are evident when reactions are represented through networks, as in the case of similar reactivity of organic compounds sharing functional groups. For the past two decades, it has been argued that network (...) reactions may be considered the core of chemistry. This network, which constitutes the basic set of chemical knowledge, provides the basis for classification and delivers routes to obtain new and known substances. In order to provide an example, we constructed and analyzed a network of chemical elements from the formation of stoichiometric binary compounds, providing to the chemistry, a formal structure of extracting the chemical knowledge. Thus, we explored all possible presence of relationships among elements. Concepts like degree centrality and centralization, the relationships among metals, semimetal and nonmetal classes, blocks, and chemical families were analyzed. We observed that the network structure had a small core set of elements of high reactivity and also a peripheral set of elements of low reactivity. The classes, blocks and families show the following increasing order of reactivity: nonmetals > semimetals > metals; p > s > d > f; and families: boron, carbon, pnictogens, chalcogens, halogens, lanthanoids > other families. This example shows, from the network perspective, that the elements and their classifications exhibit properties such as the reactivity, order, and similarity. (shrink)

The aim of this paper is to provide a contribution to the natural logic program which explores logics in natural language. The paper offers two logics called \ \) and \ \) for dealing with inference involving simple sentences with transitive verbs and ditransitive verbs and quantified noun phrases in subject and object position. With this purpose, the relational logics are introduced and a model-theoretic proof of decidability for they are presented. In the present paper we develop algebraic semantics of (...) the logics using congruence theory. (shrink)

This paper explores the motivations and experiences of British women working as lap dancers in the tourist resorts of southern Tenerife, with a particular focus on the subjective choices and processes undertaken by working-class women in the embodiment of positively evaluated identities. It uses Skeggs’ theoretical framework of ‘becoming respectable’ (1997) alongside other debates on ‘identity management’ in order to begin mapping the ways in which migrant British lap dancers produce themselves, negotiate gender and class, and seek forms of respectability, (...) reputability and honour through their work. Drawing on empirical data, it will discuss how strong disassociations with the Other are formed, and how and why important binaries, particularly distinctions between lap dancing and prostitution and lap dancing and other ‘degraded’ forms of work and lifestyle are drawn in the dancers’ own stories of themselves. It will look at notions and processes of gaining ‘respectability’ through part of a wider migrant discourse, exploring how being a migrant lap dancer can serve as a vehicle for reproducing a ‘respectable’ and otherwise positively evaluated self on several levels. (shrink)

This paper presents rules of inference for a binary quantifier I for the formalisation of sentences containing definite descriptions within intuitionist positive free logic. I binds one variable and forms a formula from two formulas. Ix[F, G] means ‘The F is G’. The system is shown to have desirable proof-theoretic properties: it is proved that deductions in it can be brought into normal form. The discussion is rounded up by comparisons between the approach to the formalisation of definite descriptions (...) recommended here and the more usual approach that uses a term-forming operator ι, where ιxF means ‘the F’. (shrink)

We give a new and elementary construction of primitive positive decomposition of higher arity relations into binary relations on finite domains. Such decompositions come up in applications to constraint satisfaction problems, clone theory and relational databases. The construction exploits functional completeness of 2-input functions in many-valued logic by interpreting relations as graphs of partially defined multivalued ‘functions’. The ‘functions’ are then composed from ordinary functions in the usual sense. The construction is computationally effective and relies on well-developed methods of (...) functional decomposition, but reduces relations only to ternary relations. An additional construction then decomposes ternary into binary relations, also effectively, by converting certain disjunctions into existential quantifications. The result gives a uniform proof of Peirce’s reduction thesis on finite domains, and shows that the graph of any Sheffer function composes all relations there. (shrink)

The ordering tendency in binary f -Ti solid solution containing 3sp or 4sp simple-metal or 3d transition-metal solute is investigated systematically by the linear muffin-tin orbital method within the atomic sphere approximation . We demonstrated that the effective pairwise interaction energy in a solid solution is equal to half the solute-solute interaction energies and can be evaluated by a supercell total energy approach. The calculations of EPI energy both with and without volume relaxation of the supercells and local density (...) of states show that the EPI energies of Ti-SM and Ti-TM solutions are dominated by different factors. For Ti-SM solutions, the EPI energies are of large absolute values with a negative sign, indicating strong ordering tendency in these solutions. The volume relaxation does not alter the EPI energy substantially. The calculated LDOS shows that the ordering tendency in Ti-SM solutions may be related to the hybridization between the electrons of the SM atoms when they are close to each other. For most Ti-TM solutions, if calculated without relaxation, the absolute EPI energies are very small; however, if calculated with relaxation, they are of relatively large positive values, indicating a clustering tendency in these solutions. By combining the calculated EPI energy and Flinn's model for short-range order strengthening, the increase in critical shear stress ‰ sro due to SRO is estimated for Ti-SM alloys, and the results qualitatively agree with experiment. (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)

_ Source: _Volume 24, Issue 2, pp 224 - 278 This article discusses the anonymous early kabbalistic work _Sefer Maʿayan ha-Ḥokhmah_, one of the pivotal works of ʿIyyun literature. The first part deals with the book’s historical and literary aspects. The second part interprets a specific formulation in light of the basic ideas of the book itself, presenting the twofold pattern as a mystical type and as a grounding for linguistic-theological theory. The third part discusses the term “positive theology” in (...) the theosophical and religious dimension, from the phenomenological perspective of extrovertive mysticism, and as a linguistic structure that provides the layer of signs as a stable basis for the restrained progress of Tongue. Acquiring the source as hidden but attendant by its constant grounding as a part of linguistic progression, uses the bifocal sight of binary extrovertive mysticism to denote the twofold structure of each being and each part of speech. (shrink)

This article reports an empirical investigation of the cognitive effort required to decide in multiattribute binary choice using a variation of the Additive Difference strategy. In contrast with other studies, this paper focuses on the effect of various context variables (rather than task variables) on cognitive effort. In order to select the context variables to be manipulated, we used the model proposed by Shugan (1980; J. Consumer Res. 75 (1980) 99). Our results indicate that there is a positive relationship (...) between the cognitive effort required to decide and the mean of the differences between the dimensions of the choice alternatives. We have also found an inverse relationship between cognitive effort and the variance of the differences between the dimensions of the choice alternatives. Finally, we have found that in negative correlation contexts the effort needed to decide is greater than in positive and null correlation contexts. (shrink)

We characterize the polynomial time operations as those which are provably total in a first order system, which comprises (untyped) combinatory logic with extensionality, together with positive “safe induction” on the set of binary strings. The formalization of safe induction is inspired by Leivants idea of ramification. We also show how to replace ramification by means of modal logic.

This article supplements Julio Tuleda, Enrique Burguete, and Justo Aznar's “The Vatican opinion on gender theory” (Linacre). It supplements their article by providing a stronger argument for the thesis that “intersex” does not violate binary sex in human beings. In their response to Timothy F. Murphy's criticism of “the Vatican's” (rightfully corrected as the Magisterium of the Catholic Church's) position on the sex binary, they argue subsidiarily that “intersex” does not violate the sex binary. However, their argument (...) against Murphy as stated is implausible; however, I provide a much stronger argument for their conclusion that intersex does not violate the sex binary. I intend to perform this supplementation in two stages, assuming the reader's familiarity with “The Vatican opinion on gender theory.” First, I provide a broader background than Murphy's to the challenge that “intersex” conditions violate the sex binary, showing both how Murphy's criticism is unoriginal and how “intersex” both has been, and continues to be, misunderstood. Second, I problematize Tuleda’s argument, and offer the strongest argument for the conclusion that “intersex” does not violate the sex binary on purely secular/nonreligious grounds (addressing Murphy's complaint). I conclude that the Magisterium of the Catholic Church remains correct that sex is binary. (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.

What are the leading forces and ideas that are shaping our age? In the West, a decade of financial disruption, austerity, and stagnant wages has produced a popular rejection of market fundamentalism that prevailed for over forty years. Mass immigration and multiculturalism have contributed to rapid changes in both family and community life that leave many people feeling dispossessed or even humiliated. Unresponsive government is exacerbating people’s sense of powerlessness and anger. The revolt against the status quo is fuelling a (...) political insurgency against the establishment that replaces the old opposition of left versus right with a similarly simplistic dichotomy pitting the people against the elites. We are witnessing the failure of dualistic thinking and this will not be resolved by substituting one binary for another. Our contemporary conjuncture is such a period of interregnum and a war of position between the hitherto hegemonic ideology of liberalism and its populist rivals. The popular revolt against liberalism, which is driving the political insurgency across the West, highlights the collapse of the authority of the professional political class dominated by liberals. In what follows I shall argue that the emergent ideologies which are vying for hegemony are hyper-liberalism, nationalist traditionalism, and tech utopianism. All of them are variously anti-humanist, to which one can oppose updated versions of one-nation conservatism and ethical socialism. Before setting out the unfolding ‘war of position,’ I will first explore the new anti-humanism that underpins the main ideological movements. (shrink)

In the current ongoing Terror War, both George W. Bush and Osama bin Laden deploy certain similar figures of speech, fusing their metaphysical and political discourses while reserving the demonology. In his speech to Congress on September 20, 2001 declaring his war against terrorism, Bush described the conflict as a war between freedom and fear. The coming Terror War was, he explained, a conflict between “those governed by fear” who “want to destroy our wealth and freedoms,” and those on the (...) side of freedom. Bush insisted that “you’re either with us, or you’re with the terrorists,” and laid down a series of non-negotiable demands to the Taliban while Congress wildly applauded. Bush’s popularity soared with a country craving blood-revenge and the head of Osama bin Laden. Moreover, proclaiming what his administration and commentators would describe as “the Bush doctrine,” Bush also asserted that his administration held accountable those nations who supported terrorism –- a position that could nurture and legitimate military interventions for years to come. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy, Psychiatry, & Psychology 9.2 (2002) 127-129 [Access article in PDF] Linguistic Markers of Recovery:Underpinnings of First Person Pronoun Usage and Semantic Positions of Patients Patrick Suppes Keywords: association, freedom, habits, psychotherapy, roles, semantics. USING LINGUISTIC EVIDENCE to evaluate recovering psychotherapy patients is an attractive and useful idea. I agree with much of Dr. van Staden's proposals for doing so. The purpose of this commentary is to give some (...) comments and criticisms on points of detail. Roles, Not Semantics A fair amount of Dr. van Staden's article is concerned with the semantics of relations. The focus on relations is a good thing. Restricting discourse about patients to properties is not sufficient, for everyone regards how a person is relating to others, and even to other things, as an important feature of normal behavior and mental health. We do not want just to report, "John was upset," but consider it definitely more informative to say, "John was upset by his father's criticisms." The English language and all other natural languages are rich in verbs for expressing relations with emotional affect between two or more persons, or a person and an event or thing. Staden's article focuses on the interesting and important case of first person pronouns. To go from saying, "She made me do it" to "I did it" is, for reasons that need not be spelled out, a sign of progress. A way to describe this change is that the speaker has indicated that in the implicit context assumed he or she has shown signs of moving from the role of being a patient to that of being an actor, from being a recipient of actions to being a performer of acts.van Staden concentrates on the semantics of relations to bring out what I call the change of roles. I would certainly agree that such change of roles is important to the semantics of affective or action verbs and verb phrases. We have no disagreement at all about this. Yet I am critical of his wanting to range much wider in his analysis of semantics. The logical or formal treatment of relations is a large topic, full of many distinctions and subtleties that seem to me not too relevant to his main theme. In a very general way he wants to say that what is usually thought of as [End Page 127] the first position in a relation, what he calls the alpha position, is occupied by the owner of the relation, and the second position, in a binary relation—the main case discussed—is occupied by the accidental to that particular relation. This second position is called the omega position.This runs contrary to much of the mathematical literature on relations, which occupy an important place in many parts of mathematics such as geometry. So when we say that one triangle is larger than another, it seems positively weird to say the second triangle is somehow accidental to the relation. But this is true and confusing even for the familiar and classical kinds of actions often cited by van Staden. In analyzing the sentence "Brutus killed Caesar intentionally" it sounds really strange to say that Caesar occupied the accidental position in the expressed relation of killing.Moreover, in the conceptual and philosophical discussion of relations, it is common practice to stress that even if the natural grammar of a sentence has a subject-predicate structure, as in "Elizabeth is the mother of Charles," no special logical force is given to what van Staden calls the first or alpha position in most mathematical relations, such as "The number 2 is less than the number 3," expressed in ordinary mathematical notation as "2 < 3."On the other hand, I stress that it is natural to distinguish in a relational sentence expressing an action between the role of actor and the role of patient, no matter which is the grammatical subject of the sentence, as in the following pair "John hurt Mary" and "Mary was hurt by John." The roles of actor... (shrink)

The academic standing of the staff working in vocational higher education must be judged as unsatisfactory according to two possible criteria: the traditional criteria, which are derived from the universities operating within the previous unitary higher education system; and the criteria outlined by the bill of the Law of Higher Education Institutions. The latter derive from the same historical institutional pattern.There are many reasons to conclude that, academically, in most fields of study, the new institutions do not reach the level (...) of the old ones. However, the mission of the new sector—the second-rank academic institutions in the eyes of the traditional academic community—is at least debatable, if not mistaken. The public university sector appears to be in deep crisis, with academics so attached to the Humboldtian university that they ignore the claims for social relevance in education.8 This is further complicated by deepening financial hardship.Using traditional criteria, it is possible that Estonia will be left with two socially irrelevant higher education sectors, instead of one functioning sector. It is also possible that the second sector, which does not fit these criteria, will be eliminated. However, the fault does not lie wholly with the dominance of traditional university attitudes. It also lies in a lack of vision on the part of the new institutions. As children of the proletariat society, they fail to recognise their vocational orientation as a benefit, and instead try to hide it. They are developing theoretically overloaded four- to five-year study programmes. None of these institutions has solved the problem of balancing the requirement of employing 50 per cent faculty full time and maintaining a satisfactory academic level. The need to demonstrate that part-time employees may actually benefit the vocational sector has not yet been understood.9As long as the sector continues to accept the rules forced upon it by the old universities, it probably has no useful role in Estonia. Its institutions, especially the public institutions, cannot compete with the traditional universities in academic fields. The universities, on the other hand, are beginning to understand that the policy they proclaimed some years ago, which was based on the clear distinction between two sectors on the German pattern, does not work in a small country with very limited resources, and an inheritance from the previous regime of a large university sector with an enrolment rate of more than 20 per cent of the age group. The universities have agreed to offer their own non-degree courses at diploma level, and now seriously threaten the small new institutions. From the financial point of view, the universities' expressed desire to swallow the small vocational institutions is beneficial since the small institutions have no clearly distinct role of their own.The private vocational higher education institutions do not conceal the fact that, according to their own vision, they have little place in the vocational sector. Some of them would like an official status equal to that of the universities, the right to offer graduate and postgraduate courses as well as diploma courses, and the registration of their diplomas and certificates on an equal basis with the public universities in the Register of Diplomas and Certificates at the Ministry of Culture and Education. In other words, they are interested in becoming fully accredited universities. This increases competition for students and—given the Estonian mechanism of public financing of higher education based on the number of students admitted provided by the Ministry of Culture and Education10—there will be less money for public universities. Here lies the origin of the principle that the universities are established by parliament and the vocational higher education institutions by executive action by the government.The existence of the new sector is seriously threatened. The current pattern of postgraduate studies has blocked the preparation of a sufficient number of research-degree holders, even at master's level.11 The new institutions cannot train their own faculty. The recent experience of Concordia International University—which depends greatly on staff with bachelor's and master's degrees from the United States, who form some 80 per cent of the faculty—demonstrates that the participation of first- or even second-rank Western academics in Estonian higher education can never be very high. If the system cannot accept experienced local staff for legal appointments in the vocational sector, unless they have a research degree, these institutions will not survive for long. Society will be back to the position where there are a large number of underpaid or unemployed academics, but a shortage of qualified individuals who could be self-employed and capable of running small and medium-size enterprises. (shrink)

Phronesis has become a buzzword in contemporary medical ethics. Yet, the use of this single term conceals a number of significant conceptual controversies based on divergent philosophical assumptions. This paper explores three of them: on phronesis as universalist or relativist, generalist or particularist, and natural/painless or painful/ambivalent. It also reveals tensions between Alasdair MacIntyre’s take on phronesis, typically drawn upon in professional ethics discourses, and Aristotle’s original concept. The paper offers these four binaries as a possible analytical framework for classifying (...) and evaluating accounts of phronesis in the medical ethics literature. It argues that to make sense of phronesis as a putative ideal in professional medical ethics—for example, with the further aim of crafting interventions to cultivate phronesis in medical ethics education—the preliminary question of which conception of phronesis is most serviceable for the aim in question needs to be answered. The paper identifies considerable lack of clarity in the current discursive field on phronesis and suggests how that shortcoming can be ameliorated. (shrink)

Addressing many social challenges requires both structural and behavioral change. The binary of an i- and s-frame obscures how behavioral science can help foster bottom-up collective action. Adopting a community-frame perspective moves toward a more integrative view of how social change emerges, and how it might be promoted by policymakers and publics in service of addressing challenges like climate change.

The discipline of nursing has long maintained that is has a unique contribution to make within the health care arena. This assertion of uniqueness lies in great part in the discipline's claim to a distinct body of knowledge. Nursing knowledge is characterized by diverse and multiple forms of knowing and underpins the work of all nurses, regardless of field of practice. Unfortunately, it has been challenging for the discipline to take full ownership of its epistemological diversity, largely due to factors (...) such as competing worldviews, and ideological and binary positioning. A philosophical middle ground stance is proposed as a way for the discipline to contemplate, discuss and develop nursing knowledge; a middle space that provides the freedom to consider competing worldviews while still allowing for the discipline to fully express itself in all of its epistemological diversity. In being able to enact its multiple forms of knowledge in a creative and open space that is open to different ideas and worldviews, not only can nursing take full ownership of its practice and its unique knowledge, it can also demonstrate how best to navigate an increasingly polarized world. In a world that is increasingly fixated on binary solutions and dualistic points of view, it is time for nursing to celebrate its epistemological diversity. (shrink)

The paper studies how the localic notion of sublocale transfers to formal topology. For any formal topology (not necessarily with positivity predicate) we define a sublocale to be a cover relation that includes that of the formal topology. The family of sublocales has set-indexed joins. For each set of base elements there are corresponding open and closed sublocales, boolean complements of each other. They generate a boolean algebra amongst the sublocales. In the case of an inductively generated formal topology, (...) the collection of inductively generated sublocales has coframe structure. Overt sublocales and weakly closed sublocales are described, and related via a new notion of "rest closed" sublocale to the binary positivity predicate. Overt, weakly closed sublocales of an inductively generated formal topology are in bijection with "lower powerpoints", arising from the impredicative theory of the lower powerlocale. Compact sublocales and fitted sublocales are described. Compact fitted sublocales of an inductively generated formal topology are in bijection with "upper powerpoints", arising from the impredicative theory of the upper powerlocale. (shrink)

Abstract.Formal topologies are today an established topic in the development of constructive mathematics. One of the main tools in formal topology is inductive generation since it allows to introduce inductive methods in topology. The problem of inductively generating formal topologies with a cover relation and a unary positivity predicate has been solved in [CSSV]. However, to deal both with open and closed subsets, a binary positivity predicate has to be considered. In this paper we will show how (...) to adapt to this framework the method used to generate inductively formal topologies with a unary positivity predicate; the main problem that one has to face in such a new setting is that, as a consequence of the lack of a complete formalization, both the cover relation and the positivity predicate can have proper axioms. (shrink)

Applying Foucault’s concepts of disciplinary power and technologies of the self to the ex-periences of social work academics in English universities, this articles reveals their carceral existences, arguing that social work academics and their students exist within a “carceral network” which controls and normalises behaviour by simultaneously trapping them with-in and excluding them from succeeding in academic practices. While social work academics become “docile bodies” as they are shaped and trained by competing norms of neoliberal higher education and professional social (...) practice, their position as insiders and outsiders to both can also enable them to resist certain disciplinary expectations. The findings of the qualitative study discussed in this article support Foucault’s analysis of powerful institu-tions but problematise binary positions of docility or resistance to disciplinary power with-in them. Lived experiences of ‘becoming academic’ in English social work education reveal how normalising judgements and hierarchical observation intersect with neoliberal forms of responsibilisation to create a carcerality rooted in “incompetence”; how “technologies of relationships” are used to mediate individual forms of responsibilisation, and how having to negotiate multiple disciplinary regimes can create opportunities for resistance to each. (shrink)

Ideological positions are often rooted in binary terms. If a group or entity holds one ideological position then it seems reasonable that they cannot hold the opposing position. This has resulted in a division between corporate public relations and grassroots movements who oppose practices they believe negatively impact society and the environment. However, what happens when corporations practice ideologically justified business decisions that were called upon by grassroots movements for change? What happens to suppliers and distributors who must operate (...) under the demands of changing manufacturing and consumerbehaviors? This paper examines the blending of corporate commercial practice with social and environmental ethos that works to form commercial grassroots activism to positively impact manufacturing and purchasing behaviors. (shrink)

The positive reception of Buber’s philosophy does not fully match Buber’s intention in terms of overcoming the problem of the subject–object binary. In other words, a number of authors have remained within the traditional way of thinking by merely replacing the subject and object with Buber’s I and You, establishing a more dogmatic normative subjectivity, paradoxically going against Buber’s intent and even seemingly not noticing this problem. In this article, we will investigate the reasons for these paradoxical readings of (...) Buber. By focusing on the structure and significance of Buber’s ontology of between-humane, we will study the concept of I–You and I–It, suggesting that these are not intentionality-oriented concepts, but a radically relationship-centered one. The theoretical problem caused by Buber himself in the process of adaptation of his dialog-philosophy to his dialog-pedagogy, namely the impossibility of complete mutuality in the educational relationship will be critically examined, based on Buber’s own declaration in his “Afterword” (1957) in I and Thou (1923). With this, we will reflect on the problematic situation of post-Buberian literature in contemporary pedagogy to pave a way to modernize Buber’s dialog-pedagogy. (shrink)

This binary also speaks more generally to how we tend to conceive of the relation between place and space: As many scholars have pointed out, place often comes valued as "the sphere of the everyday, or real and valued practices," or "a locus of denial" trailing ideas of the "closed, coherent, integrated as authentic, as 'home', a secure retreat" (Massey 2005, 5-6). Doreen Massey's descriptions speak to our perceptions of a center, of a core toward which energy flows, and (...) in so doing marking, in Michel de Certeau's words, "an instantaneous configuration of positions. (shrink)

The profession of nursing has recognized the need for contextual and relational frameworks to inform knowledge development. Two‐Eyed Seeing is a framework developed by Mi'kmaw Elders to respectfully engage with Indigenous and non‐Indigenous knowledges. Some scholars and practitioners, however, are concerned that Two‐Eyed Seeing re‐instantiates dichotomized notions regarding Western and Indigenous knowledges. As dichotomies and binaries are often viewed as polarizing devices for nursing knowledge development, this paper explores the local worldviews in which Two‐Eyed Seeing emerged, proposing that the onto‐epistemological (...) and axiological ‘roots’ of the framework are antithetical to divisiveness, paradoxically asserting space for the dichotomy to stand. Two‐Eyed Seeing, if understood as a relational, decolonial praxis, could fundamentally change the way nursing scholarship and practice operate by facilitating space for diverse knowledges, ways of being, doing and relating. In this paper, considerations for nursing scholarship and practice, as well as recommendations to support the uptake of Two‐Eyed Seeing are explored. The authors assert that conceptual divisiveness, dichotomization and exclusion can be mitigated if nursing is informed by contextual knowledge, seeks to enact accountable partnerships with Indigenous knowledge holders, and holds the Mi'kmaq worldview upon which the concept developed in positive regard. (shrink)

A phenomenon called perspectival disagreement is laid out and modelled on the basis of modifications to known consensus measures for qualitative representations of preferences and transitive values by binary relations. Cases of perspectival disagreement are of general philosophical interest, because they allow for the possibility that two or more agents judge the value positions of other agents differently even when their assessments are based on the same evidence. Various examples of perspectival disagreement are given, generalizations are discussed, and it (...) is argued that any representation by cardinal utilities also gives rise to some form of perspectivity. Although the examples strongly suggest that this phenomenon occurs in real life, it is concluded in the end that it does not pose any fundamental threat to representations of preferences and values as binary relations. Instead, position‐sensitive measures of disagreement ought to be taken as a modelling option for cases in which the relative importance of preference changes matters to an agent. (shrink)

A set of infinite binary sequences ${\cal C} \subseteq 2$ℕ is negligible if there is no partial probabilistic algorithm that produces an element of this set with positive probability. The study of negligibility is of particular interest in the context of ${\rm{\Pi }}_1^0 $ classes. In this paper, we introduce the notion of depth for ${\rm{\Pi }}_1^0 $ classes, which is a stronger form of negligibility. Whereas a negligible ${\rm{\Pi }}_1^0 $ class ${\cal C}$ has the property that one (...) cannot probabilistically compute a member of ${\cal C}$ with positive probability, a deep ${\rm{\Pi }}_1^0 $ class ${\cal C}$ has the property that one cannot probabilistically compute an initial segment of a member of ${\cal C}$ with high probability. That is, the probability of computing a length n initial segment of a deep ${\rm{\Pi }}_1^0 $ class converges to 0 effectively in n.We prove a number of basic results about depth, negligibility, and a variant of negligibility that we call tt-negligibility. We provide a number of examples of deep ${\rm{\Pi }}_1^0 $ classes that occur naturally in computability theory and algorithmic randomness. We also study deep classes in the context of mass problems, examine the relationship between deep classes and certain lowness notions in algorithmic randomness, and establish a relationship between members of deep classes and the amount of mutual information with Chaitin’s Ω. (shrink)

This paper presents a sequent calculus and a dual domain semantics for a theory of definite descriptions in which these expressions are formalised in the context of complete sentences by a binary quantifier I. I forms a formula from two formulas. Ix[F, G] means ‘The F is G’. This approach has the advantage of incorporating scope distinctions directly into the notation. Cut elimination is proved for a system of classical positive free logic with I and it is shown to (...) be sound and complete for the semantics. The system has a number of novel features and is briefly compared to the usual approach of formalising ‘the F ’ by a term forming operator. It does not coincide with Hintikka’s and Lambert’s preferred theories, but the divergence is well-motivated and attractive. (shrink)

Cultures are constituted by binary oppositions: the absolute and the relative; the perfect and the imperfect; the stable and the unstable. Many of the world’s cultures have looked to revealed religion to discover the absolute: that which transcends the human, the intellect, and space and time. By positing a God who is omniscient and omnipotent, they conceive of an eternal and absolute that continues to exist in an immutable state.In such cultures new perspectives for reinterpreting the past are continually (...) propounded. This allows history to be rewritten and re-rewritten. History simply becomes a method for becoming conscious of the past.By contrast, many East Asian cultures have not developed such a concept of revealed religion. For them, history itself constitutes an absolute, something on which one can rely. History in East Asia is endowed with a normative function, a source of authority that does not permit easy rewriting. (shrink)

Let k be a positive integer. There is a longest finite sequence x1,...,xn in k letters in which no consecutive block xi,...,x2i is a subsequence of any other consecutive block xj,...,x2j. Let n(k) be this longest length. We prove that n(1) = 3, n(2) = 11, and n(3) is incomprehensibly large. We give a lower bound for n(3) in terms of the familiar Ackerman hierarchy. We also give asymptotic upper and lower bounds for n(k). We view n(3) as a particularly (...) elemental description of an incomprehensibly large integer. Related problems involving binary sequences (two letters) are also addressed. We also report on some recent computer explorations of R. Dougherty which we use to raise the lower bound for n(3). (shrink)

Let the label binary category terms refer to natural language expressions like ‘woman’, ‘man’, ‘female’, and ‘male’. Focusing on ‘woman’ and ‘female’, I develop a novel, empirically supported theory of the meanings of English binary category terms. Given plausible assumptions about the metaphysics of sex and gender, this gender-first theory predicts that the sentence ‘Trans women are women’ expresses a truth in all contexts and the sentence ‘Women are adult human females’ expresses a truth in most ordinary contexts (...) — thus that these two sentences can and usually do express logically consistent contents. The key feature of the proposed theory is that it treats both ‘woman’ and ‘female’ as sensitive to an individual’s gender when that individual belongs to a gendered category and to an individual’s sex otherwise. The existence and plausibility of a gender-first theory of this kind opens up conceptual room for trans-inclusive positions in the philosophy of sex and gender which endorse the claim that women are adult human females, thereby both accounting for trans women’s experiences of their bodies as female and helping to disarm the sentence ‘Women are adult human females’ as a trans-exclusionary slogan. (shrink)

The use of "theory" in feminist analysis has been said to threaten feminism as a political force. This collection of work by leading feminist scholars engages with the question of the political status of poststructuralism theory within feminism. Against the view that the use of post-structuralism necessarily weakens feminism, 'Feminists Theorize the Political' affirms the contemporary debate over theory as politically rich and consequential. In laying the theoretical groundwork for the volume, Butler and Scott posed a number of questions to (...) prominent legal scholars, literary critics, philosophers, political theorists, historians, and cultural theorists. The essays do not settle the questions but generate new and productive directions for them. The volume as a whole valorizes the unsettling power and politics of theory. The essays in 'Feminists Theorize the Political' speak to the questions that emerge from the convergence of feminism and poststructuralism: What happens to feminist critique when traditional foundations--experience, history, universal norms--are called into question? Can feminist theory problematize the notion of the subject without losing its political effectivity? Which version of the subject is to questioned, and how does that questioning open up possibilities for reformulating agency, power, and sites of political resistance? What are the consequences of a specifically feminist reformulation of difference? What are the uses and limits of a poststructuralist critique of binary logic for the theorization of racial and class differences, the position of the subaltern? This anthology represents a diverse array of theoretical work within feminist theory with strong political stakes. Although not all of the authors subscribe to poststructuralism, (and few would concede post-structuralism is a monolithic enterprise), each offers an innovative feminist analysis that is in some way motivated in and by the poststructuralist challenge. 'Feminists Theorize The Political' addresses a range of feminist concerns, including productive freedom, anti-discrimination law, rape, and formulating power in terms of exclusion, difference and hierarchy. (shrink)

Since its advent, predictive DNA testing has been perceived as a technology that may have considerable impact on the quality of people’s life. The decision whether or not to use this technology is up to the individual client. However, to enable well considered decision making both the negative as well as the positive freedom of the individual should be supported. In this paper, we argue that current professional and public discourse on predictive DNA-testing is lacking when it comes to supporting (...) positive freedom, because it is usually framed in terms of risk and risk management. We show how this ‘risk discourse’ steers thinking on the good life in a particular way. We go on to argue that empirical research into the actual deliberation and decision making processes of individuals and families may be used to enrich the environment of personal deliberation in three ways: (1) it points at a richer set of values that deliberators can take into account, (2) it acknowledges the shared nature of genes, and (3) it shows how one might frame decisions in a non-binary way. We argue that the public sharing and discussing of stories about personal deliberations offers valuable input for others who face similar choices: it fosters their positive freedom to shape their view of the good life in relation to DNA-diagnostics. We conclude by offering some suggestions as to how to realize such public sharing of personal stories. (shrink)

An impressive body of recent literature posits that traditional notions of civil disobedience prevent us from properly considering potentially legitimate types of ‘uncivil’ political lawbreaking. When might uncivil (covert, legally evasive, morally offensive and potentially violent) lawbreaking prove normatively acceptable? If justifiable, what conditions should its practitioners be reasonably expected to meet? Despite some important insights, defenders of uncivil disobedience rely on a narrow and sometimes misleading view of civil disobedience, as previously practiced and theorized. Notwithstanding legitimate skepticism about Rawlsian (...) notions of civil disobedience, they reproduce its troublesome binary or ‘all-or-nothing’ view of political lawbreaking. Uncivil disobedience’s proponents tend to group a vast array of distinctive types of lawbreaking under one amorphous categorical rubric, impeding the suitably complex, nuanced analysis we need. A superior approach would pay careful attention to uncivil disobedience’s ambivalent historical record, a record suggesting that UD is more likely to reproduce authoritarian populism’s disturbing political logic than counteract it. (shrink)

Abstract:This article posits Feminist Science and Technology Studies (FSTS) as a vital tool for bridging postcolonial and decolonial thought. First, FSTS forms a bridge by providing tools for reading epistemic imperialism and scientific racism as shared conditions of possibility for disparate colonizations. Second, by foregrounding the necessary links between epistemic and material violence, FSTS helps undo the theory/praxis binary that sometimes undergirds their analytic opposition. The authors argue that the careful study of science as a set of ideas, practices, (...) and attendant institutions is vital in order to better recognize and intervene in shifting modes of colonial conquest and governance. (shrink)