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

The pigeon-inspired optimization algorithm is a category of a newly proposed swarm intelligence-based algorithm that belongs to the population-based solution technique. The MKP is a class of complex optimization problems that have many practical applications in the fields of engineering and sciences. Due to the practical applications of MKP, numerous algorithmic-based methods like local search and population-based search algorithms have been proposed to solve the MKP in the past few decades. This paper proposes a modified binary pigeon-inspired optimization algorithm (...) named (Modified-BPIO) for the 0 - 1 multidimensional knapsack problem (MKP). The utilization of the binary pigeon-inspired optimization (BPIO) for solving the multidimensional knapsack problem came with huge success. However, it can be observed that the BPIO converges prematurely due to lost diversity during the search activities. Given the above, the crossover operator is integrated with the landmark component of the BPIO to improve the diversity of the solution space. The MKP benchmarks from the Operations Research (OR) library are utilized to test the performance of the proposed binary method. Experimentally, it is concluded that the proposed Modified-BPIO has a better performance when compared with the BPIO and existing state-of-the-arts that worked on the same MKP benchmarks. (shrink)

A classical result by Słupecki states that a logic L is functionally complete for the 3-element set of truth-values THREE if, in addition to functionally including Łukasiewicz’s 3-valued logic Ł3, what he names the ‘$T$-function’ is definable in L. By leaning upon this classical result, we prove a general theorem for defining binary expansions of Kleene’s strong logic that are functionally complete for THREE.

It is proposed that the collective identification of objects is a necessary phase in the evolution of language. A procedure of identification based on the first-person perspective is assumed that is guided by object constancy, the naming insight, and other more obvious features of language production. The mental image is the basic element of this procedure. The comparison of mental images is used to define recognition, and the identification and naming of macroscopic objects by a group of persons is formulated. (...) This is shown to effect a binary relation of the order type on the set of objects that reduces to an equivalence relation in the case of observer independence. (shrink)

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

Formal topology is today an established topic in the development of constructive mathematics and constructive proofs for many classical results of general topology have been obtained by using this approach. Here we analyze one of the main concepts in formal topology, namely, the notion of formal point. We will contrast two classically equivalent definitions of formal points and we will see that from a constructive point of view they are completely different. Indeed, according to the first definition the formal points (...) of the formal topology of the real numbers can be indexed by a set whereas this is not possible according to the second one. (shrink)

This article explores the representational practices of feminist theorising around gender and violence. Adapting Liz Kelly’s notion of the continuum of women’s experiences of sexual violence, I argue that ‘continuum thinking’ can offer important interventions which unsettle binaries, recognise grey areas in women’s experiences and avoid ‘othering’ specific communities. Continuum thinking allows us to understand connections whilst nevertheless maintaining distinctions that are important conceptually, politically and legally. However, this is dependent upon recognising the multiplicity of continuums in feminist theorising – (...) as well as in policy contexts – and the different ways in which they operate. A discussion of contemporary theory and policy suggests that this multiplicity is not always recognised, resulting in a flattening of distinctions which can make it difficult to recognise the specifically gendered patterns of violence and experience. I conclude by considering how focusing on men’s behaviour might offer one way of unsettling the contemporary orthodoxy which equates gender-based violence and violence against women. (shrink)

Forenames serve as proxies for gender labels that activate gender stereotypes and gender socialization. Unlike rigid binary gender categories, they differ in the degree to which they are perceived as “masculine” or “feminine.” We examined the novel hypothesis that the ability of a forename to signal gender is associated with gender role behavior in women and men as part of a larger study evaluating forenames used in resume research. Compared to individuals endorsing a “gender-strong” forename, those perceiving their forename (...) as relatively “gender-weak” reported less gender-typical childhood social behavior and a weaker expression of gender-linked personality traits. Our findings suggest that forenames strengthen or weaken gender socialization, gender identification, and so contribute to the variable expression of gender role behavior within binary gender groups. (shrink)

I challenge the age-old binary opposition between human and animal, not as philosophers sometimes do by claiming that humans are also animals, or that animals are capable of suffering or intelligence, but rather by questioning the very category of “the animal” itself. This category groups a nearly infinite variety of living beings into one concept measured in terms of humans—animals are those creatures that are not human. In addition, I argue that the binary opposition between human and animal (...) is intimately linked to the binary opposition between man and woman. Furthermore, I suggest that thinking through animal differences or differences among various living creatures opens up the possibility of thinking beyond the dualist notion of sexual difference and enables thinking toward a multiplicity of sexual differences. (shrink)

Book Review. Jos de Mul. The Tragedy of Finitude . Dilthey’s Hermeneutics of Life . New Haven and London: Yale University Press. 2004.

Book Review. Jesús Conill-Sancho. Ética hermenéutica. Crítica desde la facticidad. [Hermeneutic Ethics. The Critique of Facticity]. Madrid: Tecnos, 2006.

[Book Review] Rudolf Makkreel and Frithjof Rodi, eds. Wilhelm Dilthey. Selected Works vol. III: The Formation of the Historical World in the Human Sciences. Princeton, N.J.: Princeton University Press, 2002.

(2008). Editorial Board/Publication Information. History of European Ideas: Vol. 34, No. 3, pp. IFC-IFC.

INTERNATIONAL STUDIES IN THE PHILOSOPHY OF SCIENCE Volume 26 Number 1 March 2012 ARTICLES An Inferential Model of Scientific Understanding Mark Newman 1 Evidence and the Assessment of Causal Rela...

This article is a report on ongoing field research and the exponential growth of the environment in which sex workers, prostitutes, call girls, and escorts operate. We look at the complexity of the conditions of such work and consider the socio-psychological and media vectors that make up the context from which its actors and stereotypes emerge. With the explosion of websites offering virtual or real sex, there is also a continuation of oppressive and violent male practices in this sector, restricting (...) the freedom of choice for women who work professionally in this field. These practices reproduce the power relations and the exclusion that has always been present in society, and are also now more diffuse as virtual reality has come to play an important role in social practice. (shrink)

In Emotions, Values & Agency, Christine Tappolet develops a sophisticated, perceptual theory of emotions and their role in wide range of issues in value theory and epistemology. In this paper, we raise three worries about Tappolet's proposal.

“Community” has long been a companion of Critical Theory, but it has always pointed in two diametrically opposed directions. One path leads us to communitarian dreams of a genuine sociability and a full life. Romantic sensibility, anxious about the modern experience of cold rationality and mechanical organization, elaborates counter-models of authentic living, embedded in organic communities deemed genuine. While the Enlightenment legacy appears to abandon us to alienated isolation—no matter how much it proclaims the importance of public discourse—the romantic community (...) provides an existential alternative, an opportunity to reclaim a human authenticity. Ferdinand Tönnies's famous conceptual binary named this drama:.. (shrink)

This chapter examines the pioneering work of Gottfried Wilhelm Leibniz (1646-1716) on various number systems, in particular binary, which he independently invented in the mid-to-late 1670s, and hexadecimal, which he invented in 1679. The chapter begins with the oft-debated question of who may have influenced Leibniz’s invention of binary, though as none of the proposed candidates is plausible I suggest a different hypothesis, that Leibniz initially developed binary notation as a tool to assist his investigations in mathematical (...) problems that were exercising him at the time, namely those concerning the divisibility of composite numbers, primality, and perfect numbers. The chapter then explores Leibniz’s development of binary, his little-known work on binary fractions and expansions, his use of binary as a symbol for creation in his philosophical-theology, and his response to the suggestion that there was a correlation between binary numeration and the hexagrams of the ancient Chinese divinatory text, the Yijing. The chapter then focuses on Leibniz’s work on other number systems, in particular his invention and exploration of hexadecimal as well as his work on duodecimal. The chapter concludes by revealing a hitherto unknown practical application of binary that Leibniz devised in the last year of his life. (shrink)

This book stands at the intersection of two topics: the decidability and computational complexity of hybrid logics, and the deductive systems designed for them. Hybrid logics are here divided into two groups: standard hybrid logics involving nominals as expressions of a separate sort, and non-standard hybrid logics, which do not involve nominals but whose expressive power matches the expressive power of binder-free standard hybrid logics.The original results of this book are split into two parts. This division reflects the division of (...) the book itself. The first type of results concern model-theoretic and complexity properties of hybrid logics. Since hybrid logics which we call standard are quite well investigated, the efforts focused on hybrid logics referred to as non-standard in this book. Non-standard hybrid logics are understood as modal logics with global counting operators ) whose expressive power matches the expressive power of binder-free standard hybrid logics. The relevant results comprise: 1. Establishing a sound and complete axiomatization for the modal logic K with global counting operators ), which can be easily extended onto other frame classes, 2. Establishing tight complexity bounds, namely NExpTime-completeness for the modal logic with global counting operators defined over the classes of arbitrary, reflexive, symmetric, serial and transitive frames ), MT), MD), MB), MK4) with numerical subscripts coded in binary. Establishing the exponential-size model property for this logic defined over the classes of Euclidean and equivalential frames ), MS5).Results of the second type consist of designing concrete deductive systems for standard and non-standard hybrid logics. More precisely, they include: 1. Devising a prefixed and an internalized tableau calculi which are sound, complete and terminating for a rich class of binder-free standard hybrid logics. An interesting feature of indicated calculi is the nonbranching character of the rule, 2. Devising a prefixed and an internalized tableau calculi which are sound, complete and terminating for non-standard hybrid logics. The internalization technique applied to a tableau calculus for the modal logic with global counting operators is novel in the literature, 3. Devising the first hybrid algorithm involving an inequality solver for modal logics with global counting operators. Transferring the arithmetical part of reasoning to an inequality solver turned out to be sufficient in ensuring termination.The book is directed to philosophers and logicians working with modal and hybrid logics, as well as to computer scientists interested in deductive systems and decision procedures for logics. Extensive fragments of the first part of the book can also serve as an introduction to hybrid logics for wider audience interested in logic.The content of the book is situated in the areas of formal logic and theoretical computer science with some elements of the theory of computational complexity. (shrink)

The binary distinction De Neys questions has been put forward many times since the beginnings of psychology, in slightly different forms and under different names. It has proved enormously useful and has received detailed empirical support and careful modeling. At heart the distinction is that between knowledge in long-term memory and control processes in short-term memory.

It is a celebrated result of McKinsey and Tarski [28] thatS4is the logic of the closure algebraΧ+over any dense-in-itself separable metrizable space. In particular,S4is the logic of the closure algebra over the realsR, the rationalsQ, or the Cantor spaceC. By [5], each logic aboveS4that has the finite model property is the logic of a subalgebra ofQ+, as well as the logic of a subalgebra ofC+. This is no longer true forR, and the main result of [5] states that each connected (...) logic aboveS4with the finite model property is the logic of a subalgebra of the closure algebraR+.In this paper we extend these results to all logics aboveS4. Namely, for a normal modal logicL, we prove that the following conditions are equivalent: (i)Lis aboveS4, (ii)Lis the logic of a subalgebra ofQ+, (iii)Lis the logic of a subalgebra ofC+. We introduce the concept of a well-connected logic aboveS4and prove that the following conditions are equivalent: (i)Lis a well-connected logic, (ii)Lis the logic of a subalgebra of the closure algebra$\xi _2^ + $over the infinite binary tree, (iii)Lis the logic of a subalgebra of the closure algebra${\bf{L}}_2^ + $over the infinite binary tree with limits equipped with the Scott topology. Finally, we prove that a logicLaboveS4is connected iffLis the logic of a subalgebra ofR+, and transfer our results to the setting of intermediate logics.Proving these general completeness results requires new tools. We introduce the countable general frame property (CGFP) and prove that each normal modal logic has the CGFP. We introduce general topological semantics forS4, which generalizes topological semantics the same way general frame semantics generalizes Kripke semantics. We prove that the categories of descriptive frames forS4and descriptive spaces are isomorphic. It follows that every logic aboveS4is complete with respect to the corresponding class of descriptive spaces. We provide several ways of realizing the infinite binary tree with limits, and prove that when equipped with the Scott topology, it is an interior image of bothCandR. Finally, we introduce gluing of general spaces and prove that the space obtained by appropriate gluing involving certain quotients ofL2is an interior image ofR. (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.

Can moral ignorance excuse? This chapter argues that philosophical debate of this question has been based on a mistaken assumption: namely that excuses are all-or-nothing affairs; to have an excuse is to be blameless. The chapter argues that we should reject this assumption. Excuses are not binary but gradable: they can be weaker or stronger, mitigating blame to greater or lesser extent. This chapter explores the notions of strength of excuses, blame miti- gation and the relationship between excuses and (...) moral responsibility. These ideas open up some principled middle-ground between the two positions staked out in the literature. Moral ignorance may well excuse but it does not exculpate. (shrink)

Name der Zeitschrift: Nietzsche-Studien Jahrgang: 46 Heft: 1 Seiten: 153-166.

In recent years, misogyny has become a central concept in philosophy as well as an established concept in public discourse and political policy. But where is misogyny’s supposed counterpart, namely, misandry? In this paper I argue for an ameliorative analysis of "misandry", arguing that it can be reformulated in an effort to reclaim it from its misogynistic weaponisation. The term "misandry" is used almost exclusively as a misogynistic rhetorical device for attributing unjust anger, hatred, or other similar emotions to a (...) speaker, thereby undermining their epistemic authority. Rather than dismissing the term as conceptually flawed and politically problematic, I argue that we ought to ameliorate misandry to instead refer to a felt anger, hostility, or fear toward the patriarchal social order and its valorisation and/or expression in misogynistic and machismo behaviour. To support these claims, I begin with a discussion of Kate Manne's analysis of misogyny before reflecting on how this can inform our understanding of misandry. I then demonstrate the various ways in which misandry is rhetorically deployed as a means of silencing speakers that express dissent against the patriarchy. Following this, I argue that we should ameliorate the term, not only to undermine these misogynistic practices, but also to articulate a legitimate affective and reactive attitude against the patriarchal imposition of a hierarchical gender binary. (shrink)

For intermediate logics, there is obtained in the paper an algebraic equivalent of the disjunction propertyDP. It is proved that the logic of finite binary trees is not maximal among intermediate logics withDP. Introduced is a logicND, which has the only maximal extension withDP, namely, the logicML of finite problems.

In this paper, I examine a contextualist thesis that has been little discussed in comparison with contextualism about knowledge, namely contextualism about evidential support. This seems surprising since, prima facie, evidential support statements seem shifty in a way parallel to knowledge ascriptions. I examine but reject the suggestion that contrastivism about evidential support is motivated by arguments analogous to those used to motivate contrastivism about knowledge including sceptical closure arguments, the nature of inquiry, the existence of explicitly contrastive evidential support (...) statements, and the intuitive shiftiness of some binary evidential support statements. I end by discussing the relations between contextualism about evidential support, evidence and knowledge. In particular, I argue that my discussion of contrastivism about evidential support undermines Neta's contextualist view about evidence, and his broader suggestion that the shiftiness of evidence statements explains the shiftiness of knowledge ascriptions. (shrink)

Assuming that votes are independent, the epistemically optimal procedure in a binary collective choice problem is known to be a weighted supermajority rule with weights given by personal log-likelihood-ratios. It is shown here that an analogous result holds in a much more general model. Firstly, the result follows from a more basic principle than expected-utility maximisation, namely from an axiom (Epistemic Monotonicity) which requires neither utilities nor prior probabilities of the ‘correctness’ of alternatives. Secondly, a person’s input need not (...) be a vote for an alternative, it may be any type of input, for instance a subjective degree of belief or probability of the correctness of one of the alternatives. The case of a profile of subjective degrees of belief is particularly appealing, since here no parameters such as competence parameters need to be known. (shrink)

A proposed measure of voting power should satisfy two conditions to be plausible: first, it must be conceptually justified, capturing the intuitive meaning of what voting power is; second, it must satisfy reasonable postulates. This paper studies a set of postulates, appropriate for a priori voting power, concerning blockers (or vetoers) in a binary voting game. We specify and motivate five such postulates, namely, two subadditivity blocker postulates, two minimum-power blocker postulates, each in weak and strong versions, and the (...) added-blocker postulate. We then test whether three measures of voting power, namely the classic Penrose-Banzhaf measure, the classic Shapley-Shubik index, and the newly proposed Recursive Measure, satisfy these postulates. We find that the first measure fails four of the postulates, the second fails two, while the third alone satisfies all five postulates. This work consequently adds to the plausibility of the Recursive Measure as a reasonable measure of voting power. (shrink)

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

We introduce Pura Vida Neutrosophic Algebra, an algebraic structure consisting of neutrosophic numbers equipped with two binary operations namely addition and multiplication. The addition can be calculated sometimes with the function min and other times with the max function. The multiplication operation is the usual sum between numbers. Pura Vida Neutrosophic Algebra is an extension of both Tropical Algebra (also known as Min-Plus, or Min-Algebra) and Max-Plus Algebra (also known as Max-algebra). Tropical and Max-Plus algebras are algebraic structures included (...) in semirings and their operations can be used in matrices and vectors. Pura Vida Neutrosophic Algebra is included in Neutrosophic semirings and can be used in Neutrosophic matrices and vectors. (shrink)

In this paper we show that some orthogeometries, i.e. projective geometries each defined using a ternary collinearity relation and equipped with a binary orthogonality relation, which are extensively studied in mathematics and quantum theory, correspond to Kripke frames, each defined using a binary relation, satisfying a few conditions. To be precise, we will define four special kinds of Kripke frames, namely, geometric frames, irreducible geometric frames, complete geometric frames and quantum Kripke frames; and we will show that they (...) correspond to pure orthogeometries, irreducible pure orthogeometries, Hilbertian geometries and irreducible Hilbertian geometries, respectively. The discovery of these correspondences raises interesting research topics and will enrich the study of logic. (shrink)

I show that the indeterminacy problem for computational structuralists is in fact far more problematic than even the harshest critic of structuralism has realised; it is not a bullet which can be bitten by structuralists as previously thought. Roughly, this is because the structural indeterminacy of logic-gates such as AND/OR is caused by the structural identity of the binary computational digits 0/1 themselves. I provide a proof that pure computational structuralism is untenable because structural indeterminacy entails absurd consequences - (...) namely, that there is only one binary computational digit. I conclude that accounting for individuation is a more important desiderata for a theory of computation than even that of triviality. -/- . (shrink)

The first brief description is given of a project aimed at searching for the neural correlates of consciousness through computer simulation. The underlying model is based on the known circuitry of the mammalian nervous system, the neuronal groups of which are approximated as binary composite units. The simulated nervous system includes just two senses - hearing and touch - and it drives a set of muscles that serve vocalisation, feeding and bladder control. These functions were chosen because of their (...) relevance to the earliest stages of human life, and the simulation has been given the name CyberChild. The system's pain receptors respond to a sufficiently low milk level in the stomach, if there is simultaneously a low level of blood sugar, and also to a full bladder and an unchanged diaper. It is believed that it may be possible to infer the presence of consciousness in the simulation through observations of CyberChild's behaviour, and from the monitoring of its ability to ontogenetically acquire novel reflexes. The author has suggested that this ability is the crucial evolutionary advantage of possessing consciousness. The project is still in its very early stages, and although no suggestion of consciousness has yet emerged, there appears to be no fundamental reason why consciousness could not ultimately develop and be observed. (shrink)

The article presents proofs of the context freeness of a family of typelogical grammars, namely all grammars that are based on a uni- ormultimodal logic of pure residuation, possibly enriched with thestructural rules of Permutation and Expansion for binary modes.

This essay reviews three books that engage the writings of Michel Foucault. It examines to what extent and in what ways Foucault has been made to ‘work’ in educational practice and research. It suggests that Foucault has been narrowly appropriated in a way that is, ultimately, ironic—namely, as either liberating us from or entrapping us within our culture's structures and practices. This essay concludes by suggesting that Foucault's work was an attempt to avoid and subvert exactly such binaries.

Propositions are the referents of the ‘that’-clauses that appear in the direct object positions of typical ascriptions of assertion, belief, and other binary cognitive relations. In that sense, propositions are the objects of those cognitive relations. Propositions are also the semantic contents (meanings, in one sense ) of declarative sentences, with respect to contexts. They are what sentences semantically express, with respect to contexts. Propositions also bear truth-values. The truth-value of a sentence, in a context, is the truth-value of (...) the proposition that it semantically expresses, in that context. This much is common ground among many (but not all) philosophers. I accept other claims about propositions that are more controversial. Propositions (I hold) are Russellian: they are structured entities whose constituents include individuals, properties, and relations. The contribution of a proper name to the proposition that a sentence semantically expresses (in a context) is the referent of that name. Thus, the semantic content of ‘Bill Clinton’ is Bill Clinton himself, and the semantic content of ‘Bill Clinton smokes’ is a proposition whose constituents are Bill Clinton and the property of smoking (ignoring tense, as I shall do from here on). Such 1 singular propositions are among the objects of belief, assertion, and other cognitive relations. This combination of a Millian view about proper names with a Russellian theory of propositions might appropriately be called ‘Millian Russellianism’, or ‘MR’ for short. David Chalmers, in his stimulating paper “Probability and Propositions,” defines a closely related view, Referentialism, as follows (see also the penultimate paragraph of his introduction). Referentialist views say that insofar as beliefs are about individuals (such as Nietzche), the objects of these belief are determined by those individuals. On one such view, the objects of belief are Russellian propositions composed from the individuals and properties that one’s belief is about.. (shrink)

The article presents proofs of the context freeness of a family of typelogical grammars, namely all grammars that are based on a uni- ormultimodal logic of pure residuation, possibly enriched with thestructural rules of Permutation and Expansion for binary modes.