Bashabi Fraser is a poet in her own right. She is also a creative translator. This is a review of her edited volume on the Partition of Bengal. The review highlights our need to read the partition event as a warning for future and ongoing genocides. The review also shows the superiority of literature over history. And finally it has something to say about translation and separately, on P Lal. For instance, this reviewer in many other reviews (...) too insists on the superiority of Fr Mignon SJ over Prof Lal's understanding of translation. (shrink)
Classical logic is usually interpreted as the logic of propositions. But from Boole's original development up to modern categorical logic, there has always been the alternative interpretation of classical logic as the logic of subsets of any given (nonempty) universe set. Partitions on a universe set are dual to subsets of a universe set in the sense of the reverse-the-arrows category-theoretic duality--which is reflected in the duality between quotient objects and subobjects throughout algebra. Hence the idea arises of a dual (...) logic of partitions. That dual logic is described here. Partition logic is at the same mathematical level as subset logic since models for both are constructed from (partitions on or subsets of) arbitrary unstructured sets with no ordering relations, compatibility or accessibility relations, or topologies on the sets. Just as Boole developed logical finite probability theory as a quantitative treatment of subset logic, applying the analogous mathematical steps to partition logic yields a logical notion of entropy so that information theory can be refounded on partition logic. But the biggest application is that when partition logic and the accompanying logical information theory are "lifted" to complex vector spaces, then the mathematical framework of quantum mechanics is obtained. Partition logic models indefiniteness (i.e., numerical attributes on a set become more definite as the inverse-image partition becomes more refined) while subset logic models the definiteness of classical physics (an entity either definitely has a property or definitely does not). Hence partition logic provides the backstory so the old idea of "objective indefiniteness" in QM can be fleshed out to a full interpretation of quantum mechanics. (shrink)
Ashapurna Devi, a prominent Bengali woman novelist (1909–1995) focused on women’s creativity and enlightenment during the colonial and postcolonial period in Bengal, India. She herself displayed immense will power, tenacity and an indomitable spirit which enabled her to eke out a prominent place for herself in the world of creative writing. Her life spanned both colonial India and independent India and these diverse experiences shaped her mind and persona and helped her to portray the emerging face of the enlightened (...) Bengali middle-class woman. Her writings trace the evolution of the Bengali woman as an enlightened and empowered individual struggling against the shackles of discriminatory norms imposed upon her by society. She traces the extremely conservative upbringing that the female members of her generation were subjected to and goes on to show how different individuals responded to these structures in different ways. Some would comply unquestioningly, some would comply simply because they did not dare to protest, while others would break free and find their own niche in the outside world. These issues are addressed by Ashapurna Devi in many short stories as well, but a critical analysis of her trilogy Pratham Pratisruti (1964), Subarnalata (1967) and Bokulkatha (1974) enables us to experience this struggle against a gradually unfolding backdrop where India moves on from being a British colony to an independent country. The trilogy traces the life of three generations of a family — Satyabati, Subarna and finally Bokul and establishes Ashapurna Devi as a path-breaking champion of women’s emancipation in an era when such endeavours were few and far between. (shrink)
The result of the doctoral work of the author, this volume reflects well her painstaking eff orts of the investigative trail into the life of Sir John Woodroffe. This book gives a concise yet overall view of the large and multifarious canvas of the personality that Woodroffe was. Including rare photographs, facsimiles of letters and notes, an elaborate bibliography and index, this book fills a void by fulfilling the long-felt need of a good biography of a soul, who preferred to (...) remain anonymous and speak to the world only through this writings under his pen name, Arthur Avalon. (shrink)
The logical basis for information theory is the newly developed logic of partitions that is dual to the usual Boolean logic of subsets. The key concept is a "distinction" of a partition, an ordered pair of elements in distinct blocks of the partition. The logical concept of entropy based on partition logic is the normalized counting measure of the set of distinctions of a partition on a finite set--just as the usual logical notion of probability based (...) on the Boolean logic of subsets is the normalized counting measure of the subsets (events). Thus logical entropy is a measure on the set of ordered pairs, and all the compound notions of entropy (join entropy, conditional entropy, and mutual information) arise in the usual way from the measure (e.g., the inclusion-exclusion principle)--just like the corresponding notions of probability. The usual Shannon entropy of a partition is developed by replacing the normalized count of distinctions (dits) by the average number of binary partitions (bits) necessary to make all the distinctions of the partition. (shrink)
Since the pioneering work of Birkhoff and von Neumann, quantum logic has been interpreted as the logic of (closed) subspaces of a Hilbert space. There is a progression from the usual Boolean logic of subsets to the "quantum logic" of subspaces of a general vector space--which is then specialized to the closed subspaces of a Hilbert space. But there is a "dual" progression. The notion of a partition (or quotient set or equivalence relation) is dual (in a category-theoretic sense) (...) to the notion of a subset. Hence the Boolean logic of subsets has a dual logic of partitions. Then the dual progression is from that logic of partitions to the quantum logic of direct-sum decompositions (i.e., the vector space version of a set partition) of a general vector space--which can then be specialized to the direct-sum decompositions of a Hilbert space. This allows the logic to express measurement by any self-adjoint operators rather than just the projection operators associated with subspaces. In this introductory paper, the focus is on the quantum logic of direct-sum decompositions of a finite-dimensional vector space (including such a Hilbert space). The primary special case examined is finite vector spaces over ℤ₂ where the pedagogical model of quantum mechanics over sets (QM/Sets) is formulated. In the Appendix, the combinatorics of direct-sum decompositions of finite vector spaces over GF(q) is analyzed with computations for the case of QM/Sets where q=2. (shrink)
Recent developments in pure mathematics and in mathematical logic have uncovered a fundamental duality between "existence" and "information." In logic, the duality is between the Boolean logic of subsets and the logic of quotient sets, equivalence relations, or partitions. The analogue to an element of a subset is the notion of a distinction of a partition, and that leads to a whole stream of dualities or analogies--including the development of new logical foundations for information theory parallel to Boole's development (...) of logical finite probability theory. After outlining these dual concepts in mathematical terms, we turn to a more metaphysical speculation about two dual notions of reality, a fully definite notion using Boolean logic and appropriate for classical physics, and the other objectively indefinite notion using partition logic which turns out to be appropriate for quantum mechanics. The existence-information duality is used to intuitively illustrate these two dual notions of reality. The elucidation of the objectively indefinite notion of reality leads to the "killer application" of the existence-information duality, namely the interpretation of quantum mechanics. (shrink)
Observe that complement questions can be either directly or indirectly conjoined, but they can only be indirectly disjoined. • What theories of questions and coordination predict this difference? • Look at Partition theory (Groenendijk & Stokhof 1984) and Inquisitive Semantics (Groenendijk & Roelofsen 2009, Ciardelli et al. 2012).
The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and functions. The analysis extends directly to other concrete categories (groups, rings, vector spaces, etc.) where the objects are sets with a certain type of structure and the morphisms are functions that preserve that structure. Then the elements & distinctions-based definitions can be (...) abstracted in purely arrow-theoretic way for abstract category theory. In short, the language of elements & distinctions is the conceptual language in which the category of sets is written, and abstract category theory gives the abstract arrows version of those definitions. (shrink)
This paper investigates the prospects for a semantic theory that treats disjunction as a modal operator. Potential motivation for such a theory comes from the way in which modals embed within disjunctions. After reviewing some of the relevant data, I go on to distinguish a variety of modal theories of disjunction. I analyze these theories by considering pairs of conflicting desiderata, highlighting some of the tradeoffs they must face.
The lattice operations of join and meet were defined for set partitions in the nineteenth century, but no new logical operations on partitions were defined and studied during the twentieth century. Yet there is a simple and natural graph-theoretic method presented here to define any n-ary Boolean operation on partitions. An equivalent closure-theoretic method is also defined. In closing, the question is addressed of why it took so long for all Boolean operations to be defined for partitions.
We propose a new account of vagueness and approximation in terms of the theory of granular partitions. We distinguish different kinds of crisp and non-crisp granular partitions and we describe the relations between them, concentrating especially on spatial examples. We describe the practice whereby subjects use regular grid-like reference partitions as a means for tempering the vagueness of their judgments, and we demonstrate how the theory of reference partitions can yield a natural account of this practice, which is referred to (...) in the literature as ‘approximation’. (shrink)
Since the early 1980s, there has been a debate in the semantics literature pertaining to whether wh-interrogatives can be directly disjoined, as main clauses and as complements. Those who held that the direct disjunction of wh-interrogatives was in conflict with certain theoretical considerations proposed that they could be disjoined indirectly. Indirect disjunction proceeds by first lifting both wh-interrogatives and then disjoining them; it assigns matrix-level scope to OR. As we will see, the notorious theoretical need for indirect disjunction has disappeared (...) by today. But the factual question remains. Are wh-complements disjoined directly or indirectly? What is the fact of the matter? This paper argues that the case for indirect disjunction remains reasonably strong. (shrink)
Classical physics and quantum physics suggest two meta-physical types of reality: the classical notion of a objectively definite reality with properties "all the way down," and the quantum notion of an objectively indefinite type of reality. The problem of interpreting quantum mechanics (QM) is essentially the problem of making sense out of an objectively indefinite reality. These two types of reality can be respectively associated with the two mathematical concepts of subsets and quotient sets (or partitions) which are category-theoretically dual (...) to one another and which are developed in two mathematical logics, the usual Boolean logic of subsets and the more recent logic of partitions. Our sense-making strategy is "follow the math" by showing how the logic and mathematics of set partitions can be transported in a natural way to Hilbert spaces where it yields the mathematical machinery of QM--which shows that the mathematical framework of QM is a type of logical system over ℂ. And then we show how the machinery of QM can be transported the other way down to the set-like vector spaces over ℤ₂ showing how the classical logical finite probability calculus (in a "non-commutative" version) is a type of "quantum mechanics" over ℤ₂, i.e., over sets. In this way, we try to make sense out of objective indefiniteness and thus to interpret quantum mechanics. (shrink)
A prominent pillar of Bayesian philosophy is that, relative to just a few constraints, priors “wash out” in the limit. Bayesians often appeal to such asymptotic results as a defense against charges of excessive subjectivity. But, as Seidenfeld and coauthors observe, what happens in the short run is often of greater interest than what happens in the limit. They use this point as one motivation for investigating the counterintuitive short run phenomenon of dilation since, it is alleged, “dilation contrasts with (...) the asymptotic merging of posterior probabilities reported by Savage (1954) and by Blackwell and Dubins (1962)” (Herron et al., 1994). A partition dilates an event if, relative to every cell of the partition, uncertainty concerning that event increases. The measure of uncertainty relevant for dilation, however, is not the same measure that is relevant in the context of results concerning whether priors wash out or “opinions merge.” Here, we explicitly investigate the short run behavior of the metric relevant to merging of opinions. As with dilation, it is possible for uncertainty (as gauged by this metric) to increase relative to every cell of a partition. We call this phenomenon distention. It turns out that dilation and distention are orthogonal phenomena. (shrink)
Dilation occurs when an interval probability estimate of some event E is properly included in the interval probability estimate of E conditional on every event F of some partition, which means that one’s initial estimate of E becomes less precise no matter how an experiment turns out. Critics maintain that dilation is a pathological feature of imprecise probability models, while others have thought the problem is with Bayesian updating. However, two points are often overlooked: (1) knowing that E is (...) stochastically independent of F (for all F in a partition of the underlying state space) is sufficient to avoid dilation, but (2) stochastic independence is not the only independence concept at play within imprecise probability models. In this paper we give a simple characterization of dilation formulated in terms of deviation from stochastic independence, propose a measure of dilation, and distinguish between proper and improper dilation. Through this we revisit the most sensational examples of dilation, which play up independence between dilator and dilatee, and find the sensationalism undermined by either fallacious reasoning with imprecise probabilities or improperly constructed imprecise probability models. (shrink)
Carl Hempel (1965) argued that probabilistic hypotheses are limited in what they can explain. He contended that a hypothesis cannot explain why E is true if the hypothesis says that E has a probability less than 0.5. Wesley Salmon (1971, 1984, 1990, 1998) and Richard Jeffrey (1969) argued to the contrary, contending that P can explain why E is true even when P says that E’s probability is very low. This debate concerned noncontrastive explananda. Here, a view of contrastive causal (...) explanation is described and defended. It provides a new limit on what probabilistic hypotheses can explain; the limitation is that P cannot explain why E is true rather than A if P assign E a probability that is less than or equal to the probability that P assigns to A. The view entails that a true deterministic theory and a true probabilistic theory that apply to the same explanandum partition are such that the deterministic theory explains all the true contrastive propositions constructable from that partition, whereas the probabilistic theory often fails to do so. (shrink)
We have a variety of different ways of dividing up, classifying, mapping, sorting and listing the objects in reality. The theory of granular partitions presented here seeks to provide a general and unified basis for understanding such phenomena in formal terms that is more realistic than existing alternatives. Our theory has two orthogonal parts: the first is a theory of classification; it provides an account of partitions as cells and subcells; the second is a theory of reference or intentionality; it (...) provides an account of how cells and subcells relate to objects in reality. We define a notion of well-formedness for partitions, and we give an account of what it means for a partition to project onto objects in reality. We continue by classifying partitions along three axes: (a) in terms of the degree of correspondence between partition cells and objects in reality; (b) in terms of the degree to which a partition represents the mereological structure of the domain it is projected onto; and (c) in terms of the degree of completeness with which a partition represents this domain. (shrink)
This article builds on C. S. Peirce’s suggestive blueprint for an inclusive outlook that grants reality to his three categories. Moving away from the usual focus on (contentious) cosmological forces, I use a modal principle to partition various ontological layers: regular sign-action (like coded language) subsumes actual sign-action (like here-and-now events) which in turn subsumes possible sign-action (like qualities related to whatever would be similar to them). Once we realize that the triadic sign’s components are each answerable to this (...) asymmetric subsumption, we obtain the means to track at which level of complexity semiosis finds itself, in a given case. Since the bulk of such a “trinitarian” metaphysics would be devoted to countenancing uninterpreted phenomena, I argue that current misgivings about sign-based ontologies are largely misplaced. (shrink)
Categorical logic has shown that modern logic is essentially the logic of subsets (or "subobjects"). Partitions are dual to subsets so there is a dual logic of partitions where a "distinction" [an ordered pair of distinct elements (u,u′) from the universe U ] is dual to an "element". An element being in a subset is analogous to a partition π on U making a distinction, i.e., if u and u′ were in different blocks of π. Subset logic leads to (...) finite probability theory by taking the (Laplacian) probability as the normalized size of each subset-event of a finite universe. The analogous step in the logic of partitions is to assign to a partition the number of distinctions made by a partition normalized by the total number of ordered pairs |U|² from the finite universe. That yields a notion of "logical entropy" for partitions and a "logical information theory." The logical theory directly counts the (normalized) number of distinctions in a partition while Shannon's theory gives the average number of binary partitions needed to make those same distinctions. Thus the logical theory is seen as providing a conceptual underpinning for Shannon's theory based on the logical notion of "distinctions.". (shrink)
The distinction between clinical research and clinical practice directs how we partition medicine and biomedical science. Reasons for a sharp distinction date historically to the work of the National Commission for the Protection of Human Subjects of Biomedical and Behavioral Research, especially to its analysis of the “boundaries” between research and practice in the Belmont Report (1978). Belmont presents a segregation model of the research-practice distinction, according to which research and practice form conceptually exclusive sets of activities and interventions. (...) This model is still the standard in federal regulations today. However, the Commission’s deliberations and conclusions about the boundaries are more complicated, nuanced, and instructive than has generally been appreciated. The National Commission did not conclude that practice needs no oversight comparable to the regulation of research. It debated the matter and inclined to the view that the oversight of practice needed to be upgraded, though the Commission stopped short of proposing new regulations for its oversight, largely for prudential political reasons. (shrink)
A computer can come to understand natural language the same way Helen Keller did: by using “syntactic semantics”—a theory of how syntax can suffice for semantics, i.e., how semantics for natural language can be provided by means of computational symbol manipulation. This essay considers real-life approximations of Chinese Rooms, focusing on Helen Keller’s experiences growing up deaf and blind, locked in a sort of Chinese Room yet learning how to communicate with the outside world. Using the SNePS computational knowledge-representation system, (...) the essay analyzes Keller’s belief that learning that “everything has a name” was the key to her success, enabling her to “partition” her mental concepts into mental representations of: words, objects, and the naming relations between them. It next looks at Herbert Terrace’s theory of naming, which is akin to Keller’s, and which only humans are supposed to be capable of. The essay suggests that computers at least, and perhaps non-human primates, are also capable of this kind of naming. (shrink)
This paper provides an axiomatic formalization of a theory of foundational relations between three categories of entities: individuals, universals, and collections. We deal with a variety of relations between entities in these categories, including the is-a relation among universals and the part-of relation among individuals as well as cross-category relations such as instance-of, member-of, and partition-of. We show that an adequate understanding of the formal properties of such relations – in particular their behavior with respect to time – is (...) critical for formal ontology. We provide examples to support this thesis from the domain of biomedicine. (shrink)
Modern categorical logic as well as the Kripke and topological models of intuitionistic logic suggest that the interpretation of ordinary “propositional” logic should in general be the logic of subsets of a given universe set. Partitions on a set are dual to subsets of a set in the sense of the category-theoretic duality of epimorphisms and monomorphisms—which is reflected in the duality between quotient objects and subobjects throughout algebra. If “propositional” logic is thus seen as the logic of subsets of (...) a universe set, then the question naturally arises of a dual logic of partitions on a universe set. This paper is an introduction to that logic of partitions dual to classical subset logic. The paper goes from basic concepts up through the correctness and completeness theorems for a tableau system of partition logic. (shrink)
Van Fraassen's Judy Benjamin problem asks how one ought to update one's credence in A upon receiving evidence of the sort ``A may or may not obtain, but B is k times likelier than C'', where {A,B,C} is a partition. Van Fraassen's solution, in the limiting case of increasing k, recommends a posterior converging to the probability of A conditional on A union B, where P is one's prior probability function. Grove and Halpern, and more recently Douven and Romeijn, (...) have argued that one ought to leave credence in A unchanged, i.e. fixed at P(A). We argue that while the former approach is superior, it brings about a Reflection violation due in part to neglect of a ``regression to the mean'' phenomenon, whereby when C is eliminated by random evidence that leaves A and B alive, the ratio P(A):P(B) ought to drift in the direction of 1:1. (shrink)
Medical terminology collects and organizes the many different kinds of terms employed in the biomedical domain both by practitioners and also in the course of biomedical research. In addition to serving as labels for biomedical classes, these names reflect the organizational principles of biomedical vocabularies and ontologies. Some names represent invariant features (classes, universals) of biomedical reality (i.e., they are a matter for ontology). Other names, however, convey also how this reality is perceived, measured, and understood by health professionals (i.e., (...) they belong to the domain of epistemology). We analyze terms from several biomedical vocabularies in order to throw light on the interactions between ontological and epistemological components of these terminologies. We identify four cases: 1) terms containing classification criteria, 2) terms reflecting detectability, modality, uncertainty, and vagueness, 3) terms created in order to obtain a complete partition of a given domain, and 4) terms reflecting mere fiat boundaries. We show that epistemology-loaded terms are pervasive in biomedical vocabularies, that the “classes” they name often do not comply with sound classification principles, and that they are therefore likely to cause problems in the evolution and alignment of terminologies and associated ontologies. (shrink)
This paper describes a cubic water tank equipped with a movable partition receiving various amounts of liquid used to represent joint probability distributions. This device is applied to the investigation of deductive inferences under uncertainty. The analogy is exploited to determine by qualitative reasoning the limits in probability of the conclusion of twenty basic deductive arguments (such as Modus Ponens, And-introduction, Contraposition, etc.) often used as benchmark problems by the various theoretical approaches to reasoning under uncertainty. The probability bounds (...) imposed by the premises on the conclusion are derived on the basis of a few trivial principles such as "a part of the tank cannot contain more liquid than its capacity allows", or "if a part is empty, the other part contains all the liquid". This stems from the equivalence between the physical constraints imposed by the capacity of the tank and its subdivisions on the volumes of liquid, and the axioms and rules of probability. The device materializes de Finetti's coherence approach to probability. It also suggests a physical counterpart of Dutch book arguments to assess individuals' rationality in probability judgments in the sense that individuals whose degrees of belief in a conclusion are out of the bounds of coherence intervals would commit themselves to executing physically impossible tasks. (shrink)
In this paper we propose a formal theory of partitions (ways of dividing up or sorting or mapping reality) and we show how the theory can be applied in the geospatial domain. We characterize partitions at two levels: as systems of cells (theory A), and in terms of their projective relation to reality (theory B). We lay down conditions of well-formedness for partitions and we define what it means for partitions to project truly onto reality. We continue by classifying well-formed (...) partitions along three axes: (a) degree of correspondence between partition cells and objects in reality; (b) degree to which a partition represents the mereological structure of the domain it is projected onto; and (c) degree of completeness and exhaustiveness with which a partition represents reality. This classification is used to characterize three types of partitions that play an important role in spatial information science: cadastral partitions, categorical coverages, and the partitions involved in folk categorizations of the geospatial domain. (shrink)
It seems intuitively obvious that metameric matching of color samples entails a loss of information, for spectrophotometrically diverse materials appear the same. This intuition implicitly relies on a conception of the function of color vision and on a related conception of how color samples should be individuated. It assumes that the function of color vision is to distinguish among spectral energy distributions, and that color samples should be individuated by their physical properties. I challenge these assumptions by articulating a different (...) conception of the function of color vision, according to which color vision serves to partition object surfaces into discrimination classes. (shrink)
Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences and distinguishability and is formalized using the distinctions of a partition. All the definitions of simple, joint, conditional and mutual entropy of Shannon information theory are derived by a uniform transformation from the corresponding definitions at the logical level. The purpose of this (...) paper is to give the direct generalization to quantum logical information theory that similarly focuses on the pairs of eigenstates distinguished by an observable, i.e., qudits of an observable. The fundamental theorem for quantum logical entropy and measurement establishes a direct quantitative connection between the increase in quantum logical entropy due to a projective measurement and the eigenstates that are distinguished by the measurement. Both the classical and quantum versions of logical entropy have simple interpretations as “two-draw” probabilities for distinctions. The conclusion is that quantum logical entropy is the simple and natural notion of information for quantum information theory focusing on the distinguishing of quantum states. (shrink)
It has been recently argued that the well-known square of opposition is a gathering that can be reduced to a one-dimensional figure, an ordered line segment of positive and negative integers [3]. However, one-dimensionality leads to some difficulties once the structure of opposed terms extends to more complex sets. An alternative algebraic semantics is proposed to solve the problem of dimensionality in a systematic way, namely: partition (or bitstring) semantics. Finally, an alternative geometry yields a new and unique pattern (...) of oppositions that proceeds with colored diagrams and an increasing set of bitstrings. (shrink)
Every domain-specific ontology must use as a framework some upper-level ontology which describes the most general, domain-independent categories of reality. In the present paper we sketch a new type of upper-level ontology, which is intended to be the basis of a knowledge modelling language GOL (for: 'General Ontological Language'). It turns out that the upper- level ontology underlying standard modelling languages such as KIF, F-Logic and CycL is restricted to the ontology of sets. Set theory has considerable mathematical power and (...) great flexibility as a framework for modelling different sorts of structures. At the same time it has the disadvantage that sets are abstract entities (entities existing outside the realm of time, space and causality), and thus a set-theoretical framework should be supplemented by some other machinery if it is to support applications in the ripe, messy world of concrete objects. In the present paper we partition the entities of the real world into sets and urelements, and then we introduce several new ontological relations between these urelements. In contrast to standard modelling and representation formalisms, the concepts of GOL provide a machinery for representing and analysing such ontologically basic relations. (shrink)
The notion of a partition on a set is mathematically dual to the notion of a subset of a set, so there is a logic of partitions dual to Boole's logic of subsets (Boolean logic is usually mis-specified as "propositional" logic). The notion of an element of a subset has as its dual the notion of a distinction of a partition (a pair of elements in different blocks). Boole developed finite logical probability as the normalized counting measure on (...) elements of subsets so there is a dual concept of logical entropy which is the normalized counting measure on distinctions of partitions. Thus the logical notion of information is a measure of distinctions. Classical logical entropy naturally extends to the notion of quantum logical entropy which provides a more natural and informative alternative to the usual Von Neumann entropy in quantum information theory. The quantum logical entropy of a post-measurement density matrix has the simple interpretation as the probability that two independent measurements of the same state using the same observable will have different results. The main result of the paper is that the increase in quantum logical entropy due to a projective measurement of a pure state is the sum of the absolute squares of the off-diagonal entries ("coherences") of the pure state density matrix that are zeroed ("decohered") by the measurement, i.e., the measure of the distinctions ("decoherences") created by the measurement. (shrink)
In this paper the sameness and difference between two distinguished Indian authors, Rokeya Sakhawat Hossain (1880–1932) and Mahasweta Devi (b. 1926), representing two generations almost a century apart, will be under analysis in order to trace the generational transformation in women’s writing in India, especially Bengal. Situated in the colonial and postcolonial frames of history, Hossain and Mahasweta Devi may be contextualized differently. At the same time their subjects are also differently categorized; the former is not particularly concerned with (...) subalterns whereas the latter specifically focuses on the effect of race and class on gender. The quest for the ‘self’ and ‘subjectivity’ is more pertinent in the latter and consequently the appeal for agency is based on a crude power struggle. Hossain, a philanthropist who championed the woman question, believed that striving for equality should be a collective process which could be achieved by spreading awareness among fellow-inmates inhabiting the prison of patriarchy. Like Euro-American first-wave feminists, Rokeya advocated the necessity of education among women in order for them to be able to comprehend their plight and ‘awake’ for the cause. She addresses fundamental issues of feminism like education and the systematized claustrophobia within the domestic space. Whereas Mahasweta Devi, has been an activist writer who is regarded as the brand ambassador for the support of the marginalized, deprived and denotified tribes of India. It is her mission to provide succour to the marginalized sections, especially tribes from the Purulia district of West Bengal, like the Kherias and Shabars. As an activist writer she explores tribal life and allied socio-political issues which reflect their agony. (shrink)
The goal of this article is twofold. First, it revises the historiographic partition proposed by John Deely in Four Ages of Understanding (2001) by arguing that the moment marking the beginning of philosophical Modernity has been vividly recorded in Descartes’ Meditations on First Philosophy with the experiment with the wax. Second, an upshot of this historical study is that it helps make sense of Deely’s somewhat iconoclastic use of the words “subject” and “subjectivity” to designate mind-independent worldly things. The (...) hope is that successfully accomplishing these twin tasks will give semiotic inquiry a better appreciation of its own history, as well as resources genial to furthering its ongoing development. (shrink)
The current image of Georg Lukács (1885-1971) is widely swayed by an interpretative standard grounded on a deep partition between his young (1910-1918),intermediate (1918-1930) and mature (1930-1971) intellectual production. Despite rejecting an undeniable discontinuity in Lukács’ philosophical evolution,especially between his pre-Marxist works (The Soul and the Forms and Theory of Romance) and the post-1918 Marxist production, I aim for a global reconsideration of Lukács’ philosophy, evaluating a greater unity in his thought. A reflection on ethical problems, specifically on the (...) matter of responsibility, emerges – and not by chance – during different turning points of Lukács’ personal life. On the poverty of Spirit (1913), Tactic and Ethic (1918) and The social responsibility of the philosopher (1960 ca.) are the three essays in which Lukács attempts in different ways to give a philosophical legitimation of some decisive biographical choices, such as his separation from Irma Seidler (1911), his adhesion to the Communist Party (1918) and his acceptance of Socialism, even after the dramatic events of Budapest in 1956. A more unitary consideration of Lukács’ thought could be reached only through a deeper reflection on the content of the ethical problem of responsibility in his thinking. Despite their differences, the essays mentioned above are united in terms of the meaning of a true responsibility,which Lukács conceives always in a direct connection – maybe in an excessively binding way ‒ between individual choice and the course of history. (shrink)
Shuford, Albert and Massengill proved, a half century ago, that the logarithmic scoring rule is the only proper measure of inaccuracy determined by a differentiable function of probability assigned the actual cell of a scored partition. In spite of this, the log rule has gained less traction in applied disciplines and among formal epistemologists that one might expect. In this paper we show that the differentiability criterion in the Shuford et. al. result is unnecessary and use the resulting simplified (...) characterization of the logarithmic rule to give novel arguments in favor of it. (shrink)
Advancement in cognitive science depends, in part, on doing some occasional ‘theoretical housekeeping’. We highlight some conceptual confusions lurking in an important attempt at explaining the human capacity for rational or coherent thought: Thagard & Verbeurgt’s computational-level model of humans’ capacity for making reasonable and truth-conducive abductive inferences (1998; Thagard, 2000). Thagard & Verbeurgt’s model assumes that humans make such inferences by computing a coherence function (f_coh), which takes as input representation networks and their pair-wise constraints and gives as output (...) a partition into accepted (A) and rejected (R) elements that maximizes the weight of satisfied constraints. We argue that their proposal gives rise to at least three difficult problems. (shrink)
The schism between analytic and continental philosophy resists repair because it is not confined to philosophers. It is a local manifestation of a far more profound and pervasive division. In 1959 C.P. Snow lamented the partition of intellectual life in to `two cultures': that of the scientist and that of the literary intellectual. If we follow the practice of most universities and bundle historical and literary studies together in the faculty of humanities on the one hand, and count pure (...) mathematics among the sciences on the other, then it is fair to say that the mutual ignorance and occasional hostility between scientists and humanists decried by Snow is still with us. And it runs through the middle of philosophy. Philosophy aspires to say something about everything, so it is unsurprising that philosophers have reproduced in miniature the division between the arts and the sciences. What is worrying is that we have failed to overcome it. (shrink)
Drawing from the results of various case studies conducted in India, Japan, China, Korea, and New York, the author focuses on the cultural interplay of Asian and American individualities. T is century has also witnessed barbarous acts of terrorism. Taking the partition of India and Pakistan and the 9/11 tragedy as his points of departure, he traces the trauma and dissociation these events entailed.
The mean majority deficit in a two-tier voting system is a function of the partition of the population. We derive a new square-root rule: For odd-numbered population sizes and equipopulous units the mean majority deficit is maximal when the member size of the units in the partition is close to the square root of the population size. Furthermore, within the partitions into roughly equipopulous units, partitions with small even numbers of units or small even-sized units yield high mean (...) majority deficits. We discuss the implications for the winner-takes-all system in the US Electoral College. (shrink)
Hugh MacColl is commonly seen as a pioneer of modal and many-valued logic, given his introduction of modalities that go beyond plain truth and falsehood. But a closer examination shows that such a legacy is debatable and should take into account the way in which these modalities proceeded. We argue that, while MacColl devised a modal logic in the broad sense of the word, he did not give rise to a many-valued logic in the strict sense. Rather, his logic is (...) similar to a “non-Fregean logic”: an algebraic logic that partitions the semantic classes of truth and falsehood into subclasses but does not extend the range of truth-values. -/- Hugh MacColl est présenté d’ordinaire comme un pionnier des logiques modales et multivalentes, suite à son introduction de modalités qui vont au-delà de la simple vérité et fausseté. Mais un examen plus attentif montre que cet héritage est discutable et devrait tenir compte de la façon dont ces modalités procédaient. Bien que MacColl ait conçu une logique modale au sens large du terme, nous montrerons qu’il n’a pas produit une logique multivalente au sens strict. Sa logique serait comparable plutôt à une « logique non-fregéenne », c’est-à-dire une logique algébrique qui effectue une partition au sein de la classe des vérités et faussetés mais n’étend pas pour autant le domaine des valeurs de vérité. (shrink)
In 2014,war in the Ukraine began. In the same year, the largest number of terrorist attacks had been committed in Ukraine since 1991. A similar increase in terrorist activity was recorded twenty years earlier, in 1994, during the conflict between the Ukraine and Russia, caused by the partition of the Black Sea Fleet, which these two countries had inherited after the Soviet Union collapse. As in 1994, the wave of terrorist attacks in 2014-2015 swept on the backdrop of a (...) new conflict with Russia, now involving regular army units and irregular armed groups on the both sides. This article explores the hypothesis that Russia is using terrorism as an instrument when confronting other statesin pursuit of its geo-political goals. In the case of Ukraine, terrorism was used as an instrument to weaken the military and political potential of the Ukraine during the preparation of a large-scale military operation by regular Russian forces. To test this hypothesis, the author uses open data sources, especially the Global Terrorism Database od the University of Maryland, as well as reports of the Ukrainian General Staff, and international organizations. (shrink)
This was written in 2014 during desultory afternoons in hinterland Bengal. The blog went on to feature in a US Bible Blog carnival. The author tried then to start a dialogue between the Gospel of Glory and Hinduism. But now, in 2018, this seems puerile and infantile to the author.
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