For regular sets in Euclidean space, previous work has identified twelve ‘basic’ computability notions to which many previous notions considered in literature were shown to be equivalent. With respect to those basic notions we now investigate on the computability of natural operations on regular sets: union, intersection, complement, convex hull, image, and pre-image under suitable classes of functions. It turns out that only few of these notions are suitable in the sense of rendering all those operations uniformly computable.

It, is shown that Birkhoff –von Neumann quantum logic (i.e., an orthomodular lattice or poset) possessing an ordering set of probability measures S can be isomorphically represented as a family of fuzzy subsets of S or, equivalently, as a family of propositional functions with arguments ranging over S and belonging to the domain of infinite-valued Łukasiewicz logic. This representation endows BvN quantum logic with a new pair of partially defined binary operations, different from the order-theoretic ones: Łukasiewicz intersection and (...) class='Hi'>union of fuzzy sets in the first case and Łukasiewicz conjunction and disjunction in the second. Relations between old and new operations are studied and it is shown that although they coincide whenever new operations are defined, they are not identical in general. The hypothesis that quantum-logical conjunction and disjunction should be represented by Łukasiewicz operations, not by order-theoretic join and meet is formulated and some of its possible consequences are considered. (shrink)

The work broadens – to a considerable extent – Z. Pawlak’s original method (1982, 1992) of approximation of sets. The approximation of sets included in a universum U goes on in the contextual approximation space CAS which consists of: 1) a sequence of Pawlak’s approximation spaces (U,Ci), where indexes i from set I are linearly ordered degrees of contexts (I, <), and Ci is the universum partition U, 2) a sequence of binary relations on sets included in U, relations called (...) context relations indexed with degrees of contexts. The introduction of relations of contexts of sets was inspired by the work of W. Ziarnko (1993). Intuitively, set X is the context of set Y to the degree i, when on the basis of knowledge of the elements of set X we can obtain knowledge about the belonging of these elements to set Y to the degree i which is a degree of uncertainty or ambiguity, or inaccuracy. The operations of approximation of sets Ci-, BNi, Ci+, called lower approximation of the degree i, boundary of the degree i, upper approximation of the degree i, are formulated in a way which is analogous with the systems of Pawlak’s approximation, by expanding their formulas accordingly. In the next part of the work, it is shown (in an analogous way to Bryniarski’s work (1989)) that one can define the following operations on contextual rough sets: the union of contextual rough sets, the intersection of contextual rough sets and the complement of contextual rough set. It is proved that the algebra of contextual rough sets is a ditributive lattice with a unit and with a zero. On the basis of the results presented above the problem of defining operations on contextual rough sets by membership relations (Bryniarski 1989) may be formulated analogously to the classical operations on sets. (shrink)

In this paper, we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), which is a set whose elements are characterized by many attributes (parameters)’ values. An attribute value v has a corresponding (fuzzy, intuitionistic fuzzy, or neutrosophic) degree of appurtenance d(x,v) of the element x, to the set P, with respect to some given criteria. In order to obtain a better accuracy for the plithogenic aggregation operators in the plithogenic set, and for a more (...) exact inclusion (partial order), a (fuzzy, intuitionistic fuzzy, or neutrosophic) contradiction (dissimilarity) degree is defined be-tween each attribute value and the dominant (most important) attribute value. The plithogenic intersection and union are linear combinations of the fuzzy operators tnorm and tconorm, while the plithogenic complement, inclusion (inequality), equality are influenced by the attribute values contradiction (dissimilarity) degrees. This article offers some examples and applications of these new concepts in our everyday life. (shrink)

We prove that every countably determined set C is U-meager if and only if every internal subset A of C is U-meager, provided that the cofinality and coinitiality of the cut U are both uncountable. As a consequence we prove that for such cuts a countably determined set C which intersects every U-monad in at most countably many points is U-meager. That complements a similar result in [KL]. We also give some partial solutions to some open problems from [KL]. We (...) prove that the set K = {1,...,H}, where H is an infinite integer, cannot be expressed as a countable union of countably determined sets each of which is U-meager for some cut U with min{cf (U), ci (U)} ≥ ω1. Also, every Borel, Σ1 m or countably determined set C which is U-meager for every cut U is a countable union of Borel, Σ1 m or countably determined sets respectively, which are U-nowhere dense for every cut U. Further, the class of Borel U-meager sets for min{cf(U), ci(U)} ≥ ω1 coincides with the least family of sets containing internal U-meager sets and closed with respect to the operation of countable union and intersection. The same is true if the phrase "U-meager sets" is replaced by "U-meager for every cut U.". (shrink)

In this paper, we have developed an Excel package to be utilized for calculating neutrosophic data and analyze them. The use of object oriented programming techniques and concepts as they may apply to the design and development a new framework to implement neutrosophic data operations, the c# programming language, NET Framework and Microsoft Visual Studio are used to implement the neutrosophic classes. We have used Excel as it is a powerful tool that is widely accepted and used for statistical analysis. (...) Figure 1 shows Class Diagram of the implemented package. Figure 2 presents a working example of the package interface calculating the complement. Our implemented Neutrosophic package can calculate Intersection, Union, and Complement of the neutrosophic set. Figure 3 presents our neutrosophic package capability to draw figures of presented neutrosophic set. Figure 4 presents charting of Union operation calculation, and figure 5 Intersection Operation. neutrosophic set are characterized by its efficiency as it takes into consideration the three data items: True, Intermediate, and False. -/- . (shrink)

The paper documents the post-war retrenchment and failure of the post-war British Consumer Co-operative Movement. In contrast to the general failure one CEO, Terry Thomas stands out both for his success in co-operative rebranding and returning to profitability the UK Co-operative Bank and because he alone amongst the top echelons of the Co-operative Groups Management based his strategies on a clearly articulated philosophy based on his understanding of the values and purpose of the co-operative movement rooted in its historical traditions (...) grounded in the writings and achievements of Robert Owen, The paper goes on to provide a case study of the bank’s process of transformation from loss-making subsidiary to the first positive co-operative national brand in the post-war period of its history. The author argues that lack of appropriate vision based on the founding values and purposes of the Co-operative Movement is the principal reason for the management’s and governance failures that have beset the UK Co-operative Group. Instead of using the past to help in understanding the present and planning for the future, the UK Co-operative Group Leadership ignored it or worse used the past successes to congratulate itself and disguise its manifest failures. In this, they were supported by an uncritical Co-operative Union. Davis argues large co-operatives cannot be managed by a civil service responsible to an elected board. Co-operatives need a servant-leadership model of professional management dedicated to the transformational goals set by the founders of the co-operative movement. This needs a radical rethink and promotion of co-operative management education and a dedicated executive recruitment that seeks out value-based professionals whose attitudes and values are compatible with Co-operative values, ownership and purpose. (shrink)

Transitive extensional well founded relations provide an intuitionistic notion of ordinals which admits transfinite induction. However these ordinals are not directed and their successor operation is poorly behaved, leading to problems of functoriality. We show how to make the successor monotone by introducing plumpness, which strengthens transitivity. This clarifies the traditional development of successors and unions, making it intuitionistic; even the (classical) proof of trichotomy is made simpler. The definition is, however, recursive, and, as their name suggests, the plump (...) ordinals grow very rapidly. Directedness must be defined hereditarily. It is orthogonal to the other four conditions, and the lower powerdomain construction is shown to be the universal way of imposing it. We treat ordinals as order-types, and develop a corresponding set theory similar to Osius' transitive set objects. This presents Mostowski's theorem as a reflection of categories, and set-theoretic union is a corollary of the adjoint functor theorem. Mostowski's theorem and the rank for some of the notions of ordinal are formulated and proved without the axiom of replacement, but this seems to be unavoidable for the plump rank. The comparison between sets and toposes is developed as far as the identification of replacement with completeness, and there are some suggestions for further work in this area. Each notion of set or ordinal defines a free algebra for one of the theories discussed by Joyal and Moerdijk, namely joins of a family of arities together with an operation s satisfying conditions such as x ≤ sx, monotonicity or s(x ∨ y) ≤ sx ∨ sy. Finally we discuss the fixed point theorem for a monotone endofunction s of a poset with least element and directed joins. This may be proved under each of a variety of additional hypotheses. We explain why it is unlikely that any notion of ordinal obeying the induction scheme for arbitrary predicates will prove the pure result. (shrink)

§1. I will start with a quick definition of descriptive set theory: It is the study of the structure of definable sets and functions in separable completely metrizable spaces. Such spaces are usually called Polish spaces. Typical examples are ℝn, ℂn, Hilbert space and more generally all separable Banach spaces, the Cantor space 2ℕ, the Baire space ℕℕ, the infinite symmetric group S∞, the unitary group, the group of measure preserving transformations of the unit interval, etc.In this theory sets are (...) classified in hierarchies according to the complexity of their definitions and the structure of sets in each level of these hierarchies is systematically analyzed. In the beginning we have the Borel sets in Polish spaces, obtained by starting with the open sets and closing under the operations of complementation and countable unions, and the corresponding Borel hierarchy. After this come the projective sets, obtained by starting with the Borel sets and closing under the operations of complementation and projection, and the corresponding projective hierarchy.There are also transfinite extensions of the projective hierarchy and even much more complex definable sets studied in descriptive set theory, but I will restrict myself here to Borel and projective sets, in fact just those at the first level of the projective hierarchy, i.e., the Borel (), analytic () and coanalytic () sets. (shrink)

There are several reasons, according to which it is worth analyzing European administrative law. First, this is a rather new branch of law. Second, the European administrative law is treated in different countries from different legal traditions positions, consequently, any effort to unify the approach to it can provide a basis for a unified European administrative law model. Third, there are no works dedicated to the analysis of the phenomenon of the European administrative law in Lithuania. Therefore, this article deals (...) with the concepts of the European administrative law. It is stated that the comprehensive image of the European administrative law reveals three European administrative law concepts. The first concept of the European administrative law characterizes it as the European Union (hereinafter – EU) administrative law, the validity of boundaries of which can be based on three aspects – functional, institutional and procedural. The second concept of the European administrative law identifies it as the law of administrative cooperation., whereas the third concept allows the European administrative law to be seen as the law common to various public administrations of European countries – ius commune. The article focuses on the analysis of the above-mentioned three approaches and the EU set of administrative procedures as an instrument to promote the development of the EU administrative law. The author comes to the conclusion that the concept of the ‘European Administrative Law’ is broader than the concept of the ‘EU Administrative Law’. The European administrative law can be perceived not only as a part of law that establishes the EU administration’s administrative legal status, its’ activity principles, forms and methods, but also as a law of administrative cooperation between states, governmental and non-governmental organizations and various corporations, based on a wide range of multilateral treaties or conventions, which cross the limits of the EU. Moreover, the European administrative law can be understood as a law with common concepts, general principles characteristic to different European countries’ public administrations as well as a science, with the help of which diverse administrative legal systems of various countries could be compared. Taking into account the content of various working documents, the author draws the conclusion that for the further development of the EU administrative law the establishment of uniform operating rules for the EU administration in its’ relations with the society is of exceptional importance. There are a number of important reasons to develop the Law on administrative procedure of the EU. First, it is generally recognized that the EU needs common binding legislation that sets out clear operating rules of the EU administration in its’ relations with legal and natural persons, and that would increase the transparency of the EU administration and its’ accessibility to citizens. Second, the drafting of the law on administrative procedure of the EU lies in the legal framework as well; the importance of the article 298 of the Treaty of the Functioning of the European Union, the articles 41 and 42 of the Charter of Fundamental Rights of the EU as well as “soft” law (i.e. codes of good administrative behavior) are obvious here. (shrink)

The dissertation deals with problems in "logic", more precisely, it deals with particular formal systems aiming at capturing patterns of valid reasoning. Sequent calculi were proposed to characterize logical connectives via introduction rules. These systems customarily also have structural rules which allow one to rearrange the set of premises and conclusions. In the "structurally free logic" of Dunn and Meyer the structural rules are replaced by combinatory rules which allow the same reshuffling of formulae, and additionally introduce an explicit marker (...) for the application of the rule---the combinator. The dissertation gives syntactic extensions of such systems introducing conjunction and disjunction . Cut elimination is proved for these systems. ;Syntactic systems as a rule are accompanied by a semantics which interprets them. The extended systems are supplied with semantics using algebraic methods. First, the Lindenbaum algebras are formed, and then these algebras are represented in an algebra of sets. This gives a so called Kripke-style semantics for the systems. The representation for the distributive extension utilizes well-known techniques; it uses sets of prime filters and set theoretical operations on them to deal with conjunction and disjunction, plus a ternary accessibility relation to accommodate the intensional operators as fusion and implication. The representation theorem is proven generally, i.e., for arbitrary sets of combinators using the "squeeze lemma" of Routley and Meyer. ;The non-distributive calculi require a different representation since union and intersection are distributive. Two previous representations for lattices are overviewed, and a modification of the Hartonas-Dunn representation is successfully augmented with the intensional operations. Instead of sets of filters, sets of pairs of minimally inconsistent filters and ideals are used and the representation theorem is proven. The representation results provide soundness and completeness for the systems. The dissertation also investigates properties of dual combinators , proving a series of lemmas about dual combinatory systems not being Church-Rosser and being inconsistent. Combinatorially definable classes of lambda-terms are considered as well. (shrink)

Assuming that $0^\#$ exists, we prove that there is a structure that can effectively interpret its own jump. In particular, we get a structure $\mathcal A$ such that \[ \textit{Sp}({\mathcal A}) = \{{\bf x}'\colon {\bf x}\in \textit{Sp}({\mathcal A})\}, \] where $\textit{Sp}({\mathcal A})$ is the set of Turing degrees which compute a copy of $\mathcal A$. More interesting than the result itself is its unexpected complexity. We prove that higher-order arithmetic, which is the union of full $n$th-order arithmetic for all (...) $n$, cannot prove the existence of such a structure. (shrink)

Multi-space is the notion combining different fields in to a unifying field, which is more applicable in our daily life. In this paper, we introduced the notion of multi-soft space which is the approximated collection of the multi-subspaces of a multi-space . Further, we defined some basic operations such as union, intersection, AND, OR etc. We also investigated some properties of multi-soft spaces.

This article aims to shed some light on the concepts embedded in the expressions ‘services of general interest’ (‘SGI’), ‘services of general economic interest’ (‘SGEI’), ‘non-economic services of general interest’ (‘NSGI’) and ‘social services of general interest’ (‘SSGI’). It is submitted that the expression ‘SGI’ conveys a general concept which comprises both SGEI and NSGI. SGEI may be distinguished from NSGI in that only the former involve an economic activity. In contrast to SGI, SGEI and NSGI, the expression ‘SSGI’ is (...) nowhere to be found in primary EU law. This means that it is for the EU legislator and, as the case may be, for the Member States to define such expression. Furthermore, this article supports the contention that a definition of the principles and conditions underpinning the operation of SGI must be capable of adapting to changing times and social perceptions, whilst being respectful of the vertical and horizontal allocation of powers set out in the Treaties. Vertically, a definition of SGI must not impinge upon the powers retained by the Member States. In the absence of harmonisation, it is for the Member States to define the services they consider to be of general interest, unless they commit a manifest error of assessment. In the presence of EU harmonising measures, the margin of discretion enjoyed by the Member States is, if still existent, narrowed down, given that national authorities are required to comply with the objectives pursued by the EU legislator. Horizontally, a definition of SGI must not encroach upon the prerogatives of the Commission in the realm of competition law. Moreover, in light of Article 9 TFEU and secondary EU legislation, the specific features of SSGI must be taken into consideration when determining the compatibility with EU State aid rules of public service compensation awarded to the providers of those services. An EU conceptual framework for the SGI must thus be the result of a constructive dialogue between the different levels of governance, as well as of a balanced solution among different policy areas in relation to which the EU enjoys competences. (shrink)

The traditional soft set is a mapping from a parameter set to family of all crisp subsets of a universe. Molodtsov introduced the soft set as a generalized tool for modelling complex systems involving uncertain or not clearly defined objects. In this paper, the notion of neutrosophic soft set is reanalysed. The novel theory is a combination of neutrosophic set theory and soft set theory. The complement, “and”, “or”, intersection and union operations are defined on the neutrosophic soft sets. (...) The neutrosophic soft relations accompanied with their compositions are also defined. The basic properties of the neutrosophic soft sets, neutrosophic soft relations and neutrosophic soft compositions are also discussed. (shrink)

The set of $$\textsf{ST}$$ ST -valid inferences is neither the intersection, nor the union of the sets of $$\textsf{K}_3$$ K 3 -valid and $$\textsf{LP}$$ LP -valid inferences, but despite the proximity to both systems, an extensional characterization of $$\textsf{ST}$$ ST in terms of a natural set-theoretic operation on the sets of $$\textsf{K}_3$$ K 3 -valid and $$\textsf{LP}$$ LP -valid inferences is still wanting. In this paper, we show that it is their relational product. Similarly, we prove that the (...) set of $$\textsf{TS}$$ TS -valid inferences can be identified using a dual notion, namely as the relational sum of the sets of $$\textsf{LP}$$ LP -valid and $$\textsf{K}_3$$ K 3 -valid inferences. We discuss links between these results and the interpolation property of classical logic. We also use those results to revisit the duality between $$\textsf{ST}$$ ST and $$\textsf{TS}$$ TS. We present a notion of duality on which $$\textsf{ST}$$ ST and $$\textsf{TS}$$ TS are dual in exactly the same sense in which $$\textsf{LP}$$ LP and $$\textsf{K}_3$$ K 3 are dual to each other. (shrink)

In this paper, we study when a set-continuous operator has a fixed-point that is the intersection of a directed family. The framework of our study is the Kelley-Morse theory KMC– and the Gödel-Bernays theory GBC–, both theories including an Axiom of Choice and excluding the Axiom of Foundation. On the one hand, we prove a result concerning monotone operators in KMC– that cannot be proved in GBC–. On the other hand, we study conditions on directed superclasses in GBC– in order (...) that their intersection is a fixed-point of a set-continuous operator. Finally, we illustrate our results with a solution to the liar paradox and a construction of maximal bisimulations. (shrink)

Given two internal sets X and Y we prove that every Borel function whose graph is a subset of the product X x Y is a member of the least set containing the class of all internal functions and closed with respect to the operations of monotone countable union and intersection. We also prove that any Souslin function can be extended to a Borel function and obtain, as a corollary, a new proof of the recent result of Henson and (...) Ross about the measure preserving property of injective Souslin functions. Further we give a new proof of the fact that injective Borel functions map Borel sets into Borel. A structural result for Souslin graphs all of whose Y-sections are of cardinality n is given. (shrink)

In Aczel [1], the existence of largest fixed points of set continuous operators is proved assuming the schema version of dependent choices in Zermelo-Fraenkel set theory without the axiom of Foundation. In the present paper, we study whether the existence of largest fixed points of set continuous operators is provable without the schema version of dependent choices, using Boffa's weak antifoundation axioms.

Accretive and monotone operator theory are central branches of nonlinear functional analysis and constitute the abstract study of certain set-valued mappings between function spaces. This paper deals with the computational properties of these accretive and (generalized) monotone set-valued operators. In particular, we develop (and extend) for this field the theoretical framework of proof mining, a program in mathematical logic that seeks to extract computational information from prima facie “non-computational” proofs from the mainstream literature. To this end, we establish logical metatheorems (...) that guarantee and quantify the computational content of theorems pertaining to accretive and (generalized) monotone set-valued operators. On the one hand, our results unify a number of recent case studies, while they also provide characterizations of central analytical notions in terms of proof theoretic ones on the other, which provides a crucial perspective on needed quantitative assumptions in future applications of proof mining to these branches. (shrink)

We consider finite multisets over some set of urelements equipped only with additive union [uplus ] and show that the {[otimes], -0}-Horn fragment of Intuitionistic Linear Logic has a sound and complete interpretation in them by interpreting [otimes] as [uplus ]. The linear implication is interpreted by ordered pairs of multisets expressing replacement. The operator ! is also defined in an asymptotic way. Soundness, completeness and partial completeness results are proved for the {×, -0, !}-Horn fragment as well.

In lieu of an abstract, here is a brief excerpt of the content:Buddhist-Christian Studies 21.1 (2001) 37-41 [Access article in PDF] What I Know and Don't Know: A Christian Reflects on Buddhist Practice Mary Frohlich Catholic Theological Union To reflect and write on spiritual practice for publication in an academic journal requires a delicate balancing act. It is not appropriate simply to recount one's experience; nor is it appropriate merely to theorize. I am assisted in this balancing act by (...) a set of categories proposed some years ago by Walter Principe and generally accepted as standard now within the academic field of spirituality. Principe observed that spirituality operates on three interrelated yet distinct levels and that it is crucial for the academician to be clear about which level or levels are being presented. The three are: (1) experience; (2) articulation within wisdom traditions; (3) academic interpretation. 1 My understanding of what is desired in the present context is some of all three but with a primary emphasis on the second. What does Buddhist practice look like from my stance within my Christian "wisdom traditions"? Thus, this is the horizon within which I will present both experience and academic insights.First a bit of autobiographical context. I became a Christian as a young adult, after having been raised in a secular humanist household. My first attempts at a form of meditation as a teenager came from reading Taoist books; in college I experimented with drugs (at that time this was often seen as "spiritual practice") and spent a couple of years very seriously practicing transcendental meditation. Only after all this did I seek baptism and church membership. Since then, my certainty that my call is to be a Christian has not wavered. I spent several years in a Carmelite contemplative monastery, and I now belong to another Roman Catholic religious order.Yet I have repeatedly been drawn to periods of engagement with various practices having Hindu and Buddhist roots.This context is important to describe because I am aware that for me (and for many spiritual seekers today) there can never be a "pure" insertion in a single tradition. I reflected on that recently in an airplane at twenty-five thousand feet, looking down and seeing how totally human constructive activity has reshaped the contours of the land, the rivers, and everything that depends on them. I realized then that the same must be said of the inner contours of my soul. Nearing fifty, I bear the marks [End Page 37] of everything that I have ever done or touched or suffered or known. As I approach this task of reflecting on Buddhist practice from the point of view of a Christian, I cannot do it as a pure outsider. My spiritual practice is Christian in its core, but it has been inextricably shaped by so many other influences--including varieties of Buddhist practice.It is also important to acknowledge the limits of my knowledge about Buddhism and Buddhist practices. My academic exposure to Buddhism is about equivalent to an introductory undergraduate course. As for Buddhist practice, I have participated in a total of five weekend retreats, three one-week retreats, and one three-week retreat. These were all from either Vipassana (Insight Meditation) or Zen (Kwan Um or Diamond Sangha) traditions. Occasionally, I have also had even briefer exposure to other Buddhist traditions. I am very aware that there is much I do not know, or that perhaps I just plain misunderstand, about Buddhism.Yet dialogue requires that I honestly state my views, in their present form, with the hope that in the dialogical process what is misinformed or insensitive can eventually be corrected.Spiritual practice (for Buddhists as well as Christians) involves many different kinds of practices. Practices of charity, such as hospitality or almsgiving, perhaps present the fewest obstacles to mutual understanding, because the practices may be generally similar in both traditions. The ritual practices of a religious tradition, on the other hand, can feel extremely alien to those who do not belong to that religious culture. Paul Hanvey has noted that our reaction to... (shrink)

In the present paper we concentrate on fundamental problems concerning ω-operations over partial enumerated sets. The notion of “HOM-lifts” seems to be an adequate tool for this kind of investigations. MSC: 03D45, 18A30.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Callimachus in Context: From Plato to the Augustan Poets by Benjamin Acosta-Hughes, Susan A. StephensIvana PetrovicBenjamin Acosta-Hughes and Susan A. Stephens. Callimachus in Context: From Plato to the Augustan Poets. Cambridge: Cambridge University Press 2012. xvi + 328 pp. 4 maps. Cloth, $99.Callimachus is a scholar’s poet, not just because his poetry is difficult and challenging, but also because we tend to see a reflection of ourselves in (...) him: self-assured to the point of arrogance, delighting in recondite words and fun facts, a target of unfair criticism from malevolent and envious colleagues. Callimachus was for decades perceived as antiquarian, bookish, a scholar whose poetry was divorced from the performative setting, not championing civic values, but rather l’art pour l’art avant la lettre. The main focus of scholarship used to be Callimachus’ relationship with the Greek poetic tradition, and virtuoso studies in intertextuality demonstrated just how rich and wide-ranging the tapestry of his allusions is, from poetry to technical writings in prose. However, in the last couple of decades, this image of Callimachus as the ivory-tower scholar-poet began to change. In his ground-breaking monograph Callimachus and His Critics (Princeton 1995), Alan Cameron argued that Callimachus was a prominent and active figure at the Alexandrian court, and far from an armchair intellectual.In recent years, numerous scholars have looked into the way Callimachus was indeed a child of his own time. Brill’s 2011 Companion to Callimachus (edited by the authors of the present book and Luigi Lehnus) is a good illustration of the current state of affairs in Callimachus scholarship: six out of twenty-seven papers discuss Callimachus’ relationship with the royal family and explore his status as a court-poet, his attitude to contemporary religion, and the geopoetics of his poetry and its political implications.This book is a successful union of the two aforementioned approaches to the poet. First, the authors set out to “contextualize Callimachus within his intellectual traditions and within his physical and social environments”; second, they pose five questions: “Why do there appear to be so many Platonic tangents in Callimachus? Why, in a poet considered the model of the ‘bookish’ author, are there so many indications of poetic performance? What is the rapport between the Ptolemies and their political interests and a remarkably diffuse body of work of one court poet? Why is Callimachus an ongoing feature of Roman poetic culture, and in such a particular way?” (viii). They provide an answer to each of these questions in separate chapters, carefully and meticulously negotiating between the study of intertexts and Callimachus’ social contexts.The introduction is fast-paced and fact-based. It provides an overview of Callimachus’ career and the political and cultural history of his native city, Cyrene, and his adopted home, Alexandria. It is the choice of facts and the sharp eye for detail that sets this section apart from a mere collection of data: by discussing the poetic production of the lesser-known Cyrenaean epic poet Eugamon, the authors provide “a glimpse into regional poetics and how it operated within the broader Panhellenic context” (6); careful reading of inscriptions and an assessment of the archaeological remains allows them to offer an interesting suggestion regarding [End Page 365] the dramatic performances of dithyrambic choruses in connection with the festival of the Carneia, which Callimachus memorably described in his Hymn to Apollo.A succinct discussion of Cyrenaean cults brings together results of decades of archaeological study and allows material culture to inform and enrich our view of Callimachus’ poetry: there was a bronze Delian palm in the Cyrenaean sanctuary of Leto (cf. H. Ap. 1–2); the local temple of Zeus Olympius had a cult statue that replicated Phidias’ (cf. Iambus 6); Thesmophoria were probably celebrated in the Cyrenaen sanctuary of Demeter and Kore (cf. H. Dem.); a number of local statue-groups and reliefs coincide with figures in Callimachus’ poetry. By juxtaposing the old and venerable city Cyrene with the newly founded cosmopolitan Alexandria in Egypt, the authors emphasize the cultural contrast between Callimachus’ native city and his chosen home. Since Callimachus was a poet active in a city... (shrink)

This volume presents a sketch of the Meaning-Text linguistic approach, richly illustrated by examples borrowed mainly, but not exclusively, from English. Chapter 1 expounds the basic idea that underlies this approach—that a natural language must be described as a correspondence between linguistic meanings and linguistic texts—and explains the organization of the book. Chapter 2 introduces the notion of linguistic functional model, the three postulates of the Meaning-Text approach (a language is a particular meaning-text correspondence, a language must be described by (...) a functional model and linguistic utterances must be treated at the level of the sentence and that of the word) and the perspective “from meaning to text” for linguistic descriptions. Chapter 3 contains a characterization of a particular Meaning-Text model: formal linguistic representations on the semantic, the syntactic and the morphological levels and the modules of a linguistic model that link these representations. Chapter 4 covers two central problems of the Meaning-Text approach: semantic decomposition and restricted lexical cooccurrence (≈ lexical functions); particular attention is paid to the correlation between semantic components in the definition of a lexical unit and the values of its lexical functions. Chapter 5 discusses five select issues: 1) the orientation of a linguistic description must be from meaning to text (using as data Spanish semivowels and Russian binominative constructions); 2) a system of notions and terms for linguistics (linguistic sign and the operation of linguistic union; notion of word; case, voice, and ergative construction); 3) formal description of meaning (strict semantic decomposition, standardization of semantemes, the adequacy of decomposition, the maximal block principle); 4) the Explanatory Combinatorial Dictionary (with a sample of complete lexical entries for Russian vocables); 5) dependencies in language, in particular—syntactic dependencies (the criteria for establishing a set of surface-syntactic relations for a language are formulated). Three appendices follow: a phonetic table, an inventory of surface-syntactic relations for English and an overview of all possible combinations of the three types of dependency (semantic, syntactic, and morphological). The book is supplied with a detailed index of notions and terms, which includes a linguistic glossary. (shrink)

The quantified relevant logic RQ is given a new semantics in which a formula for all xA is true when there is some true proposition that implies all x-instantiations of A. Formulae are modelled as functions from variable-assignments to propositions, where a proposition is a set of worlds in a relevant model structure. A completeness proof is given for a basic quantificational system QR from which RQ is obtained by adding the axiom EC of 'extensional confinement': for all x(A V (...) B) -> (A V for all xB). with x not free in A. Validity of EC requires an additional model condition involving the boolean difference of propositions. A QR-model falsifying EC is constructed by forming the disjoint union of two natural arithmetical structures in which negation is interpreted by the minus operation. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Talmud Meets Church HistoryDaniel Boyarin (bio)Virginia Burrus. Chastity as Autonomy: Women in the Stories of the Apocryphal Acts. New York: Edwin Mellen, 1987.———. ‘“Equipped for Victory’: Ambrose and the Gendering of Orthodoxy.” Journal of Early Christian Studies 4.4 (1996): 461–75.———. The Making Of A Heretic: Gender, Authority, And The Priscillianist Controversy. Berkeley: U of California P, 1995.———. “Reading Agnes: The Rhetoric of Gender in Ambrose and Prudentius.” Journal (...) of Early Christian Studies 3.1 (1995): 25–46.———. “Word and Flesh: The Bodies and Sexuality of Ascetic Women in Christian Antiquity.” Journal of Feminist Studies in Religion 10.1 (1994): 27–51.[1] Prologue: Morningside Heights, 1941—A Talmudist Meets a Church HistorianIn 1944, my teacher Saul Lieberman published a classic essay in which he treated talmudic martyrology in the context of patristic literature. 1 The article had been written under the inspiration of his meeting and friendship with Henri Gregoire, the great Belgian church historian, then a refugee from the Nazis in the Morningside Heights neighborhood in New York, where Lieberman, the great Lithuanian talmudist, had also found refuge and where the two met. Nearly a half-century later, this student of Lieberman’s met another church historian, Virginia Burrus, in Morningside Heights under happier circumstances, when both of us were participants at a conference on asceticism at Union Theological Seminary, and a similar intellectual interaction began. This paper represents some of the first fruits of that second encounter and aspires to modestly continue the enterprise begun by the first.[2] Intertextuality and InterdisciplinarityAveril Cameron has recently written:The myth of early Christianity as the resort of the poor and underprivileged is precisely that, and a very convenient one it has been. It is a myth that rests, moreover, on the fallacy of an original Christianity uncontaminated by external influences; but its holders then have to explain how this “new” faith could make [End Page 52] the leap to center stage. Thus, we have been told, “the naiveté of the early Christian speech came in the course of time to wed itself to the cultures of the world.” But while much of current New Testament scholarship is directed at the internal (that is, theological) articulation of the texts, there is also a perceptible trend towards a mode of interpretation that balances the external and internal factors operative in the literary texts. It is thus less a question of the degree of “influence” of Greco-Roman or Jewish literary or philosophical elements on early Christian writing than of their integral relationship.[37–38]Judaism also (and Jewish scholarship) has had a stake in inscribing itself as pure and uncontaminated, for reasons that Philip Alexander has articulated: “The attempt to [lay down a norm for Judaism in the first century] barely conceals apologetic motives—in the case of Christianity a desire to prove that Christianity transcended or transformed Judaism, in the case of Jews a desire to suggest that Christianity was an alien form of Judaism which deviated from the true path” [3]. Indeed, the very distinctness of Judaism has been articulated by Jews as precisely its distance from a “syncretistic” Christianity whose defining feature is that it is somehow a composite of Judaism and Hellenism. 2In this essay, in conversation with some of the work of Burrus, I wish to begin to suggest a few of the ways that study of the Talmud can be further enriched through the engagement of talmudic scholars with the recent sophisticated (and especially gender-oriented) work being done on early Christianity. Indeed, I will be hinting (and in future work explicitly arguing) that we have to begin seriously thinking about Judaeo-Christianity as a single cultural system: contentious, dialectical, polemical, and sometimes friendly, but—I hasten to add—not moralistic in the homogenized “family values” sense implied by the modern usage of this term. I put forth here, as a case in point, that the richest contexts for understanding the sets of cultural tensions that gave rise to a particular talmudic text are to be uncovered in contemporary patristic literature. From the point of view of a New Historicist approach to talmudic literature, this suggests that the... (shrink)

This paper is about partially ordered multisets (pomsets for short). We investigate a particular class of pomsets that we call order-deterministic, properly including all partially ordered sets, which satisfies a number of interesting properties: among other things, it forms a distributive lattice under pomset prefix (hence prefix closed sets of order-deterministic pomsets are prime algebraic), and it constitutes a reflective subcategory of the category of all pomsets. For the order-deterministic pomsets we develop an algebra with a sound and (-) complete (...) equational theory. The operators in the algebra are concatenation and join, the latter being a variation on the more usual disjoint union of pomsets. This theory is then extended in order to capture refinement of pomsets by incorporating homomorphisms between models as objects in the algebra and homomorphism application as a new operator. (shrink)

In intuitionistic analysis, a subset of a Polish space like or is called positively Borel if and only if it is an open subset of the space or a closed subset of the space or the result of forming either the countable union or the countable intersection of an infinite sequence of (earlier constructed) positively Borel subsets of the space. The operation of taking the complement is absent from this inductive definition, and, in fact, the complement of a (...) positively Borel set is not always positively Borel itself (see Veldman, 2008a). The main result of Veldman (2008a) is that, assuming Brouwer's Continuity Principle and an Axiom of Countable Choice, one may prove that the hierarchy formed by the positively Borel sets is genuinely growing: every level of the hierarchy contains sets that do not occur at any lower level. The purpose of the present paper is a different one: we want to explore the truly remarkable fine structure of the hierarchy. Brouwer's Continuity Principle again is our main tool. A second axiom proposed by Brouwer, his Thesis on Bars is also used, but only incidentally. (shrink)

The final portion of the thesis surveys proposals for the introduction of hidden variables into quantum mechanics, proofs of the impossibility of such hidden-variable proposals, and criticisms of these impossibility proofs. And arguments in favour of the partial-Boolean algebra, rather than the orthomodular lattice, formalization of the quantum propositional structures are reviewed. ;As for , each quantum state-induced expectation-function on a P truth-functionally assigns 1 and 0 values to the elements in a ultrafilter and dual ultraideal of P, where in (...) general the union of an ultrafilter and its dual ultraideal is smaller than the entire structure. Thus it is argued that each expectation-function is the quantum analog of a classical semantic mapping, even though the domain where each expectation-function is bivalent and truth-functional is usually a non-Boolean substructure of P. ;In classical propositional logic, propositions form a Boolean algebra, and each semantic mapping assigns the value 1 to the members of a certain subset of the algebra, namely, an ultrafilter, and assigns 0 to the members of the dual ultraideal, where the union of these two subsets is the entire algebra. The propositional structures of classical mechanics are likewise Boolean algebras, so one can straightforwardly provide a classical semantics, which also satisfies . However, quantum propositional structures are non-Boolean, so it is an open question whether a semantics satisfying , and can be provided. ;Von Neumann first proposed that the algebraic structures of the subspaces of Hilbert space be regarded as the propositional structures P of quantum mechanics. These structures have been formalized in two ways: as orthomodular lattices which have the binary operations "and", "or", defined among all elements, compatible and incompatible ; and as partial-Boolean algebras which have the binary operations defined among only compatible elements. In the thesis, two basic senses in which these structures are non-Boolean are discriminated. And two notions of truth-functionality are distinguished: truth-functionality ,) applicable to the Plattices; and truth-functionality ) applicable to both the Plattices and partial-Boolean algebras. Then it is shown how the lattice definitions of "and", "or", among incompatibles rule out a bivalent, truth-functional ,) semantics for any PQM lattice containing incompatible elements. In contrast, the Gleason and Kochen-Specker proofs of the impossibility of hidden-variables for quantum mechanics show the impossibility of a bivalent, truth-functional ) semantics for three-or-higher dimensional Hilbert space PQM structures; and the presence of incompatible elements is necessary but is not sufficient to rule out such a semantics. ;The thesis investigates the possibility of a classical semantics for quantum propositional structures. A classical semantics is defined as a set of mappings each of which is bivalent, i.e., the value 1 or 0 is assigned to each proposition, and truth-functional, i.e., the logical operations are preserved. In addition, this set must be "full", i.e., any pair of distinct propositions is assigned different values by some mapping in the set. When the propositions make assertions about the properties of classical or of quantum systems, the mappings should also be "state-induced", i.e., values assigned by the semantics should accord with values assigned by classical or by quantum mechanics. (shrink)

First published in 1848, Frederick Grimke's book, in the words of the editor, "deserves comparison with Tocqueville's justly famous work, Democracy in America, and is in certain ways superior. It is the single best book written by an American in the nineteenth century on the meaning of our political way of life." A second edition of Grimke's work was published in 1856, and a third edition appeared posthumously in 1871, but since then this classic in American thought has been almost (...) completely lost to sight. Grimke was born in South Carolina in 1791, and later moved to Ohio where he became a judge. He remained a bachelor, led a rich and cosmopolitan intellectual life, and accumulated an excellent library. His sisters Angelina (wife of the abolitionist Theodore Weld) and Sarah were both famous for deserting their South Carolina heritage and becoming active in the abolition and woman suffrage movements. In 1842 Grimke retired from the bench to devote the remainder of his life to study and writing, setting himself the task of educating his contemporaries in the nature of their society. His major achievement was The Nature and Tendency of Free Institutions. Grimke's range of topics includes the right of the majority, the character and operation of elective governments, the function of political parties, the American contrasted with the English and French constitutions, and the separation of powers in the American political systems. He sees governmental institutions as the expression of the general structure of society which calls them into being. In his Introduction, Mr. Ward points to Grimke's thesis "that the separation of powers in the frame of the American constitution works not because power is distributed within the government but because all branches of the government are, directly or indirectly, responsible to the will of the majority of the people outside the doors of government." As a result of the party system, Grimke wrote, "we may vary the paraphernalia of government as much as we please, but it still obstinately persists in every one of its departments to be a government based upon the popular will." Mr. Ward calls attention to Grimke's passionate belief that "freedom is its own justification" and that its ultimate value is that "it created the kind of character which made freedom possible." He held that "the only way to make a man fit for freedom is to give him freedom." Yet, unlike his sisters, he shared a view of race that was pervasive in his time and was unable to imagine the extension of freedom to the slave. In contradiction to his views of government and freedom, he upheld Negro slavery even to the extent of sanctioning secession to protect it. To him, "the open affirmation of the right of secession would serve to maintain the Union, not destroy it.". (shrink)

Nick Dyer-Witheford and Greig de Peuter. Games of Empire: Global Capitalism and Video Games . Minneapolis: University of Minnesota Press. 2009. 320pp. pbk. $19.95 ISBN-13: 978-0816666119. In Games of Empire , Nick Dyer-Witheford and Greig de Peuter expand an earlier study of “the video game industry as an aspect of an emerging postindustrial, post-Fordist capitalism” (xxix) to argue that videogames are “exemplary media of Empire” (xxix). Their notion of “Empire” is based on Michael Hardt and Antonio Negri’s Empire (2000), which (...) characterizes the contemporary world order as a decentralized system of global economic, political, and economic power that transcends national boundaries. In the view of the authors, Hardt and Negri’s account sets itself apart from other analyses of international politics by offering a “comprehensive account of conditions of work, forms of subjectivity, and types of struggle in contemporary capital” (xx). Dyer-Witheford and de Peuter thus divide Games of Empire into three sections to reflect each of these aspects of Empire ’s argument, seeing their work as the first account to explore “virtual games within a system of global ownership, privatized property, coercive class relations, military operations, and radical struggle” (xxix). Books in the University of Minnesota Press’s Electronic Mediations series “explore the humanistic and social implications” of new technologies that spark “significant changes in society and culture, politics and economics, thinking and being.” That’s an abstract goal, and one that Games of Empire surely meets. Yet at times it can be difficult to understand exactly which specific intervention this book seeks to make. It is unclear whether the authors of Games of Empire see their work as an indictment of game scholars’ lack of attention to political economy, or whether it’s a work of political theory hoping to show that other disciplines should be paying more attention to the production and play of videogames. Because Dyer-Witheford and de Peuter don’t directly criticize previous political critiques of gaming—such as Edward Castronova’s exploration of the “porous membrane” allowing two-way traffic between virtual economies and those of the real world, or Alexander Galloway’s unraveling of control protocols in algorithmic design, or Ian Bogost’s idea of political procedural rhetoric—they sometimes leave the reader wondering how to situate the book in the broader discourse on games and politics, either separately or together. Thus, Games of Empire might best be seen as an introduction to the writings of Hardt and Negri for game players and designers, rather than as a text for communicating the basic concepts of game studies and design. It is neither a truly new theory of games or digital media, nor is it a new theory of Empire—and that’s not a criticism. It is instead an introduction to Empire through popular culture, as Zizek does for Lacan in Looking Awry . If one were teaching an introductory course on contemporary political theory, this book would offer obvious inroads into Negri and Hardt’s thinking for a number of reasons. Despite its radical ideological bent, the book isn’t off-putting to readers who don’t necessarily share the authors’ politics. It synthesizes complex ideas from difficult thinkers like Marx, Foucault, and Guattari while integrating modifications and critiques of Empire theory itself. And although the book is dense, sometimes feeling longer than it actually is (just over 200 pages), Games of Empire maintains a breezy readability by tightly coupling core concepts of Empire theory to well-known games and widely-publicized conflicts within the videogame industry. The first section of the book focuses on immaterial labor, the accumulation of “cognitive capital,” and the global process of manufacturing videogame consoles. It is significant for the authors that videogames began as hacker experiments within research institutes of the military industrial complex, programmed on stolen time, before becoming a commodity (7). This is the first in a string of examples showing how creative dissidence and conflict fuel the continuing evolution of Empire’s control. Dyer-Witheford and de Peuter explain that the videogame industry now constitutes an international production apparatus dominating both creative work in developed nations and manual labor in developing ones. Because game industries in the United States, Western Europe, and Japan are predominately non-unionized, they serve as an exemplary system for analyzing how global capital exploits contemporary intellectual work—including an excellent analysis of the “EA Spouse” scandal of 2004. On the side of the consumer, the authors argue that rabid “console races” that drive the industry forward from a technological perspective serve to structure gamer identity and combat piracy; later in the book, these machines offer a window into the worlds of Congolese coltan mining and electronic waste (222-224). In the second section, Dyer-Witheford and de Peuter move on to deep case studies of individual games to show how the most popular game genres embed imperial assumptions about conflict, exchange, and urban life. First they argue that military training games such as Full Spectrum Warrior —co-developed by university researchers, industry developers, and military contractors—contribute to the “banalization” of war, a subjective state wherein perpetual preparedness for war is accepted as a part of everyday life (100). Chapter five covers Michel Foucalt’s notion of “biopower,” the extension of capital accumulation to life itself. The authors argue that virtual worlds such as World of Warcraft , which take market capitalism as a given and force players into essentialist roles and racial antagonisms, are organized to maximize control and profit (often on the backs of virtual currency “farmers” in China and southeast Asia). Finally, they criticize the naïve assumption that humor and cynicism in the popular sandbox game franchise Grand Theft Auto offer any remedy to its racialized, violent content. Instead, such games indulge and normalize the fantasy of getting rich at any cost by keeping the realities of contemporary urban life and corporate greed at a safe distance (181). Part three of Games of Empire focuses on “games of multitude,” a preliminary attempt to escape from Empire’s order through alternate modes of videogame development and play. Multitude is defined dialectically, as “the engine and the enemy” of Empire (187). This is the most important, yet also most contradictory section of the text. It lays bare the process by which Empire and its media feed our creative and intellectual development to overabundance. At a certain point, the force of the multitude reaches such a level that it threatens the stability of Empire; however, instead of following Hardt and Negri’s utopian assumptions about the radical potential of the multitude, the authors here follow Paolo Virno’s warning that Empire is “very good at adopting apparently iconoclastic practices and utopian ideas as management techniques and revenue sources” (188). At every turn, advances in player configurative power provide new sources of revenue and advertising angles for the game industry. A disappointing shortcoming of these latter pages is the lack of truly new examples for radical resistance within game development. Instead, it turns out that the radical left seems satisfied with the same mild successes that the left-of-center also has celebrated: artist’s mods, virtual world activism, and critical counterplay within strategy- and wargames. Having been frequently cited by many authors before Dyer-Witheford and de Peuter, this idea of subversion or resistance through play feels tired and unpersuasive. It is unclear if the authors believe it is possible to embrace game design itself as a way of pursuing what they call “exodus” from Empire, or if an all-too-fashionable subversion is the only workable strategy. While the book does explore how the earliest independent game studios were eventually subverted and incorporated into the game industry proper, it doesn’t affirm or critique more recent non-commercial, DIY game development projects such as Klik-of-the-Month Club and Ludum Dare. Dyer-Witheford and de Peuter’s analysis of so-called “tactical games,” including the editorial works of La Molleindustria, leads to an even more ambivalent take on the contemporary design ecology. At the conclusion of his essay on “Countergaming,” Galloway asserts that avant-garde videogame artists “should create new grammars of action […] should create alternative algorithms” (Galloway 125). Yet Dyer-Witheford and de Peuter characterize works such as McDonald’s Video Game and Oiligarchy as didactic, suggesting that the role of radical political games might be “limited to that of agitprop” (199). They are concerned that games like those of Molleindustria rigidly structure the activities of their players in order to prove a point. Yet, despite their repeated assertion that the equation of greater interactivity with democratic digital liberation is flawed, the authors see potential in policy simulators that “allow players to edit or tweak” (202) their parameters in response to what Bogost has called simulation fever , the simultaneous drive toward and fear of simulation (Bogost 108). The possibility of practicing radical design is bucked, and early attempts at critical game development like those of Molleindustria’s seem to be relegated to the status of exceptions that prove the rule for player-centered exodus. Overall, there is one glaring question Games of Empire leaves unanswered: how exactly are videogames the “exemplary media” of Empire, and what are the implications of videogames being exemplary in this way? Presumably Dyer-Witheford and de Peuter want to avoid essentialist claims, so they’re not keen on following Wark’s desire to mark “the game’s difference from [legacy media] as something that speaks to changes in the overall structure of social and technical relations” (Wark 225). It is also unclear how the production apparatuses, labor standards, and subjectivizing processes involved in the creation and use of other any other kind of digital media would fail to justify their equally exemplary status. Even the book’s concluding paragraph holds that virtual games “are one molecular component of this undecidable collective mutation” (Dyer-Witheford and de Peuter 229) of intellect, labor, and daily life. In the end, the authors seem to back away from their focus on games as exemplary to bring their work in line with broader theories of the gradual digitization of the everyday, in line with Galloway and Manovich. Despite these flaws, there is an undeniable elegance to Games of Empire ’s contrasting of gaming’s overwhelmingly imperial content with its multitudinous form . And its ambivalence about the potential of independent or political game development might be seen by scholars of Empire as a strength rather than a weakness, an acceptance that every new expression of multitude offers another opportunity for the expansion of Empire. The book also functions as a strong, all-encompassing call to greater responsibility on the part of mainstream game developers to be more conscious of the ideologies they embed in their work, of the way their intellectual property is used and manipulated by those who employ them, and of the material impact their industry has on the world at large. For players it offers a toolbox of concepts for radical examinations of their own play activities, asking them to be more cognizant of the consequences of their consumption of digital media and the ways in which their virtual lives interface with the real. REFERENCES Bogost, Ian. Unit Operations: An Approach to Videogame Criticism . Cambridge, Mass.: MIT Press, 2006. Castranova, Edward. Synthetic Worlds: The Business and Culture of Online Games . Chicago, Illinois: University of Chicago Press, 2006. Dyer-Witheford, Nick and de Peuter, Greig. Games of Empire: Global Capitalism and Video Games . Minneapolis, Minnesota: University of Minnesota Press, 2009. Galloway, Alexander. Gaming: Essays on Algorithmic Culture . Minneapolis, Minnesota: University of Minnesota Press, 2006). Wark, McKenzie. Gamer Theory . Cambridge, Mass.: Harvard University Press, 2007. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Continental and Feminist Philosophical PedagogiesConditionsSina KramerIn thinking through what it means to teach continental and feminist philosophy, I keep coming back to a somewhat enigmatic line from Adorno’s essay, “Why Still Philosophy?”: “Because philosophy is good for nothing, it is not yet obsolete” (Adorno 2005, 15). I believe that this dialectical aphorism has everything to do with the conditions under which we as teachers practice philosophy today, and continental (...) and feminist philosophy in particular.On the one hand, Adorno’s remark is made in the context of the specific conditions—political, economic, philosophical, etc.—of his own time. On the other hand, Adorno writes that if philosophy is still necessary (and we should always take seriously this “if,” as well as the “not yet” of the quote above) then it is for the same reasons that philosophy has always been necessary: as critique. Philosophy is thus both spatially and temporally specific in that it plays particular roles in particular places and times, and it is universal in that its operation as critique has always been the same. We must therefore spell out the particular conditions of our historical moment in order for philosophy to play the critical role that it has purportedly always played. What are the conditions under which we teach continental and feminist philosophy today?I would point here to a few phenomena. First, President Barack Obama announced in his 2011 “State of the Union” address that in order for America to “win the future” we must invest in education, to reach the goal of having the [End Page 68] highest proportion of college graduates in the world by the end of the decade (Obama 2011). The president described investment in education as part of the larger of goal of supporting the competitive advantage of American workers. The president cast education in entirely economic terms: a greater quantity of graduates for the sake of a more economically prosperous nation.At the same time, some universities, especially those that depend in part upon dwindling state resources, have chosen to cut programs in the humanities in general or in philosophy in particular: at UNLV, at the University of Louisiana at Lafayette, or at Middlesex University.1 Under the logic of fiscal austerity, universities are deciding that they can no longer “afford” to keep departments that are losing money or, which may amount to the same thing, programs that are no longer central to the mission of the university.Finally, recent research indicates that only about one-third of all teachers in higher education in the United States are tenured or on the tenure track; teaching has been farmed out, outsourced, or subcontracted to a contingent labor force with less job security, lower wages, and fewer benefits than those on the tenure track.2 And shortly after the president’s “State of the Union” address, the book Academically Adrift and accompanying articles in the Chronicle of Higher Education and the New York Times argued that college students are learning less, according to measurable metrics, even as they are paying more—that is, going into greater debt—for a degree that is less and less a guarantee of a stable middle-class income (Arum and Roksa 2011; Glenn 2011a, 2011b).In his dialectical aphorism, Adorno seems to set up a contradiction between philosophy and utility, between learning as an end in itself, and learning as an instrument toward some other end—a contradiction that goes back as far as philosophy’s stories about its own origins, to Thales and the olive-press. But this contradiction must be examined in each context in which it is raised. For instance, W. E. B. Du Bois seems to set up the same contradiction in The Souls of Black Folk, when he writes that “the true college will ever have one goal: not to earn meat, but to know the end and aim of that life which meat nourishes” (Du Bois 1997, 86). While this seems like the statement of a universal truth, it must be understood in the context of the larger argument in Souls, in which Du Bois argues that black people have a right to an education as... (shrink)

This work is an attempt to lay foundations for a theory of interactive computation and bring logic and theory of computing closer together. It semantically introduces a logic of computability and sets a program for studying various aspects of that logic. The intuitive notion of computational problems is formalized as a certain new, procedural-rule-free sort of games between the machine and the environment, and computability is understood as existence of an interactive Turing machine that wins the game against any possible (...) environment. The formalism used as a specification language for computational problems, called the universal language, is a non-disjoint union of the formalisms of classical, intuitionistic and linear logics, with logical operators interpreted as certain—most basic and natural—operations on problems. Validity of a formula is understood as being “always computable”, and the set of all valid formulas is called the universal logic. The name “universal” is related to the potential of this logic to integrate, on the basis of one semantics, classical, intuitionistic and linear logics, with their seemingly unrelated or even antagonistic philosophies. In particular, the classical notion of truth turns out to be nothing but computability restricted to the formulas of the classical fragment of the universal language, which makes classical logic a natural syntactic fragment of the universal logic. The same appears to be the case for intuitionistic and linear logics . Unlike classical logic, these two do not have a good concept of truth, and the notion of computability restricted to the corresponding two fragments of the universal language, based on the intuitions that it formalizes, can well qualify as “intuitionistic truth” and “linear-logic truth”. The paper also provides illustrations of potential applications of the universal logic in knowledgebase, resourcebase and planning systems, as well as constructive applied theories. The author has tried to make this article easy to read. It is fully self-contained and can be understood without any specialized knowledge of any particular subfield of logic or computer science. (shrink)

The powerset operator, [MATHEMATICAL SCRIPT CAPITAL P], is compared with other operators of similar type and logical complexity. Namely we examine positive operators whose defining formula has a canonical form containing at most a string of universal quantifiers. We call them ∀-operators. The question we address in this paper is: How is the class of ∀-operators generated ? It is shown that every positive ∀-operator Γ such that Γ ≠ ∅, is finitely generated from [MATHEMATICAL SCRIPT CAPITAL P], the identity (...) operator Id, constant operators and certain trivial ones by composition, ∪ and ∩. This extends results of [3] concerning bounded positive operators. (shrink)

Let R be an o-minimal expansion of an ordered group R has no poles, R cannot define a real closed field with domain R and order R is eventually linear and every R -definable set is a finite union of cones. As a corollary we get that Th has quantifier elimination and universal axiomatization in the language with symbols for the ordered group operations, bounded R -definable sets and a symbol for each definable endomorphism of the group.

We consider countable so‐called rich subsemigroups of ; each such semigroup T gives a variety CPEAT that is axiomatizable by a finite schema of equations taken in a countable subsignature of that of ω‐dimensional cylindric‐polyadic algebras with equality where substitutions are restricted to maps in T. It is shown that for any such T, if and only if is representable as a concrete set algebra of ω‐ary relations. The operations in the signature are set‐theoretically interpreted like in polyadic equality set (...) algebras, but such operations are relativized to a union of cartesian spaces that are not necessarily disjoint. This is a form of guarding semantics. We show that CPEAT is canonical and atom‐canonical. Imposing an extra condition on T, we prove that atomic algebras in CPEAT are completely representable and that CPEAT has the super amalgamation property. If T is rich and finitely represented, it is shown that CPEAT is term definitionally equivalent to a finitely axiomatizable Sahlqvist variety. Such semigroups exist. This can be regarded as a solution to the central finitizability problem in algebraic logic for first order logic with equality if we do not insist on full fledged commutativity of quantifiers. The finite dimensional case is approached from the view point of guarded and clique guarded (relativized) semantics of fragments of first order logic using finitely many variables. Both positive and negative results are presented. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Instinct of Nature: Natural Law, Synderesis, and the Moral SenseRobert A. Greene“Instinct is a great matter.”—Sir John FalstaffThis essay traces the evolution of the meaning of the expression instinctus naturae in the discussion of the natural law from Justinian’s Digest through its association with synderesis to Francis Hutcheson’s theory of the moral sense. The introduction of instinctus naturae into Ulpian’s definition of the natural law by Isidore of Seville (...) in the seventh century posed a problem of definition for medieval commentators. Some said that it meant a universal and providential natura naturans; some defined it as the urge to self and species preservation in animals, degenerating in man into sensual and shameful impulses; some advanced the humanistic and paradoxical notion that it referred to a unique exercise of human reason in coming to know the natural law. The contemporaneous revival in the twelfth century of St. Jerome’s puzzling new term “synderesis,” and its gradual definition as the immediate apprehension of the first practical moral principles of the natural law, brought the two terms into proximity and loose association.A half-century later St. Bonaventure made explicit what had remained latent in the thinking of Thomas Aquinas by relocating synderesis in the affective rather than the intellectual part of man’s nature. Accordingly the moral discoveries of synderesis came to be spoken of as not only non-discursive but instinctive in nature—apprehensions for which no reason could be given, apprehensions somehow rooted in affective human experience. During the bilingual early modern period an increasingly secularized, internalized, and reified instinctus [End Page 173] naturae, together with its abbreviated vernacular cognate, “instinct,” came to serve as a substitute and synonym for the obsolescent synderesis. Edward Herbert’s attention to instinctus naturae in his De Veritate (1624), Sir Matthew Hale’s speculations about the place of rational instinct in the natural law, and Francis Hutcheson’s theory of a moral sense all exemplify this semantic legacy.The first entry in Justinian’s Digest has had a disproportionate influence on later speculation about the natural law. It begins a chapter that gives pride of place to general definitions of justice, law, jus naturale and jus gentium, and it is drawn from the writings of the Roman jurisconsult Domitius Ulpianus (d. 223), whose work constitutes forty percent of the Digest. Ulpian defines the natural law, with insistent repetition, as that which nature has taught to, or is common to, all animals:Jus naturale is that which nature has taught to all animals; for it is not a law specific to mankind but is common to all animals—land animals, sea animals, and the birds as well. Out of this comes the union of man and woman [male and female] which we call marriage, and the procreation of children, and their rearing. So we can see that the other animals, wild beasts included, are rightly understood to be acquainted with this law. Jus gentium, the law of the nations, is that which all human peoples observe. That it is not coextensive with natural law can be grasped easily, since this latter is common to all animals whereas jus gentium is common only to human beings among themselves. 1Justinian’s compilers gave Ulpian’s definition striking prominence at the beginning of the Digest and then in the same short chapter quoted the incompatible and more traditional definitions of his contemporaries Gaius and Paulus. They confined the operation of the natural law to mankind and spoke of reason as its source. 2 The compilers had been charged to eliminate just such conflicts; yet here at the very outset they set a conundrum that perplexed commentators [End Page 174] and invited explanation from Isidore of Seville to Hugo Grotius. Their selection of quotations suggests that as lawyers they regarded such general definitions as “for legal purposes no more than ornament to discussion.” 3 For those of a more speculative bent, however, the dilemmas could not have been more fundamental. How was the natural law to be defined in relation to those appetitive and self-preservative urges that man seemed to share with animals? Or did the term law apply only... (shrink)

We show that considerable sets of positive linear operators namely their extensions as closures, adjoints or Friedrichs positive self-adjoint extensions form operator (generalized) effect algebras. Moreover, in these cases the partial effect algebraic operation of two operators coincides with usual sum of operators in complex Hilbert spaces whenever it is defined. These sets include also unbounded operators which play important role of observables (e.g., momentum and position) in the mathematical formulation of quantum mechanics.

As is well known, any preorder R on a set U induces an Alexandrov topology on U. In some interesting cases related to data mining an Alexandrov topology can be transformed into different types of logico-algebraic models. In some cases, (pre)topological operators provided by Pointless Topology may define a topological space on U even if R is not a preorder. If this is the case, then we call R a crypto-preorder. The paper studies the conditions under which a relation R (...) is a crypto-preorder and how to transform a crypto-preorder into a proper preorder. (shrink)

We present an extension of constructive Zermelo{Fraenkel set theory [2]. Constructive sets are endowed with an applicative structure, which allows us to express several set theoretic constructs uniformly and explicitly. From the proof theoretic point of view, the addition is shown to be conservative. In particular, we single out a theory of constructive sets with operations which has the same strength as Peano arithmetic.

We introduce a way of relativizing operational set theory that also takes care of application. After presenting the basic approach and proving some essential properties of this new form of relativization we turn to the notion of relativized regularity and to the system OST that extends OST by a limit axiom claiming that any set is element of a relativized regular set. Finally we show that OST is proof-theoretically equivalent to the well-known theory KPi for a recursively inaccessible universe.

The strongly innovative theory of whole-parts relations outlined by Husserl in his Third logical Investigation—to which he attributed a basic value for his entire phenomenology—has recently attracted a renewed interest. Although many important issues have been clarified (especially by Kit Fine) the subject seems still worth being revisited. To this aim Husserlian universes are introduced. These are lower bounded distributive lattices endowed with a unary operation of defect and a binary relation of isogeneity. Husserl's contents are identified with nonzero (...) elements of a Husserlian universe and the dependence relations among contents are defined and studied starting from the idea that the defect of xis what x needs in order to ‘exist’ i.e., in order to be ‘closed’ with respect to the closure operation defined as the sup of x and its defect. It turns out that there are (at least) eight dependence relations which are worth to be considered. Many other questions concerning the world of contents (among them the proofs of the famous Husserl's Sätze) may now be discussed and clarified. Then the theory of species and genera is developed. Ultimate species (for short: species) are identified with equivalence classes of contents modulo isogeneity, and species in general (for short: genera) are identified with arbitrary unions of species. On the basis of the relation obtaining among two contents when they are isogeneous to two contents the first of which is a part of the second it becomes possible to develop a rather satisfying interpretation of Husserl's theory of the dependencies among species and genera and of the material a priori laws. By strengthening the notion of Husserlian universe into the notion of rigid Husserlian universe, the theory of species and genera obtains a stronger version. Three models of the theory are exhibited. The first one, suggested by combinatorial-topological considerations, identifies contents with finite non-empty sets of natural numbers; the second one identifies contents with non-empty sets of formulas of a formal language; the third one (not totally ‘rigid’) identifies contents with positive integers. (shrink)

We consider the question of randomness of the probability ΩU[X] that an optimal Turing machine U halts and outputs a string in a fixed set X. The main results are as follows: ΩU[X] is random whenever X is $\Sigma _{n}^{0}$-complete or $\Pi _{n}^{0}$-complete for some n ≥ 2. However, for n ≥ 2, ΩU[X] is not n-random when X is $\Sigma _{n}^{0}$ or $\Pi _{n}^{0}$ Nevertheless, there exists $\Delta _{n+1}^{0}$ sets such that ΩU[X] is n-random. There are $\Delta _{2}^{0}$ sets (...) X such that ΩU[X] is rational. Also, for every n ≥ 1, there exists a set X which is $\Delta _{n+1}^{0}$ and $\Sigma _{n}^{0}$-hard such that ΩU[X] is not random. We also look at the range of ΩU as an operator. We prove that the set {ΩU[X]: X ⊆ 2<ω} is a finite union of closed intervals. It follows that for any optimal machine U and any sufficiently small real r, there is a set X ⊆ 2<ω recursive in ∅′ ⊕ r, such that ΩU[X] = r. The same questions are also considered in the context of infinite computations, and lead to similar results. (shrink)

Any set x is uniquely specified by the graph of the membership relation on the set obtained by adjoining x to the transitive closure of x. Thus any operation on sets can be looked at as an operation on these graphs. We look at the operations of ordinal arithmetic of sets in this light. This turns out to be simplest for a modified ordinal arithmetic based on the Zermelo ordinals, instead of the usual von Neumann ordinals. In this (...) arithmetic, addition of sets corresponds to concatenating graphs, and multiplication corresponds to replacing each edge of a graph by a copy of another graph. Characterizations for the von Neumann case are also given. (shrink)

We follow [8] in asking when a set of ordinals $X \subseteq \alpha$ is a countable union of sets in K, the core model. We show that, analogously to L, and X closed under the canonical Σ 1 Skolem function for K α can be so decomposed provided K is such that no ω-closed filters are put on its measure sequence, but not otherwise. This proviso holds if there is no inner model of a weak Erdős-type property.