Let X be an infinite internal set in an ω1-saturated nonstandard universe. Then for any coloring of [X] k , such that the equivalence E of having the same color is countably determined and there is no infinite internal subset of [X] k with all its elements of different colors (i.e., E is condensating on X), there exists an infinite internal set Z⊆X such that all the sets in [Z] k have the same color. This Ramsey-type result is obtained (...) as a consequence of a more general one, asserting the existence of infinite internal Q-homogeneous sets for certain Q ⊆ [[X] k ] m , with arbitrary standard k≥ 1, m≥ 2. In the course of the proof certain minimal condensating countably determined sets will be described. (shrink)

Clinical biobanks processing data of participants in the European Union fall under the scope of the General Data Protection Regulation, which among others includes requirements for consent. These requirements are further specified by the Article 29 Working Party —an EU advisory body currently known as the European Data Protection Board. Unfortunately, their guidance is cause for some confusion. While the GDPR allows participants to give broad consent for research when specific research purposes are still unknown, the WP29 guidelines suggest that (...) additional consent for specific uses should be obtained in addition to broad consent when this becomes applicable. This discrepancy elicits the question whether clinical biobanks can fail the requirement of consent if they obtain broad consent, but not a specific consent for each biomedical study. We analysed this discrepancy within the framework of contextual integrity, in order to describe the context-relative informational norms that govern information flows in clinical biobanks. However, our analysis demonstrates that there is no uniform set of norms that can be applied to all clinical biobanks. As such, neither the GDPR nor the WP29 guidance can act as a “one size fits all” approach to all clinical biobanks. Rather, differences between clinical biobanks—especially regarding the scientific aims and patient populations—make the case for context-relative norms that determine the appropriate type of consent. (shrink)

Organisms' environments are thought to play a fundamental role in determining their fitness and hence in natural selection. Existing intuitive conceptions of environment are sufficient for biological practice. I argue, however, that attempts to produce a general characterization of fitness and natural selection are incomplete without the help of general conceptions of what conditions are included in the environment. Thus there is a "problem of the reference environment"—more particularly, problems of specifying principles which pick out those environmental conditions which (...) determine fitness. I distinguish various reference environment problems and propose solutions to some of them. While there has been a limited amount of work on problems concerning what I call "subenvironments", there appears to be no earlier work on problems of what I call the "whole environment". The first solution I propose for a whole environment problem specifies the overall environment for natural selection on a set of biological types present in a population over a specified period of time. The second specifies an environment relevant to extinction of types in a population; this kind of environment is especially relevant to certain kinds of long-term evolution. (shrink)

This paper is concerned with English noun phrases that denote generalized instances: they do not refer to actual spatio-temporal instances, but to virtual ones that are abstracted from a limited number of actual instances, e.g., a student in Three times, a student complained (Langacker, Foundations of Cognitive Grammar. Volume II: Descriptive application, Stanford University Press, 1991, Dynamicity, fictivity, and scanning: The imaginative basis of logic and linguistic meaning, Cambridge University Press, 2005, forthcoming). Langacker likens generalized instances to generic ones, which (...) constitute “global” generalizations over all actual instances of a type. On the basis of authentic data, I argue that, even though the profiled instance denoted by generic and generalized noun phrases is similar, the way the respective instances are accessed in discourse is very different. My data set consists of English noun phrases that are explicitly marked for generalized instantiation by the addition of a secondary determiner such as same in The twin brothers bought the same car or kind of in There was no way we could match that kind of offer. I compare noun phrases of four sets of secondary determiners, viz. adjectives of multiple exposure (usual), of identity (same, identical), of similarity (similar, comparable) and type noun constructions (kind of/type of/sort of). These data also allow me to refine the concept of generalized instantiation in terms of its semantic subtypes, the semantic interaction between secondary determiner and primary determiner, and the selection criteria for secondary determiners that can express it. (shrink)

It is commonly argued that natural language has the expressive power of quantifying over intensional entities, such as times, worlds, or situations. A standard way of modelling this assumes that there are unpronounced but syntactically represented variables of the corresponding type. Not all that much as has been said, however, about the exact syntactic location of these variables. Meanwhile, recent work has highlighted a number of problems that arise because the interpretive options for situation pronouns seem to be subject (...) to various restrictions. This paper is primarily concerned with situation pronouns inside of determiner phrases, arguing that they are introduced as arguments of (certain) determiners. Verbal predicates, on the other hand, are assumed to not combine with a situation pronoun. The various restrictions on their interpretation are shown to fall out from the semantic system that is developed based on that view. Further support for such an account comes from situation semantic analyses of donkey sentences as well as data on the temporal interpretation of nominal predicates. Its ability to account for this full range of data in a unified manner is shown to set it apart from previous proposals. The paper closes with an outlook on further extensions, including an account of quantifier domain restriction based on situation pronouns. (shrink)

Short-term motor practice leads to plasticity in the primary motor cortex. The purpose of this study is to investigate the factors that determine the increase in corticospinal tract excitability after motor practice, with special focus on two factors; “the level of muscle activity” and “the presence/absence of a goal of keeping the activity level constant.” Fifteen healthy subjects performed four types of rapid thumb adduction in separate sessions. In the “comfortable task” and “forceful task”, the subjects adducted their thumb using (...) comfortable and strong forces. In the “comfortable with a goal task” and “forceful with a goal task”, subjects controlled the muscle activity at the same level as in the C and F, respectively, by adjusting the peak electromyographic amplitude within the target ranges. Paired associative stimulation, which combines peripheral nerve stimulation and transcranial magnetic stimulation, with an inter-stimulus interval of 25 ms was also done. Before and after the motor tasks and PAS25, TMS was applied to the M1. None of the four tasks showed any temporary changes in behavior, meaning no learning occurred. Motor-evoked potential amplitude increased only after the FG and it exhibited a positive correlation with the MEP increase after PAS25, suggesting that FG and PAS25 share at least similar plasticity mechanisms in the M1. Resting motor threshold decreased only after FG, suggesting that FG would also be associated with the membrane depolarization of M1 neurons. These results suggest task-dependent plasticity from the synergistic effect of forceful muscle activity and of setting a goal of keeping the activity level constant. (shrink)

This paper deals with Gärdenfors’ theory of conceptual spaces. Let ${\mathcal {S}}$ be a conceptual space consisting of 2-type fuzzy sets equipped with several kinds of metrics. Let a finite set of prototypes $\tilde{P}_1,\ldots,\tilde{P}_n\in \mathcal {S}$ be given. Our main result is the construction of a classification algorithm. That is, given an element ${\tilde{A}}\in \mathcal {S},$ our algorithm classifies it into the conceptual field determined by one of the given prototypes $\tilde{P}_i.$ The construction of our algorithm uses some physical (...) analogies and the Newton potential plays a significant role here. Importantly, the resulting conceptual fields are not convex in the Euclidean sense, which we believe is a reasonable departure from the assumptions of Gardenfors’ original definition of the conceptual space. A partitioning algorithm of the space $\mathcal {S}$ is also considered in the paper. In the application section, we test our classification algorithm on real data and obtain very satisfactory results. Moreover, the example we consider is another argument against requiring convexity of conceptual fields. (shrink)

Even though there are many views on consciousness theory in the pertinent literature, there remains a need for a unifying framework for specifying the features of specific states of consciousness. In order to know what kinds of experiences conscious states have in common, researchers need to elicit testimony that is more direct and finer-grained than has been previously available. This dissertation endeavors to fill a gap in current research by addressing concepts and methods for making requisite distinctions and illuminates the (...) question of whether specific states of consciousness can be reliably and validly distinguished from each other. In order to do this, 41 individuals were invited to be interviewed. The interview was designed as a conversational-type synthesis of 5 well-known questionnaires pertinent to states of consciousness, but without their explicit and implicit assumptions; that is, the volunteers’ responses would not conform to predetermined questions. Encoding their responses allowed me to develop a model that helped to answer the research question (“Are there identifiable features that can reliably and validly distinguish among states of consciousness thought to be distinct from each other?”) by formulating a model in which any given conscious state can be catalogued in terms of its component factors (background, resistances, setting, induction, tradition, energies, and breakthrough events). The results of this study provide much-needed insights into people’s internal experiences of their various states, thus forming a basis for improved treatments and analyses. Better understanding of these states can be an impetus for social change by allowing for more incisive analyses and treatments, as well as fostering improved interpersonal communications. (shrink)

Incidences of organizational wrongdoing have become wide spread throughout the whole business world. The management of organizational wrongdoings is of growing concern in organizations globally, since these types of acts can be detrimental to financial well being. Wrongdoing occurs within organizational settings and organizational members commonly have knowledge of and thus the opportunity to report the wrongdoing. An employee’s decision to report individual or organizational misconduct, i.e. blow the whistle, is a complex phenomenon that is based upon organizational, situational and (...) personal factors. The purpose of this study is to examine the relationship between value orientations of individuals and choices for particular whistleblowing modes. Our results show that there are significant relationships between these variables. We contribute to the extant literature by choosing Turkey as context as most studies have been conducted in the US and Europe, and little has been reported about the actions taken by employees in non-Western cultures when they observe wrongdoing in their organizations. (shrink)

Classical generalized quantifier (GQ) theory posits that quantificational determiners (Q-dets) combine with a nominal argument of type et, a first order predicate, to form a GQ. In a recent paper, Matthewson (2001) challenges this position by arguing that the domain of a Q-det is not of type et, but e, an entity. In this paper, I defend the classical GQ view, and argue that the data that motivated Matthewson’s revision actually suggest that the domain set can, and indeed (...) in certain languages must, be contextually restricted overtly. (shrink)

The aim of the article is to show how the use of diagnostic methods allows identifying patterns and problems of corporations functioning, providing identification of directions and strategies for further development of their business. Theoretical and methodological basis of the research is a scientific works of scientists in the field of business diagnostics and strategic development, who studied diagnostics in the system of responding to business development problems, identifying areas for improving strategic management, financial statements of corporations of Daimler Group (...) (Germany), Tesla Motors (USA) and Toyota Motor (Japan) and own research results. The methodological basis of the study is a set of general and special methods used to achieve the goal of the research and includes: theoretical generalization and synthesis – in analyzing the content of scientific works on business diagnostics and strategic management; observation – to obtain primary information about the state of business of automotive companies in the world; indicator and integrated assessment – to assess the state of business and the effectiveness of strategic management of automotive corporations; information and logical analysis – when determining the issues and patterns of business development of corporations; problem-target method – to justify the choice of business development strategies; causation-result method – to obtain definitive conclusions. The results of the study of the state of business of the world's leading automotive corporations revealed the dependence of business efficiency on the degree of efficiency of strategic management of their activities, and identified types of strategies that will promote further development of automotive corporations – integrated, concentrated, diversified or globalized growth. The practical significance of the obtained results lies in their usefulness for strategic management for Daimler Group, Tesla Motors, Toyota Motor Corporation. (shrink)

This article focuses on discursive regularities that can generally be observed in text corpora produced in similar communication situations (medical interviews, political debates, teaching classes, etc.). One type of such regularities is related to the so-called ‘discourse genres’, considered as a set of tacit instructions broadly constraining the forms of utterances in a given discursive practice. Those regularities highlight the relatively regulated, non-random nature of most of our discursive practices and epitomize the necessary constrained creativity of meaning making in (...) discourse. In this perspective, we suggest that the concepts of Thirdness and Habit, as theorized by Charles S. Peirce, can be fruitful in describing the role and importance of such regularities in our sociodiscursive life. More specifically, we believe that discourse regularities are ideal case studies if one wishes to investigate instances of predictability in semiotic (discursive) processes. Overall, we suggest that their study can be one of many research orientations through which a prediction-based scientific conception of semiotics could be applied. (shrink)

To encourage corporations to contribute positively to the environment in which they operate, voluntary self-regulatory codes (SRC) have been enacted and refined over the past 15 years. Two of the most prominent are the United Nations Global Compact and the Global Reporting Initiative. In this paper, we explore the impact of different stakeholders' pressures on the selection of strategic choices to join SRCs. Our results show that corporations react differently to different sets of stakeholder pressures and that the SRC selection (...) depends on the type and intensiveness of the stakeholder pressures as well as the resources at hand to respond to those pressures. Our contribution offers a more specific and finely variegated analysis of firmstakeholder interactions. (shrink)

A synaptic algebra is a generalization of the self-adjoint part of a von Neumann algebra. In this article we extend to synaptic algebras the type-I/II/III decomposition of von Neumann algebras, AW∗-algebras, and JW-algebras.

The model of the structural part of Object Determination Logic (LDO) is translated and interpreted in the Formal Concept Analysis (FCA) model. In this article, we start from the premise that the modeling of a real problem has as its starting point a cognitive level that can be translated into the framework of a logic model and, subsequently, a mathematical model. We take these steps by considering the structural model of LDO, a lesser known and analyzed logic, and translating it (...) into the FCA approach. Then, using the results of the analysis of the FCA model, we return to their interpretation within the LDO framework. Translation, i.e. the transition from the LDO model to the FCA model, is achieved by encoding in the FCA model, as faithfully as possible, each notion and constraint imposed by the LDO model. We illustrate this “methodology” by applying it to three situations corresponding to the cognitive elements of the LDO. The results obtained are interpreted from the point of view of cognitive elements of LDO. They enable us to establish the relationship between the LDO model and the FCA model, as well as the limits of each of the two models. On the basis of these limits, we propose an opening towards other types of mathematical models based on Soft Sets (SS) as parameterized sets. (shrink)

Data access committees (DAC) gatekeep access to secured genomic and related health datasets yet are challenged to keep pace with the rising volume and complexity of data generation. Automated decision support (ADS) systems have been shown to support consistency, compliance, and coordination of data access review decisions. However, we lack understanding of how DAC members perceive the value add of ADS, if any, on the quality and effectiveness of their reviews. In this qualitative study, we report findings from 13 semi-structured (...) interviews with DAC members from around the world to identify relevant barriers and facilitators to implementing ADS for genomic data access management. Participants generally supported pilot studies that test ADS performance, for example in cataloging data types, verifying user credentials and tagging datasets for use terms. Concerns related to over-automation, lack of human oversight, low prioritization, and misalignment with institutional missions tempered enthusiasm for ADS among the DAC members we engaged. Tensions for change in institutional settings within which DACs operated was a powerful motivator for why DAC members considered the implementation of ADS into their access workflows, as well as perceptions of the relative advantage of ADS over the status quo. Future research is needed to build the evidence base around the comparative effectiveness and decisional outcomes of institutions that do/not use ADS into their workflows. (shrink)

The article concerns the definition of the problem field of a new type of modern terrorist activity in the information space under the conditions of globalization - information terrorism.The findings systematized, which are presented in the domestic social and political discourse and can serve as the basis for its further comprehensive research in the direction of building its corresponding model / concept. The research strategy of the well-known American methodologist L. Coser used for the analysis of elements of social (...) reality - the search for a set of interrelated indicators (variables) that can clarify the content, conditions for the emergence and development of this research subject.It substantiated that when constructing the problem field of the analysis of information terrorism as an element of social reality, such indicators can be: first, the interpretation of the very concept of «information terrorism»;secondly, the analysis of the causes and conditions of the spread of terrorist activity in the information space; thirdly, the classification of the main forms of manifestation of information terrorism; fourth, the analysis of the main technologies and methods of carrying out terrorist activities of an informational nature; fifth, substantiation of conditions and development of mechanisms against the wide spread of information terrorism in the modern world.The analysis of the essence of information terrorism from the standpoint of constructing an analytical (five-link) scheme for researching the problematic field of this type of terrorist activity provides a basis for generalizing and interpreting this new form of terrorism as the use of information and information infrastructure by certain (states, organizations, structures), on the one hand, for violence against people’s consciousness, manipulation of their behavior using certain methods and methods of influence, and on the other hand – to influence the information and technical structure of the state, with the aim of exerting pressure on the adoption of favorable decisions by states, groups of people or individuals by creating conditions for chaos, panic, etc. (shrink)

Recent semantic approaches to scientific structuralism, aiming to make precise the concept of shared structure between models, formally frame a model as a type of set-structure. This framework is then used to provide a semantic account of (a) the structure of a scientific theory, (b) the applicability of a mathematical theory to a physical theory, and (c) the structural realist’s appeal to the structural continuity between successive physical theories. In this paper, I challenge the idea that, to be so (...) used, the concept of a model and so the concept of shared structure between models must be formally framed within a single unified framework, set-theoretic or other. I first investigate the Bourbaki-inspired assumption that structures are types of set-structured systems and next consider the extent to which this problematic assumption underpins both Suppes’ and recent semantic views of the structure of a scientific theory. I then use this investigation to show that, when it comes to using the concept of shared structure, there is no need to agree with French that “without a formal framework for explicating this concept of ‘structure-similarity’ it remains vague, just as Giere’s concept of similarity between models does ...” (French, 2000, Synthese, 125, pp. 103–120, p. 114). Neither concept is vague; either can be made precise by appealing to the concept of a morphism, but it is the context (and not any set-theoretic type) that determines the appropriate kind of morphism. I make use of French’s (1999, From physics to philosophy (pp. 187–207). Cambridge: Cambridge University Press) own example from the development of quantum theory to show that, for both Weyl and Wigner’s programmes, it was the context of considering the ‘relevant symmetries’ that determined that the appropriate kind of morphism was the one that preserved the shared Lie-group structure of both the theoretical and phenomenological models. (shrink)

An ω-language is a set of infinite sequences on a countable language, and corresponds to a set of real numbers in a natural way. Languages may be described by logical formulas in the arithmetical hierarchy and also may be described as the set of words accepted by some type of automata or Turing machine. Certain families of languages, such as the equation image languages, may enumerated as P0, P1, … and then an index set associated to a given property (...) R of languages is just the set of e such that Pe has the property. The complexity of index sets for 7 types of languages is determined for various properties related to the size of the language. (shrink)

This book is a contribution to the flourishing field of formal and philosophical work on truth and the semantic paradoxes. Our aim is to present several theories of truth, to investigate some of their model-theoretic, recursion-theoretic and proof-theoretic aspects, and to evaluate their philosophical significance. In Part I we first outline some motivations for studying formal theories of truth, fix some terminology, provide some background on Tarski’s and Kripke’s theories of truth, and then discuss the prospects of classical type-free (...) truth. In Chapter 4 we discuss some minimal adequacy conditions on a satisfactory theory of truth based on the function that the truth predicate is intended to fulfil on the deflationist account. We cast doubt on the adequacy of some non-classical theories of truth and argue in favor of classical theories of truth. Part II is devoted to grounded truth. In chapter 5 we introduce a game-theoretic semantics for Kripke’s theory of truth. Strategies in these games can be interpreted as reference-graphs of the sentences in question. Using that framework, we give a graph-theoretic analysis of the Kripke-paradoxical sentences. In chapter 6 we provide simultaneous axiomatizations of groundedness and truth, and analyze the proof-theoretic strength of the resulting theories. These range from conservative extensions of Peano arithmetic to theories that have the full strength of the impredicative system ID1. Part III investigates the relationship between truth and set-theoretic comprehen- sion. In chapter 7 we canonically associate extensions of the truth predicate with Henkin-models of second-order arithmetic. This relationship will be employed to determine the recursion-theoretic complexity of several theories of grounded truth and to show the consistency of the latter with principles of generalized induction. In chapter 8 it is shown that the sets definable over the standard model of the Tarskian hierarchy are exactly the hyperarithmetical sets. Finally, we try to apply a certain solution to the set-theoretic paradoxes to the case of truth, namely Quine’s idea of stratification. This will yield classical disquotational theories that interpret full second-order arithmetic without set parameters, Z2- . We also indicate a method to recover the parameters. An appendix provides some background on ordinal notations, recursion theory and graph theory. (shrink)

This paper introduces some of the main components of a novel type theoretical semantics for quantifi- cation with plural noun phrases. This theory, unlike previous ones, sticks to the standard generalized quantifier treatment of singular noun phrases and uses only one lifting operator per semantic category (predicate, quantifier and determiner) for quantification with plurals. Following Bennett (1974), plural individuals are treated as functions of type ¢¡ . Plural nouns and other plural predicates accordingly denote £ ¢¡¥¤¦¡ functions. Such (...) predicates do not match the standard £ ¢¡¥¤ £§£ ¢¡¨¤©¡¥¤ type of determiners. Following Partee and Rooth (1983), type mismatches are resolved using type shifting operators. These operators derive collectivity with plurals, keeping the analysis of singular noun phrases, where no type mismatch arises, as in Barwise and Cooper (1981). A single type shifting operator for determiners combines into one reading the existential shift and the counting (neutral) shift of Scha (1981) and Van der Does (1993). This operator combines the conservativity principle of generalized quantifier theory with Szabolcsi’s (1997) existential quantification over witness sets. The unified lift prevents unmotivated ambiguity as well as the monotonicity ill of existential lifts pointed out by Van Benthem.. (shrink)

Biological type specimens are a particular kind of voucher specimen stored in natural history collections. Their special status and practical use are discussed in relation to the description and naming of taxonomic zoological diversity. Our current system, known as Linnaean nomenclature, is governed by the International Code of Zoological Nomenclature. The name of a species is fixed by its name-bearing type specimen, linking the scientific name of a species to the type specimen first designated for that species. (...) The name-bearing type specimen is not necessarily a typical example of the species, while establishment of the boundaries of a species requires empirical taxonomic studies. The International Code of Zoological Nomenclature allows for the naming of new species in the absence of preserved specimens. However, photos and DNA sequences should not function as primary type material, while new species should not be described and named without deposition of at least one type specimen in a collection. Philosophically, species are individuals, spatiotemporally restricted entities. Therefore, Linnaean species names are proper names, which do not define the taxon but serve as a label, providing an ostensive definition of a species. Paratypes have no name-bearing function but, nevertheless, are highly valued specimens in natural history collections. Paratypes should be restricted to those specimens originating from the same sample as the holotype. Diagnosis of a species taxon involves establishment of a connection between a Linnaean name and determination of the boundaries of the species. A first step in this process is the choice of an appropriate species concept. It is not the examination of holotypes and paratypes that necessarily provides the best estimate of the taxonomic boundaries of a species, but this is facilitated by a set of voucher specimens known as the hypodigm. Dissatisfaction with the present nomenclatural code led some researchers to propose emendations. Other taxonomists suggested abandoning Linnaean nomenclature and proposed the alternative PhyloCode, albeit that it relegates the naming of species taxa to the traditional nomenclatural codes. (shrink)

The aim of this paper is to introduce an alternative to Łukasiewicz’s 4-valued modal logic Ł. As it is known, Ł is afflicted by “Łukasiewicz type paradoxes”. The logic we define, PŁ4, is a strong paraconsistent and paracomplete 4-valued modal logic free from this type of paradoxes. PŁ4 is determined by the degree of truth-preserving consequence relation defined on the ordered set of values of a modification of the matrix MŁ characteristic for the logic Ł. On the other (...) hand, PŁ4 is a rich logic in which a number of connectives can be defined. It also has a simple bivalent semantics of the Belnap–Dunn type. (shrink)

Since virtually every mathematical theory can be interpreted in Zermelo-Fraenkel set theory, it is a foundation for mathematics. There are other foundations, such as alternate set theories, higher-order logic, ramified type theory, and category theory. Whether set theory is the right foundation for mathematics depends on what a foundation is for. One purpose is to provide the ultimate metaphysical basis for mathematics. A second is to assure the basic epistemological coherence of all mathematical knowledge. A third is to serve (...) mathematics, by lending insight into the various fields and suggesting fruitful techniques of research. A fourth purpose of a foundation is to provide an arena for exploring relations and interactions between mathematical fields. While set theory does better with regard to some of these and worse with regard to others, it has become the de facto arena for deciding questions of existence, something one might expect of a foundation. Given the different goals, there is little point to determining a single foundation for all of mathematics. (shrink)

Mitchell, J.C. and E. Moggi, Kripke-style models for typed lambda calculus, Annals of Pure and Applied Logic 51 99–124. The semantics of typed lambda calculus is usually described using Henkin models, consisting of functions over some collection of sets, or concrete cartesian closed categories, which are essentially equivalent. We describe a more general class of Kripke-style models. In categorical terms, our Kripke lambda models are cartesian closed subcategories of the presheaves over a poset. To those familiar with Kripke models of (...) modal or intuitionistic logics, Kripke lambda models are likely to seem adequately ‘semantic’. However, when viewed as cartesian closed categories, they do not have the property variously referred to as concreteness, well- pointedness or having enough points. While the traditional lambda calculus proof system is not complete for Henkin models that may have empty types, we prove strong completeness for Kripke models. In fact, every set of equations that is closed under implication is the theory of a single Kripke model. We also develop some properties of logical relations over Kripke structures, showing that every theory is the theory of a model determined by a Kripke equivalence relation over a Henkin model. We discuss cartesian closed categories but present the main definitions and results without the use of category theory. (shrink)

The notion of a natural model of type theory is defined in terms of that of a representable natural transfomation of presheaves. It is shown that such models agree exactly with the concept of a category with families in the sense of Dybjer, which can be regarded as an algebraic formulation of type theory. We determine conditions for such models to satisfy the inference rules for dependent sums Σ, dependent products Π, and intensional identity types Id, as (...) used in homotopy type theory. It is then shown that a category admits such a model if it has a class of maps that behave like the abstract fibrations in axiomatic homotopy theory: they should be stable under pullback, closed under composition and relative products, and there should be weakly orthogonal factorizations into the class. It follows that many familiar settings for homotopy theory also admit natural models of the basic system of homotopy type theory. (shrink)

One objective of this paper is the determination of the proof-theoretic strength of Martin-Löf's type theory with a universe and the type of well-founded trees. It is shown that this type system comprehends the consistency of a rather strong classical subsystem of second order arithmetic, namely the one with Δ 2 1 comprehension and bar induction. As Martin-Löf intended to formulate a system of constructive (intuitionistic) mathematics that has a sound philosophical basis, this yields a constructive consistency (...) proof of a strong classical theory. Also the proof-theoretic strength of other inductive types like Aczel's type of iterative sets is investigated in various contexts.Further, we study metamathematical relations between type theories and other frameworks for formalizing constructive mathematics, e.g. Aczel's set theories and theories of operations and classes as developed by Feferman. (shrink)

The article is devoted to the analysis of the theological-academic ontological doctrine of the three types of being formulated within the framework of the Russian theological-academic philosophy of the 19th century. The study of this problem in the context of the general analysis of the phenomenon of theological-academic philosophy allows expanding our understanding of the genesis of Russian philosophy and its religious-philosophical component. The main aim of the article is the historical-philosophical analysis (on the material of philosophical courses of Russian (...) theological academies and original works of professors of academies) of the doctrine about three types of being, which was developed within the framework of the theological-academic philosophy in Russia in the 19th century. The set goal is achieved by means of textual and religious analysis methods, as well as historical-functional, historical-genetic, and comparative research methods. The authors conclude that the specificity of theological-academic philosophizing was determined by confessional affiliation and consisted in its theistic form: the transversal theme of all theological-academic interpretations was the problem of being. Thus, theological-academic ontology took the form of the doctrine of God as an absolute being and the world as its derivative. The theological-academic doctrine of the three types of being and the synthesizing function of the absolute in relation to theological and material being cannot be characterized as quite logical and consistent. The notion of God as an absolute being is conditioned by the aspiration of theological-academic philosophers not to go beyond traditional orthodoxy and is one of the main specific features of theological-academic philosophical interpretations of religious consciousness. At the same time, the historical and philosophical analysis of the works of professors from Russian theological academies allows tracing how the powerful ideological and theoretical potential accumulated in Russian theological academies after their reforms in the 19th century contributed to the development of professional philosophy in Russia, the development of a philosophical categorical apparatus and the systematic formation of Russian philosophical thought. The development of this theme responds to the urgent research tasks of the history of philosophy. Further, this topic is very interesting not only for historians of philosophy but also for historians of religion, historians of orthodoxy, and culturologists. (shrink)

The aim of the present study was to determine statistical differences in a set of badminton competition matches in five different modalities with regard to competition level (Group Phase versus Eliminatory Phase). Data from 453 sets (125 in men’s singles; 108 sets in women’s singles; 77 sets in men’s doubles; 73 in women’s doubles and 70 in mixed doubles) from the RIO 2016 Olympics Games were recorded and classified in two groups of variables to analyse variables related to match (5) (...) and set (15). A descriptive analysis and univariate test (Mann Whitney U) for non-parametric data were conducted. The results show in men’s and women’s singles all the variables related to match were higher in the Elimination Phase than in the Group Phase (p<0.01). In Sets 1 and 3, the longest set duration, rally and average rally were found in the Elimination Phase than Group Stage (p<0.05). In women’s singles, these differences were also recorded in Set 2. For doubles, the results are more stable among groups. Men’s doubles had a longer duration of the match and set (set 1 and set 2) (p<0.01), and also scored highest for average rally strokes (set 1 and set 3) (p<0.05) and shuttles used in the Elimination Phase versus the Group Phase along the match (p<0.01). In women’s doubles, more shuttles were used in a match in the Elimination than in the Group Phase. Moreover, the same results are established for Set 2, including for average rally. Mixed doubles saw no match going to three sets. However, the greatest differences showed a longer rally and average rally being registered in the Elimination than in the Group Phase. In conclusion, the timing factors of the badminton singles and doubles games were different in the Elimination and Group Phases. This information may help players and coaches prepare and administer different types of workouts or, more specifically, competition schedules adapted to the characteristics of modern badminton. (shrink)

The problem of unification in a normal modal logic $L$ can be defined as follows: given a formula $\varphi$, determine whether there exists a substitution $\sigma$ such that $\sigma $ is in $L$. In this paper, we prove that for several non-symmetric non-transitive modal logics, there exists unifiable formulas that possess no minimal complete set of unifiers.

In this paper we continue the study of inner models of the type studied inInner models for set theory—Part I.The present paper is concerned exclusively with a particular kind of model, the ‘super-complete models’ defined in section 2.4 of I. The condition of 2.4 and the completeness condition 1.42 imply that such a model is uniquely determined when its universal class Vmis given. Writing condition and the completeness conditions 1.41, 1.42 in terms of Vm, we may state the definition (...) in the form:3.1. Dfn.A classVmis said to determine a super-complete model if the model whose basic notions are defined by,satisfies axiomsA, B, C.N. B. This definition is not necessarily metamathematical in nature. If desired, it could be written out quite formally as the definition of a notion ‘SCM’ thus:whereψ is the propositional function expressing in terms ofUthe fact that the model determined byUaccording to 3.1 satisfies the relativization of axioms A, B, C. E.g. corresponding to axiom A1m, i.e.,,ψ contains the equivalent term. All the relativized axioms can be similarly expressed in this way by first writing out the relativized form and then replacing ‘ϕ bywhich is in turn replaced by, and similarly replacing ‘ϕ’ by ‘ϕ’ by ‘), andThusψ is obtained in primitive notation. (shrink)

Detailed coverage of Canon's four speedlite-580EX II, 430 EX II, 220 EX and the new 270 EX-built exclusively for Canon DSLRs If you use a digital SLR camera, then you understand just how critical it is to have a capable flash. Canon Speedlite shines a whole new light on taking photos with a Canon DSLR. This full-color, in-depth guide takes you beyond the standard manual that accompanies the Speedlite and shows you the types of settings you can use on your (...) camera when working with the Speedlite. You'll explore the possibilities of wireless lighting with multiple speedlites as well as the creative effects you can achieve. Author and professional photographer Brian McLernon demystifies setting up the speedlite, synchronizing the speedlite equipment, and determining lighting ratios. Canon DSLRs are only growing in popularity and the Speedlite system is a must-have accessory for exploring a new world of digital photo possibilities Shows you how to create an inexpensive and portable wireless studio lighting system that can go where you go Demystifies setting up the speedlite, synchronizing the equipment, and figuring out lighting ratios Covers other Canon lighting system components, such as the ST-E2 Speedlite Transmitter, Macro Ring Lite, and Macro Twin Lite Real-world information on using these speedlites illustrated by full-color examples and untangles the complexities of using the Canon Speedlite system. (shrink)

ABSTRACTColleen Murphy has argued that in circumstances of societal transition only one special type of justice is applicable: ‘transitional justice’, a type of justice not reducible to any other type or types. I take issue with Murphy’s conclusion, showing that retributive, distributive and corrective justice all feature as isolable component parts in her own positive account of transitional justice. I also argue that restorative justice is applicable and important in transitional societies when the state itself has perpetrated (...) serious wrongs. Murphy claims that each distinct type of justice is a response to a unique ‘basic problem of justice’, triggered by a background set of ‘circumstances’. However, I argue that identifying such a basic problem neither necessarily means the circumstances in question call for a unique type of justice, nor is sufficient to determine which type of justice is most salient in the circumstances. What is more, I show that Murphy applies her own methodology inconsistently in her treatment of transitional societies and stable democracies. I argue that what Murphy calls ‘transitional justice’ is composed of familiar types of justice as well as other moral values, but also regrettable – though often unavoidable – injustice. (shrink)

Given an abstract logic L = L(Q i ) i ∈ I generated by a set of quantifiers Q i , one can construct for each type τ a topological space S τ exactly as one constructs the Stone space for τ in first-order logic. Letting T be an arbitrary directed set of types, the set $S_T = \{(S_\tau, \pi^\tau_\sigma)\mid\sigma, \tau \in T, \sigma \subset \tau\}$ is an inverse topological system whose bonding mappings π τ σ are naturally determined (...) by the reduct operation on structures. We relate the compactness of L to the topological properties of S T . For example, if I is countable then L is compact iff for every τ each clopen subset of S τ is of finite type and S τ is homeomorphic to $\underset{lim}S_T$ , where T is the set of finite subtypes of τ. We finally apply our results to concrete logics. (shrink)

Ambitious targets to reduce greenhouse gas emissions from agriculture have been set by both national governments and their respective livestock sectors. We hypothesize that farmer self-identity influences their assessment of climate change and their willingness to implement measures which address the issue. Perceptions of climate change were determined from 286 beef/sheep farmers and evaluated using principal component analysis. The analysis elicits two components which evaluate identity, and two components which evaluate behavioral capacity to adopt mitigation and adaptation measures. Subsequent Cluster (...) Analyses reveal four farmer types based on the PCA scores. ‘The Productivist’ and ‘The Countryside Steward’ portray low levels of awareness of climate change, but differ in their motivation to adopt pro-environmental behavior. Conversely, both ‘The Environmentalist’ and ‘The Dejected’ score higher in their awareness of the issue. In addition, ‘The Dejected’ holds a high sense of perceived risk; however, their awareness is not conflated with an explicit understanding of agricultural GHG sources. With the exception of ‘The Environmentalist’, there is an evident disconnect between perceptions of agricultural emission sources and their contribution towards GHG emissions amongst all types. If such linkages are not conceptualized, it is unlikely that behavioral capacities will be realized. Effective communication channels which encourage action should target farmers based on the groupings depicted. Therefore, understanding farmer types through the constructs used in this study can facilitate effective and tailored policy development and implementation. (shrink)

Rooth & Partee (1982) and Rooth (1985) have shown that the English-specific rule-by-rule system of PTQ can be factored out into function application plus two transformations for resolving type mismatch (type lifting and variable binding). Building on these insights, this article proposes a universal system for type-driven translation, by adding two more innovations: local type determination for gaps (generalizing Montague 1973) and a set of semantic filters (extending Cooper 1983). This system, dubbed Cross-Linguistic Semantics (XLS), is (...) shown to account for various phenomena — including scope relations in English and Greenlandic Eskimo, internally headed relative clauses in Lakhota, serial verbs in Yoruba and VP ellipsis in English. (shrink)

Time and resource constraints, combined with competing priorities, mean that research prioritization is a critical ethical consideration in pandemics and emergencies, given the increased need for relevant research findings to address health needs, and the multiple adverse ways that emergencies can impact capacities to conduct research. At international, national and local levels, careful consideration is needed of which research topics should be prioritized and on what grounds. This needs to take into account the ethically significant considerations that should inform prioritization; (...) existing frameworks to guide prioritization decisions; and the consequences associated with prioritizing or de-prioritizing research. The need to prioritize research that is directly responsive to the pandemic may generate debate about which types of research should be prioritised, and within fields of research, which studies should be continued, paused, or re-oriented. In determining which research proposals may have the greatest likelihood of reducing urgent epidemic health burdens, both the nature and distribution of such burdens are key considerations. Epidemics and pandemics typically disproportionately affect the most disadvantaged and vulnerable people in society, highlighting the necessity of inclusive and responsive approaches, which evaluate not just which research approaches have the greatest potential public health benefit, but also the likelihood that they will help address inequities. Key questions also arise when determining if current studies should be de-escalated or stopped, particularly when this may result in highly compromised results. It is also important to consider what obligations arise for research communities (including funders) to pledge to taking the outcomes of research prioritisation processes into account. The case studies in this chapter prompt consideration of how qualitative research into the impacts of isolation should be prioritised, and whether and how research prioritization measures should be responsive to widespread use of traditional medicine and off-label use of medications. The cases also highlight issues that research teams may face as research priorities are re-evaluated in pandemics, including whether and how to redesign proposed research in response to the logistical challenges posed by the pandemic and evolving pandemic research priorities. (shrink)

Saunders Mac Lane has drawn attention many times, particularly in his book Mathematics: Form and Function, to the system of set theory of which the axioms are Extensionality, Null Set, Pairing, Union, Infinity, Power Set, Restricted Separation, Foundation, and Choice, to which system, afforced by the principle, , of Transitive Containment, we shall refer as . His system is naturally related to systems derived from topos-theoretic notions concerning the category of sets, and is, as Mac Lane emphasises, one that is (...) adequate for much of mathematics. In this paper we show that the consistency strength of Mac Lane's system is not increased by adding the axioms of Kripke–Platek set theory and even the Axiom of Constructibility to Mac Lane's axioms; our method requires a close study of Axiom H, which was proposed by Mitchell; we digress to apply these methods to subsystems of Zermelo set theory , and obtain an apparently new proof that is not finitely axiomatisable; we study Friedman's strengthening of , and the Forster–Kaye subsystem of , and use forcing over ill-founded models and forcing to establish independence results concerning and ; we show, again using ill-founded models, that proves the consistency of ; turning to systems that are type-theoretic in spirit or in fact, we show by arguments of Coret and Boffa that proves a weak form of Stratified Collection, and that is a conservative extension of for stratified sentences, from which we deduce that proves a strong stratified version of ; we analyse the known equiconsistency of with the simple theory of types and give Lake's proof that an instance of Mathematical Induction is unprovable in Mac Lane's system; we study a simple set theoretic assertion—namely that there exists an infinite set of infinite sets, no two of which have the same cardinal—and use it to establish the failure of the full schema of Stratified Collection in ; and we determine the point of failure of various other schemata in . The paper closes with some philosophical remarks. (shrink)

The overall aim of this thesis is to present a model for rational goal-setting and to illustrate how it can be applied in evaluations of public policies, in particular policies concerning sustainable development and environmental quality. The contents of the thesis are divided into two sections: a theoretical section and an empirical section. Paper I identifies a set of rationality criteria for single goals and discusses them in relation to the typical function of goals. It is argued that goals are (...) typically set to enhance goal achievement. A goal that successfully furthers its achievement is “achievement-inducing”. It holds for each of the identified criteria that, ceteris paribus, improved satisfaction of a criterion makes a goal better in the achievement-inducing sense.Paper II contains an analysis of the notion of goal system coherence. It is argued that the coherence of a goal system is determined by the relations that hold among the goals in the system, in particular the relations of operationalization, means and ends, support, and conflict. Paper III investigates the rationality of utopian goals. The paper analyzes four arguments that support the normative criterion of attainability: that utopian goals are too imprecise and too far-reaching to guide action effectively, counterproductive, and morally objectionable. A tentative defence of utopian goal-setting is built on counter-arguments that can be put forward to weaken each of the four objections. Paper IV investigates the nature of self-defeating goals. The paper identifies three types of situations in which self-defeating mechanisms obstruct goal achievement: situations in which the goal itself carries the seeds of its own non-fulfilment, situations in which the activity of goal-setting contributes to goal failure, and situations in which disclosure of the goal interferes with progress. Paper V provides a brief description of the Swedish system of environmental objectives and a preliminary inventory of the management difficulties that attach to this goal system.Paper VI contains an investigation into the rationality of five Swedish environmental objectives through an application of the rationality criteria identified in Papers I-II. The paper identifies and discusses some difficulties that are associated with management by objectives and the use of goals in environmental policy. Paper VII analyses the rationality of the Swedish environmental quality objective A good built environment. Among the conclusions drawn in the paper are that some of the sub-goals to the objective are formulated in terms that are unnecessarily vague from an action-guiding standpoint and that others are problematic from the viewpoint of evaluability. (shrink)

This thesis presents a proof theoretical investigation of some constructive set theories with restricted set induction. The set theories considered are various systems of Constructive Zermelo Fraenkel set theory, CZF ([1]), in which the schema of $\in$ - Induction is either removed or weakened. We shall examine the theories $CZF^\Sigma_\omega$ and $CZF_\omega$, in which the $\in$ - Induction scheme is replaced by a scheme of induction on the natural numbers (only for  formulas in the case of the first theory, (...) for arbitrary formulas in the second theory). Of particular interest is the system CZF− + INAC, which is obtained by removing $\in$ - Induction and by adding an axiom, INAC, for inaccessible sets. The main outcome is that CZF− + INAC is a predicative set theory with inaccessible sets, its proof theoretic ordinal being $\Gamma_0$. The proof theoretic strength of these theories, has been determined by means of proof theoretical reductions. The upper bounds have been obtained by interpreting the set theories in classical theories of (iterated) inductive definitions with ordinals. A significant feature of these interpretations is that they are realizability interpretations, which make an indirect use of Aczel’s interpretation of CZF in Martin Löf type theory, and, in the case of CZF− + INAC, also employ a maximum bisimulation relation to represent equality between sets. The lower bounds are obtained by interpreting appropriate subsystems of intuitionistic second order arithmetic in the set theories. At the conclusion of the thesis we present work unrelated to the previous chapters. It is a preliminary study of the constructible hierarchy in CZF. We begin by formalizing the notion of definability in constructive set theory and then introduce Gödel’s L in CZF. We prove that intuitionistic L is a model of a subsystem of CZF strong enough to include intuitionistic Kripke-Platek set theory, and also that L is a model of the axiom of constructibility, provably in CZF. (shrink)

Background: Positive effects of acute exercise on cognitive performances in general inspired research that investigated the effects of acute exercise on specific cognitive subdomains. Many existing studies examined beneficial effects of acute exercise on subsequent set shifting performance in healthy adults. Set shifting, a subdomain of executive function, is the ability to switch between different cognitive sets. The results of existing studies are inconsistent. Therefore, a meta-analysis was conducted that pooled available effect sizes. Additionally, moderator analyses were carried out to (...) identify covariates that determine the magnitude of exercise-induced set shifting benefits.Methods: Medline, PsycINFO, and SPORTDiscus were searched for eligible studies. Hedges' g corrected standardized mean difference values were used for analyses. Random-effects weights were applied to pool effects. Potential moderation of the effect of acute exercise on subsequent set shifting performance by exercise intensity, type of exercise, participants' age, and type of control group were examined.Results: Twenty-two studies were included into analysis. All aggregated effect sizes ranged from small to moderate. Overall, a small significant beneficial effect was revealed. Heterogeneity of included effect sizes was moderate and significant. Moderator analyses revealed a larger average effect in older adults than for studies examining younger adults. Light exercise led to larger effects than moderate or vigorous exercise. Studies testing acute exercise against active control groups showed a noticeably smaller average effect than studies that used passive or cognitive engaging control groups. Interestingly, application of resistance or aerobic exercise led to no different average effect sizes. However, none of the tested covariates reached statistical significance.Conclusion: Acute exercise improves subsequent set shifting performance. However, effect sizes are small, making the relevance for everyday life questionable. The results indicate that older adults benefit more from acute exercise than younger adults do. Light intensity exercise seems most effective while the type of exercise does not seem to influence the magnitude of effects. Research designs with active control groups show the smallest average effect, raising concerns about placebo effects.PROSPERO registration number: CRD42019138799. (shrink)

Cardiovascular disease is a major complication of type 2 diabetes mellitus. In addition to traditional risk factors, psychological determinants play an important role in CVD risk. This study applied Deep Neural Network to develop a CVD risk prediction model and explored the bio-psycho-social contributors to the CVD risk among patients with T2DM. From 2017 to 2020, 834 patients with T2DM were recruited from the Department of Endocrinology, Affiliated Hospital of Harbin Medical University, China. In this cross-sectional study, the patients' (...) bio-psycho-social information was collected through clinical examinations and questionnaires. The dataset was randomly split into a 75% train set and a 25% test set. DNN was implemented at the best performance on the train set and applied on the test set. The receiver operating characteristic curve analysis was used to evaluate the model performance. Of participants, 272 were diagnosed with CVD. The developed ensemble model for CVD risk achieved an area under curve score of 0.91, accuracy of 87.50%, sensitivity of 88.06%, and specificity of 87.23%. Among patients with T2DM, the top five predictors in the CVD risk model were body mass index, anxiety, depression, total cholesterol, and systolic blood pressure. In summary, machine learning models can provide an automated identification mechanism for patients at CVD risk. Integrated treatment measures should be taken in health management, including clinical care, mental health improvement, and health behavior promotion. (shrink)

This research aims to explore the relationship between corporate governance and CSR: What are the major factors that play a direct role in the establishment of this relationship? How does context and institutional background impact upon the relationship between CSR and Governance? Using in-depth semi-structured interviews from two types of governance systems in three countries over three years, this study has demonstrated that in practice, within different settings, CSR is being used both as a strategy as well as a reaction (...) to different drivers. We call this adaptive governance where governance can be defined as a flexible system of action incorporating strategic and monitoring activities that determines the way a company enacts its responsibilities to its shareholders and stakeholders and which is determined at any given time by the interrelationship of institutional drivers and behavioural norms. Governance systems and their interrelationships with CSR are demonstrated as fluid according to the national and institutional context, economic situation and industry impact. In the eyes of practitioners corporate governance includes both structural and behavioural factors as well as responsibilities and actions towards shareholders and stakeholders. Contextual factors that this research highlights to be important to the incorporation of CSR into governance include the economic environment, national governance system, regulation and soft law, shareholders, national culture, behavioural norms and industry impacts. Hypotheses on the impact of institutional contexts, industry impacts and economic situations on different types of CSR actions are proposed for further research. (shrink)

Playing traditional games has a direct impact on the mood states of the players, and this is the reason why physical education is an ideal setting for teaching how to recognize them and be aware about how they can swing. The objective of the study was to determine if participating in traditional opposition games causes changes to the participants' mood states. A total of 102 students participated. Each participant recorded the intensity of the mood state experienced at the beginning and (...) at the end of the sessions, using the validated Profile of Mood States instrument. The pedagogical experience was planned as 4 sessions with 6 and 5 opposition games each: with competition in mixed groups, equally and unequally mixed; without competition in mixed groups, equally and unequally mixed; with competition in same-gender groups; and without competition in same-gender groups. When comparing the different mood states according to session, the mood states of the depression, fatigue, and vigor dimensions were significantly different, with higher scores in the sessions with competition for the mood states of vigor and fatigue. Also, when comparing the mood states depending on session grouping and group type, the results showed differences in the scores obtained for the dimensions fatigue and anger, and general mood state. These differences were found at the start of the session and at the end, with the dimension fatigue being the only one with differences in both situations when comparing the same-gender, equally-mixed, and unequally-mixed groups for the two types of traditional opposition games compared. In addition, after an analysis of the mood states depending on gender was performed, the results and therefore the significant differences found, were very similar to those obtained according to group type. Lastly, it was concluded that the type of group, and gender were decisive, causing variations in the mood states of the students. This provides valuable information for teaching professionals about the structuring and organization of PE sessions, aiming to promoting positive motor experiences. (shrink)

Qiyās, or “correlational inference”, comprises a primary set of methodological tools recognized by a majority of premodern Sunnī jurists. Its elements, valid modes, and proper applications were the focus of continual argument and refinement. A particular area of debate was the methodology of determining or justifying the ʿilla: the legal cause giving rise to a ruling in God’s Law. This was most often discussed under the rubric of “the modes of causal justification”. Among these modes was the much debated (...) test of dawarān. In brief, proponents of dawarān employed it to justify claims that a property occasioned the ruling in an authoritative source-case. In concert with other considerations, the demonstrated co-presence and co-absence of property and ruling—that is, their concomitance “in existence” and “in nonexistence” — was taken as an indication that the property was the ruling’s ʿilla. Delving further into dawarān and causation, the current study interprets “in existence” and “in nonexistence” not as a kind of metaphor for true and false, but as an accurate terminology vis-à-vis the meaning of causality statements, fully compatible with dominant Islamicate views on causal agency. In brief, a deeper logical and linguistic analysis of the different existential modes of dawarān strongly suggests that we should distinguish property and ruling as types as opposed to tokens. Our reading of dawarān as shaped by a finer-grained structure not only allows us to identify the efficient occasioning process as a function which takes some particular token of the ʿilla and renders a token of the general ruling type, but it allows us to elucidate the role of taʿlīl in shaping an epistemological theory of argument to the best explanation: a sophisticated, premodern manifestation of abductive reasoning. (shrink)

Qiyās, or “correlational inference” (often glossed as “analogy”), comprises a primary set of methodological tools recognized by a majority of premodern Sunnī jurists. Its elements, valid modes, and proper applications were the focus of continual argument and refinement. A particular area of debate was the methodology of determining or justifying the ʿilla: the legal cause (or occasioning factor, or ratio legis) giving rise to a ruling in God’s Law. This was most often discussed (and disputed) under the rubric of (...) “the modes of causal justification” (masālik al-taʿlīl). Among these modes was the much debated test of dawarān (concomitance of presumed cause and effect). In brief, proponents of dawarān employed it to justify claims that a property (waṣf) occasioned the ruling (ḥukm) in an authoritative source-case (aṣl). In concert with other considerations, the demonstrated co-presence (ṭard) and co-absence (ʿaks) of property and ruling—that is, their concomitance “in existence” (wujūdan) and “in nonexistence” (ʿadaman)— was taken as an indication that the property was the ruling’s ʿilla. Delving further into dawarān and causation (ʿilliyya), the current study interprets “in existence” and “in nonexistence” not as a kind of metaphor for true and false (within the framework of a classical truth-functional formal semantics), but as an accurate terminology vis-à-vis the meaning of causality statements, fully compatible with dominant Islamicate views on causal agency. In brief, a deeper logical and linguistic analysis of the different existential modes of dawarān strongly suggests that we should distinguish property (or phenomenon) and ruling (or effect) as types (concepts or propositions linguistically expressed by a sentence) as opposed to tokens (instantiations of the type; the real, ontological events that verify the proposition). Our reading of dawarān as shaped by a finer-grained structure not only allows us to identify the efficient occasioning process as a function which takes some particular token of the ʿilla (arguably, the property or properties which provide the ruling’s material cause) and renders a token of the general ruling type, but it allows us to elucidate the role of taʿlīl (causal justification) in shaping an epistemological theory of argument to the best explanation: a sophisticated, premodern manifestation of abductive reasoning. (shrink)

We characterize, in terms of determinacy, the existence of the least inner model of "every object of type k has a sharp." For k ∈ ω, we define two classes of sets, (Π 0 k ) * and (Π 0 k ) * + , which lie strictly between $\bigcup_{\beta and Δ(ω 2 -Π 1 1 ). Let ♯ k be the (partial) sharp function on objects of type k. We show that the determinancy of (Π 0 k (...) ) * follows from $L \lbrack\ sharp_k \rbrack \models "\text{every object of type} k \text{has a sharp},$ and we show that the existence of indiscernibles for L[ ♯ k ] is equivalent to a slightly stronger determinacy hypothesis, the determinacy of (Π 0 k ) * +. (shrink)

This paper argues that for Nietzsche it is only when the strong type decays on its own terms that it is possible for a weak type to come into dominance by inverting the values of the strong. It sets right a latent inconsistency in Deleuze’s work, Nietzsche and Philosophy , which traces back the origin of decadence to the subterranean struggle between reactive forces. I show that Deleuze’s reading runs contrary to his own contention that for Nietzsche the (...) negative is a result of activity. I argue that the decadence of the strong is a consequence of its very creative activity and abundant health. Relying on Nietzsche’s later works, I isolate and analyze four typical traits of the strong type which not only determine this type as what it is but also make it vulnerable to decadence. (shrink)

This brief article is intended to introduce the reader to the field of algebraic set theory, in which models of set theory of a new and fascinating kind are determined algebraically. The method is quite robust, applying to various classical, intuitionistic, and constructive set theories. Under this scheme some familiar set theoretic properties are related to algebraic ones, while others result from logical constraints. Conventional elementary set theories are complete with respect to algebraic models, which arise in a variety of (...) ways, including topologically, type-theoretically, and through variation. Many previous results from topos theory involving realizability, permutation, and sheaf models of set theory are subsumed, and the prospects for further such unification seem bright. (shrink)

Continuing work begun in [10], we utilize a notion of forcing for which the generic objects are structures and which allows us to determine whether these “generic” structures compute certain sets and enumerations. The forcing conditions are bounded complexity types which are consistent with a given theory and are elements of a given Scott set. These generic structures will “represent” this given Scott set, in the sense that the structure has a certain weak saturation property with respect to bounded complexity (...) types in the Scott set. For example, if ? is a nonstandard model of PA, then ? represents the Scott set ? = n∈ω | ?⊧“the nth prime divides a” | a∈?.The notion of forcing yields two main results. The first characterizes the sets of natural numbers computable in all models of a given theory representing a given Scott set. We show that the characteristic function of such a set must be enumeration reducible to a complete existential type which is consistent with the given theory and is an element of the given Scott set.The second provides a sufficient condition for the existence of a structure ? such that ? represents a countable jump ideal and ? does not compute an enumeration of a given family of sets ?. This second result is of particular interest when the family of sets which cannot be enumerated is ? = Rep[Th(?)]. Under this additional assumption, the second result generalizes a result on TA [6] and on certain other completions of PA [10]. For example, we show that there also exist models of completions of ZF from which one cannot enumerate the family of sets represented by the theory. (shrink)