This is a book about sensory states and their apparent characteristics. It confronts a whole series of metaphysical and epistemological questions and presents an argument for type materialism: the view that sensory states are identical with the neural states with which they are correlated. According to type materialism, sensations are only possessed by human beings and members of related biological species; silicon-based androids cannot have sensations. The author rebuts several other rival theories, and explores a number of important (...) issues: the forms and limits of introspective awareness of sensations, the semantic properties of sensory concepts, knowledge of other minds, and unity of consciousness. The book is a significant contribution to the philosophy of mind, and has much to say to psychologists and cognitive scientists. (shrink)

Bridget Pratt and Jantina de Vries1 have made an insightful contribution to enhancing epistemic justice in global health ethics. Their elaboration details intellectual (external) exclusion—described as non-representation—across three levels, and at its core, proposes inclusion to rectify this. To extend this work, we contend that it is worth probing the nuances and challenges associated with inclusion as a response to epistemic injustice. These include (A) the meaning of inclusion outside binary vocabularies of north and south; (B) the possibility of forms (...) of inclusion that produce exclusion and (C) inclusion as a politics of belonging with intellectual confinement as a possible epistemic harm. How the problem of injustice is described influences the substantive meaning of inclusion. In describing epistemic injustice, north and south (centre and periphery) are used as relational markers of power, inclusion, authority and exclusion. While this binary vocabulary is seductive, it can appear to confer proprietary rights to the concepts, theories and values described as originating in the global north (and south). However, such inscriptions of ownership are not always a correct reading of the problem. Sometimes, the ostensible western-ness and non-western-ness of ideas are taken for granted, particularly …. (shrink)

In recent years, several formalisms for program construction have appeared. One such formalism is the type theory developed by Per Martin-L f. Well suited as a theory for program construction, it makes possible the expression of both specifications and programs within the same formalism. Furthermore, the proof rules can be used to derive a correct program from a specification as well as to verify that a given program has a certain property. This book contains a thorough introduction to (...) class='Hi'>type theory, with information on polymorphic sets, subsets, monomorphic sets, and a full set of helpful examples. (shrink)

We present an extension of the basic revision theory of circular definitions with a unary operator, □. We present a Fitch-style proof system that is sound and complete with respect to the extended semantics. The logic of the box gives rise to a simple modal logic, and we relate provability in the extended proof system to this modal logic via a completeness theorem, using interpretations over circular definitions, analogous to Solovay’s completeness theorem forGLusing arithmetical interpretations. We adapt our proof to (...) a special class of circular definitions as well as to the first-order case. (shrink)

Abstract: Tomatoes are part of the major crops in food security. Tomatoes are plants grown in temperate and hot regions of South American origin from Peru, and then spread to most countries of the world. Tomatoes contain a lot of vitamin C and mineral salts, and are recommended for people with constipation, diabetes and patients with heart and body diseases. Studies and scientific studies have proven the importance of eating tomato juice in reducing the activity of platelets in diabetics, which (...) helps in protecting them from developing deadly blood clots. A tomato classification approach is presented with a data set containing approximately 5,266 images with 7 species belonging to tomatoes. The Neural Network Algorithms (CNN), a deep learning technique applied widely in image recognition, is used for this task. (shrink)

In this report I motivate and develop a type-free logic with predicate quantifiers within the general ontological framework of properties, relations, and propositions. In Part I, I present the major ideas of the system informally and discuss its philosophical significance, especially with regard to Russell's paradox. In Part II, I prove the soundness, consistency, and completeness of the logic.

I assess Robert Kane's view that global Frankfurt-type cases don't show that freedom to do otherwise is never required for moral responsibility. I first adumbrate Kane's indeterminist account of free will.This will help us grasp Kane's notion of ultimate responsibility, and his claim that in a global Frankfurt-type case, the counterfactual intervener could not control all of the relevant agent's actions in the Frankfurt manner, and some of those actions would be such that the agent could have done (...) otherwise. Appealing to considerations of responsibility and luck, I then show that the global cases survive Kane's objections. (shrink)

In this article we will focus our attention on the variety of distributive bisemilattices and some linguistic expansions thereof: bounded, De Morgan, and involutive bisemilattices. After extending Balbes’ representation theorem to bounded, De Morgan, and involutive bisemilattices, we make use of Hartonas–Dunn duality and introduce the categories of 2spaces and 2spaces\. The categories of 2spaces and 2spaces\ will play with respect to the categories of distributive bisemilattices and De Morgan bisemilattices, respectively, a role analogous to the category of Stone spaces (...) with respect to the category of Boolean algebras. Actually, the aim of this work is to show that these categories are, in fact, dually equivalent. (shrink)

‘Type’ in biology is a polysemous term. In a landmark article, Paul Farber (Journal of the History of Biology 9(1): 93–119, 1976) argued that this deceptively plain term had acquired three different meanings in early nineteenth century natural history alone. ‘Type’ was used in relation to three distinct type concepts, each of them associated with a different set of practices. Important as Farber’s analysis has been for the historiography of natural history, his account conceals an important dimension (...) of early nineteenth century ‘type talk.’ Farber’s taxonomy of type concepts passes over the fact that certain uses of ‘type’ began to take on a new meaning in this period. At the closing of the eighteenth century, terms like ‘type specimen,’ ‘type species,’ and ‘type genus’ were universally recognized as referring to typical, model members of their encompassing taxa. But in the course of the nineteenth century, the same terms were co-opted for a different purpose. As part of an effort to drive out nomenclatural synonymy – the confusing state of a taxon being known to different people by different names – these terms started to signify the fixed and potentially atypical name-bearing elements of taxa. A new type concept was born: the nomenclatural type. In this article, I retrace this perplexing nineteenth century shift in meaning of ‘type.’ I uncover the nomenclatural disorder that the new nomenclatural type concept dissolved, and expose the conceptual confusion it left in its tracks. What emerges is an account of how synonymy was suppressed through the coinage of a homonym. (shrink)

In section 24 of The Antichrist, Nietzsche notes a problem namely “the origin of Christianity.” He offers two propositions toward its solution: the first is that “Christianity can only be understood on the soil where it grew:” and the second is that “the psychological type of the Galilean is still recognizable, but it had to assume a completely degenerate form (simultaneously mutilated and full of alien features) before it came to be used as a redeemer of humanity” (A 24). (...) Significantly this passage suggests that the origins of Christianity rest on a reinterpretation of the type of the redeemer. This paper seeks to clarify the nature of such a modification and to identify some of its key ramifications. After clarifying the type, the paper argues that the type, thus understood, serves as a link between the texts On the Genealogy of Morality and The Antichrist and, as such, reveals the connection between Nietzsche's genealogical methods and the wider project of reevaluation. Though this reading is not the standard interpretive strategy, the paper argues that it is the strategy that Nietzsche himself recommends. (shrink)

Results of a study investigating the relation between personality traits and ethical-orientation indicate sex is not an good predictor for differences in Machiavellian-, Type A personality- or ethical-orientation. Intelligence is found to be positively associated with Machiavellian- and Type A personality-orientation but negatively associated with ethical-orientation. Machiavellians tend to have Type A personalities, but tend to be less ethically-oriented than Nonmachiavellians. Type A personalities are more ethically-orientated than Type B personalities.

We formulate and explore two basic axiomatic systems of type-free subjective probability. One of them explicates a notion of finitely additive probability. The other explicates a concept of infinitely additive probability. It is argued that the first of these systems is a suitable background theory for formally investigating controversial principles about type-free subjective probability.

We show that basic hybridization makes it possible to give straightforward Henkin-style completeness proofs even when the modal logic being hybridized is higher-order. The key ideas are to add nominals as expressions of type t, and to extend to arbitrary types the way we interpret \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$@_i$\end{document} in propositional and first-order hybrid logic. This means: interpret \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$@_i\alpha _a$\end{document}, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} (...) \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\alpha _a$\end{document} is an expression of any type \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$a$\end{document}, as an expression of type \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$a$\end{document} that rigidly returns the value that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\alpha_a$\end{document} receives at the i-world. The axiomatization and completeness proofs are generalizations of those found in propositional and first-order hybrid logic, and we automatically obtain a wide range of completeness results for stronger logics and languages. Our approach is deliberately low-tech. We don’t, for example, make use of Montague’s intensional type s, or Fitting-style intensional models; we build, as simply as we can, hybrid logicover Henkin’s logic. (shrink)

Background: The prevalence of sedentary behavior in adolescents has aroused social attention. The association between sedentary behavior and cognitive flexibility remains unclear, and it may vary depending on the type of sedentary behavior. This study aimed to investigate the associations between specific-type sedentary behaviors and cognitive flexibility in adolescents.Method: A total of 700 Chinese adolescents aged 10–15 years were recruited. The self-report questionnaire was used to assess total sedentary time, recreational screen-based sedentary time, and educational sedentary time. The (...) More-odd shifting task was used to assess cognitive flexibility.Results: The correlation analysis showed that recreational screen-based sedentary time was negatively correlated with cognitive flexibility, whereas educational sedentary time was positively correlated with cognitive flexibility. The regression analysis also further revealed that a significantly negative association between recreational screen-based sedentary time and cognitive flexibility, while a significantly positive association existed between educational sedentary time and cognitive flexibility.Conclusion: The findings shown that the association between recreational screen-based sedentary behavior and cognitive flexibility differs from educational sedentary behavior in adolescents, providing new ideas for a more comprehensive understanding of the association between sedentary behavior and cognitive flexibility in adolescents. (shrink)

A Polish space is not always homeomorphic to a computably presented Polish space. In this article, we examine degrees of non-computability of presenting homeomorphic copies of compact Polish spaces. We show that there exists a $\mathbf {0}'$ -computable low $_3$ compact Polish space which is not homeomorphic to a computable one, and that, for any natural number $n\geq 2$, there exists a Polish space $X_n$ such that exactly the high $_{n}$ -degrees are required to present the homeomorphism type of (...) $X_n$. Along the way we investigate the computable aspects of Čech homology groups. We also show that no compact Polish space has a least presentation with respect to Turing reducibility. (shrink)

In a lengthy review article, C. Anthony Anderson criticizes the approach to property theory developed in Quality and Concept (1982). That approach is first-order, type-free, and broadly Russellian. Anderson favors Alonzo Church’s higher-order, type-theoretic, broadly Fregean approach. His worries concern the way in which the theory of intensional entities is developed. It is shown that the worries can be handled within the approach developed in the book but they remain serious obstacles for the Church approach. The discussion focuses (...) on: (1) the fine-grained/coarse-grained distinction, (2) proper names and definite descriptions, (3) the paradox of analysis and Mates’ puzzle, and (4) the logical, semantical, and intentional paradoxes. (shrink)

There has been a plethora of studies outlying the various factors which may affect undergraduate student cheating, generally focusing on individual, situational and deterrent factors. But beyond these factors, does the type of cheating affect students’ perceptions of cheating? We found that there were differences in regards to gradable cheating such as cheating on homework, tests and papers versus non-gradable cheating such as illegally downloading software/music from the Internet or photocopying materials which violate the university’s academic integrity policy. Gender, (...) discussion of ethical issues in class and enforcement of cheating reduces the acceptance of cheating across types of cheating. Less time spent on the Internet reduces the acceptance of only non-gradable cheating and the type of institution and knowing the consequences of cheating reduces the acceptance of only gradable cheating. (shrink)

SummaryHow can the immense amount of suffering and waste inherent in the evolutionary process be reconciled with the existence of a perfectly good and omnipotent God? A widely embraced proposal in the area of “evolutionary theodicy” is the so-called “Only Way”-argument. This argument contends that certain valuable goods – in particular, creaturely independence and human freedom – can only come about through a genuinely indeterministic and partly uncontrolled process of evolution. In a previous article, I have argued that the “Only (...) Way”-argument can be defeated by a “Twin Earth”-thought experiment: If God is omnipotent, he could have created – directly, without evolution – creatures that are molecule-for-molecule identical to those that he actually created through evolution. If the creatures that he actually created have freedom and independence, there is no valid reason to deny that the non-evolved “twin creatures” would also be free and independent. Recently, Eikrem and Søvik have suggested a way of blocking my Twin Earth-argument by appealing to the distinction between type-values and token-values. While ES admit that the Twin Earth-argument shows the non-necessity of evolution for the existence of certain type-goods, they argue that an evolutionary creation can be justified by appeal to valuable token-goods that could not have existed without evolution. In this article, I respond to ES’s token-goods argument by showing that it is incompatible with a basic presupposition of “Only Way” evolutionary theodicies, namely the claim that the evolutionary process is genuinely indeterministic and partly uncontrolled. (shrink)

This Element is an exposition of second- and higher-order logic and type theory. It begins with a presentation of the syntax and semantics of classical second-order logic, pointing up the contrasts with first-order logic. This leads to a discussion of higher-order logic based on the concept of a type. The second Section contains an account of the origins and nature of type theory, and its relationship to set theory. Section 3 introduces Local Set Theory, an important form (...) of type theory based on intuitionistic logic. In Section 4 number of contemporary forms of type theory are described, all of which are based on the so-called 'doctrine of propositions as types'. We conclude with an Appendix in which the semantics for Local Set Theory - based on category theory - is outlined. (shrink)

This paper is part of a broader project whose aim is to present a coherent unified approach to natural language dialogue semantics using tools from type theory. Here we explore aspects of our approach which relate to situation theory and situation semantics. We first point out a relationship between type theory and the Austinian notion of truth. We then consider how records in type theory might be used to represent situations and how dependent record types can be (...) used to model constraints on situations. We then sketch treatments of attitude phenomena for which Barwise and Perry proposed situation semantic analyses (perception complements, belief, the Pierre puzzle) as well as two other intensional phenomena (intensional verbs and intentional identity). Finally we give a characterisation of the type theory used and a small illustrative fragment of English. (shrink)

We present a generalisation of the type-theoretic interpretation of constructive set theory into Martin-Löf type theory. The original interpretation treated logic in Martin-Löf type theory via the propositions-as-types interpretation. The generalisation involves replacing Martin-Löf type theory with a new type theory in which logic is treated as primitive. The primitive treatment of logic in type theories allows us to study reinterpretations of logic, such as the double-negation translation.

Church’s type theory, aka simple type theory, is a formal logical language which includes classical first-order and propositional logic, but is more expressive in a practical sense. It is used, with some modifications and enhancements, in most modern applications of type theory. It is particularly well suited to the formalization of mathematics and other disciplines and to specifying and verifying hardware and software. It also plays an important role in the study of the formal semantics of natural (...) language. When utilizing it as a meta-logic to semantically embed expressive non-classical logics further topical applications are enabled in artificial intelligence and philosophy. A great wealth of technical knowledge can be expressed very naturally in it. With possible enhancements, Church’s type theory constitutes an excellent formal language for representing the knowledge in automated information systems, sophisticated automated reasoning systems, systems for verifying the correctness of mathematical proofs, and a range of projects involving logic and artificial intelligence. Some examples and further references are given in Sections 1.2.2 and 5 below. Type theories are also called higher-order logics, since they allow quantification not only over individual variables, but also over function, predicate, and even higher order variables. Type theories characteristically assign types to entities, distinguishing, for example, between numbers, sets of numbers, functions from numbers to sets of numbers, and sets of such functions. As illustrated in Section 1.2.2 below, these distinctions allow one to discuss the conceptually rich world of sets and functions without encountering the paradoxes of naive set theory. Church’s type theory is a formulation of type theory that was introduced by Alonzo Church in Church 1940. In certain respects, it is simpler and more general than the type theory introduced by Bertrand Russell in Russell 1908 and Whitehead & Russell 1927a. Since properties and relations can be regarded as functions from entities to truth values, the concept of a function is taken as primitive in Church’s type theory, and the λ-notation which Church introduced in Church 1932 and Church 1941 is incorporated into the formal language. Moreover, quantifiers and description operators are introduced in a way so that additional binding mechanisms can be avoided, λ-notation is reused instead. λ-notation is thus the only binding mechanism employed in Church’s type theory. (shrink)

This study explores the type-based vocational education system from the perspective of China. General education and vocational education are equal types of education in status, but not based on different levels of education in China. Specifically, the connotation of vocational education as type-based education is mainly embodied in ‘three directions’. The outstanding problems of vocational education as a type-based education include ‘four aspects’. Vocational education as a type-based education reform path is considered as ‘four reforms’. We (...) should strengthen management, improve the comprehensive quality of vocational college students and make clear the direction and explore the new path of reform and development of vocational colleges. In addition, we need to optimize investment and make innovations in the system and mechanism of funding for China’s vocational education. (shrink)

There may be two and a half bagels on the table. When there are two and a half, it is false that there are exactly two. As obvious as these claims are, they can’t be accounted for on the most straightforward and familiar views of counting and the semantics of number words. I develop a view on which counting is a type of measuring. In particular, counting involves a specific measure function. I then analyze that function and show how (...) it can account for the cases in which counting is sensitive to partiality, e.g. partial bagels. (shrink)

Among the most interesting features of Homotopy Type Theory is the way it treats identity, which has various unusual characteristics. We examine the formal features of “identity types” in HoTT, and how they relate to its other features including intensionality, constructive logic, the interpretation of types as concepts, and the Univalence Axiom. The unusual behaviour of identity types might suggest that they be reinterpreted as representing indiscernibility. We explore this by defining indiscernibility in HoTT and examine its relationship with (...) identity. We argue that identity types are a primitive component of HoTT and cannot be reduced to indiscernibility. (shrink)

Unbound anaphoric pronouns or ‘E-type pronouns’ have presented notorious problems for semantic theory, leading to the development of dynamic semantics, where the primary function of a sentence is not considered that of expressing a proposition that may act as the object of propositional attitudes, but rather that of changing the current information state. The older, ‘E-type’ account of unbound anaphora leaves the traditional notion of proposition intact and takes the unbound anaphor to be replaced by a full NP (...) whose semantics is assumed to be known (e.g. a definite description). In this paper, I argue that there are serious problems with any version of the E-type account as well as the (original form of the) dynamic account. I will explore a new account based on structured propositions, which can be considered a conservative extension of a traditional proposition-based semantics, but which at the same time incorporates some crucial insights of the dynamic account. (shrink)

This paper discusses some of the ways in which Martin-Löf type theory differs from set theory. The discussion concentrates on conceptual, rather than technical, differences. It revolves around four topics: sets versus types; syntax; functions; and identity. The difference between sets and types is spelt out as the difference between unified pluralities and kinds, or sorts. A detailed comparison is then offered of the syntax of the two languages. Emphasis is put on the distinction between proposition and judgement, drawn (...) by type theory, but not by set theory. Unlike set theory, type theory treats the notion of function as primitive. It is shown that certain inconveniences pertaining to function application that afflicts the set-theoretical account of functions are thus avoided. Finally, the distinction, drawn in type theory, between judgemental and propositional identity is discussed. It is argued that the criterion of identity for a domain cannot be formulated in terms of propositional identity. It follows that the axiom of extensionality cannot be taken as a statement of the criterion of identity for sets. (shrink)

The core thesis of anti-luck epistemology is the incompatibility thesis, that is, knowledge is incompatible with veritic epistemic luck. Traditionally, anti-luck epistemologists hold that there are two distinct types of veritic epistemic luck, viz, intervening luck and environmental luck. The former occurs when something luckily intervenes between the subject’s belief and the target fact, which renders the subject’s belief luckily true. The latter can be found in cases where the subject’s belief is luckily true when she is in an unfriendly (...) epistemic environment. This paper purports to show that there is another long-neglected type of veritic epistemic luck—I name it ‘interpretative luck’. It refers to the type of luck occurring when the subject accidentally chooses the correct interpretation of evidence and thus her belief is luckily true. I will demonstrate that no proper reasons can support the incompatibility between interpretative luck and knowledge. Instead, the price for insisting this incompatibility would be unacceptably high. Therefore, the existence of interpretative luck falsifies the incompatibility thesis of anti-luck epistemology. (shrink)

In historical discussions of twentieth-century logic, it is typically assumed that model theory emerged within the tradition that adopted first-order logic as the standard framework. Work within the type-theoretic tradition, in the style of Principia Mathematica, tends to be downplayed or ignored in this connection. Indeed, the shift from type theory to first-order logic is sometimes seen as involving a radical break that first made possible the rise of modern model theory. While comparing several early attempts to develop (...) the semantics of axiomatic theories in the 1930s, by two proponents of the type-theoretic tradition and two proponents of the first-order tradition, we argue that, instead, the move from type theory to first-order logic is better understood as a gradual transformation, and further, that the contributions to semantics made in the type-theoretic tradition should be seen as central to the evolution of model theory. (shrink)

This paper contains a novel and coherent reading of Weberian ideal type construction, based on recent philosophical approaches to conceptual engineering. This reading makes transparent the dialectics of Weber's approach, resulting in a more nuanced interpretation of his methodological work. It will become apparent that Weber, when introducing his notion of an ideal type, did not merely summarize his views on methodology in the social sciences, but, rather, presented a two-step argument in favor of these views. The reconstruction (...) will directly bear on issues in the methodology of the social sciences. Weber not only presented a methodology that is, at some level of abstraction, strikingly similar to Carnapian explication (the canonical point of reference in the contemporary debate on conceptual engineering). He also diagnosed, in a systematic fashion, types of problems we face when dealing with ordinary and scientific concepts that play a key role in the description of social reality, and he foreshadowed what is today sometimes described as “debunking” projects. From a philosophy of science perspective, I propose Weber's view (on the reconstruction proposed here) as a serious candidate for an adequate theory of concept replacement in the social sciences. (shrink)

This paper discusses the Indo-Iranian reduplicated i-adjectives of the type Ved. cákri-, Av. caxri- ‘doing’. These adjectives are formally associated with the weak stem of the corresponding perfect, but their lexical semantics are not always those expected of an adjectival derivative of the perfect stem. A subgroup of forms is associated with synchronically resultative perfects, but pattern functionally as present participles, often with iterative or intensive readings. I show that these “form-meaning mismatch” formations share a number of syntactic properties (...) both in Vedic and in Avestan and are likely to be the starting point of the type. I conclude from this that the synchronic association of the cákri-type with the perfect stem is secondary, and that its original derivational basis must have been a different reduplicated verbal category. I furthermore provide arguments that this cannot be one of the synchronic Indo-Iranian reduplicated verbal categories. (shrink)

In this paper I undertake to resolve a main pragmatic puzzle triggered by Bank-type cases. After accepting ‘sanitized’ intuitions about Truth-Values, as reflected in x-phi experiments, the pragmatic puzzle about whether the husband is inconsistent remains, and if he isn’t, which intuitively is the case, how are we to explain it. The context in such cases is pragmatic, with awareness of high risks, and the treatment I propose is pragmatic as well, but not Gricean. I offer a new Pragmatics (...) whose main tools are Steering Thrust and Posting. It focuses on what I call Action-Directed Pragmatics. An overall view of Pragmatics centers on the primary resort to Sayability rather than to Truth-Values, and to the Pragmatic phenomenon of co-present operative norm-types, which can conflict in some cases vis-à-vis particular actions and about what subjects can say. The very satisfactory explanation of the above puzzle that I offer is in such terms. In particular, attention is focused on the phenomenon of Negative-Polarity Pragmatic Functors. (shrink)

The first main result isolates some conditions which fail for the class of graphs and hold for the class of Abelian p-groups, the class of Abelian torsion groups, and the special class of "rank-homogeneous" trees. We consider these conditions as a possible definition of what it means for a class of structures to have "Ulm type". The result says that there can be no Turing computable embedding of a class not of Ulm type into one of Ulm (...) class='Hi'>type. We apply this result to show that there is no Turing computable embedding of the class of graphs into the class of "rank-homogeneous" trees. The second main result says that there is a Turing computable embedding of the class of rank-homogeneous trees into the class of torsion-free Abelian groups. The third main result says that there is a "rank-preserving" Turing computable embedding of the class of rank-homogeneous trees into the class of Boolean algebras. Using this result, we show that there is a computable Boolean algebra of Scott rank ${\mathrm{\omega }}_{1}^{\mathrm{C}\mathrm{K}}$. (shrink)

Due to the advance computer technology, the use of probability distributions has been raised up to solve the real life problems. These applications are found in reliability engineering, computer sciences, economics, psychology, survival analysis, and some others. This study offers a new probability model called Marshall–Olkin Extended Gumbel Type-II which can model various shapes of the failure rate function. The proposed distribution is capable to model increasing, decreasing, reverse J-shaped, and upside down bathtub shapes of the failure rate function. (...) Various statistical properties of the proposed distribution are derived such as alternate expressions for the density and distribution function, special cases of MOEGT-II distribution, quantile function, Lorenz curve, and Bonferroni curve. Estimation of the unknown parameters is carried out by the method of maximum likelihood. A simulation study is conducted using three different iterative methods with different samples of sizes n. The usefulness and potentiality of the MOEGT-II distribution have been shown using three real life data sets. The MOEGT-II distribution has been demonstrated as better fit than Exponentiated Gumbel Type-II, Marshall–Olkin Gumbel Type-II, Gumbel Type-II, Marshall–Olkin–Frechet, Frechet, Burr III, Log Logistic, Beta Inverse Weibull, and Kumaraswamy Inverse Weibull distributions. (shrink)

The notion of cognitive act is of importance for an epistemology that is apt for constructive type theory, and for epistemology in general. Instead of taking knowledge attributions as the primary use of the verb 'to know' that needs to be given an account of, and understanding a first-person knowledge claim as a special case of knowledge attribution, the account of knowledge that is given here understands first-person knowledge claims as the primary use of the verb 'to know'. This (...) means that a cognitive act is an act that counts as cognitive from a first-person point of view. The method of linguistic phenomenology is used to explain or elucidate our epistemic notions. One of the advantages of the theory is that an answer can be given to some of the problems in modern epistemology, such as the Gettier problem. (shrink)

This article examines the new type of hero created by Ayn Rand and finds its roots in Chernyshevsky's “new human.” Rand's characters share such features as extremism, asceticism, escapism, and the desire to transform the world. Moreover, Rand's heroes exhibit the self-building and “wholeness” traits of the “superhuman” as found in myths and in Renaissance and Masonic ideas.