Higher types can readily be added to set theory, Bernays-Morse set theory being an example. A type for each ordinal is added in [2]. Adding higher types to set theory provides a neat solution to the problem of how to handle higher type categories. We give the basic definitions, and prove cocompleteness of some higher type categories. MSC: 14A15.

Instead of the half-century old foundational feud between set theory and category theory, this paper argues that they are theories about two different complementary types of universals. The set-theoretic antinomies forced naïve set theory to be reformulated using some iterative notion of a set so that a set would always have higher type or rank than its members. Then the universal u_{F}={x|F(x)} for a property F() could never be self-predicative in the sense of u_{F}∈u_{F}. But the mathematical theory (...) of categories, dating from the mid-twentieth century, includes a theory of always-self-predicative universals--which can be seen as forming the "other bookend" to the never-self-predicative universals of set theory. The self-predicative universals of category theory show that the problem in the antinomies was not self-predication per se, but negated self-predication. They also provide a model (in the Platonic Heaven of mathematics) for the self-predicative strand of Plato's Theory of Forms as well as for the idea of a "concrete universal" in Hegel and similar ideas of paradigmatic exemplars in ordinary thought. (shrink)

We use the category of presheaves over PTIME-functions in order to show that Cook and Urquhart's higher-order function algebra PV ω defines exactly the PTIME-functions. As a byproduct we obtain a syntax-free generalisation of PTIME-computability to higher types. By restricting to sheaves for a suitable topology we obtain a model for intuitionistic predicate logic with ∑ 1 b -induction over PV ω and use this to re-establish that the provably total functions in this system are polynomial time computable. (...) Finally, we apply the category-theoretic approach to a new higher-order extension of Bellantoni-Cook's system BC of safe recursion. (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)

In the dialogue of scientists and theologians, participants experienced differences in linguistic usage of the various disciplines, for example different concepts, grammatical rules, characteristic terminology, specific phrases, and expressions. A fascinating subject of this dialogue concerned God’s agency in human history within space-time, where the concepts of ‘God’ and ‘divine agency’ were unusual. In the church tradition, believers learned to use these concepts using biblical training with narratives such as the Exodus or Babylon stories. But to handle these narratives in (...) historical situations, we need to analyse the concepts of ‘history’ and its ambiguity, and the ‘historical method of explanation’ to answer the question: ‘How does God act in history?’ The central question of this article was: Is history a domain of Divine Agency? It is imperative to pay attention to the specific grammar of religious language and to distinguish it categorically from the computational language of the natural sciences. History as such should be deconstructed into history 1 and history 2. However, religious and technical activities are of different logical types, so we cannot combine them in one conceptual scheme on the same level. Nevertheless, it is conceivable that coherence might be possible at a higher conceptual level. A qualitative method of a critical literature review across disciplines was used and a subsequent contemplative conceptualisation was proposed. Contribution: This article illustrated the difference between religious and scientific concepts to address Divine Agency in history. If reality or the universe can be described as an information-bearing entity in process, and if this is hierarchically structured, then we can imagine God interacting with this hierarchy. (shrink)

We can perceive not only low-level features of events such as color and motion, but also seemingly higher-level properties such as causality. A prototypical example of causal perception is the ”launching effect’: one object moves toward a stationary second object until they are adjacent, at which point A stops and B starts moving in the same direction. Beyond these motions themselves --- and regardless of any higher-level beliefs --- this display induces a vivid visual impression of causality, wherein (...) A is seen to cause B’s motion. Do such percepts reflect a unitary category of visual processing, or might there be multiple distinct forms of causal perception? While launching is often simply equated with causal perception, researchers have sometimes described other phenomena such as ”triggering’ and ”entraining’. We used psychophysical methods to determine whether these labels really carve visual processing at its joints, and how putatively different forms of causal perception relate to each other. Previous research demonstrated retinotopically specific adaptation to causality: exposure to causal launching makes subsequent ambiguous events in that same location more likely to be seen as non-causal ”passing’. Here, after replicating this effect, we show that exposure to triggering also yields retinotopically specific adaptation for subsequent ambiguous launching displays, but that exposure to entraining does not. Collectively, these results reveal that visual processing distinguishes some types of causal interactions. (shrink)

Martin-Löf's constructive type theory forms the basis of this paper. His central notions of category and set, and their relations with Russell's type theories, are discussed. It is shown that addition of an axiom - treating the category of propositions as a set and thereby enabling higher order quantification - leads to inconsistency. This theorem is a variant of Girard's paradox, which is a translation into type theory of Mirimanoff's paradox (concerning the set of all well-founded (...) sets). The occurrence of the contradiction is explained in set theoretical terms. Crucial here is the way a proof-object of an existential proposition is understood. It is shown that also Russell's paradox can be translated into type theory. The type theory extended with the axiom mentioned above contains constructive higher order logic, but even if one only adds constructive second order logic to type theory the contradictions arise. (shrink)

Much evidence suggests that, from a young age, humans are able to generalize information learned about a subset of a category to the category itself. Here, we propose that—beyond simply being able to perform such generalizations—people are biased to generalize to categories, such that they routinely make spontaneous, implicit category generalizations from information that licenses such generalizations. To demonstrate the existence of this bias, we asked participants to perform a task in which category generalizations would distract from the main (...) goal of the task, leading to a characteristic pattern of errors. Specifically, participants were asked to memorize two types of novel facts: quantified facts about sets of kind members and generic facts about entire kinds. Moreover, half of the facts concerned properties that are typically generalizable to an animal kind, and half concerned properties that are typically more idiosyncratic. We predicted that—because of the hypothesized bias—participants would spontaneously generalize the quantified facts to the corresponding kinds, and would do so more frequently for the facts about generalizable properties. In turn, these generalizations would lead to a higher rate of quantified-to-generic memory errors for the generalizable properties. The results of four experiments supported this prediction. Moreover, the same generalizable-versus-idiosyncratic difference in memory errors occurred even under cognitive load, which suggests that the hypothesized bias operates unnoticed in the background, requiring few cognitive resources. In sum, this evidence suggests the presence of a powerful bias to draw generalizations about kinds. (shrink)

We define a class of higher inductive types that can be constructed in the category of sets under the assumptions of Zermelo‐Fraenkel set theory without the axiom of choice or the existence of uncountable regular cardinals. This class includes the example of unordered trees of any arity.

Higher-order logic, with its type-theoretic apparatus known as the simple theory of types (STT), has increasingly come to be employed in theorizing about properties, relations, and states of affairs—or ‘intensional entities’ for short. This paper argues against this employment of STT and offers an alternative: ordinal type theory (OTT). Very roughly, STT and OTT can be regarded as complementary simplifications of the ‘ramified theory of types’ outlined in the Introduction to Principia Mathematica (on a realist reading). While (...) STT, understood as a theory of intensional entities, retains the Fregean division of properties and relations into a multiplicity of categories according to their adicities and ‘input types’ and discards the division of intensional entities into different ‘orders’, OTT takes the opposite approach: it retains the hierarchy of orders (though with some modifications) and discards the categorisation of properties and relations according to their adicities and input types. In contrast to STT, this latter approach avoids intensional counterparts of the Epimenides and related paradoxes. Fundamental intensional entities lie at the base of the proposed hierarchy and are also given a prominent part to play in the individuation of non-fundamental intensional entities. (shrink)

In this paper we show that the membership problem for second order non-linear Abstract Categorial Grammars is decidable. A consequence of that result is that Montague-like semantics yield to a decidable text generation problem. Furthermore the proof we propose is based on a new tool, Higher Order Intersection Signatures, which grasps statically dynamic properties of λ-terms and presents an interest in its own.

The purpose of this informal survey article is to introduce the reader to a new and surprising connection between Logic, Geometry, and Algebra which has recently come to light in the form of an interpretation of the constructive type theory of Per Martin-Löf into homotopy theory and higher-dimensional category theory.

Cartesian closed categories (CCCs) have played and continue to play an important role in the study of the semantics of programming languages. An axiomatization of the isomorphisms which hold in all Cartesian closed categories discovered independently by Soloviev and Bruce, Di Cosmo and Longo leads to seven equalities. We show that the unification problem for this theory is undecidable, thus settling an open question. We also show that an important subcase, namely unification modulo the linear isomorphisms, is NP-complete. (...) Furthermore, the problem of matching in CCCs is NP-complete when the subject term is irreducible. CCC-matching and unification form the basis for an elegant and practical solution to the problem of retrieving functions from a library indexed by types investigated by Rittri. It also has potential applications to the problem of polymorphic type inference and polymorphic higher-order unification, which in turn is relevant to theorem proving and logic programming. (shrink)

Higher order unification is a way of combining information (or equivalently, solving equations) expressed as terms of a typed higher order logic. A suitably restricted form of the notion has been used as a simple and perspicuous basis for the resolution of the meaning of elliptical expressions and for the interpretation of some non-compositional types of comparative construction also involving ellipsis. This paper explores another area of application for this concept in the interpretation of sentences containing intonationally marked (...) focus, or various semantic constructs which are sensitive to focus.Similarities and differences between this approach, and theories using alternative semantics, structured meanings, or flexible categorial grammars, are described. The paper argues that the higher order unification approach offers descriptive advantages over these alternatives, as well as the practical advantage of being capable of fairly direct computational implementation. (shrink)

Dual-process and dual-system theories in both cognitive and social psychology have been subjected to a number of recently published criticisms. However, they have been attacked as a category, incorrectly assuming there is a generic version that applies to all. We identify and respond to 5 main lines of argument made by such critics. We agree that some of these arguments have force against some of the theories in the literature but believe them to be overstated. We argue that the dual-processing (...) distinction is supported by much recent evidence in cognitive science. Our preferred theoretical approach is one in which rapid autonomous processes are assumed to yield default responses unless intervened on by distinctive higher order reasoning processes. What defines the difference is that Type 2 processing supports hypothetical thinking and load heavily on working memory. (shrink)

In this book the authors reconcile two different viewpoints of the foundations of mathematics, namely mathematical logic and category theory. In Part I, they show that typed lambda-calculi, a formulation of higher order logic, and cartesian closed categories are essentially the same. In Part II, it is demonstrated that another formulation of higher order logic is closely related to topos theory. Part III is devoted to recursive functions. Numerous applications of the close relationship between traditional logic and (...) the algebraic language of category theory are given. The authors have included an introduction to category theory and develop the necessary logic as required, making the book essentially self-contained. Detailed historical references are provided throughout, and each section concludes with a set of exercises. Thus it is well-suited for graduate courses and research in mathematics and logic. Researchers in theoretical computer science, artificial intelligence and mathematical linguistics will also find this an accessible introduction to a subject of increasing application to these disciplines. (shrink)

Let T be the theory of dense cyclically ordered sets with at least two elements. We determine the classifying space of $\mathsf {Mod}(T)$ to be homotopically equivalent to $\mathbb {CP}^\infty $. In particular, $\pi _2(\lvert \mathsf {Mod}(T)\rvert )=\mathbb {Z}$, which answers a question in our previous work. The computation is based on Connes’ cycle category $\Lambda $.

Few contemporary researchers in psychology, philosophy, and the cognitive sciences have any doubt about whether mental phenomena occur without being conscious. There is extensive and convincing clinical and experimental evidence for the existence of thoughts, desires, and related mental states that aren’t conscious. We characterize thoughts, desires, intentions, expectations, hopes, and many other mental states in terms of the things they are about and, more fully, in terms of their content, as captured by a sentence nominalization, such as a clause (...) beginning with the word ‘that’. The philosophical literature follows Franz Brentano’s adaptation of Thomist terminology in referring to all such states as intentional states. But there is another type of mental phenomena, which lack intentionality and whose mental nature consists instead of some qualitative feature. These states include bodily sensations, such as aches and pains, and perceptual states, such as visual sensations of color and tactile sensations of heat and cold. And these states all exhibit some mental quality or another, such as the mental quality distinctive of pain or the mental quality of red or blue.1 And even theorists who acknowledge that intentional states can and do occur without being conscious have sometimes insisted that qualitative states cannot. There is, according to these theorists, nothing to a state’s being qualitative or exhibiting some mental quality unless that state is conscious – unless it is, as we might metaphorically say, “lighted up”. It’s striking that Freud himself seems to have adopted this double standard toward the two types of mental state. In his metapsychological paper, “The Unconscious”, for example, he writes that “all the categories which we employ to describe conscious mental acts, such as ideas, purposes, resolutions, and so forth, can be applied to [unconscious mental occurrences]” (Freud 1915e, p. 168). But he seems here to have in.. (shrink)

The eta rule for a set A says that an arbitrary element of A is judgementally identical to an element of constructor form. Eta rules are not part of what may be called canonical Martin-Löf type theory. They are, however, justified by the meaning explanations, and a higher-order eta rule is part of that type theory. The main aim of this paper is to clarify this somewhat puzzling situation. It will be argued that lower-order eta rules do (...) not, whereas the higher-order eta rule does, accord with the understanding of judgemental identity as definitional identity. A subsidiary aim is to clarify precisely what an eta rule is. This will involve showing how such rules relate to various other notions of type theory, proof theory, and category theory. (shrink)

The role of emotional creativity in practicing creative leisure activities and in the preference of college majors remains unknown. The present study aims to explore how emotional creativity measured by the Emotional Creativity Inventory (ECI; Averill, 1999) is interrelated with the real-life involvement in different types of specific creative leisure activities and with four categories of college majors. Data were collected from 251 university students, university graduates and young adults (156 women and 95 men). Art students and graduates scored (...) significantly higher on the ECI than other majors. Humanities scored significantly higher than technical/economic majors. Five creative leisure activities were significantly correlated with the ECI, specifically, writing, painting, composing music, performing drama, and do-it-yourself home improvement. Keywords: Creativity, Emotional Creativity, Emotions, Creativeness, Affect, Feelings, Leisure Activities, Creative Ability, Artistic Creativity, Creative Thinking, Creativeness, Aging, Cognitive Deficits, Performance. MeSH Headings: Emotions, Creativity, Leisure, Leisure Activities, Hobbies, Recreation, Affect Affective Symptoms, Creativeness. (shrink)

In this paper I compare two well studied approaches to topological semantics – the domain-theoretic approach, exemplified by the category of countably based equilogical spaces, Equ and Typ Two Effectivity, exemplified by the category of Baire space representations, Rep . These two categories are both locally cartesian closed extensions of countably based T0-spaces. A natural question to ask is how they are related.First, we show that Rep is equivalent to a full coreflective subcategory of Equ, consisting of the so-called (...) 0-equilogical spaces. This establishes a pair of adjoint functors between Rep and Equ. The inclusion Rep → Equ and its coreflection have many desirable properties, but they do not preserve exponentials in general. This means that the cartesian closed structures of Rep and Equ are essentially different. How ever, in a second comparison we show that Rep and Equ do share a common cartesian closed subcategory that contains all countably based-T0 spaces. Therefore, the domain-theoretic approach and TTE yield equivalent topological semantics of computation for all higher-order types over countably based T0-spaces. We consider several examples involving the natural numbers and the real numbers to demonstrate how these comparisons make it possible to transfer results from one setting to another. (shrink)

Positive public perceptions of academic quality and professional ethics are critical to the long-term legitimacy of American colleges and universities. Faculty codes of conduct are one mechanism whereby the professoriate can define acceptable practice, exercise social control, and maintain public confidence in higher education, yet the drivers of their adoption are not well understood. Building upon previous research into such organizational behavior by institutional type, this study examined the prevalence and content of publicly posted faculty codes of conduct (...) within an organizational field of institutions that share a common religious identity but differ in their institutional types and employment structures. Faculty handbooks from American member institutions of the Council for Christian Colleges & Universities, an international association of faith-based institutions, were gathered and analyzed. Although only 27% of CCCU member institutions in the U.S. publicly posted faculty codes of conduct, the average number of tenets present in each code was higher than suggested by previous research. Study findings also revealed that membership category, institutional type, and employment structures influence the content of faculty codes of conduct, indicating that isomorphic pressures operate within this particular organizational field. The piece concludes by commending publicly posted codes of conduct as an affirmation of the personal responsibility, fairness, and care exercised by ethical professionals in the academy. (shrink)

In the paper there are introduced and discussed the concepts of an indexed category with quantifications and a higher level indexed category to present an algebraic characterization of some version of Martin-Löf Type Theory. This characterization is given by specifying an additional equational structure of those indexed categories which are models of Martin-Löf Type Theory. One can consider the presented characterization as an essentially algebraic theory of categorical models of Martin-Löf Type Theory. The paper contains (...) a construction of an indexed category with quantifications from terms and types of the language of Martin-Löf Type Theory given in the manner of Troelstra [11]. The paper contains also an inductive definition of a valuation of these terms and types in an indexed category with quantifications. (shrink)

Ambiguity is a property of syntactic expressions which is ubiquitous in all informal languages–natural, scientific and mathematical; the efficient use of language depends to an exceptional extent on this feature. Disambiguation is the process of separating out the possible meanings of ambiguous expressions. Ambiguity is typical if the process of disambiguation can be carried out in some systematic way. Russell made use of typical ambiguity in the theory of types in order to combine the assurance of its (apparent) consistency (“having (...) the cake”) with the freedom of the informal untyped theory of classes and relations (“eating it too”). The paper begins with a brief tour of Russell’s uses of typical ambiguity, including his treatment of the statement Cls ∈ Cls. This is generalized to a treatment in simple type theory of statements of the form A ∈ B where A and B are class expressions for which A is prima facie of the same or higher type than B. In order to treat mathematically more interesting statements of self membership we then formulate a version of typical ambiguity for such statements in an extension of Zermelo-Fraenkel set theory. Specific attention is given to how the“naive” theory of categories can thereby be accounted for. (shrink)

Still, some may still want to say it. If so, my replies may gain nothing better than a stalemate against such persistence, though I can hope that earlier revelations will discourage others from persisting. But two replies are possible. Both come down, one circuitously, to an issue with us from the beginning: whether the language of the right side of (10) is suspect. For if (10) is to support instances for (6) which are about objects, that clause must itself be (...) about objects. (These would be ones assigned by variants of I it mentions to constants it mentions.) Yet Barwise and I would call it implicitly about functions. Ironically, the discussion surrounding (10), hoping to settle that issue, could only do so if the issue were already settled, revealing decisively the ontology of (10). If irritating, this is also inevitable, given the Tarskian spirit of the ensivioned semantics for QLB.A second reply begins by noting that a QLB semantics which implies (10) cannot simply be assumed. Even a QL semantics augmented to imply (11) is not trivial to frame, as I will let readers confirm. On the QLB project, Barwise comments thus:It is not possible to explain the meaning of an essential use of branching quantification ... inductively, by treating one quantifier at a time in a first-order fashion. Some use of higher-type abstract objects is essential. (BQE75)But believers in a modest ontology for QLB can claim a non sequitur here. For (10), as they read it, succeeds without mentioning abstract objects, though not in the “one quantifier at a time” way which Barwise rightly finds impossible. This is not yet to say the same about a QLB semantics implying (10). But that too can be said, as it happens, with as good a conscience as with (10). A suitable treatment can begin by somehow linearizing non QL sentences like (6). Still assuming prefixes whose rows each consist, speaking loosely, of n universal quantifiers followed by a single existential, we could simply line up these rows in any order, with unique deconcatenatability being assured. From then on, it gets both tedious and complex. A full syntax is essential, and some surprising categories arose in mine. I will spare readers all details, except to say that one can indeed “treat one quantifier at a time”, if not “in first-order fashion”: schematic rules for treating n quantifiers at once can be eschewed. Unsurprisingly, heavy use is made of the “depending only on” idiom seen in (10). Nor does it surprise me that this semantics can succeed, with that idiom available. Roughly, if open talk about functions works in a semantics for QLF, what I read as implicit talk about them should work in a semantics for QLB See [6] for a start on a semantics aspiring to handle sentences like (6) without invoking abstract objects. See also my comments on its notion of dependence, in [9]. . So even from a bare sketch, we can see that this new semantics settles nothing. It just leads back to the stalemate. Barwise and I will read crucial clauses as talking implicitly about functions, but this general charge against an idiom is equally deniable wherever the idiom occurs: in a reading for (6), say, or in the metalanguage can hardly repress a motherhood slogan: better dead than obscurely read. But that just denies the denial, unhelpfully. A better comment is the reminder that the claim stays alive only in a form which no one has ever imagined for it. The QLB quantifiers that cannot be shown not to range over objects are not the items anyone would ever have pointed to in illustrating the unkillable claim. (shrink)

Nietzsche’s Anti-Darwinism. By Dirk R. Johnson (Cambridge: Cambridge University Press, 2010) In this substantial and incisive monograph, Dirk R. Johnson traces in minute detail Nietzsche’s stance towards Darwin at the various stages of his intellectually productive life. Johnson’s book is in two principal parts: Part 1 is on Nietzsche’s early Darwinism, which turned into anti-Darwinism, and Part 2 is a close reading of all three essays of Nietzsche’s Genealogy of Morals in their historical context since together they constitute “his most (...) systematic, thorough, and far-reaching analysis of the theories of Darwin and their followers” (81, 111). The author concedes that Nietzsche’s exchange with Darwin (1809–82), who was a contemporary of Nietzsche (1944–1900), is often implicit only and that he leads his explicit discussions of Darwin mostly in his unpublished notebooks. I agree with Johnson’s view that Nietzsche knew Darwin’s thought and its implications both “early and well’ (3). Johnson provides compelling evidence of the “increased personalization” of Nietzsche’s opposition to Darwinism during his last productive years after Zarathustra. For instance, Nietzsche entitled section 9,14 of Twilight of the Idols “Anti-Darwin,” and explained that “his position at this stage resulted both from his critical reappraisal of Darwin’s genealogical perspectives in the middle period and his attempt in Zarathustra to define the parameters of an affirmative, anti-metaphysical vision beyond Darwinism” (79). He argues that Zarathustra trans-values Darwinian categories such as “reason.” For him, “the work’s literary self-expression is the message,” since the superior well-being of the future higher type “can only be conjured through poetic affirmation” (48, 50). (shrink)

A hyperintensional semantics for natural language is proposed which is agnostic about the question of whether propositions are sets of worlds or worlds are sets of propositions. Montague’s theory of intensional senses is replaced by a weaker theory, written in standard classical higher-order logic, of fine-grained senses which are in a many-to-one correspondence with intensions; Montague’s theory can then be recovered from the proposed theory by identifying the type of propositions with the type of sets of worlds (...) and adding an axiom to the effect that each world is the set of propositions which are true there. Senses are compositionally assigned to linguistic expressions by a categorial grammar with only two rule schemas, based on the implicative fragment of intuitionistic linear propositional logic, and a fully explicit grammar fragment is provided that illustrates the compositional assignment of sense to a variety of constructions, including dummy-subject constructions, infinitive complements, predicative adjectives and nominals, raising to subject, ‘tough-movement’, and quantifier scope ambiguities. Notably, the grammar and the derivations that it licenses never make reference to either worlds or to the extensions of senses. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...) propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develops a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for two-dimensional (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between Elohim's hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for two-dimensional hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. Elohim invents a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Elohim provides a counter-example to epistemic closure for logical deduction. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

Life strategy in personal dimension could be identified as a complex phenomenon, which includes main key dimensions and categories that characterize person’s life and behavior. Life strategy is a way of life self-determining, self-establishing, self-expression and self-organizing as well as the ability to bring living conditions according with personality own values and individual uniqueness. The student life strategies directly connected with higher education. Author’s sociological research examines the main features of life strategies of modern Ukrainian students. In the (...) article, the author's typology of the main types of life strategies of students is proposed. The tipology reflects the crucial connection with the appropriate understanding of the place and role of higher education: career-pragmatic, universal education, and adaptive-conformist. (shrink)

Often professors of higher education do not recognize the difference between teaching subject matter and teaching students. They emulate their former professor mentors without much analysis of the assets/liabilities of classroom behaviors. The absence of teaching methods in the teaching curriculum of college/university contributes to the problem. The following article describes a composite picture of the esteemed professorate depicted by an accumulation of life experiences, student stories, professorial reputations and caricatures. The categories of professorial type do not (...) represent exclusivity, but indeed are anticipated to overlap. The professorate needs to strive to use teaching methods which empower students to learn, just as we all strive to encourage the corporate world to empower their employees. (shrink)

This study investigates the types of misinformation spread on Twitter that evokes scientific authority or evidence when making false claims about the antimalarial drug hydroxychloroquine as a treatment for COVID-19. Specifically, we examined tweets generated after former U.S. President Donald Trump retweeted misinformation about the drug using an unsupervised machine learning approach called the biterm topic model that is used to cluster tweets into misinformation topics based on textual similarity. The top 10 tweets from each topic cluster were content coded (...) for three types of misinformation categories related to scientific authority: medical endorsements of hydroxychloroquine, scientific information used to support hydroxychloroquine’s use, and a comparison group that included scientific evidence opposing hydroxychloroquine’s use. Results show a much higher volume of tweets featuring medical endorsements and use of supportive scientific information compared to accurate and updated scientific evidence, that misinformation-related tweets propagated for a longer time frame, and the majority of hydroxychloroquine Twitter discourse expressed positive views about the drug. Metadata from Twitter accounts found that prominent users within misinformation discourse were more likely to have media or political affiliation and explicitly expressed support for President Trump. Conversely, prominent accounts within the scientific opposition discourse primarily consisted of medical doctors or scientists but had far less influence in the Twitter discourse. Implications of these findings and connections to related social media research are discussed, as well as cognitive mechanisms for understanding susceptibility to misinformation and strategies to combat misinformation spread via online platforms. (shrink)

By comparing three types of hybrid organizations—18th-century scientific academies, 19th-century institutions of higher vocational education, and 20th-century industrial research institutes—it is the purpose here to answer the question of why new hybrid organizations are continuously formed. Traditionally, and often implicitly, it is often assumed that emerging groups of potential knowledge users have their own organizational preferences and demands influencing the setup of new hybrid organizations. By applying the concepts epistemic and academic drift, it will be argued here, however, that (...) internal organizational dynamics are just as important as changing historical conjunctures in the uses of science when understanding why new hybrid organizations are formed. Only seldom have older hybrid organizations sought to make themselves relevant to new categories of knowledge users as the original ones have been marginalized. Instead, they have tended to accede to ideals supported by traditional academic organizations with higher status in terms of knowledge management, primarily universities. Through this process, demand has been generated for the founding of new hybrid organizations rather than the transformation of existing ones. Although this study focuses on Swedish cases, it is argued that since Sweden strove consistently to implement existing international policy trends during the periods in question, the observations may be generalized to apply to other national and transnational contexts. (shrink)

We study, from a classical point of view, how the truth of a statement about higher type functionals depends on the underlying model. The models considered are the classical set-theoretic finite type hierarchy and the constructively more meaningful models of continuous functionals, hereditarily effective operations, as well as the closed term model of Gödel's system T. The main results are characterisations of prenex classes for which truth in the full set-theoretic model transfers to truth in the other (...) models. As a corollary we obtain that the axiom of choice is not conservative over Gödel's system T with classical logic for closed ∃2-formulas. We hope that this study will contribute to a clearer delineation and perception of constructive mathematics from a classical perspective. (shrink)

Life strategy in personal dimension could be identified as a complex phenomenon, which includes main key dimensions and categories that characterize person’s life and behavior. Life strategy is a way of life self-determining, self-establishing, self-expression and self-organizing as well as the ability to bring living conditions according with personality own values and individual uniqueness. The student life strategies directly connected with higher education. Author’s sociological research examines the main features of life strategies of modern Ukrainian students. In the (...) article, the author's typology of the main types of life strategies of students is proposed. The tipology reflects the crucial connection with the appropriate understanding of the place and role of higher education: career-pragmatic, universal education, and adaptive-conformist. (shrink)

It is shown how to restrict recursion on notation in all finite types so as to characterize the polynomial-time computable functions. The restrictions are obtained by using a ramified type structure, and by adding linear concepts to the lambda calculus.

In this article, we analyzed the effect of various factors on moral judgment and ethical attitudes of working persons. It was found that the effect of various socio-demographic factors on ethical attitudes varied between the two different categories of ethical issues under study, issues which involve explicit violation of laws vis-à-vis issues which involved social concerns. Our results did not support the implication of Callahan’s hypothesis that males are more sensitive to rule-based ethical issues while women are to issues (...) involving social concerns; it was found that females have a lower acceptability of unethical behaviors related to both categories of issues in Hong Kong, whereas gender effect was not statistically significant in Mainland China. University education also had no significant effect on ethical attitudes. Religion played an important role in affecting ethical attitudes, however, its effect varied with different types of religions; Christianity was found to be most favorable to higher ethical standards, but people of traditional Chinese religion had a higher acceptability of unethical behaviors involving social concerns compared to people with no religion. Our finding also indicated that employees in state-owned enterprises, private employees, employees in foreign-investment firms, and employers in Mainland China all had a higher acceptability of unethical law-breaking behaviors compared to workers in collectives, throwing doubt on the validity of convergence theory in Mainland China. (shrink)

In previous work the author has introduced a lambda calculus SLR with modal and linear types which serves as an extension of Bellantoni–Cook's function algebra BC to higher types. It is a step towards a functional programming language in which all programs run in polynomial time. In this paper we develop a semantics of SLR using BCK -algebras consisting of certain polynomial-time algorithms. It will follow from this semantics that safe recursion with arbitrary result type built up from (...) N and ⊸ as well as recursion over trees and other data structures remains within polynomial time. In its original formulation SLR supported only natural numbers and recursion on notation with first-order functional result type. (shrink)

Student authentication and authorship checking systems are intended to help teachers address cheating and plagiarism. This study set out to investigate higher education teachers’ perceptions of the prevalence and types of cheating in their courses with a focus on the possible changes that might come about as a result of an increased use of e-assessment, ways of addressing cheating, and how the use of student authentication and authorship checking systems might impact on assessment practice. This study was carried out (...) within the context of the project TeSLA (an Adaptive Trust-based e-assessment System for Learning) which is developing a system intended for integration within an institution’s Virtual Learning Environment (VLE) offering a variety of instruments to assure student authentication and authorship checking. Data was collected at two universities that were trialling the TeSLA system, one in Turkey, where the main modes of teaching are face-to-face teaching and distance education, and one in Bulgaria, where the main modes of teaching are face-to-face teaching and blended learning. The study used questionnaires and interviews, building on existing TeSLA project evaluation activities and extending these to explore the specific areas we wished to examine in more depth.In three of the four contexts cheating was seen by teachers as a serious and growing problem, the exception was the distance education context where the teachers believed that the existing procedures were effective in controlling cheating. Most teachers in all four contexts expected cheating to become a greater problem with increased use of e-assessment. Student authentication was not seen as a major problem in any of the contexts, as this was felt to be well controlled through face-to-face proctored assessments, though the problem of assuring effective authentication was seen by many teachers as a barrier to increased use of e-assessment. Authorship checking was seen as a major issue in all contexts, as copying and pasting from the web, ghost writing and plagiarism were all reported as widely prevalent, and authorship checking was seen as becoming even more important with increased use of e-assessment. Teachers identified a third category of cheating behaviours, which was the accessing of information from other students, from written materials, and from the internet during assessments.Teachers identified a number of approaches to addressing the problem of cheating: education, technology, assessment design, sanctions, policy, and surveillance. Whilst technology was not seen as the most important approach to prevention, student authentication and authorship checking systems were seen as relevant in terms of reducing reliance on face-to-face proctored examinations, and in improving the quality of assessment through supporting the employment of a wider range of assessment methods. The development of authorship checking based on computational linguistic approaches was an area of particular interest. Student authentication and authorship checking systems were not seen as being able to address the third category of cheating behaviours that the study identified. (shrink)

In recent years, there has been an increasing interest in unethical work behavior. Several types of survey instruments to collect information about unethical work behavior are available. Nevertheless, to date little attention has been paid to design issues of those surveys. There are, however, several important problems that may influence reliability and validity of questionnaire data on the topic, such as social desirability bias. This paper addresses two important issues in the design of online surveys on unethical work behavior: the (...) response scale for questions regarding the frequency of certain types of unethical work behavior and the location of the background questions in an online survey. We present the results of an analysis of a double split-ballot experiment in a large sample (n = 3,386) on governmental integrity. We found that, when comparing response scales that have labels for all categories with response scales that only have anchors at the end, the latter provided answers with higher validity. The study did not provide support for the conventional practice of asking background questions at the end. (shrink)

The structure of people’s conceptual knowledge of concrete nouns has traditionally been viewed as hierarchical (Collins & Quillian, 1969). For example, superordinate concepts (vegetable) are assumed to reside at a higher level than basic‐level concepts (carrot). A feature‐based attractor network with a single layer of semantic features developed representations of both basic‐level and superordinate concepts. No hierarchical structure was built into the network. In Experiment and Simulation 1, the graded structure of categories (typicality ratings) is accounted for by (...) the flat attractor network. Experiment and Simulation 2 show that, as with basic‐level concepts, such a network predicts feature verification latencies for superordinate concepts (vegetable ). In Experiment and Simulation 3, counterintuitive results regarding the temporal dynamics of similarity in semantic priming are explained by the model. By treating both types of concepts the same in terms of representation, learning, and computations, the model provides new insights into semantic memory. (shrink)

The pervasive use of distributional semantic models or word embeddings for both cognitive modeling and practical application is because of their remarkable ability to represent the meanings of words. However, relatively little effort has been made to explore what types of information are encoded in distributional word vectors. Knowing the internal knowledge embedded in word vectors is important for cognitive modeling using distributional semantic models. Therefore, in this paper, we attempt to identify the knowledge encoded in word vectors by conducting (...) a computational experiment using Binder et al.'s (2016) featural conceptual representations based on neurobiologically motivated attributes. In an experiment, these conceptual vectors are predicted from text‐based word vectors using a neural network and linear transformation, and prediction performance is compared among various types of information. The analysis demonstrates that abstract information is generally predicted more accurately by word vectors than perceptual and spatiotemporal information, and specifically, the prediction accuracy of cognitive and social information is higher. Emotional information is also found to be successfully predicted for abstract words. These results indicate that language can be a major source of knowledge about abstract attributes, and they support the recent view that emphasizes the importance of language for abstract concepts. Furthermore, we show that word vectors can capture some types of perceptual and spatiotemporal information about concrete concepts and some relevant word categories. This suggests that language statistics can encode more perceptual knowledge than often expected. (shrink)

According to one productive and influential approach to cognition, categorization, object recognition, and higher level cognitive processes operate on a set of fixed features, which are the output of lower level perceptual processes. In many situations, however, it is the higher level cognitive process being executed that influences the lower level features that are created. Rather than viewing the repertoire of features as being fixed by low-level processes, we present a theory in which people create features to subserve (...) the representation and categorization of objects. Two types of category learning should be distinguished. Fixed space category learning occurs when new categorizations are representable with the available feature set. Flexible space category learning occurs when new categorizations cannot be represented with the features available. Whether fixed or flexible, learning depends on the featural contrasts and similarities between the new category to be represented and the individual's existing concepts. Fixed feature approaches face one of two problems with tasks that call for new features: If the fixed features are fairly high level and directly useful for categorization, then they will not be flexible enough to represent all objects that might be relevant for a new task. If the fixed features are small, subsymbolic fragments (such as pixels), then regularities at the level of the functional features required to accomplish categorizations will not be captured by these primitives. We present evidence of flexible perceptual changes arising from category learning and theoretical arguments for the importance of this flexibility. We describe conditions that promote feature creation and argue against interpreting them in terms of fixed features. Finally, we discuss the implications of functional features for object categorization, conceptual development, chunking, constructive induction, and formal models of dimensionality reduction. Key Words: concept learning; conceptual development; features; perceptual learning; stimulus encoding. (shrink)

Generalized databases will be examined, in which attributes can be sets of attributes, or sets of sets of attributes, and other higher type constructs. A precise semantics will be developed for such databases, based on a higher type modal/intensional logic.

In 1936, Gerhard Gentzen published a proof of consistency for Peano Arithmetic using transfinite induction up to ε0, which was considered a finitistically acceptable procedure by both Gentzen and Paul Bernays. Gentzen’s method of arithmetising ordinals and thus avoiding the Platonistic metaphysics of set theory traces back to the 1920s, when Bernays and David Hilbert used the method for an attempted proof of the Continuum Hypothesis. The idea that recursion on higher types could be used to simulate the limit-building (...) in transfinite recursion seems to originate from Bernays. The main difficulty, which was already discovered in Gabriel Sudan’s nearly forgotten paper of 1927, was that measuring transfinite ordinals requires stronger methods than representing them. This paper presents a historical account of the idea of nominalistic ordinals in the context of the Hilbert Programme as well as Gentzen and Bernays’ finitary interpretation of transfinite induction. (shrink)

We show that the Lascar group $\operatorname {Gal}_L$ of a first-order theory T is naturally isomorphic to the fundamental group $\pi _1|)$ of the classifying space of the category of models of T and elementary embeddings. We use this identification to compute the Lascar groups of several example theories via homotopy-theoretic methods, and in fact completely characterize the homotopy type of $|\mathrm {Mod}|$ for these theories T. It turns out that in each of these cases, $|\operatorname {Mod}|$ is aspherical, (...) i.e., its higher homotopy groups vanish. This raises the question of which homotopy types are of the form $|\mathrm {Mod}|$ in general. As a preliminary step towards answering this question, we show that every homotopy type is of the form $|\mathcal {C}|$ where $\mathcal {C}$ is an Abstract Elementary Class with amalgamation for $\kappa $ -small objects, where $\kappa $ may be taken arbitrarily large. This result is improved in another paper. (shrink)

BackgroundResearch misconduct is a global concern in biomedical science. There are no comprehensive data regarding the perception and situation of scientific misconduct among the Iranian medical faculty members. We conducted a nationwide survey to assess the research misconduct among the medical faculty members in Iran.MethodsWe used the Persian version of the research misconduct questionnaire (PRMQ) on the Google Forms platform. We sent the survey link to a systematic random sample of medical faculty members in Iran (N = 4986). Descriptive analyses (...) were performed on the individual items of the PRMQ, with frequencies and percentages for categorical and Likert-type response items, and means and standard deviation (S.D.) for continuous variables. Chi-square analysis was conducted to test hypotheses examining differences in the frequency of responses related to factors influencing misconduct. We also defined four tenure categories (TC) based on the working years of the participants as tenured faculty members. All the analyses were performed using R 3.6.0.ResultsThe response rate was 13.8% (692 responses). Nearly 70% of the respondents agreed that their publication output would be of higher quality if there were no publication pressure. Approximately three-quarters (N =499, 72.1%) of the respondents had been aware of some instances of research misconduct during the previous year according to their understanding of misconduct. Among the participants, 18.5% perceived the effectiveness of their associated organisation’s rules for reducing research misconduct to be high or very high. Pressure for tenure was identified as the item most frequently perceived with a strong behavioural influence on engaging in research misconduct (80.2%).ConclusionsThis study confirms that research misconduct needs to be actively addressed among the medical faculty members. Making policies with a focus on boosting awareness regarding the occasions of scientific misconduct and its management seems to be indispensable in the future in Iran. (shrink)

He maintained that there are two main categories of truth: those that are a result of natural laws and those that are completely necessary since their opposite suggests contradiction. God can dispense solely with the latter rules, such as the law of human mortality. Although a doctrine of faith may conflict with second-type realities, it can never contradict first-type truths. Therefore, reason may not be able to completely understand an article of religion, even though it cannot be (...) self-contradictory. Simply put, mysteries like the Trinity are "above reason." However, how can we balance the odds in favor of a religious belief with those based on natural law and common experience? The presence and character of God, as well as the global harmony that underpins the providential creation and order of the universe, must all be considered when we make these choices. On the other hand, moving from the higher to the lower classes is also feasible. Since goodness has an immediate order to the higher pattern of the universal source of being, rational creatures are able to understand "the meaning of the good as such" (II-IIae q.2, a.3). The last good that theologians and philosophers examine is different; the former is the bonum ultimum, which can only be understood with the help of revelation, while the later is the beatific vision, which reason can understand. Both conceptions of the ultimate good have significant implications since they serve as the foundation for the political division between secular and ecclesiastical authority as well as the moral division between natural and supernatural virtues. (shrink)

Until Tarski’s semantic truth definition, the concept of truth was used informally in metalogic (metamathematics) or even proposed to be eliminated in favour of syntactic concepts, as in Rudolf Carnap’s early programme of philosophy via logical syntax. Tarski demonstrated that the concept of truth can be defined using precise mathematical devices. If L is a language for which the truth definition is given, it must be done in the metalanguage ML. According to this construction, semantics for L must be performed (...) in ML. The most important example concerns the arithmetic of natural numbers. According to Tarski’s theorem of undefinability, the set of truths of this theory cannot be defined in it – such a definition can be formulated in the metatheory. This fact illuminates the relation between syntax and semantics. If Th is a rich theory and presented as a syntactic theory (a calculus), its semantics is not reducible to its syntax. According to Tarski’s view, related to his work in the simple theory of types, semantics for L can be always constructed in the morphology of ML, provided that L is of the finite order. Two problems arise: what does the word “morphology” mean and how to formulate these ideas, when the framework is based on the distinction between first‑order logic and higher‑order logic. As far as the issue concerns morphology, it is possible to consider it as an extended syntax, i.e. vocabulary which does not refer to semantic concepts or defines such notions by not‑semantic, e.g. set‑theoretical, categories. If the hierarchy of logical types is replaced by the distinction of logics of various orders, in particular between first‑order and higher‑order (it is sufficient to use second‑order), it is possible to show that semantics of first‑order rich theories cannot be defined inside them. (shrink)

The current widespread belief that taxonomic methods used before Darwin were essentialist is ill-founded. The essentialist method developed by followers of Plato and Aristotle required definitions to state properties that are always present. Polythetic groups do not obey that requirement, whatever may have been the ontological beliefs of the taxonomist recognizing such groups. Two distinct methods of forming higher taxa, by chaining and by examplar, were widely used in the period between Linnaeus and Darwin, and both generated polythetic groups. (...) Philosopher William Whewell congratulated pre-Darwinian taxonomists for not adhering to the rigid ideal of definition used in the mathematical sciences. What he called the method of types is here called the method of exemplars because typology has been equated with essentialism, whereas the use of a type species as the reference point or prototype for a higher category was a practice inconsistent with essentialism. The story that the essentialism of philosophers dominated the development of systematics may prove to be a myth. (shrink)