Epstein et al. fail to show that L2 learners have full access to UG because they do not explain the relationship between UG and functional categories (FCs). Nor do they provide an explanation of why learners with (supposed) full knowledge of FCs fail to use them in a native-like way.

This commentary focuses on whether the full set of categories is available to beginning L2 learners. After critiquing Epstein et al.'s experimental evidence for the presence of functional categories, I outline the results of an experiment involving English speakers learning Japanese as a second language that does indeed point toward the early presence of fuuctional categories.

A notion of resource-bounded Baire category is developed for the class PC[0,1] of all polynomial-time computable real-valued functions on the unit interval. The meager subsets of PC[0,1] are characterized in terms of resource-bounded Banach-Mazur games. This characterization is used to prove that, in the sense of Baire category, almost every function in PC[0,1] is nowhere differentiable. This is a complexity-theoretic extension of the analogous classical result that Banach proved for the class C[0, 1] in 1931.

A notion of resource‐bounded Baire category is developed for the classPC[0,1]of all polynomial‐time computable real‐valued functions on the unit interval. The meager subsets ofPC[0,1]are characterized in terms of resource‐bounded Banach‐Mazur games. This characterization is used to prove that, in the sense of Baire category, almost every function inPC[0,1]is nowhere differentiable. This is a complexity‐theoretic extension of the analogous classical result that Banach proved for the classC[0, 1] in 1931. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim).

IN THE FIRST EDITION TRANSCENDENTAL DEDUCTION of the categories Kant does not mention the logical functions of judgment. In the second edition the Deduction can be said to be dominated by the logical functions of judgment. A transcendental deduction supplies a method for showing that pure concepts can have applicability. My contention is that the two deductions constitute exactly the same method, and so are the exact same deduction. The difference between them, rather, is in the characterization of the (...) pure concepts that the method is supposed to be a method for. The undifferentiated categories of the A edition become the logical functions together with their schemata in the B edition. This does not mean that Kant has split the A edition notion of categories since the A edition categories are equivalent to just the schemata themselves. (shrink)

The relevance of the research is defined by the need to create a set of linguistic means, which would contribute to effective communication with the general public, and the need to study different functional-semantic categories, including appeals, for the competent formation of public opinion in the political context. The research aims to comprehend the functioning of linguistic means used as appeals in the example of political propaganda texts in the English media field. The methodology is based on the (...) theoretical study of the works of modern linguists, linguistic, structural, and communicative analysis of appeal linguistic units and contexts. The research considered the linguistic means that form the functional-semantic category of the appeal, examples of political contexts from the British and American media were presented, the functions of appeal were presented using specific examples, an idea of the communicative side of political propaganda texts and audience participation in this process was formed, emphasis was placed on different types of propaganda (white, black, gray), the following groups of appeals were characterized: imperatives (volitional and involuntary). The materials presented in this research can be used to form an idea of the functional-semantic category of appeal, the choice of linguistic means for the purpose of information promotion in the media or social networks, the study of communicative strategies in linguistics and their successful implementation, consideration of political propaganda texts, increasing efficiency when influencing the audience, further implementation of means of appeal in machine learning. (shrink)

This paper introduces λ-grammar, a form of categorial grammar that has much in common with LFG. Like other forms of categorial grammar, λ-grammars are multi-dimensional and their components are combined in a strictly parallel fashion. Grammatical representations are combined with the help of linear combinators, closed pure λ-terms in which each abstractor binds exactly one variable. Mathematically this is equivalent to employing linear logic, in use in LFG for semantic composition, but the method seems more practicable.

The characteristics of the meaning of inexpressible is given in the article. It is shown that in the Russian language semantics of inexpressible is represented as a binary functional-semantic category. It was determined that the nuances of semantics of inexpressible can be represented in the form of a gradational scale on which they are distributed within the opposition ‘complete inexpressibleness - complete expressibility‘. The components of the situation of inexpressibleness inherent the means of transference of the value of inexpressible (...) are described. It is shown that the definition of the components of situation of inexpressible contribute to the modeling of the field of semantics of inexpressible: what the concept of inexpressible means, in which situations semantics of inexpressible manifests itself; for whom this situation arises, how it is solved, can it be solved; by what means of language, speech and other semiotic systems it is expressed. It is determined that the situation of inexpressible includes seven components: the subject of speech inexpressibleness; an action that is impossible to express the statement; inexpressibility result of the process; objectivity of the situation described; reasons of inexpressibleness; the object of this situation; spatial area of the situation of inexpressibleness. It is shown that the central part of the functional-semantic field model components number 2, 3 and 4. The private values of the field of semantics of inexpressible were described for the first time. The definition of gradation nuances of inexpressibleness considering the paradigmatic and syntagmatic aspects of the study of the semantics were carried out for the first time. (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)

The goal of this paper is to develop a systematic taxonomy of cognitive artifacts, i.e., human-made, physical objects that functionally contribute to performing a cognitive task. First, I identify the target domain by conceptualizing the category of cognitive artifacts as a functional kind: a kind of artifact that is defined purely by its function. Next, on the basis of their informational properties, I develop a set of related subcategories in which cognitive artifacts with similar properties can be grouped. In (...) this taxonomy, I distinguish between three taxa, those of family, genus, and species. The family includes all cognitive artifacts without further specifying their informational properties. Two genera are then distinguished: representational and non-representational (or ecological) cognitive artifacts. These genera are further divided into species. In case of representational artifacts, these species are iconic, indexical, or symbolic. In case of ecological artifacts, these species are spatial or structural. Within species, token artifacts are identified. The proposed taxonomy is an important first step towards a better understanding of the range and variety of cognitive artifacts and is a helpful point of departure, both for conceptualizing how different artifacts augment or impair cognitive performance and how they transform and are integrated into our cognitive system and practices. (shrink)

General extenders are phrases like 'or something', 'and everything', 'and things ', 'and stuff ', and 'and so on'. Although they are an everyday feature of spoken language, are crucial in successful interpersonal communication, and have multiple functions in discourse, they have so far gone virtually unnoticed in linguistics. This pioneering work provides a comprehensive description of this new linguistic category. It offers new insights into ongoing changes in contemporary English, the effect of grammaticalization, novel uses as associative plural markers (...) and indicators of intertextuality, and the metapragmatic role of extenders in interaction. The forms and functions of general extenders are presented clearly and accessibly, enabling students to understand a number of different frameworks of analysis in discourse-pragmatic studies. From an applied perspective, the book presents a description of translation equivalents, an analysis of second language variation, and practical exercises for teaching second language learners of English. (shrink)

The aim of this investigation is to discuss the merits of the three radically divergent views as to the nature and function of the categories held by Kant, Ward and Alexander.

It may seem trivial to state that one of the major trends in biological investigation consists in an attempt to explain the structural and functional aspects of living matter in chemical terms, in an effort to obtain insight into the equivalent of macroscopic phenomena on the molecular level. I am sure you are aware of, and this meeting of the Association has brought ample additional evidence, in how many fields this tendency has become apparent. It can be recognized in (...) genetics with the molecular analysis of chromosomes and the enzymatic or metabolic interpretation of hereditary properties like the eyecolor of Drosophila. In a purely morphological branch like histology we do not ask merely for a differentiation of stained cell structure but we ask for the nature of the staining reaction; in nerve physiology we try to interpret conduction as alterations of protein lipoid layers; or in pathology where the age old syndrome of inflammation is explored with biochemical methods. I should mention molecular models of membranes and cell surfaces, the molecular interpretation of secretion and of the macroscopic phenomena of metabolism. Yet insofar as this yield of data could be designated as a trend, it would rather seem to be the natural outcome to be expected from the application of the analytic method of science. In one instance, however, this approach has been carried farther than in all the other fields, and it would seem to be worthwhile to pause for one moment to ask whether this case is important merely because of its technical implications or whether it is meaningful in a wider sense. (shrink)

I defend the view that many biological categories are defined by homology against a series of arguments designed to show that all biological categories are defined, at least in part, by selected function. I show that categories of homology are `abnormality inclusive'—something often alleged to be unique to selected function categories. I show that classifications by selected function are logically dependent on classifications by homology, but not vice-versa. Finally, I reject the view that biologists must use (...) considerations of selected function to abstract away from variation and pathology to form a canonical description of a class of biological systems. (shrink)

The sound system of a language must be able to support a perceptual contrast between different words in order to signal communicatively relevant meaning distinctions. In this paper, we use a simple agent-based exemplar model in which the evolution of sound-category systems is understood as a co-evolutionary process, where the range of variation within sound categories is constrained by functional pressure to keep different words perceptually distinct. We show that this model can reproduce several observed effects on the (...) range of sound variation. We argue that phonological systems can be seen as finding a relative optimum of variation: Efficient communication is sustained while at the same time, hidden category variation provides pathways for future evolution. (shrink)

Verbs and nouns gear θ-dependencies, Case, agreement, or construal relations. Building on Chomsky’s 1974 decomposition of such categories into ±N, ±V features, by translating said features into ±1, ±i scalars that allow for the construction of a vector space, this paper studies the possibility of organizing said features into 2 × 2 square matrices. In the system proposed to explore “head-complement” relations, operating on nouns yields a measurable/observable (Hermitian matrix), which in turn limits other potential combinations with abstract lexical (...) categories. Functional/grammatical categories in the system deploy the same features, albeit organized differently in the matrix diagonal and off-diagonal. The algebraic result is a group with well-defined mathematical properties, which properly includes the Pauli group of standard use in quantum computation. In the system, the presumed difference between categories and interactions—here, in a context of the head-complement sort—reduces to whether the magnitude of the matrix eigenvalue is 1 or not, in the latter instance inducing asymmetric interactions. (shrink)

An introduction to category theory as a rigorous, flexible, and coherent modeling language that can be used across the sciences. Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics. This book shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences. Information is inherently dynamic; the same (...) ideas can be organized and reorganized in countless ways, and the ability to translate between such organizational structures is becoming increasingly important in the sciences. Category theory offers a unifying framework for information modeling that can facilitate the translation of knowledge between disciplines. Written in an engaging and straightforward style, and assuming little background in mathematics, the book is rigorous but accessible to non-mathematicians. Using databases as an entry to category theory, it begins with sets and functions, then introduces the reader to notions that are fundamental in mathematics: monoids, groups, orders, and graphs—categories in disguise. After explaining the “big three” concepts of category theory—categories, functors, and natural transformations—the book covers other topics, including limits, colimits, functor categories, sheaves, monads, and operads. The book explains category theory by examples and exercises rather than focusing on theorems and proofs. It includes more than 300 exercises, with solutions. Category Theory for the Sciences is intended to create a bridge between the vast array of mathematical concepts used by mathematicians and the models and frameworks of such scientific disciplines as computation, neuroscience, and physics. (shrink)

Previous research has found a rich lexicon of shame and guilt terms in Chinese, but how comparable these terms are to “shame” or “guilt” in English remains a question. We identified eight commonly used Chinese terms translated as “shame” and “guilt”. Study 1 assessed the Chinese terms’ intensities, social characteristics, and action tendencies among 40 Chinese speakers. Testing term production in the reverse direction, Study 2 asked another Chinese-speaking sample (N = 85) to endorse emotion terms in response to eight (...) eliciting scenarios generated using each term’s social characteristics from Study 1. A native English-speaking sample (N = 83) was also included to examine the production of English emotion terms and compare motivational tendencies cross-culturally. Using this cross-referencing method, we found that some of the Chinese terms shared similar social-functional characteristics to their English translation, but some had distinct profiles. The two large shame-like and guilt-like term categories yielded in Study 1 were replicated in Study 2’s Chinese term-production task where larger-scale correspondences between categorised elicitors and term clusters were found. Meanwhile, English speakers’ term use provided further evidence for the equivalence between some Chinese terms and “shame” or “guilt” both in terms of their social and motivational characteristics. (shrink)

One well known problem regarding quantifiers, in particular the 1storder quantifiers, is connected with their syntactic categories and denotations. The unsatisfactory efforts to establish the syntactic and ontological categories of quantifiers in formalized first-order languages can be solved by means of the so called principle of categorial compatibility formulated by Roman Suszko, referring to some innovative ideas of Gottlob Frege and visible in syntactic and semantic compatibility of language expressions. In the paper the principle is introduced for categorial (...) languages generated by the Ajdukiewicz’s classical categorial grammar. The 1st-order quantifiers are typically ambiguous. Every 1st-order quantifier of the type k > 0 is treated as a two-argument functorfunction defined on the variable standing at this quantifier and its scope (the sentential function with exactly k free variables, including the variable bound by this quantifier); a binary function defined on denotations of its two arguments is its denotation. Denotations of sentential functions, and hence also quantifiers, are defined separately in Fregean and in situational semantics. They belong to the ontological categories that correspond to the syntactic categories of these sentential functions and the considered quantifiers. The main result of the paper is a solution of the problem of categories of the 1st-order quantifiers based on the principle of categorial compatibility. (shrink)

Philosophers of evolutionary biology favor the so-called etiological concept of function according to which the function of a trait is its evolutionary purpose, defined as the effect for which that trait was favored by natural selection. We term this the selected effect (SE) analysis of function. An alternative account of function was introduced by Robert Cummins in a non-evolutionary and non-purposive context. Cummins''s account has received attention but little support from philosophers of biology. This paper will show that a similar (...) non-purposive concept of function, which we term causal role (CR) function, is crucial to certain research programs in evolutionary biology, and that philosophical criticisms of Cummins''s concept are ineffective in this scientific context. Specifically, we demonstrate that CR functions are a vital and ineliminable part of research in comparative and functional anatomy, and that biological categories used by anatomists are not defined by the application of SE functional analysis. Causal role functions are non-historically defined, but may themselves be used in an historical analysis. Furthermore, we show that a philosophical insistence on the primary of SE functions places practicing biologists in an untenable position, as such functions can rarely be demonstrated (in contrast to CR functions). Biologists who study the form and function of organismal design recognize that it is virtually impossible to identify the past action of selection on any particular structure retrospectively, a requirement for recognizing SE functions. (shrink)

One well known problem regarding quantifiers, in particular the 1st order quantifiers, is connected with their syntactic categories and denotations.The unsatisfactory efforts to establish the syntactic and ontological categories of quantifiers in formalized first-order languages can be solved by means of the so called principle of categorial compatibility formulated by Roman Suszko, referring to some innovative ideas of Gottlob Frege and visible in syntactic and semantic compatibility of language expressions. In the paper the principle is introduced for categorial (...) languages generated by the Ajdukiewicz’s classical categorial grammar. The 1st-order quantifiers are typically ambiguous. Every 1st-order quantifier of the type k > 0 is treated as a two-argument functor-function defined on the variable standing at this quantifier and its scope (the sentential function with exactly k free variables, including the variable bound by this quantifier); a binary function defined on denotations of its two arguments is its denotation. Denotations of sentential functions, and hence also quantifiers, are defined separately in Fregean and in situational semantics. They belong to the ontological categories that correspond to the syntactic categories of these sentential functions and the considered quantifiers. The main result of the paper is a solution of the problem of categories of the 1st-order quantifiers based on the principle of categorial compatibility. (shrink)

Focusing on Weibo and Twitter, this study adopts computer-mediated discourse analysis to examine how influencers use emoji sequences when engaging in self-presentation. It identified a variety of text-based speech acts, emoji functions, and functional relations by conducting speech act and pragmatic function analysis. ‘Claim’ is the most common text-based speech act accompanying with emoji sequences in both data groups; however, the former had a higher percentage than the later. Moreover, emoji functioning as a combination of ‘stance and action’ in (...) sequences comprise the most prominent category in the Twitter data, whereas the ‘concept’ function accounts for the largest percentage within the Weibo data. Finally, emoji sequences serving as ‘emphasis on text’ is most employed in connection with accompanying texts in both data. This study also observed how a lack of user-desired emoji may be compensated for through collocation of emoji sequences, a device which involves significant creativity and intricacy. (shrink)

Category-specific impairments of object recognition and naming are among the most intriguing disorders in neuropsychology, affecting the retrieval of knowledge about either living or nonliving things. They can give us insight into the nature of our representations of objects: Have we evolved different neural systems for recognizing different categories of object? What kinds of knowledge are important for recognizing particular objects? How does visual similarity within a category influence object recognition and representation? What is the nature of our semantic (...) knowledge about different objects? We review the evidence on category-specific impairments, arguing that deficits even for one class of object cannot be accounted for in terms of a single information processing disorder across all patients; problems arise at contrasting loci in different patients. The same apparent pattern of impairment can be produced by damage to different loci. According to a new processing framework for object recognition and naming, the hierarchical interactive theory, we have a hierarchy of highly interactive stored representations. HIT explains the variety of patients in terms of lesions at different levels of processing and different forms of stored knowledge used both for particular tasks and for particular categories of object. Key Words: category-specific deficits; functional imaging; hierarchical models; interactive activation models; neuropsychology; object recognition; perceptual and functional knowledge. (shrink)

Numerous research groups are now utilizing Basic Formal Ontology as an upper-level framework to assist in the organization and integration of biomedical information. This paper provides elucidation of the three existing BFO subcategories of realizable entity, namely function, role, and disposition. It proposes one further sub-category of tendency, and considers the merits of recognizing two sub-categories of function for domain ontologies, namely, artifactual and biological function. The motivation is to help advance the coherent ontological treatment of functions, roles, and (...) dispositions, to help provide the potential for more detailed classification, and to shed light on BFO’s general make-up and use. (shrink)

I defend the historical definition of "function" originally given in my Language, Thought and Other Biological Categories (1984a). The definition was not offered in the spirit of conceptual analysis but is more akin to a theoretical definition of "function". A major theme is that nonhistorical analyses of "function" fail to deal adequately with items that are not capable of performing their functions.

“Functional homology” appears regularly in different areas of biological research and yet it is apparently a contradiction in terms—homology concerns identity of structure regardless of form and function. I argue that despite this conceptual tension there is a legitimate conception of ‘homology of function’, which can be recovered by utilizing a distinction from pre-Darwinian physiology (use versus activity) to identify an appropriate meaning of ‘function’. This account is directly applicable to molecular developmental biology and shares a connection to the (...) theme of hierarchy in homology. I situate ‘homology of function’ within existing definitions and criteria for structural assessments of homology, and introduce a criterion of ‘organization’ for judging function homologues, which focuses on hierarchically interconnected interdependencies (similar to relative position and connection for skeletal elements in structural homology). This analysis of biological concepts has at least three broad philosophical consequences: (1) it provides the grounds for the study of behavior and psychological categories as homologues; (2) it demonstrates that philosophers who take selected effect function as primary effectively ignore large portions of comparative, structural, and experimental research, thereby misconstruing biological reasoning and knowledge; and, (3) it underwrites causal generalizations, which illuminates inferences made from model organisms in experimental biology. (shrink)

The notion of function is indispensable to our understanding of distinctions such as that between being broken and being in working order (for artifacts) and between being diseased and being healthy (for organisms). A clear account of the ontology of functions and functioning is thus an important desideratum for any top-level ontology intended for application to domains such as engineering or medicine. The benefit of using top-level ontologies in applied ontology can only be realized when each of the categories (...) identified and defined by a top-level ontology is integrated with the others in a coherent fashion. Basic Formal Ontology (BFO) has from the beginning included function as one of its categories, exploiting a version of the etiological account of function that is framed at a level of generality sufficient to accommodate both biological and artifactual functions. This account has been subjected to a series of criticisms and refinements. We here articulate BFO’s account of function, provide some reasons for favoring it over competing views, and defend it against objections. (shrink)

Dominical categories are categories in which the notions of partial morphisms and their domains become explicit, with the latter being endomorphisms rather than subobjects of their sources. These categories form the basis for a novel abstract formulation of recursion theory, to which the present paper is devoted. The abstractness has of course its usual concomitant advantage of generality: it is interesting to see that many of the fundamental results of recursion theory remain valid in contexts far removed (...) from their classic manifestations. A principal reason for introducing this new formulation is to achieve an algebraization of the generalized incompleteness theorem, by providing a category-theoretic development of the concepts and tools of elementary recursion theory that are inherent in demonstrating the theorem.Dominical recursion theory avoids the commitment to sets and partial functions which is characteristic of other formulations, and thus allows for an intrinsic recursion theory within such structures as polyadic algebras. It is worthy of notice that much of elementary recursion theory can be developedwithout referencetoelements.By Gödel's generalized incompleteness theorem for consistent arithmetical systemTwe mean any statement of the following sort: if every recursive set is definable inT, thenTis essentially undecidable [41]; or if all recursive functions are definable inT, thenTis essentially undecidable [41]; or if every recursive set is definable inT, thenT0andR0 are recursively inseparable [39]; or if all re sets are representable inT, thenT0is creative [28], [39]; or ifTis a Rosser theory, thenT0andR0are effectively inseparable [39]. (shrink)

We develop a category theoretical scheme for the comprehension of the information structure associated with a complex system, in terms of families of partial or local information carriers. The scheme is based on the existence of a categorical adjunction, that provides a theoretical platform for the descriptive analysis of the complex system as a process of functorial information communication.

The contest between “Lockeian liberalism” and “classical republicanism” as explanatory frameworks for the intellectual history of the American Revolution, and therefore of the present-day United States, has been one of the longest running and most distinguished in recent U.S. historiography. It also has major implications for the history of political thought in the North Atlantic Anglophone world more widely. Yet this debate was merely suspended when it was held to have ended in an ill-defined compromise. Although some U.S. historians expressed (...) doubts and qualifications, attention in U.S. historiography moved on to other themes while leaving the initial problem unsolved. This article reopens the question; it suggests that a historicization of both these two categories is now both possible and necessary, and that their supersession will advance understanding of the Revolution. It seeks to help solve this problem by the same means that the debate began: that is, by re-establishing a link between U.S. and U.K. historiographies. (shrink)

The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and functions. The analysis extends directly to other concrete categories (groups, rings, vector spaces, etc.) where the objects are sets with a certain type of structure and the morphisms are functions that preserve that structure. Then the elements & distinctions-based definitions can (...) be abstracted in purely arrow-theoretic way for abstract category theory. In short, the language of elements & distinctions is the conceptual language in which the category of sets is written, and abstract category theory gives the abstract arrows version of those definitions. (shrink)

A century after the discovery of quantum mechanics, the meaning of quantum mechanics still remains elusive. This is largely due to the puzzling nature of the wave function, the central object in quantum mechanics. If we are realists about quantum mechanics, how should we understand the wave function? What does it represent? What is its physical meaning? Answering these questions would improve our understanding of what it means to be a realist about quantum mechanics. In this survey article, I review (...) and compare several realist interpretations of the wave function. They fall into three categories: ontological interpretations, nomological interpretations, and the sui generis interpretation. For simplicity, I will focus on non-relativistic quantum mechanics. (shrink)

We develop a conceptual framework that connects biological heredity and organization. We refer to heredity as the cross-generation conservation of functional elements, defined as constraints subject to organizational closure. While hereditary objects are functional constituents of biological systems, any other entity that is stable across generations—and possibly involved in the recurrence of phenotypes—belongs to their environment. The central outcome of the organizational perspective consists in extending the scope of heredity beyond the genetic domain without merging it with the (...) broad category of cross-generation stability. After discussing some implications, we conclude with a reflection on the relationship between stability and variation. 1Introduction2From Extended Heredity to Cross-generation Stability 2.1Extending the scope of heredity: A brief state of the art2.2Rethinking heredity: Conceptual challenges3Biological Heredity in Light of Organization 3.1Biological organization within organisms and beyond3.2Extending organization in time3.3What is biological heredity?4Implications and Objections 4.1Heredity as a specific kind of cross-generation stability4.2Heredity at various levels of description4.3Non-functional and dysfunctional objects5Conclusions: From Conservation to Variation. (shrink)