: This article presents a new approach to considering the categories and concepts necessary for praxeology based on the theoretical framework proposed by Anna Wierzbicka and Cliff Goddard. Natural semantic metalanguage theory can be a comprehensive method for defining the conceptual foundations of human action and of rational discussion in general. Behind the very premise of ….

Journal Name: Semiotica Issue: Ahead of print.

In ‘Reification and the Consciousness of the Proletariat’, Lukács analyses the commodity-structure as ‘the universal category’ that frames society as a whole. Taking seriously the aspiration to follow Marx in going ‘to the root of the matter’, Lukács examines the ways and extent to which the commodity structure extends into and remoulds society, focusing on living individuals, their needs and relations to things as use values. We propose a reading drawing on the idea of concern-in-indifference, which addresses the complexity (...) of the practice of owning that underpins Lukács’s analysis. We argue that attention to this complexity enables us to shine a light on the commodity structure’s capacity to conceal, directing us away from Lukács’s focus to an appreciation of the significance of the universal category’s power to deny a future ethical substantiality of togetherness while giving rise to singular beings for whom this substantiality remains an orienting vision. (shrink)

When we think of the problem of ‘universals’, we tend first of all to identify this issue with medieval philosophy. In that period the arguments ran hot and heavy, and the result was that philosophers almost came to be classified according to the position each took about the relation between the individual and universal concepts. Of course, the fact is that the problem of universals has been important in every philosophical age in western thought. Metaphysics as an enterprise may (...) rise and fall in popularity, but the problem of universals is always with us. Yet, like most philosophical problems of importance, it has not always meant one thing. (shrink)

The aim of this paper is to address a longstanding concern about the linguistic ‘relativ- ity’ of ontological categories, and resulting limitations in the scope of ontological theo- ries. Given recent evidence on the influence of language on cognitive dispositions, do we have empirical reasons to doubt that there are ontological categories that have uni- versal scope across languages? I argue that this is the case, at least if we retain the stan- dard ‘inferential’ approach within analytical ontology, (...) i.e., if we evaluate ontological interpretations of L-sentences relative to certain material inferences in L. Research in linguistic typology suggests that types of entities postulated for the domain of Indo- European languages cannot capture the ontological commitments of the (much larger group of) non-Indo-European languages. Ontological category theory thus seems to have three options. The first option is to abandon the standard ‘inferential’ approach to ontological category theory. Alternatively, if we stay with the inferential approach, we face the following choice. Either ontology must let go of its ambitions to provide general domain descriptions for any language and settle for the more modest project of reconstructing the ontological commitments of a group of natural languages. Or else analytical ontologists should turn to linguistic typology in order to accommodate the diversity of inferential structures embedded in natural languages. I recommend and ex- plore this third option, illustrating a strategy for how to construct a domain theory that can be used across languages. In a first step I show how linguistic research on the se- mantics of verbs and nouns (studies on so-called “Aktionsarten” and “Seinsarten”) can be used to identify the inferential patterns of ten basic concepts of modes of existence in time and space. In a second step I show how these inferential data can be inter- preted ontologically within General Process Theory, an ontological framework based on nonparticular individuals (“dynamics”). -/- . (shrink)

This article aims to analyze the manifestation of the universal axiological cultural category of sinfulness in the media space. The study's subject was this category's properties and functions, which are actualized when represented in digital media. In accordance with this goal, we used such methods as continuous sampling and observation of the facts of the representation of cultural categories, which allowed us to determine the linguistic material for analysis and a statistical method for quantitative analysis. The content analysis (...) of the units selected for the study was used to identify the role, properties, and main functions of the universal axiological category of sinfulness. The novelty of the research lies in the fact that, for the first time, the universal nature of the category of sinfulness, its functions and properties, represented in media publications, were considered. Main conclusions: the study of the facts of actualization of the category of sinfulness in the media space allowed us to assert that the phenomenon under study is associated with topics such as politics, crime (in news media), and the assessment of citizens' behavior and morality (in religious media). These facts indicate that the primary function of the category of sinfulness is regulatory, aimed at evaluating and correcting the actions of members of society, as well as creating public opinion. In addition, the article proves that the category of sinfulness has transcultural properties, penetrating and being realized in all cultural layers, from local to global. In these cultural layers, the nature of the category acquires a different shade. In particular, at the global level, the category of sinfulness acquires the meaning of guilt, which is a consequence of the significant influence of Western culture on the global culture. It seems that the revealed properties of the category indicate its high importance for modern Russian society. The established regulatory function will make it possible to apply this category, including within the framework of regulating and managing public opinion and promoting basic values. (shrink)

For classical sets one has with the cumulative hierarchy of sets, with axiomatizations like the system ZF, and with the category SET of all sets and mappings standard approaches toward global universes of all sets.We discuss here the corresponding situation for fuzzy set theory. Our emphasis will be on various approaches toward (more or less naively formed) universes of fuzzy sets as well as on axiomatizations, and on categories of fuzzy sets.

Rather than approaching Kant's moral theory in the normal way through a consideration of The Groundwork of the Metaphysics of Morals and The Critique of Practical Reason, I do so from the perspective of an extended analysis of other aspects of his work that bear on his moral philosophy . Consideration of the Doctrine of Right suggests that the universal principle of Right Kant identifies is a restricted version of the CI applied to the limited domain of relations between (...) persons at issue in this context. Given that duties of Right deriving from this principle are also regarded as perfect ethical duties, an analysis of the nature and scope of the universal principle of Right can, I argue, be expected to be informative with respect to our understanding of perfect duties and the contradiction in conception from which these are said to derive. Allowing for the more limited scope of merely external duties of Right, analysis of these duties suggests that ethical duties of Right are obligations concerned with ensuring the capacity of rational agents to govern themselves on the basis of reason . This kind of analysis, I argue, is both confirmed and clarified by Kant's subsequent discussion of perfect and imperfect duties of virtue we owe to ourselves under the rubric of concerns with our moral health and moral prosperity. ;The resulting view is, I claim, a promising one that allows us to integrate the different treatments of duties in these two works and accommodate the various duties Kant discusses. In particular, understood in terms of the notions of moral health and prosperity, the concerns engendered here require careful consideration of the particular nature and psychology of human agency and yield a much more subtle and interesting account of duty and of the moral life than those typically associated with Kant. (shrink)

Since its formal definition over sixty years ago, category theory has been increasingly recognized as having a foundational role in mathematics. It provides the conceptual lens to isolate and characterize the structures with importance and universality in mathematics. The notion of an adjunction (a pair of adjoint functors) has moved to center-stage as the principal lens. The central feature of an adjunction is what might be called "internalization through a universal" based on universal mapping properties. A recently developed (...) "heteromorphic" theory of adjoint functors allows the concepts to be more easily applied empirically. This suggests a conceptual structure, albeit abstract, to model a range of selectionist mechanisms (e.g., in evolution and in the immune system). Closely related to adjoints is the notion of a "brain functor" which abstractly models structures of cognition and action (e.g., the generative grammar view of language). (shrink)

With the six volumes of the Writings edited by the Peirce Edition Project at Indiana University since 1982, the monumental work of Charles S. Peirce has finally received the care, respect, and love that it deserves. The sixth volume, object of attention of this review, represents a thorough selection and edition of Peirce's writings from 1886 to 1890.

As philosophers, we may be accustomed to asking ourselves—or at least having to explain to others—why we do philosophy. In Categories We Live By: The Construction of Sex, Gender, Race, and Other So...

We investigate the family of concepts that an agent comes to know through a set of defining features, and examine the role played by these features in the process of categorization. In a qualitative framework, categorial membership is evaluated through an order relation among the objects at hand, which translates the fact that an object may fall more than another under a given concept. For concepts defined by their features, this global membership order depends on the degree with which each (...) feature applies to the objects of the universe. The passage from these individual membership degrees to a global membership order poses a problem analogous to vote aggregation in social choice theory. This similarity leads to an original solution that is particularly well-adapted to the framework of cognitive psychology. The resulting membership order extends to compound concepts, and provides a good description of the guppy paradox and the conjunction effect. (shrink)

_The Universal_ proposes a radically new philosophical system that moves from ontology to ethics. Drawing on the work of De Beauvoir, Sartre, and Le Doeuff, among others, and addressing a range of topics from the Asian sex trade to late capitalism, quantum gravity, and Merleau-Ponty's views on cinema, Dorothea Olkowski stretches the mathematical, political, epistemological, and aesthetic limits of continental philosophy and introduces a new perspective on political structures. Straddling a course between formalism and conventionalism, Olkowski develops the concept of (...) an ontological unconscious that arises from our "sensible" relation to the world-the information we absorb and emit that affects our encounters with the environment and others. In this "realm of the senses," or the field of vulnerability defined by our experience with pleasure and pain, Olkowski is able to rethink the space-time relations put forth by Irigaray's notion of the "interval," Bergson's "recollection," Merleau-Ponty's idea of the "flesh," and Deleuze's "plane of immanence." This aesthetic sense is shared by all humankind and nonhuman entities in the organic and inorganic world. The sensible universal can be applied to categories of pure and practical reason; experiential binaries of male-female and subject-object; and issues of autonomy, moral laws, and the regulation of perception. (shrink)

This essay endeavors to define the concept of indefinite extensibility in the setting of category theory. I argue that the generative property of indefinite extensibility for set-theoretic truths in category theory is identifiable with the Grothendieck Universe Axiom and the elementary embeddings in Vopenka's principle. The interaction between the interpretational and objective modalities of indefinite extensibility is defined via the epistemic interpretation of two-dimensional semantics. The semantics can be defined intensionally or hyperintensionally. By characterizing the modal profile of $\Omega$-logical validity, (...) and thus the generic invariance of mathematical truth, modal coalgebras are further capable of capturing the notion of definiteness for set-theoretic truths, in order to yield a non-circular definition of indefinite extensibility. (shrink)

Category Theory has developed rapidly. This book aims to present those ideas and methods which can now be effectively used by Mathe­ maticians working in a variety of other fields of Mathematical research. This occurs at several levels. On the first level, categories provide a convenient conceptual language, based on the notions of category, functor, natural transformation, contravariance, and functor category. These notions are presented, with appropriate examples, in Chapters I and II. Next comes the fundamental idea of an (...) adjoint pair of functors. This appears in many substantially equivalent forms: That of universal construction, that of direct and inverse limit, and that of pairs offunctors with a natural isomorphism between corresponding sets of arrows. All these forms, with their interrelations, are examined in Chapters III to V. The slogan is "Adjoint functors arise everywhere". Alternatively, the fundamental notion of category theory is that of a monoid -a set with a binary operation of multiplication which is associative and which has a unit; a category itself can be regarded as a sort of general­ ized monoid. Chapters VI and VII explore this notion and its generaliza­ tions. Its close connection to pairs of adjoint functors illuminates the ideas of universal algebra and culminates in Beck's theorem characterizing categories of algebras; on the other hand, categories with a monoidal structure lead inter alia to the study of more convenient categories of topological spaces. (shrink)

The concept that peope have of themselves as a 'person' is one of the most intimate notions that they hold. Yet the way in which the category of the person is conceived varies over time and space. In this volume, anthropologists, philosophers, and historians examine the notion of the person in different cultures, past and present. Taking as their starting point a lecture on the person as a category of the human mind, given by Marcel Mauss in 1938, the contributors (...) critically assess Mauss's speculation that ntions of the person, rather than being primarily philosophical or psychological, have a complex social and ideological origin. Discussing societies ranging from ancient Greece, India, and China to modern Africa and Papua New Guinea, they provide fascinating descriptions of how these different cultures define the person. But they also raise deeper theoretical issues: What is universally constant and what is culturally variable in people's thinking about the person? How can these variations be explained? Has there been a general progressive development toward the modern Western view of the person? What is distinctive about this? How do one's notions of the person inform one's ability to comprehend alternative formulations? These questions are of compelling interest for a wide range of anthropologists, philosophers, historians, psychologists, sociologists, orientalists, and classicists. The book will appeal to any reader concerned with understanding one of the most fundamental aspects of human existence. (shrink)

Category theory and topos theory have been seen as providing a structuralist framework for mathematics autonomous vis-a-vis set theory. It is argued here that these theories require a background logic of relations and substantive assumptions addressing mathematical existence of categories themselves. We propose a synthesis of Bell's many-topoi view and modal-structuralism. Surprisingly, a combination of mereology and plural quantification suffices to describe hypothetical large domains, recovering the Grothendieck method of universes. Both topos theory and set theory can be carried (...) out relative to such domains; puzzles about ‘large categories’ and ‘proper classes’ are handled in a uniform way, by relativization, sustaining insights of Zermelo. (shrink)

The more one reads about the topic of natural kinds, the more one is reminded of that famous scene in The Hitchhiker’s Guide to the Galaxy in which Deep Thought—after a mere 7.5 million years of doing calculations—reveals that the answer to the Ultimate Question of Life, the Universe and Everything was 42. Faced with bewildered reactions from the eager audience, Deep Thought explains: “I think the problem, to be quite honest with you, is that you’ve never actually known what (...) the question is” .In the case of the growing literature on natural kinds, it is easy to get a feeling that something similar is going on. While philosophers keep advancing novel accounts of natural kinds, at the same time there is considerable disagreement about what exactly the problem is that such accounts should solve. To some, natural kinds are real kinds in nature that exist in the world independently of human interests and practices. At the very least, they are human-made kinds that correspon .. (shrink)

Analytical categories of scientific cultures have typically been used both exclusively and universally. For instance, when styles of scientific research are employed in attempts to understand and narrate science, styles alone are usually employed. This article is a thought experiment in interweaving categories. What would happen if rather than employ a single category, we instead investigated several categories simultaneously? What would we learn about the practices and theories, the agents and materials, and the political-technological impact of science (...) if we analyzed and applied styles, paradigms, and models simultaneously? I address these questions in general and for a specific case study: a brief history of systematics. (shrink)

This paper is an essay in what Austin (_Proc Aristotel Soc_ 57: 1–30, 1956–1957) called "linguistic phenomenology". Its focus is on showing how the grammatical features of ordinary causal verbs, as revealed in the kinds of linguistic constructions they can figure in, can shed light on the nature of the processes that these verbs are used to describe. Specifically, drawing on the comprehensive classification of English verbs founds in Levin (_English verb classes and alternations: a preliminary investigation_, University of Chicago (...) Press, Chicago, 1993), I divide the forms of productive causal processes into five classes, corresponding to Aristotle's ontological categories: there are processes that cause change in location, in state, and in quantity; and that lead to the creation and destruction of substances. These broader categories are then subdivided into other ones, corresponding to different Levin classes, according to further differences in the causal processes they involve. I conclude by discussing the relevance of this argument to research in metaphysics and experimental philosophy. (shrink)

Peirce's Law of Triviality: The Implementation of the Trivium of Logic, Rhetoric and Grammar. Basic Categories for Linguistics and Literature Studies from a Universal Semiotic Theory This article focuses on the aspects that refer to linguistics in the works of Charles S. Peirce. His pragmatic philosophy implemented many other sciences and among them is the traditional trivium of logic, grammar, and rhetoric, which Peirce divided into different kinds of logic, grammar, and rhetoric. While the impact of the work (...) of Peirce on theses sciences is weak, the integration of the sciences in his philosophy is interesting as a step in the history of science and his work is an example for ecclecticism and historism of science in the 19th century and the universalism of science deducted from a philosophy that uses the sign as an unitarian principle. Triple constructions are a very common feature in the writings of Peirce, and the trivium is an example of an academic construction Peirce implemented. (shrink)

Kendall Walton’s “Categories of Art” (1970) is one of the most important and influential papers in twentieth-century aesthetics. It is almost universally taken to refute traditional aesthetic formalism/empiricism, according to which all that matters aesthetically is what is manifest to perception. Most commentators assume that the argument of “Categories” applies to works of literature. Walton himself notes a word of caution: “The aesthetic properties of works of literature are not happily called ‘perceptual’ … (The notion of perceiving a (...) work in a category … is not straightforwardly applicable to literary works)” (335 n.5). However, he goes on to say that although he focuses “on visual and musical works … the central points I make concerning them hold, with suitable modifications, for novels, plays, and poems as well” (335 n.5). Here I consider what “suitable modifications” are required to extend the account to literature. (shrink)

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)

A key figure in the history of Aristotelianism, Porphyry (AD 232/3 - c. 305) was born in Tyre and was a student of Longinus' in Athens and of Plotinus' in Rome. In his commentary on the Categories, Porphyry provided an authoritative interpretation of a notoriously controversial work. Commentators on Aristotle had disagreed fundamentally over whether the Categories was a work of logic, concerning simple terms or the simple concepts they represent, or a metaphysical work addressing the classification by (...) genera of simple entities or concepts. Approaching the Categories as the first of Aristotle's works in logic, Porphyry adopted an earlier Peripatetic view of the Categories as being concerned principally with terms or linguistic items, which he calls "predicates." He successfully defended the Categories against Plotinus, arguing that while it seemed to attack orthodox Platonism by denying the separation of forms and the ontological priority of the universal, it was in fact entirely compatible with Platonism. Because of Porphyry's intervention, the Categories came to serve as a basic textbook of logic for subsequent Neoplatonist teaching. His commentary influenced the Arabic tradition, and Boethius drew heavily on it as well. The full text of Porphyry's commentary was lost, but the extant version is available here in Steven K. Strange's new translation. Ancient philosophers, historians of philosophy, classicists, and medievalists will welcome its appearance in English. (shrink)

In this paper an Artificial Neural Network (ANN) model, for predicting the category of a tumor was developed and tested. Taking patients’ tests, a number of information gained that influence the classification of the tumor. Such information as age, sex, histologic-type, degree-of-diffe, status of bone, bone-marrow, lung, pleura, peritoneum, liver, brain, skin, neck, supraclavicular, axillar, mediastinum, and abdominal. They were used as input variables for the ANN model. A model based on the Multilayer Perceptron Topology was established and trained using (...) data set which its title is “primary tumor” and was obtained from the University Medical Centre, Institute of Oncology, Ljubljana, Yugoslavia Test data evaluation shows that the ANN model is able to correctly predict the tumor category with 76.67 % accuracy. (shrink)

For the most part, the papers collected in this volume stern from presentations given at a conference held in Tucson over the weekend of May 31 through June 2, 1985. We wish to record our gratitude to the participants in that conference, as well as to the National Science Foundation and the University of Arizona SBS Research Institute for their financial support. The advice we received from Susan Steele on organizational matters proved invaluable and had many felicitous consequences for the (...) success of the con­ ference. We also would like to thank the staff of the Departments of Linguistics of the University of Arizona and the University of Massachusetts at Amherst for their help, as weIl as a number of individuals, including Lin Hall, Kathy Todd, and Jiazhen Hu, Sandra Fulmer, Maria Sandoval, Natsuko Tsujimura, Stuart Davis, Mark Lewis, Robin Schafer, Shi Zhang, Olivia Oehrle-Steele, and Paul Saka. Finally, we would like to express our gratitude to Martin Scrivener, our editor, for his patience and his encouragement. Vll INTRODUCTION The term 'categorial grammar' was introduced by Bar-Rillel as a handy way of grouping together some of his own earlier work and the work of the Polish logicians and philosophers Lesniewski and Ajdukiewicz, in contrast to approaches to linguistic analysis based on phrase structure grammars. (shrink)

In this paper I argue that category theory ought to be seen as providing the language for mathematical discourse. Against foundational approaches, I argue that there is no need to reduce either the content or structure of mathematical concepts and theories to the constituents of either the universe of sets or the category of categories. I assign category theory the role of organizing what we say about the content and structure of both mathematical concepts and theories. Insofar, then, as (...) the structuralist sees mathematics as talking about structures and their morphology, I contend that category theory furnishes a framework for mathematical structuralism. (shrink)

Journal of Mathematical Logic, Volume 22, Issue 02, August 2022. We introduce bounded category forcing axioms for well-behaved classes [math]. These are strong forms of bounded forcing axioms which completely decide the theory of some initial segment of the universe [math] modulo forcing in [math], for some cardinal [math] naturally associated to [math]. These axioms naturally extend projective absoluteness for arbitrary set-forcing — in this situation [math] — to classes [math] with [math]. Unlike projective absoluteness, these higher bounded category forcing (...) axioms do not follow from large cardinal axioms but can be forced under mild large cardinal assumptions on [math]. We also show the existence of many classes [math] with [math] giving rise to pairwise incompatible theories for [math]. (shrink)

"Categories in Distress," given as one of two Hanna Lectures at Hamline University, April 22, 1999. A revision of this lecture was given at the meeting of the Midwest Division of the Society for Women in Philosophy, Fall 1999.

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)