Traditionally, heated philosophical debates regarding the status of categories have turned on questions of "nominal" vs "real" existence, where the role and significance of rhetoric and politics is obscured. Feminists in the late 20th century acknowledge a variety of elements involved in the construction of categories such as "human," "nature," rhetoric and logic. I argue for a position which undercuts the traditional debates between nominalism and realism, and using "wo men" as a case study, demonstrate the intricacies of the (...) relationship of logic and rhetoric in category construction. (shrink)

The current consensus is that most natural categories are not organized around strict definitions (a list of singly necessary and jointly sufficient features) but rather according to a family resemblance (FR) principle: Objects belong to the same category because they are similar to each other and dissimilar to objects in contrast categories. A number of computational models of category construction have been developed to provide an account of how and why people create FR categories (Anderson, 1990; Fisher, (...) 1987). Surprisingly, however, only a few experiments on category construction or free sorting have been run and they suggest that people do not sort examples by the FR principle. We report several new experiments and a two‐stage model for category construction. This model is contrasted with a variety of other models with respect to their ability to account for when FR sorting will and will not occur. The experiments serve to identify one basis for FR sorting and to support the two‐stage model. The distinctive property of the two‐stage model is that it assumes that people impose more structure than the examples support in the first stage and that the second stage adjusts for this difference between preferred and perceived structure. We speculate that people do not simply assimilate probabilistic structures but rather organize them in terms of discrete structures plus noise. (shrink)

We are women, we are men. We are refugees, single mothers, people with disabilities, and queers. We belong to social categories and they frame our actions, self-understanding, and opportunities. But what are social categories? How are they created and sustained? How does one come to belong to them? Ásta approaches these questions through analytic feminist metaphysics. Her theory of social categories centers on an answer to the question: what is it for a feature of an individual to be socially meaningful? (...) In a careful, probing investigation, she reveals how social categories are created and sustained and demonstrates their tendency to oppress through examples from current events. To this end, she offers an account of just what social construction is and how it works in a range of examples that problematize the categories of sex, gender, and race in particular. The main idea is that social categories are conferred upon people. Ásta introduces a 'conferralist' framework in order to articulate a theory of social meaning, social construction, and most importantly, of the construction of sex, gender, race, disability, and other social categories. (shrink)

This paper addresses the question of how human science categories yield projectable inferences by critically examining Ron Mallon’s ‘social role’ account of human kinds. Mallon contends that human categories are projectable when a social role produces a homeostatic property cluster (HPC) kind. On this account, human categories are projectable when various social mechanisms stabilize and entrench those categories. Mallon’s analysis obscures a distinction between transitory and robust projectable inferences. I argue that the social kinds discussed by Mallon yield the former, (...) while classifications of biological kinds yield the latter. Classifications from psychiatry (‘schizophrenia,’ ‘hysteria’) are discussed as examples. (shrink)

Real kinds, both natural and social categories, are characterized by rich inductive potential. They have relatively stable sets of conceptually independent projectable properties. Somewhat surprisingly, even some purely social categories show such multiple projectability. The article explores the origin of the inductive richness of social categories and concepts. I argue that existing philosophical accounts provide only a partial explanation, and mechanisms of boundary formation and stabilization must be brought into view for a more comprehensive account of inductively rich social categories.

Categories We Live by: The Construction of Sex, Gender, Race, and Other Social Categories, by Ásta. Oxford: OUP, 2018. Pp. 160.

This paper argues that grammatical constructions, specifically argument structure constructions that determine the “who did what to whom” part of sentence meaning and how this meaning is expressed syntactically, can be considered a kind of relational category. That is, grammatical constructions are represented as the abstraction of the syntactic and semantic relations of the exemplar utterances that are expressed in that construction, and it enables the generation of novel exemplars. To support this argument, I review evidence that there (...) are parallel behavioral patterns between how children learn relational categories generally and how they learn grammatical constructions specifically. Then, I discuss computational simulations of how grammatical constructions are abstracted from exemplar sentences using a domain-general relational cognitive architecture. Last, I review evidence from adult language processing that shows parallel behavioral patterns with expert behavior from other cognitive domains. After reviewing the evidence, I consider how to integrate this account with other theories of language development. (shrink)

I describe an account of ontological categories which does justice to the facts that not all categories are ontological categories and that ontological categories can stand in containment relations. The account sorts objects into different categories in the same way in which grammar sorts expressions . It then identifies the ontological categories with those which play a certain role in the systematization of collections of categories. The paper concludes by noting that on my account what ontological categories there are is (...) partially interest-relative, and that furthermore no object can belong essentially to its ontological category. (shrink)

When formalizing mathematics in constructive type theories, or more practically in proof assistants such as Coq or Agda, one is often using setoids. In this note we consider two categories of setoids with equality on objects and show, within intensional Martin-Löf type theory, that they are isomorphic. Both categories are constructed from a fixed proof-irrelevant family F of setoids. The objects of the categories form the index setoid I of the family, whereas the definition of arrows differs. The first (...) class='Hi'>category has for arrows triples →F)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\,\rightarrow \,F)$$\end{document} where f is an extensional function. Two such arrows are identified if appropriate composition with transportation maps makes them equal. In the second category the arrows are triples 2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^2)$$\end{document} where R is a total functional relation between the subobjects F,F↪Σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F, F \hookrightarrow \Sigma $$\end{document} of the setoid sum of the family. This category is simpler to use as the transportation maps disappear. Moreover we also show that the full image of a category along an E-functor into an E-category is a category. (shrink)

Depuis le début du siècle, la lutte contre les mariages de complaisance est devenue un élément central des politiques migratoires européennes. En Belgique, le gouvernement a instauré une procédure d’évaluation des mariages « mixtes » entre des citoyen·nes belges et des individu·es provenant d’un pays hors Union Européenne afin de détecter – et empêcher – les mariages de complaisance, c'est-à-dire des unions matrimoniales entreprises uniquement dans le but d’obtenir un titre de séjour. A travers l’analyse de plusieurs documents juridiques et (...) politiques provenant de la Belgique et de l’Union Européenne, cet article vise à examiner les éléments discursifs de la définition juridico-administrative d’un « mariage de complaisance » dans ces enquêtes. Dans un premier temps, nous montrons que cette définition constitue le produit d’un processus de construction discursive et explorons la manière dont cette définition est façonnée et codifiée par l’ensemble de textes et de pratiques sur lesquels reposent les enquêtes. Nous exposons ensuite en quoi ce processus laisse la place à des discriminations – et notamment à des discriminations genrées – ainsi que des cas de « gardiennage » moral. (shrink)

The article asks, how one of the basic notions of cultural-political identity — we — is constructed in mass media, viz. which kind of semiotic and linguistic facilities are used in constructing a political unity. The approach used in this article is based on Lotman’s semiotic theory of culture and on the analysis of pronouns in political texts, using Emil Benvenist’s theory of deixis. Our case study concentrates on the years 1940–1941 which mark one of the most crucial periods in (...) Estonian nearest history. The source material of the analysis consists of speeches of new political elite in power, all of which were published in major daily newspapers at the time. In outline, first year of soviet power in Estonia can be divided in two periods. First period would be from June 21 to “July elections” in 1940. In political rhetoric, new political elite tried to create a monolithic subject, the unity between themselves and people (people’s will) by emphasizing activity and freedom of self-determination. Nevertheless, starting from “elections”, especially from the period after “accepting” Soviet Republic of Estonia as a full member of Soviet Union, a transition of we-concept from an active subject to mere passive recipient can be detected. From that time on, people’s will was envisaged as entirely determined by marxist-leninist ideology and “the Party”. (shrink)

The present study explores discursive constructions of us- and them-groups within the context of the debates on the placement of the US anti-ballistic missile defence system in Central and Eastern Europe. The study is based on the data collected by the authors in the Polish and Russian press. Using the framework that is informed by Critical Discourse Analysis and Membership Categorization Analysis, the authors define strategies and specific linguistic means used to represent ‘us’ and ‘them’ and provide a picture of (...) chronological transformations that these representations undergo in the investigated newspapers. (shrink)

_ Categories We Live by: The Construction of Sex, Gender, Race, and Other Social Categories _ By ÁstaOxford University Press, 2018. xiv + 140 pp.

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...

Résumé Les linguistes adoptant des objets transphrastiques travaillent avec des unités qui coïncident rarement avec les catégories traditionnelles. Ces unités ne sont pas une donnée déjà là, elles le deviennent a posteriori par le travail analytique. Il en va ainsi de la définition à laquelle nous nous intéressons en termes de catégorie discursive dans trois contextes discursifs, – le roman épistolaire, le slogan publicitaire et l’article de journal – pour observer comment elle contribue à l’analyse des discours. L’objectif vise à (...) la contextualiser dans différents univers discursifs, qui lui affectent une pertinence singulière, déterminée par les effets de généricité à l’œuvre dans le corpus et par les autres catégories construites par la textualité. Il s’agit de montrer quels sont les indices qui concourent à son identification, en nous attachant au caractère hétérogène de ces unités, et que ces catégories ne deviennent discursives que dans le mouvement de l’interprétation. Ce dernier consiste à les situer par rapport à une finalité inscrite dans la compétence générique des interactants et dans leurs représentations socio-idéologiques. Nous découvrirons que la définition n’a d’existence que dans son interaction avec d’autres unités, mais également que cette interaction nécessaire à l’identification du procédé discursif résultant participe à la construction de nouveaux indices. (shrink)

In this article I shall argue that the categories a subject employs to codify her perceptions are emergent elements of the social niche her community inhabits. Hence, I defend the claim that categories are primarily elements of the social ontology a certain subject experiences. I then claim that public representations shared in a social niche play a crucial regulative role for the members of that community: in fact, they offer a rule to conceive a certain type or a certain (...) class='Hi'>category, e.g. ‘movement’, ‘time’ or ‘space’. In this sense, categories function as normative elements. (shrink)

Foundational ontologies, central constructs in ontological investigations and engineering alike, are based on ontological categories. Firstly proposed by Aristotle as the very ur- elements from which the whole of reality can be derived, they are not easy to identify, let alone partition and/or hierarchize; in particular, the question of their number poses serious challenges. The late medieval philosopher Dietrich of Freiberg wrote around 1286 a tutorial that can help us today with this exceedingly difficult task. In this paper, I discuss (...) ontological categories and their importance for foundational ontologies from both the contemporary perspective and the original Aristotelian viewpoint, I provide the translation from the Latin into English of Dietrich's De origine II with an introductory elaboration, and I extract a foundational ontology–that is in fact a single-category one–from this text rooted in Dietrich's specification of types of subjecthood and his conception of intentionality as causal operation. (shrink)

Caster Semenya is done with track and field. At 29, her hopes for a continued career as a professional middle-distance runner are dashed. After her case against International Association for Athletics Federation 1 was dismissed by the Court for Arbitration of Sport on 1 May 2019, she has switched to football later in the year.1 Semenya’s case may have come to its legal conclusion, however it has generated an aporia regarding the binary classification in athletics, which has yet to be (...) solved.2 It is time the implications of the fair equality of opportunity principle as a normative basis for the construction of categories in sport are taken seriously to move forward the debate on unfair advantages in sport. Loland conditionally justifies restricting the women’s category to athletes with testosterone levels below a certain threshold, on the basis of the FEO principle, and of a distinction between stable and dynamic inequalities between athletes. …. (shrink)

This paper considers the nature and role of axioms from the point of view of the current debates about the status of category theory and, in particular, in relation to the “algebraic” approach to mathematical structuralism. My aim is to show that category theory has as much to say about an algebraic consideration of meta-mathematical analyses of logical structure as it does about mathematical analyses of mathematical structure, without either requiring an assertory mathematical or meta-mathematical background theory as (...) a “foundation”, or turning meta-mathematical analyses of logical concepts into “philosophical” ones. Thus, we can use category theory to frame an interpretation of mathematics according to which we can be algebraic structuralists all the way down. (shrink)

I defend a one category ontology: an ontology that denies that we need more than one fundamental category to support the ontological structure of the world. Categorical fundamentality is understood in terms of the metaphysically prior, as that in which everything else in the world consists. One category ontologies are deeply appealing, because their ontological simplicity gives them an unmatched elegance and spareness. I’m a fan of a one category ontology that collapses the distinction between particular (...) and property, replacing it with a single fundamental category of intrinsic characters or qualities. We may describe the qualities as qualitative charactersor as modes, perhaps on the model of Aristotelian qualitative (nonsubstantial) kinds, and I will use the term “properties” interchangeably with “qualities”. The qualities are repeatable and reasonably sparse, although, as I discuss in section 2.6, there are empirical reasons that may suggest, depending on one’s preferred fundamental physical theory, that they include irreducibly intensive qualities. There are no uninstantiated qualities. I also assume that the fundamental qualitative natures are intrinsic, although physics may ultimately suggest that some of them are extrinsic. On my view, matter, concrete objects, abstract objects, and perhaps even spacetime are constructed from mereological fusions of qualities, so the world is simply a vast mixture of qualities, including polyadic properties (i.e., relations). This means that everything there is, including concrete objects like persons or stars, is a quality, a qualitative fusion, or a portion of the extended qualitative fusion that is the worldwhole. I call my view mereological bundle theory. (shrink)

The project of Categories We Live By is to offer a metaphysics of social categories. The strategy is to give a theory of social properties of individuals. The main components of the theory are a conferralist framework for properties; an account of social meaning; and an account of social construction; accompanying is also an account of social identity. This theory can be applies to offer concrete conferralist proposals of categories such as sex, gender, race, disability, religion, and LGBTQ categories. (...) This précis describes the main components (conferralist framework, social meaning, social construction, social identity) briefly, but leaves discussions of applications for another time. (shrink)

This paper aims to bring a novel approach to the discussion of unfair advantages in sport by looking for a local criterion of fairness instead of a universal criterion. A local criterion of fairness would not solve the general dispute over what counts as an unfair advantage, but it would be beneficial in evaluating specific cases and could guide further discussion about them. We seek a local criterion of fairness by comparing the specific property advantages of Caster Semenya and Eero (...) Mäntyranta. South African Semenya is a middle‐distance runner whose right to compete in the female category has been challenged owing to her assumed difference of sex development and related high level of testosterone. Finnish Mäntyranta was a cross‐country skier with an exceptionally high haematocrit level. We examine whether there is a relevant difference between their advantages that would justify treating the athletes differently. We propose that the criterion ‘not attainable by other athletes in the same category’ could stand as a local criterion of fairness under certain conditions. However, its proper application requires further discussion on how to justify categories in sport. (shrink)

The precondition of any feminist politics – a usable category of ‘woman’ – has proved to be difficult to construct, even proposed to be impossible, given the ‘problem of exclusion’. This is the inevitable exclusion of at least some women, as their lives or experiences do not fit into the necessary and sufficient condition(s) that denotes group membership. In this paper, I propose that the problem of exclusion arises not because of inappropriate category membership criteria, but because of (...) the presumption that categories can only be organised by identity relations or shared properties among their members. This criterion of sameness as well as the characterisation of this exclusion as essentialism attests to a metaphysics that is not conducive to resistance and liberatory projects. Following a strain of hybrid thinking in feminist and post-colonial theory, I outline an alternative pluralist logic that confronts oppressive binaries that impede theory work in gender, sexuality, and race theory, and limit political action and resistance. The problem of exclusion is neither irresolvable nor is it essentialism. Instead it is a denial of subjectivity due to pseudodualistic self/Other dichotomies that can be resisted by adopting a new categorial logic. While this paper focuses on the specific problem of formulating a category of ‘woman’, it has implications for other areas of gender, critical race, and postcolonial theory. Rather than working toward an inclusive category founded on sameness, theorists need to develop independent and positive categories grounded in difference. Our current categorial logic does not permit such a project, and therefore a new metaphysics must be adopted. (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 child directed speech of twelve English‐speaking motherswas analyzed in terms of utterance‐level constructions. First, the mothers' utterances were categorized in terms of general constructional categories such as Wh‐questions, copulas and transitives. Second, mothers' utterances within these categories were further specified in terms of the initial words that framed the utterance, item‐based phrases such as Are you …, I'll …, It's …, Let's …, What did … The findings were: (i) overall, only about 15% of all maternal utterances had SVO (...) form (most were questions, imperatives, copulas, and fragments); (ii) 51% of all maternal utterances began with one of 52 item‐based phrases, mostly consisting of two words or morphemes (45% began with one of just 17 words); and (iii) children used many of these same item‐based phrases, in some cases at a rate that correlated highly with their own mother's frequency of use. We suggest that analyses of adult–child linguistic interaction should take into account not just general constructional categories, but also the item‐based constructions that adults and children use and the frequency with which they use them. (shrink)

The deployment of the Albanian admirative as well as the evidential particles kinse ‘allegedly’ and gjoja ‘supposedly’ in Kosovar electronic news sources to render either dubitative or neutral reports — depending on both the source and the timing — contributed to the project of an independent Kosovo. The usages can be divided into three periods: 1994–1997, 1998–1999, and post-1999. During the first period, usage was exclusively dubitative and deployed for Serbian news sources. During the second period, which corresponded to the (...) intensification of the armed uprising, usage shifted to neutrality, and during the third period, after the NATO bombing campaign, it returned somewhat to dubitativity, this time aimed at UN and NATO sources. The discussion demonstrates how pragmatics and grammatical categories contribute to the construction of political narratives and argues that a socially informed linguistic analysis is crucial to understanding how politics is performed in the world. (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)

This is an introduction to, and survey of, the constructive approaches to pure mathematics. The authors emphasise the viewpoint of Errett Bishop's school, but intuitionism. Russian constructivism and recursive analysis are also treated, with comparisons between the various approaches included where appropriate. Constructive mathematics is now enjoying a revival, with interest from not only logicans but also category theorists, recursive function theorists and theoretical computer scientists. This account for non-specialists in these and other disciplines.

This chapter discusses some of the central Aristotelian doctrines founded on dialectical argument. It focuses on the Topics and Categories, which deal at length with some of the central problems classified as ‘logical’ as opposed to physical or ethical. In the Topics, Aristotle shows how to argue about the four predicables: coincident, proprium, genus, and definition. The categories or ‘kinds of predicates’ are introduced as a tenfold division of each of the four predicables, the four possible types of properties predicted (...) in a dialectical proposition or discussed in a dialectical problem. The distinctions underlying this tenfold division are presented at greater length in the Categories. (shrink)

In a message posted to one of the cognitive science discussion groups the author asked, to paraphrase roughly, what should be read to get an up-to-date account of research into color naming? My advice is (and was) to consider the two books under review here: C. L. Hardin and Luisa Maffi’s excellent collection of essays on color language research; Robert MacLaury’s magnum opus on color naming and cognition.

After Kant, the school which further developed Kant's philosophy is the neo-kantianism. This neo-kantianism scholarship is characterized by the simultaneous development of Kant's epistemological and ontological problems. The ontological problem developed around Hartmann, and the epistemological problem developed around Cohen. Here we can see Cohen's achievements. Cohen completes epistemology in Logic of pure awareness(Logik der reinen Erkenntnis). In order to establish his own epistemology, Cohen first completes the problem of aspect category. And Cohen brings the problem of this aspect (...) category in the form of Plato and Aristotle. He connects these aspect categories and Kant's aspect categories. Like this, Cohen completes his perception logic in this aspect category. Plato, Aristotle, and Kant have different categories. Cohen first deals with the problem of the aspect based on the epistemology based on Plato's a priori. Next, he accepts metaphysical aspects of Aristotle's ten categories. Kant's aspect category is different from the other two philosophers. It is, soon, the basis of judgment. Cohen accepts Kant's aspect category of the very basis of his judgment for his epistemology. In this article, we first look at how Cohen embraced Plato, Aristotle, and Kant's view categories for his cognitive logic, and then see how he completed his aspect category. Whether epistemological or ontological, the construction of aspect category is for category theory, which is ultimately related to the laws of nature. Cohen also completes his categorization system in 12 categories, like Kant, centering on three aspect categories. Aristotle's ten categories, Kant's twelve categories, and Cohen's twelve categories eventually start with judgment. And so far, the number of these categories has been limited to twelve. Cohen argues that the number of these categories is likely to increase sufficiently. As science develops and societies become more complex, the number of categories is not as limited as Aristotle and Kant's view, but has the idea that there can be as many. Cohen explains his thoughts as Judgment of Methodology(Ureile der Methodik). We find here the merits of Cohen's cognitive logic. However, Cohen did not leave his view of the increasing number of categories or numbers. This is his disadvantage. The conclusion of this paper is to point out a problem with Cohen's aspect category by discussing the possibility of expanding or increasing the number of categories claimed by Cohen. (shrink)

Developing some suggestions of Ramsey (1925), elementary logic is formulated with respect to an arbitrary categorial system rather than the categorial system of Logical Atomism which is retained in standard elementary logic. Among the many types of non-standard categorial systems allowed by this formalism, it is argued that elementary logic with predicates of variable degree occupies a distinguished position, both for formal reasons and because of its potential value for application of formal logic to natural language and natural science. This (...) is illustrated by use of such a logic to construct a theory of quantity which is argued to be scientifically superior to existing theories of quantity based on standard categorial systems, since it yields real-valued scales without the need for unrealistic existence assumptions. This provides empirical evidence for the hypothesis that the categorial structure of the physical world itself is non-standard in this sense. (shrink)

Language exists because human subjects define themselves in the circumstance they are in. This is possible because they are able to know, not directly through their senses only, but adding something new to the construct they create in their conscience. The main thing they add to the construct created is categories, something invented or fabricated by the human subject at the moment of speaking.

We give a new Esakia-style duality for the category of Sugihara monoids based on the Davey-Werner natural duality for lattices with involution, and use this duality to greatly simplify a construction due to Galatos-Raftery of Sugihara monoids from certain enrichments of their negative cones. Our method of obtaining this simplification is to transport the functors of the Galatos-Raftery construction across our duality, obtaining a vastly more transparent presentation on duals. Because our duality extends Dunn's relational semantics for (...) the logic R-mingle to a categorical equivalence, this also explains the Dunn semantics and its relationship with the more usual Routley-Meyer semantics for relevant logics. (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)