Journal of Mathematical Logic, Ahead of Print. We study classes of modules closed under direct sums, [math]-submodules and [math]-epimorphic images where [math] is either the class of embeddings, RD-embeddings or pure embeddings. We show that the [math]-injective modules of theses classes satisfy a Baer-like criterion. In particular, injective modules, RD-injective modules, pure injective modules, flat cotorsion modules and [math]-torsion pure injective modules satisfy this criterion. The argument presented is a model theoretic one. We use in an essential way stable independence (...) relations which generalize Shelah’s non-forking to abstract elementary classes. We show that the classical model theoretic notion of superstability is equivalent to the algebraic notion of a noetherian category for these classes. We use this equivalence to characterize noetherian rings, pure semisimple rings, perfect rings and finite products of finite rings and artinian valuation rings via superstability. (shrink)

We study classes of modules closed under direct sums, [Formula: see text]-submodules and [Formula: see text]-epimorphic images where [Formula: see text] is either the class of embeddings, RD-embeddings or pure embeddings. We show that the [Formula: see text]-injective modules of theses classes satisfy a Baer-like criterion. In particular, injective modules, RD-injective modules, pure injective modules, flat cotorsion modules and [Formula: see text]-torsion pure injective modules satisfy this criterion. The argument presented is a model theoretic one. We use in an essential (...) way stable independence relations which generalize Shelah’s non-forking to abstract elementary classes. We show that the classical model theoretic notion of superstability is equivalent to the algebraic notion of a noetherian category for these classes. We use this equivalence to characterize noetherian rings, pure semisimple rings, perfect rings and finite products of finite rings and artinian valuation rings via superstability. (shrink)

Let A be the category of all reduced compact complex spaces, viewed as a multi-sorted first order structure, in the standard way. Let U be a sub-category of A, which is closed under the taking of products and analytic subsets, and whose morphisms include the projections. Under the assumption that Th(U) is unidimensional, we show that Morley rank is equal to Noetherian dimension, in any elementary extension of U. As a result, we are able to show that Morley degree (...) is definable in Th(U), when Th(U) is unidimensional. (shrink)

Probably colour is the best worked-out example of allegedly neurophysiologically innate response categories determining percepts and percepts determining concepts, and hence biology fixing the basic categories implicit in the use of language. In this paper I argue against this view and I take C. L. Hardin's Color for Philosophers [1988] as my main target. I start by undermining the view that four unique hues stand apart from all other colour shades (Section 2) and the confidence that the solar (...) spectrum is naturally divided into four categories (Section 3). For such categories to be truly universal, they have to be true for all peoples and in Section 4 I show that Berlin and Kay's [1969] widely quoted theory of basic colour categories is not sufficiently supported to lend it any credibility.Having disposed of the view that inspection of language or ‘pure’ perception unveils the universal colour categories. I turn to neurophysiological and psychophysical theories of colour vision to see whether they provide a more solid basis for deciding what the innate response categories are. In Section 5 I show that Hardin's account of the opponent-process theory neither supports his view that ‘colour-coding’takes place early in the visual neural pathway, nor his view that knowledge of colour vision science will help us solve many philosophical mysteries about colour.In Section 6 I give a more detailed review of what is known today about the neurophysiology of colour vision and I show that there's nothing in the brain which could be called a colour module, let alone a module with homunculi for particular basic colour categories. In Section 7 I show that psychophysical models do not support such rigid constraints on category formation either. Hence (Section 8), at least in the case of colour, current science supports a plasticity in the formation of categories that goes far beyond the requirements of those naturalistic philosophers who would like to ground primitive concepts in biology. (shrink)

A classification of models of reduction into three categories — theory reductionism, explanatory reductionism, and constitutive reductionism — is presented. It is shown that this classification helps clarify the relations between various explications of reduction that have been offered in the past, especially if a distinction is maintained between the various epistemological and ontological issues that arise. A relatively new model of explanatory reduction, one that emphasizes that reduction is the explanation of a whole in terms of its parts (...) is also presented in detail. Finally, the classification is used to clarify the debate over reductionism in molecular biology. It is argued there that while no model from the category of theory reduction might be applicable in that case, models of explanatory reduction might yet capture the structure of the relevant explanations. (shrink)

Biology and Philosophy, forthcoming 2007.

In Experience and Education, John Dewey described how learning should occur in schools, and what the results of that learning should be. Critiquing both the traditional educational practices of his time and the progressive schools that took some of their ideas from his own work, Dewey put forth what he called the "educative" experience (LW 13: 11) as the aim of formal instruction. The educative experience is affectively engaging, intelligently directed, and disciplined by the demands of purposeful and social activity. (...) It leads to growth in possibilities for perception and action. Dewey contrasted the educative experience to those experiences he labeled as "mis-educative" (LW 13: 11), which, lacking some or all of .. (shrink)

Gärdenfors (Conceptual spaces, 2000) argues that the semantic domains that natural language deals with have a geometrical structure. He gives evidence that simple natural language adjectives usually denote natural properties, where a natural property is a convex region of such a “conceptual space.” In this paper I will show that this feature of natural categories need not be stipulated as basic. In fact, it can be shown to be the result of evolutionary dynamics of communicative strategies under very general (...) assumptions. (shrink)

The cuteness of the avant-garde -- Merely interesting -- The zany science.

The social categories to which we belong—Latino, disabled, American, woman— causally influence our lives in deep and unavoidable ways. One might be pulled over by police because one is Latino, or one might receive a COVID vaccine sooner because one is American. Membership in these social categories most often falls outside of our control. This paper argues that membership in social categories constitutes a restriction on human agency, creating a situation of non-ideal agency for many human individuals. (...) -/- However, there are ways to resist the causal influence of social categories, and certain socially marginalized groups can be understood as attempting to do just this. I discuss two instances of social category resistance: gender pronouns and the rights of trans individuals. I suggest that the intentional declaration of gender pronouns (“she/her” or “they/them”) can be understood as an attempt to resist the causal powers of nonconsensual social categorization. Similarly, one among many reasons to support the rights of trans individuals is that their self-declarations of gender identity can be viewed as a reclamation of agency in the face of causal constraints imposed by socially defined and imposed gender categories. This lesson can be generalized to people belonging to a broad range of marginalized groups. (shrink)

Kant's transcendental deduction yields twelve and only twelve categories, but behind the argument lie two assumptions: 1) newtonian physics gives unalterable and certain knowledge of phenomena; 2) the subject-predicate logic is the correct tool for the analysis of knowledge. this article examines the place of both assumptions in kant's doctrine and the relevance of each today. both assumptions must be discarded, and with them goes the rigidity of the categories; but the article shows how kant's important insights into (...) the place of the categories in knowledge can be salvaged. (shrink)

A pluralistic view of psychiatric classification is defended, according to which psychiatric categories take a variety of structural forms. An ordered taxonomy of these forms—non-kinds, practical kinds, fuzzy kinds, discrete kinds, and natural kinds—is presented and exemplified. It is argued that psychiatric categories cannot all be understood as pragmatically grounded, and at least some reflect naturally occurring discontinuities without thereby representing natural kinds. Even if essentialist accounts of mental disorders are generally mistaken, they are not implied whenever a (...) psychiatric category that is not pragmatically grounded is posited. (shrink)

The method of morphisms is a well-known application of Dialectica categories to set theory. In a previous work, Valeria de Paiva and the author have asked how much of the Axiom of Choice is needed in order to carry out the referred applications of such method. In this paper, we show that, when considered in their full generality, those applications of Dialectica categories give rise to equivalents of either the Axiom of Choice or Partition Principle —which is a (...) consequence of $\textbf{AC}$ whose precise status of its relationship with$\textbf{AC}$ itself is an open problem for more than a hundred years. (shrink)

This book develops an account of what substance is in terms of the notion of independence. As the authors note, there is a tradition of defining substance as independent that begins with Aristotle. But what notion of independence can provide an adequate definition of substance? The authors find traditional attempts to define independence, including Aristotle’s, inadequate on a number of grounds, and they propose an alternative account. As a preface to this undertaking, the authors consider and reject a number of (...) standard objections to their project, and as an afterword, they argue that the notion of spiritual substance is as intelligible as the notion of material substance. (shrink)

We explore the possibility and some potential payoffs of using the theory of accessible categories in the study of categories of logics. We illustrate this by two case studies focusing on the category of finitary structural logics and its subcategory of algebraizable logics.

In Predication and Ontology A. Kalbarczyk provides the first monograph-length study of the Arabic reception of Aristotle’s Categories. At the center of attention is the critical reappraisal of that treatise by Ibn Sīnā, better known in the Latin West as Avicenna. Ibn Sīnā’s reading of the Categories is examined in the context of his wider project of rearranging the transmitted body of philosophical knowledge. Against the background of the late ancient commentary tradition and subsequent exegetical efforts, Ibn Sīnā’s (...) Kitāb al-Maqūlāt of the Šifāʾ is interpreted as a milestone in the gradual reshuffle of the relationship between logic proper and ontology. In order to assess the philosophical impact of this realignment, some of the subsequent developments in Ibn Sīnā’s writings and in the emerging post-Avicennian tradition are also taken into account. The thematic focus lies on the two fundamental classification schemes which Aristotle introduces in the treatise: the fourfold division of Cat. 2 and the tenfold scheme of Cat. 4. They both pose the question of whether and how the manner in which an expression is predicated relates to extra-linguistic reality. As the study intends to show, this question is one of the driving forces of Ibn Sīnā’s momentous reform of the Aristotelian curriculum. (shrink)