We explore some topics in the model theory of sheaves of modules. First we describe the formal language that we use. Then we present some examples of sheaves obtained from quivers. These, and other examples, will serve as illustrations and as counterexamples. Then we investigate the notion of strong minimality from model theory to see what it means in this context. We also look briefly at the relation between global, local and pointwise versions of properties related to acyclicity.

Elementary duality between left and right modules over a ring, especially its interpretation in terms of the relevant functor categories, is discussed, as is the relationship between these categories of functors and sorts in theories of modules. A topology on the set of indecomposable pure-injective modules over a ring is introduced. This topology is dual to the Ziegler topology and may be seen as a generalisation of the Zariski topology.

Rings which, from the ring-theoretic point of view, are very different may well have categories of modules which are extremely similar. More generally, the category of modules over a ring may contain many other categories of modules. Ideas from model theory are of use in elucidating this state of affairs. In particular we investigate the model-theoretic effect of tilting functors between categories of modules.

Abstract:In this paper, we explore challenges in conveying the culturally constructed meanings of local Indigenous musics and the worldviews they manifest to students in K-12 school music classes, when foundational aspects of the English language, historical and current discourse, and English language habits function to thwart the transmission of those meanings. We recount how, in settler colonial societies in North America, speakers of the dominant English language have historically misrepresented, discredited, and obscured cultural meanings that inhere in local Indigenous musics. (...) First, we examine three ways in which the use of English has distorted the cultural meanings of those musics. Next, we explain how historical discourses in English have intentionally undervalued or discredited the values intrinsic to those musics, also describing how some current music education discourse in English might work against the embedding of Indigenous meanings in school music education settings. We then consider additional factors distinguishing Indigenous languages from European languages (especially English) to show how a people’s “language habits” influence their perception of and thus their relationship with their natural environment. We conclude by considering the role of music education in revitalizing local Indigenous languages and musics and advancing the cultural values of their originating communities. (shrink)

Using the description of the Ziegler spectrum we characterise modules with various stability-theoretic properties (ω-stability, superstability, categoricity) over certain classes of finite-dimensional algebras. We also show that, for modules over the algebras we consider, having few types is equivalent to being ω-stable.

The central aim of this book is to understand modules and the categories they form through associated structures and dimensions, which reflect the complexity of these, and similar, categories.

In the model theory of modules the Ziegler spectrum, the space of indecomposable pure-injective modules, has played a key role. We investigate the possibility of defining a similar space in the context of G-sets where G is a group.

This collection addresses a post-WWII shift in the hierarchy of scientific explanations, where the highest goal moves from reductionism towards some ...

A formulação habermasiana de racionalidade aponta a possibilidade de renovação da base justificadora da educação, pela emergência do universal na comunicação entre as diferentes experiências dos atores, nutridas pelas particularidades do mundo vivido. Isso permite à educação orientar-se por uma racionalidade que assegure a pluralidade e as diferenças, bem como formar a identidade de sujeitos racionais capazes de assumir compromissos éticos.

In much of the current academic and public discussion, conspiracy theories are portrayed as a negative phenomenon, linked to misinformation, mistrust in experts and institutions, and political propaganda. Rather surprisingly, however, philosophers working on this topic have been reluctant to incorporate a negatively evaluative aspect when either analyzing or engineering the concept conspiracy theory. In this paper, we present empirical data on the nature of the concept conspiracy theory from five studies designed to test the existence, prevalence and exact form (...) of an evaluative dimension to the ordinary concept conspiracy theory. These results reveal that, while there is a descriptive concept of conspiracy theory, the predominant use of conspiracy theory is deeply evaluative, encoding information about epistemic deficiency and often also derogatory and disparaging information. On the basis of these results, we present a new strategy for engineering conspiracy theory to promote theoretical investigations and institutional discussions of this phenomenon. We argue for engineering conspiracy theory to encode an epistemic evaluation, and to introduce a descriptive expression—such as ‘conspiratorial explanation’—to refer to the purely descriptive concept conspiracy theory. (shrink)

Let G be a finite group. For every formula ø in the language of groups, let K denote the class of groups H such that ø is a normal abelian subgroup of H and the quotient group H;ø is isomorphic to G. We show that if G is nilpotent and its order is not square-free, then there exists a formula ø such that the theory of K is undecidable.

Contingency is the presence of non-actualized possibility in the world. Fatalism is a view of reality on which there is no contingency. Since it is contingency that permits agency, there has traditionally been much interest in contingency. This interest has long been embarrassed by the contention that simple and plausible assumptions about the world lead to fatalism. I begin with an Aristotelian argument as presented by Richard Taylor. Appreciation of this argument has been stultified by a question pertaining to the (...) source of necessity and possibility and a closely related one regarding the nature of metaphysics itself. Answering these questions reveals the crucial issue here, to wit, necessity and possibility in a temporal world. This issue is investigated through an important later criticism of Taylor by David Foster Wallace. Wallace’s critique is significant because it brings to the fore the pivotal notion for understanding contingency in a temporal world, that of synchronic possibility, the idea that incompatible states of affairs are possible at a single moment. This notion provides the basis of distinguishing two systematic accounts of truth, modality and time: two metaphysics of contingency. On one account, Taylor’s Aristotelian argument is straightforwardly valid and compelling; on the other, it is fallacious. In closing, I present reasons why the former account, supporting the Aristotelian views of time and truth, is correct and make some comments to ameliorate this conclusion. (shrink)

For the theorists of crisis, the revolutionary state comes into existence through violence, and due to its inability to provide an authoritative katechon (restrainer) against internal and external violence, it perpetuates violence until it self-destructs. Writing during extreme economic depression and growing social and political violence, the crisis theorists––Joseph de Maistre, Juan Donoso Cortés, and Carl Schmitt––each sought to blame the chaos of their time upon the Janus-faced postrevolutionary ideals of liberalism and socialism by urging a return to pre-revolutionary moral (...) and religious values. They are united by three counterrevolutionary principles, all of which are purported to remedy revolutionary violence: traditional constitutional fidelity, the philosophy of the decision, and opposition to bourgeois liberalism. This essay is followed by the first complete English translation and publication of Donoso’s letter of October 24, 1851, which contains Donoso’s only reference to the “discussing class,” a political entity later popularized by Schmitt in his 1922 work Political Theology. (shrink)

The X-ray and bulk densities of PdIn alloys have been determined at ambient temperature on samples annealed at 1273 and 1373 K and quenched in water-ice mixtures. From these measurements the vacancy concentrations in this intermetallic phase have been obtained as a function of In concentration at these two temperatures. In addition, a generalized thermodynamic model is presented which considers the existence of antisite and vacancy defects on both sublattices without any dilute solution approximations. This model uses three energy parameters, (...) whose values have been obtained for PdIn using the measured vacancy concentrations and the chemical potentials of In. This model is able to describe all the available vacancy data and is suitable for calculating these values at compositions and temperatures when such data are not available. In addition, the model permits the calculation of the concentrations of the minority point defects. It is shown that dilute-solution approximations, which have invariably been used in this kind of modelling, are unsatisfactory. The present results and their analysis confirm that PdIn is a near-triple-defect type of intermetallic and not a near-Schottky type, as has been claimed recently. (shrink)

Reprint of paper first published in Philosophy and Phenomenological Research in 1984.

Early in his Essays on Intellectual Powers, Reid draws a distinction between mental power, mental operation, and mental capacity (EIP 21). To the untrained eye, these terms could probably be used interchangeably, and Reid believes this is correct, up to a point. He argues that, if we are interested in understanding exactly how the human mind works, we must use these terms with more precise meanings. This is part of his more general strategy of trying to always use the words (...) with their common meanings, as much as possible, but also pointing out that certain philosophical distinctions are needed to carry out the project of laying out the foundations of the science of the mind. This paper explains what the distinction between power, operation, and capacity is, according to Reid, with the goal of understanding why it is important to draw such a distinction, not only for the Reidian project, but for action theory, more generally. (shrink)

This volume provides a philosophical introduction to and analysis of the study of metaphor. By proceeding from the concrete analysis of complex metaphors, White is able to identify a range of features which are incompatible with standard accounts of the way words function in metaphor.

In this short text, a distinguished philosopher turns his attention to one of the oldest and most fundamental philosophical problems of all: How it is that we are able to sort and classify different things as being of the same natural class? Professor Armstrong carefully sets out six major theories—ancient, modern, and contemporary—and assesses the strengths and weaknesses of each. Recognizing that there are no final victories or defeats in metaphysics, Armstrong nonetheless defends a traditional account of universals as the (...) most satisfactory theory we have.This study is written for advanced students, but as Armstrong goes considerably beyond his earlier work on this topic, it will interest professional scholars as well. Carefully plotted and clearly written, Universals is both a paradigm of exposition and a case study on the value of careful analysis of fundamental issues in philosophy. (shrink)

Bioethics has paid surprisingly little attention to the special problems faced by women and to feminist analyses of current health care issues other than ...

In this important study D. M. Armstrong offers a comprehensive system of analytical metaphysics that synthesises but also develops his thinking over the last twenty years. Armstrong's analysis, which acknowledges the 'logical atomism' of Russell and Wittgenstein, makes facts the fundamental constituents of the world, examining properties, relations, numbers, classes, possibility and necessity, dispositions, causes and laws. All these, it is argued, find their place and can be understood inside a scheme of states of affairs. This is a comprehensive and (...) rigorously this-worldly account of the most general features of reality, argued from a distinctive philosophical perspective, and it will appeal to a wide readership in analytical philosophy. (shrink)

Arguably no concept is more fundamental to science than that of causality, for investigations into cases of existence, persistence, and change in the natural world are largely investigations into the causes of these phenomena. Yet the metaphysics and epistemology of causality remain unclear. For example, the ontological categories of the causal relata have been taken to be objects (Hume 1739), events (Davidson 1967), properties (Armstrong 1978), processes (Salmon 1984), variables (Hitchcock 1993), and facts (Mellor 1995). (For convenience, causes and effects (...) will usually be understood as events in what follows.) Complicating matters, causal relations may be singular (Socrates’s drinking hemlock caused Socrates’s death) or general (Drinking hemlock causes death); hence the relata might be tokens (e.g., instances of properties) or types (e.g., types of events) of the category in question. Other questions up for grabs are: Are singular causes metaphysically and/or epistemologically prior to general causes or vice versa (or neither)? What grounds the intuitive asymmetry of the causal relation? Are macro-causal relations reducible to micro-causal relations? And perhaps most importantly: Are causal facts (e.g., the holding of causal relations) reducible to non-causal facts (e.g., the holding of certain spatiotemporal relations)? (shrink)