The sex aetates mundi was the central framework of Early Christian, Late Antique, and early medieval Christian eschatology and historiography. This article is the second part of a study of the development and history of this motif. Part I summarised the emergence of this framework in biblical and patristic writings up to the late fourth-century, concluding with the work of the North African theologian, Tyconius. The second part of this study investigates the treatment of this subject in the writings of (...) Augustine of Hippo, Dionysius Exiguus, Isidore of Seville, and the Venerable Bede. The majority of the examination is devoted to tracing Augustine’s understanding of the six ages – which was strongly influenced by Tyconius – since Augustine is frequently credited with being the main proponent of this conceptualisation of sacred history. This investigation of Augustine’s writings is mostly focused on De civitate Dei, the work that addresses the six ages framework most thoroughly, but analyses references to this historiography throughout his corpus. The conclusion of this examination argues that Augustine engaged with this commonplace view of history, but only insofar as it points mankind towards reflection of the world to come. This study argues that Isidore is the scholar who should be credited with popularising this notion in the early medieval Latin West. How the developments in calendrical reckoning put forward by Dionysius Exiguus and Bede intersect with and influence the six ages model is also charted. Overall, this study provides an in-depth examination of the six ages of history model in the thought of the fathers of Late Antique and early medieval Latin exegesis, pinpointing key moments in the evolution of the sex aetates model. (shrink)

Theories of discourse bring to realism new ideas about how knowledge develops and how representations of reality are influenced. We gain an understanding of the conceptual aspect of social life and the processes by which meaning is produced. This collection reflects the growing interest realist critics have shown towards forms of discourse theory and deconstruction. The diverse range of contributions address such issues as the work of Derrida and deconstruction, discourse theory, Eurocentrism and poststructuralism. What unites all of the contributions (...) is a sense that it is essential to provide a realist alternative to the hitherto dominance of social constructionism, hermeneutics and postmodernism, over many of the issues discussed. By developing a realist perspective the different authors attempt to embed discourse within the structured nature of the reality of the world. Realism can situate language, discourse and ideology within context specific, or 'causally efficacious' circumstances. Realism can help to uncover issues of power, representation, and subjectivity and how discursive and other social practices produce real effects. This can help us understand the manner in which social structures are reproduced through various forms of ideology and discourse. And by knowing this, we can start to address questions concerning human emancipation and how the world is to be transformed. (shrink)

Topics covered in Discrete Mathematics have become essential tools in many areas of studies in recent years. This is primarily due to the revolution in technology, communications, and cyber security. The book treats major themes in a typical introductory modern Discrete Mathematics course: Propositional and predicate logic, proof techniques, set theory (including Boolean algebra, functions and relations), introduction to number theory, combinatorics and graph theory. An accessible, precise, and comprehensive approach is adopted in the treatment of each topic. The ability (...) of abstract thinking and the art of writing valid arguments are emphasized through detailed proof of (almost) every result. Developing the ability to think abstractly and roguishly is key in any areas of science, information technology and engineering. Every result presented in the book is followed by examples and applications to consolidate its comprehension. The hope is that the reader ends up developing both the abstract reasoning as well as acquiring practical skills. All efforts are made to write the book at a level accessible to first-year students and to present each topic in a way that facilitates self-directed learning. Each chapter starts with basic concepts of the subject at hand and progresses gradually to cover more ground on the subject. Chapters are divided into sections and subsections to facilitate readings. Each section ends with its own carefully chosen set of practice exercises to reenforce comprehension and to challenge and stimulate readers. As an introduction to Discrete Mathematics, the book is written with the smallest set of prerequisites possible. Familiarity with basic mathematical concepts (usually acquired in high school) is sufficient for most chapters. However, some mathematical maturity comes in handy to grasp some harder concepts presented in the book. (shrink)

A theorem on the extendability of certain subsets of a Boolean algebra to ultrafilters which preserve countably many infinite meets (generalizing Rasiowa-Sikorski) is used to pinpoint the mechanism of the Barwise proof in a way which bypasses the set theoretical elaborations.

The present note is a reworking and streamlining of Daigneault and Monk's Representation Theory for Polyadic Algebras. MSC: 03G15.

The point of Hegel's dissatisfaction with Kant -- Rethinking Peirce's fallibilism -- Pragmatism's future : a touch of prophecy.

CONTEMPORARY ISSUES IN BUSINESS ETHICS, 6E introduces readers to business ethics by focusing on the influence of market mechanisms and social values on workplace norms. And because business is increasingly a global enterprise, this edition emphasizes the role of ethics both at home and abroad.

There is a growing body of empirical evidence which shows that infants and non-human primates have the ability to represent the mental states of other agents, i.e. that they possess a Theory of Mind. We will argue that this evidence also suggests that infants and non-human primates possess the concept of truth, which, as we will explain, is good news for primitivists about truth. First, we will offer a brief overview of alethic primitivism, focusing on Jamin Asay’s conceptual version of (...) the view. Next, we will survey relevant work on Theory of Mind which indicates that children younger than two and non-human primates are able to attribute false beliefs. Then, we will bring these false-belief data to bear on Asay’s form of primitivism, arguing that the data support two of the four distinctive theses of this view and offering some remarks about the empirical evaluability of the two remaining theses. We hope that our discussion will help to bridge the gap between psychological and philosophical inquiry and that it will encourage further empirical research on the cognitive significance of the concept of truth for humans and other thinking creatures. (shrink)

Belief storage is often modeled as having the structure of a single, unified web. This model of belief storage is attractive and widely assumed because it appears to provide an explanation of the flexibility of cognition and the complicated dynamics of belief revision. However, when one scrutinizes human cognition, one finds strong evidence against a unified web of belief and for a fragmented model of belief storage. Using the best available evidence from cognitive science, we develop this fragmented model into (...) a nascent theory of the cognitive architecture of belief storage. (shrink)