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This edited collection casts light on central issues within contemporary philosophy of mathematics such as the realism/anti-realism dispute; the relationship between logic and metaphysics; and the question of whether mathematics is a science of objects or structures. The discussions offered in the papers involve an in-depth investigation of, among other things, the notions of mathematical truth, proof, and grounding; and, often, a special emphasis is placed on considerations relating to mathematical practice. A distinguishing feature of the book is the multicultural nature of the community that has produced it. Philosophers, logicians, and mathematicians have all contributed high-quality articles which will prove valuable to researchers and students alike.
This book develops a novel generalization of possible world semantics, called ‘world line semantics’, which recognizes worlds and links between world-bound objects (world lines) as mutually independent aspects of modal semantics. Addressing a wide range of questions vital for contemporary debates in logic and philosophy of language and offering new tools for theoretical linguistics and knowledge representation, the book proposes a radically new paradigm in modal semantics. This framework is motivated philosophically, viewing a structure of world lines as a precondition of modal talk. The author provides a uniform analysis of quantification over individuals (physical objects) and objects of thought (intentional objects). The semantic account of what it means to speak of intentional objects throws new light on accounts of intentionality and singular thought in the philosophy of mind and offers novel insights into the semantics of intensional transitive verbs.
This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. An Introduction to Substrucural Logics is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered: * Proof Theory * Propositional Structures * Frames * Decidability * Coda Both students and professors of philosophy, computing, linguistics, and mathematics will find this to be an important addition to their reading.
Logics of Worlds is the sequel to Alain Badiou's masterpiece, Being and Event. Tackling the questions that had been left open by Being and Event, and answering many of his critics in the process, Badiou supplements his pioneering treatment of multiple being with a daring and complex theory of the worlds in which truths and subjects make their mark - what he calls a materialist dialectic. Drawing on his most ambitious philosophical predecessors - Leibniz, Kant, Hegel, Kierkegaard, Lacan, Deleuze – Badiou ends this important later work with an impassioned call to 'live for an Idea'.
This book provides a collection of chapters on the development of scientific philosophy and symbolic logic in the early twentieth century. The turn of the last century was a key transitional period for the development of symbolic logic and scientific philosophy. The Peano school, the editorial board of the Revue de Métaphysique et de Morale, and the members of the Vienna Circle are generally mentioned as champions of this transformation of the role of logic in mathematics and in the sciences. The scholarship contained provides a rich historical and philosophical understanding of these groups and research areas. Specifically, the contributions focus on a detailed investigation of the relation between structuralism and modern mathematics. In addition, this book provides a closer understanding of the relation between symbolic logic and previous traditions such as syllogistics. This volume also informs the reader on the relation between logic, the history and didactics in the Peano School. This edition appeals to students and researchers working in the history of philosophy and of logic, philosophy of science, as well as to researchers on the Vienna Circle and the Peano School.
The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bell’s own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic (William Lawvere, Peter Aczel, Graham Priest, Giovanni Sambin); analytical philosophy (Michael Dummett, William Demopoulos), philosophy of science (Michael Redhead, Frank Arntzenius), philosophy of mathematics (Michael Hallett, John Mayberry, Daniel Isaacson) and decision theory and foundations of economics (Ken Bimore). Most articles are contributions to current philosophical debates, but contributions also include some new mathematical results, important historical surveys, and a translation by Wilfrid Hodges of a key work of arabic logic.
This book presents the leading edge in several related fields, specifically object orientated programming, open distributed systems and formal methods for object oriented systems. With increased support within industry regarding these areas, this book captures the most up-to-date information on the subject. Many topics are discussed, including the following important areas: object oriented design and programming; formal specification of distributed systems; open distributed platforms; types, interfaces and behaviour; formalisation of object oriented methods.
Building a foundational understanding of the digital, Logic of the Digital reveals a unique digital ontology. Beginning from formal and technical characteristics, especially the binary code at the core of all digital technologies, Aden Evens traces the pathways along which the digital domain of abstract logic encounters the material, human world. How does a code using only 0s and 1s give rise to the vast range of applications and information that constitutes a great and growing portion of our world? Evens' analysis shows how any encounter between the actual and the digital must cross an ontological divide, a gap between the productive materiality of the human world and the reductive abstraction of the binary code. Logic of the Digital examines the distortions of this ontological crossing, considering the formal abstraction that persists in exemplary digital technologies and techniques such as the mouse, the Web, the graphical user interface, and the development of software. One crucial motive for this research lies in the paradoxical issue of creativity in relation to digital technologies: the ontology of abstraction leaves little room for the unpredictable or accidental that is essential to creativity, but digital technologies are nevertheless patently creative. Evens inquires into the mechanisms by which the ostensibly sterile binary code can lend itself to such fecund cultural production. Through clarification of the digital's ontological foundation, Evens points to a significant threat to creativity lurking in the nature of the digital and so generates a basis for an ethics of digital practice. Examining the bits that give the digital its ontology, exploring the potentials and limitations of programming, and using gaming as an ideal test of digital possibility, Logic of the Digital guides future practices and shapes academic research in the digital.
This book constitutes the refereed proceedings of the 4th International Conference on Deductive and Object-Oriented Databases, DOOD '95, held in Singapore in December 1995. Besides two keynote papers by Stefano Ceri and Michael Kifer, the book contains revised full versions of 28 papers selected from a total of 88 submissions. The volume gives a highly competent state-of-the-art report on DOOD research and advanced applications. The papers are organized in sections on active databases, query processing, semantic query optimization, transaction management, authorization, implementation, and applications.