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Free logic - i.e., logic free of existential presuppositions in general and with respect to singular terms in particular- began to come into its own as a field of research in the 1950s. As is the case with so many developments in Western philosophy, its roots can be traced back to ancient Greek philo sophy. It is only during the last fifty years, however, that it has become well established as a branch of modern logic. The name of Karel Lambert is most closely connected with this development: he gave it its name and its profile as a well defined field of research. After a development of fifty years, it is time to look back and take stock while at the same time scanning for new perspectives. This is the purpose of the papers collected in this volume. The first paper is written by Karel Lambert himself who also comments on all the papers of the other authors. In an introductory essay we give a survey of the present status of and new directions in free logic.
This volume contains a collection of recent papers on Free Logic which cover a wide range of topics. These topics show that Free Logic is applied not only in traditional philosophical areas, but also in various contexts of modern formal logic as well as in the discussion of theoretical aspects of programming. Part I of the book covers theories of names and definite descriptions. Part II contains papers on various topics in the logic of modalities. Part III is devoted to semantics and programming. In part IV Free Logic is used to analyse and discuss topics from the history of philosophy. In addition, one of the founders of Free Logic, Karel Lambert, not only contributes an article to this volume, but he also comments the papers of all the other authors. So this book will be of interest not only to philosophers and logicians, but also to computer scientists and researchers interested in foundational aspects of computer programming.
Questions about truth and questions about reality are intimately connected. One can ask whether numbers exist by asking "Are there numbers?" But one can also ask what arguably amounts to the same question by asking "Is the sentence 'There are numbers' true?" Such semantic ascent implies that reality can be investigated by investigating our true sentences. This line of thought was dominant in twentieth century philosophy, but is now beginning to be called into question. In From Truth to Reality, Heather Dyke brings together some of the foremost metaphysicians to examine approaches to truth, reality, and the connections between the two. This collection features new and previously unpublished material by JC Beall, Mark Colyvan, Michael Devitt, John Heil, Frank Jackson, Fred Kroon, D. H. Mellor, Luca Moretti, Alan Musgrave, Robert Nola, J. J. C. Smart, Paul Snowdon, and Daniel Stoljar.
Free logic is an important field of philosophical logic that first appeared in the 1950s. J. Karel Lambert was one of its founders and coined the term itself. The essays in this collection (written over a period of 40 years) explore the philosophical foundations of free logic and its application to areas as diverse as the philosophy of religion and computer science. Amongst the applications on offer are those to the analysis of existence statements, to definite descriptions and to partial functions. The volume contains a proof that free logics of any kind are non-extensional and then uses that proof to show that Quine's theory of predication and referential transparency must fail. The purpose of this collection is to bring an important body of work to the attention of a new generation of professional philosophers, computer scientists and mathematicians.
Bertrand Russell, the recipient of the 1950 Nobel Prize for Literature, was one of the most distinguished, influential, and prolific philosophers of the twentieth century. Part of his importance consists in the significant contributions he made to mathematical logic, epistemology, philosophy of language, philosophy of mind, metaphysics, and philosophy of science. But he is also widely recognized for his achievements as a public figure, social activist, and gifted popularizer who brought philosophy and science outside of the ivory tower with rare clarity and wit. Both of these elements harmoniously come together in his 1912 "The Problems of Philosophy," a deceptively short book originally intended for a mass-audience of working adults but which has since become a core reading in the philosophical canon. This volume brings together 10 new essays on "The Problems of Philosophy" by some of the foremost scholars of Russell s life and works. These essays reexamine Russell s famous distinction between knowledge by acquaintance and knowledge by description, his developing views about our knowledge of physical reality, and his views about our knowledge of logic, mathematics, and other abstract matters. In addition, it includes an editors introduction, which summarizes Russell s book, highlights its continued significance for contemporary philosophy, and presents new biographical details about how and why Russell wrote it. "
In this exciting new collection, a distinguished international group of philosophers contribute new essays on central issues in philosophy of language and logic, in honor of Michael Dummett, one of the most influential philosophers of the late twentieth century. The essays are focused on areas particularly associated with Professor Dummett. Five are contributions to the philosophy of language, addressing in particular the nature of truth and meaning and the relation between language and thought. Two contributors discuss time, in particular the reality of the past. The last four essays focus on Frege and the philosophy of mathematics. The volume represents some of the best work in contemporary analytical philosophy.
A diverse group of contributors reflect on the philosophical legacy of Fred Sommers and his efforts to revive and refashion traditional Aristotelian logic for a post-Fregean world.
This edited volume collects essays on the four-valued logic known as Belnap-Dunn logic, or first-degree entailment logic (FDE). It also looks at various formal systems closely related to it. These include the strong Kleene logic and the Logic of Paradox. Inside, readers will find reprints of seminal papers written by the fathers of the field: Nuel Belnap and Michael Dunn. In addition, the collection also features a well-known but previously unpublished manuscript of Dunn, an interview with Belnap, and a new essay by Dunn. Besides the original, monumental papers, the book also includes research by leading scholars. They consider the extraordinary importance of Belnap-Dunn logic from several perspectives. They look at how, philosophically, it has served as a basic system of inconsistency-tolerant reasoning, as the core of underlying logics for theories based on dialetheism, and, more recently, for theories based on Buddhist philosophy. Coverage also explores its contributions to computer science, such as knowledge representation and information processing. This mix of seminal papers and insightful analysis by top scholars offers readers a comprehensive outlook on Belnap-Dunn logic and its related expansions, which have been agenda setting for the debate on philosophical logic as well as philosophy of logic. The book will also enhance further discussion on the philosophical issues related to nonclassical logics in general.
Starting with simple examples showing the relevance of cutting and pasting logics, the monograph develops a mathematical theory of combining and decomposing logics, ranging from propositional and first-order based logics to higher-order based logics as well as to non-truth functional logics. The theory covers mechanisms for combining semantic structures and deductive systems either of the same or different nature. The issue of preservation of properties is addressed.
These are exciting times for philosophical theorizing about propositions, with the last 15 years seeing the development of new approaches and the emergence of new theorists. Propositions have been invoked to explain thought and cognition, the nature and attribution of mental states, language and communication, and in philosophical treatments of truth, necessity and possibility. According to Frege and Russell, and their followers, propositions are structured mind- and language-independent abstract objects which have essential and intrinsic truth-conditions. Some recent theorizing doubts whether propositions really exist and, if they do, asks how we can grasp, entertain and know them? But most of the doubt concerns whether the abstract approach to propositions can really explain them. Are propositions really structured, and if so where does their structure come from? How does this structure form a unity, and does it need to? Are the representational and structural properties of propositions really independent of those of thinking and language? What does it mean to say that an object occurs in or is a constituent of a proposition? The volume takes up these and other questions, both as they apply to the abstract object approach and also to the more recently developed approaches. While the volume as a whole does not definitively and unequivocally reject the abstract objection approach, for the most part, the papers explore new critical and constructive directions. This book was originally published as a special issue of the Canadian Journal of Philosophy.