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Vague Objects and Vague Identity
This unique anthology of new, contributed essays offers a range of perspectives on various aspects of ontic vagueness. It seeks to answer core questions pertaining to onticism, the view that vagueness exists in the world itself. The questions to be addressed include whether vague objects must have vague identity, and whether ontic vagueness has a distinctive logic, one that is not shared by semantic or epistemic vagueness. The essays in this volume explain the motivations behind onticism, such as the plausibility of mereological vagueness and indeterminacy in quantum mechanics and they offer various arguments both for and against ontic vagueness; onticism is also compared with other, competi...
Pluralisms in Truth and Logic
This edited volume brings together 18 state-of-the art essays on pluralism about truth and logic. Parts I and II are dedicated to respectively truth pluralism and logical pluralism, and Part III to their interconnections. Some contributors challenge pluralism, arguing that the nature of truth or logic is uniform. The majority of contributors, however, defend pluralism, articulate novel versions of the view, or contribute to fundamental debates internal to the pluralist camp. The volume will be of interest to truth theorists and philosophers of logic, as well as philosophers interested in relativism, contextualism, metaphysics, philosophy of language, semantics, paradox, epistemology, or normativity.
Foundations of Logical Consequence
Logical consequence is the relation that obtains between premises and conclusion(s) in a valid argument. Orthodoxy has it that valid arguments are necessarily truth-preserving, but this platitude only raises a number of further questions, such as: how does the truth of premises guarantee the truth of a conclusion, and what constraints does validity impose on rational belief? This volume presents thirteen essays by some of the most important scholars in the field of philosophical logic. The essays offer ground-breaking new insights into the nature of logical consequence; the relation between logic and inference; how the semantics and pragmatics of natural language bear on logic; the relativity of logic; and the structural properties of the consequence relation.
Pluralism in Mathematics: A New Position in Philosophy of Mathematics
This book is about philosophy, mathematics and logic, giving a philosophical account of Pluralism which is a family of positions in the philosophy of mathematics. There are four parts to this book, beginning with a look at motivations for Pluralism by way of Realism, Maddy’s Naturalism, Shapiro’s Structuralism and Formalism. In the second part of this book the author covers: the philosophical presentation of Pluralism; using a formal theory of logic metaphorically; rigour and proof for the Pluralist; and mathematical fixtures. In the third part the author goes on to focus on the transcendental presentation of Pluralism, and in part four looks at applications of Pluralism, such as a Pluralist approach to proof in mathematics and how Pluralism works in regard to together-inconsistent philosophies of mathematics. The book finishes with suggestions for further Pluralist enquiry. In this work the author takes a deeply radical approach in developing a new position that will either convert readers, or act as a strong warning to treat the word ‘pluralism’ with care.
Epistemology versus Ontology
This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice (ZFC). This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively pursued today is predicativistic constructivism based on Martin-Löf type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-Löf. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-Löf and Wittgensteinian or other accounts of meaning-as-use? What can proof-theoretical analyses tell us about the scope and limits of constructive and predicative mathematics?
Judgement and the Epistemic Foundation of Logic
This compelling reevaluation of the relationship between logic and knowledge affirms the key role that the notion of judgement must play in such a review. The commentary repatriates the concept of judgement in the discussion, banished in recent times by the logical positivism of Wittgenstein, Hilbert and Schlick, and the Platonism of Bolzano. The volume commences with the insights of Swedish philosopher Per Martin-Löf, the father of constructive type theory, for whom logic is a demonstrative science in which judgement is a settled feature of the landscape. His paper opens the first of four sections that examine, in turn, historical philosophical assessments of judgement and reason; their pl...
Paraconsistency: Logic and Applications
A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change this situation. The book includes almost every major author currently working in the field. The papers are on the ...
Special Sciences and the Unity of Science
Science is a dynamic process in which the assimilation of new phenomena, perspectives, and hypotheses into the scientific corpus takes place slowly. The apparent disunity of the sciences is the unavoidable consequence of this gradual integration process. Some thinkers label this dynamical circumstance a ‘crisis’. However, a retrospective view of the practical results of the scientific enterprise and of science itself, grants us a clear view of the unity of the human knowledge seeking enterprise. This book provides many arguments, case studies and examples in favor of the unity of science. These contributions touch upon various scientific perspectives and disciplines such as: Physics, Computer Science, Biology, Neuroscience, Cognitive Psychology, and Economics.
Vagueness in the Exact Sciences
The book starts with the assumption that vagueness is a fundamental property of this world. From a philosophical account of vagueness via the presentation of alternative mathematics of vagueness, the subsequent chapters explore how vagueness manifests itself in the various exact sciences: physics, chemistry, biology, medicine, computer science, and engineering.
The Nature of Truth
The book offers a characterization of the meaning and role of the notion of truth in natural languages and an explanation of why, in spite of the big amount of proposals about truth, this task has proved to be resistant to the different analyses. The general thesis of the book is that defining truth is perfectly possible and that the average educated philosopher of language has the tools to do it. The book offers an updated treatment of the meaning of truth ascriptions from taking into account the latest views in philosophy of language and linguistics.
