Foundations Of Logic And Language
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Logical Form
Logical form has always been a prime concern for philosophers belonging to the analytic tradition. For at least one century, the study of logical form has been widely adopted as a method of investigation, relying on its capacity to reveal the structure of thoughts or the constitution of facts. This book focuses on the very idea of logical form, which is directly relevant to any principled reflection on that method. Its central thesis is that there is no such thing as a correct answer to the question of what is logical form: two significantly different notions of logical form are needed to fulfill two major theoretical roles that pertain respectively to logic and to semantics. This thesis has a negative and a positive side. The negative side is that a deeply rooted presumption about logical form turns out to be overly optimistic: there is no unique notion of logical form that can play both roles. The positive side is that the distinction between two notions of logical form, once properly spelled out, sheds light on some fundamental issues concerning the relation between logic and language.
Mathematical Logic
Author: Wei Li
language: en
Publisher: Springer Science & Business Media
Release Date: 2010-02-26
Mathematical logic is a branch of mathematics that takes axiom systems and mathematical proofs as its objects of study. This book shows how it can also provide a foundation for the development of information science and technology. The first five chapters systematically present the core topics of classical mathematical logic, including the syntax and models of first-order languages, formal inference systems, computability and representability, and Gödel’s theorems. The last five chapters present extensions and developments of classical mathematical logic, particularly the concepts of version sequences of formal theories and their limits, the system of revision calculus, proschemes (formal descriptions of proof methods and strategies) and their properties, and the theory of inductive inference. All of these themes contribute to a formal theory of axiomatization and its application to the process of developing information technology and scientific theories. The book also describes the paradigm of three kinds of language environments for theories and it presents the basic properties required of a meta-language environment. Finally, the book brings these themes together by describing a workflow for scientific research in the information era in which formal methods, interactive software and human invention are all used to their advantage. This book represents a valuable reference for graduate and undergraduate students and researchers in mathematics, information science and technology, and other relevant areas of natural sciences. Its first five chapters serve as an undergraduate text in mathematical logic and the last five chapters are addressed to graduate students in relevant disciplines.
Philosophy of Language
Author: Scott Soames
language: en
Publisher: Princeton University Press
Release Date: 2012-09-24
A masterful overview of the philosophy of language from one of its most important thinkers In this book one of the world's foremost philosophers of language presents his unifying vision of the field—its principal achievements, its most pressing current questions, and its most promising future directions. In addition to explaining the progress philosophers have made toward creating a theoretical framework for the study of language, Scott Soames investigates foundational concepts—such as truth, reference, and meaning—that are central to the philosophy of language and important to philosophy as a whole. The first part of the book describes how philosophers from Frege, Russell, Tarski, and Carnap to Kripke, Kaplan, and Montague developed precise techniques for understanding the languages of logic and mathematics, and how these techniques have been refined and extended to the study of natural human languages. The book then builds on this account, exploring new thinking about propositions, possibility, and the relationship between meaning, assertion, and other aspects of language use. An invaluable overview of the philosophy of language by one of its most important practitioners, this book will be essential reading for all serious students of philosophy.