Coherent, well organized text familiarizes readers with complete theory of logical inference and its applications to math and the empirical sciences. Part I deals with formal principles of inference and definition; Part II explores elementary intuitive set theory, with separate chapters on sets, relations, and functions. Last section introduces numerous examples of axiomatically formulated theories in both discussion and exercises. Ideal for undergraduates; no background in math or philosophy required.

Logical Atomism is a philosophy that sought to account for the world in all its various aspects by relating it to the structure of the language in which we articulate information. In _The Philosophy of Logical Atomism,_ Bertrand Russell, with input from his young student Ludwig Wittgenstein, developed the concept and argues for a reformed language based on pure logic. Despite Russell’s own future doubts surrounding the concept, this founding and definitive work in analytical philosophy by one of the world’s (...) most significant philosophers is a remarkable attempt to establish a novel way of thinking. (shrink)

By a `denoting phrase' I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the present King of France, the center of mass of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. Thus a phrase is denoting solely in virtue of its form. We may distinguish (...) three cases: (1) A phrase may be denoting, and yet not denote anything; e.g., `the present King of France'. (2) A phrase may denote one definite object; e.g., `the present King of England' denotes a certain man. (3) A phrase may denote ambiguously; e.g. `a man' denotes not many men, but an ambiguous man. The interpretation of such phrases is a matter of considerably difficulty; indeed, it is very hard to frame any theory not susceptible of formal refutation. All the difficulties with which I am acquainted are met, so far as I can discover, by the theory which I am about to explain. (shrink)

Introduction: Science and Common Sense Long before the beginnings of modern civilization, men ac- quired vast funds of information about their environment. ...

This is the third edition of Chomsky's outstanding collection of essays on language and mind, first published in 2006. The first six chapters, originally published in the 1960s, made a groundbreaking contribution to linguistic theory. This edition complements them with an additional chapter and a new preface, bringing Chomsky's influential approach into the twenty-first century. Chapters 1-6 present Chomsky's early work on the nature and acquisition of language as a genetically endowed, biological system, through the rules and principles of which (...) we acquire an internalized knowledge. Over the past fifty years, this framework has sparked an explosion of inquiry into a wide range of languages, and has yielded some major theoretical questions. The final chapter revisits the key issues, reviewing the 'biolinguistic' approach that has guided Chomsky's work from its origins to the present day, and raising some novel and exciting challenges for the study of language and mind. (shrink)