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The work of Bertrand Russell has a decisive influence on the emergence of analytic philosophy, and on its subsequent development. The essays in this text recapture aspects of Russell's philosophical vision during his most influential period, the two decades following his break with Idealism in 1899.
This text is designed for graduate-level courses in real analysis. Real Analysis, 4th Edition, covers the basic material that every graduate student should know in the classical theory of functions of a real variable, measure and integration theory, and some of the more important and elementary topics in general topology and normed linear space theory. This text assumes a general background in undergraduate mathematics and familiarity with the material covered in an undergraduate course on the fundamental concepts of analysis.
This graduate-level text gives a thorough overview of the analysis of Boolean functions, beginning with the most basic definitions and proceeding to advanced topics.
This is a major, wide-ranging history of analytic philosophy since 1900, told by one of the tradition's leading contemporary figures. The first volume takes the story from 1900 to mid-century. The second brings the history up to date. As Scott Soames tells it, the story of analytic philosophy is one of great but uneven progress, with leading thinkers making important advances toward solving the tradition's core problems. Though no broad philosophical position ever achieved lasting dominance, Soames argues that two methodological developments have, over time, remade the philosophical landscape. These are (1) analytic philosophers' hard-won success in understanding, and distinguishing the notions of logical truth, a priori truth, and necessary truth, and (2) gradual acceptance of the idea that philosophical speculation must be grounded in sound prephilosophical thought. Though Soames views this history in a positive light, he also illustrates the difficulties, false starts, and disappointments endured along the way. As he engages with the work of his predecessors and contemporaries--from Bertrand Russell and Ludwig Wittgenstein to Donald Davidson and Saul Kripke--he seeks to highlight their accomplishments while also pinpointing their shortcomings, especially where their perspectives were limited by an incomplete grasp of matters that have now become clear. Soames himself has been at the center of some of the tradition's most important debates, and throughout writes with exceptional ease about its often complex ideas. His gift for clear exposition makes the history as accessible to advanced undergraduates as it will be important to scholars. Despite its centrality to philosophy in the English-speaking world, the analytic tradition in philosophy has had very few synthetic histories. This will be the benchmark against which all future accounts will be measured.
Propositions are routinely invoked by philosophers, linguists, logicians, and other theorists engaged in the study of meaning, communication, and the mind. To investigate the nature of propositions is to investigate the very nature of our connection to each other, and to the world around us. As one of the only volumes of its kind, The Routledge Handbook of Propositions provides a comprehensive overview of the philosophy of propositions, from both historical and contemporary perspectives. Comprising 33 original chapters by an international team of scholars, the volume addresses both traditional and emerging questions concerning the nature of propositions, and our capacity to engage with them in thought and in communication. The chapters are clearly organized into the following three sections: I. Foundational Issues in the Theory of Propositions II. Historical Theories of Propositions III. Contemporary Theories of Propositions Essential reading for philosophers of language and mind, and for those working in neighboring areas, The Routledge Handbook of Propositions is suitable for upper-level undergraduate study, as well as graduate and professional research.
A Spiral Workbook for Discrete Mathematics covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions,relations, and elementary combinatorics, with an emphasis on motivation. The text explains and claries the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a nal polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a dierent perspective or at a higher level of complexity, in order to slowly develop the student's problem-solving and writing skills.
This is a major, wide-ranging history of analytic philosophy since 1900, told by one of the tradition's leading contemporary figures. The first volume takes the story from 1900 to mid-century. The second brings the history up to date. As Scott Soames tells it, the story of analytic philosophy is one of great but uneven progress, with leading thinkers making important advances toward solving the tradition's core problems. Though no broad philosophical position ever achieved lasting dominance, Soames argues that two methodological developments have, over time, remade the philosophical landscape. These are (1) analytic philosophers' hard-won success in understanding, and distinguishing the notions of logical truth, a priori truth, and necessary truth, and (2) gradual acceptance of the idea that philosophical speculation must be grounded in sound prephilosophical thought. Though Soames views this history in a positive light, he also illustrates the difficulties, false starts, and disappointments endured along the way. As he engages with the work of his predecessors and contemporaries--from Bertrand Russell and Ludwig Wittgenstein to Donald Davidson and Saul Kripke--he seeks to highlight their accomplishments while also pinpointing their shortcomings, especially where their perspectives were limited by an incomplete grasp of matters that have now become clear. Soames himself has been at the center of some of the tradition's most important debates, and throughout writes with exceptional ease about its often complex ideas. His gift for clear exposition makes the history as accessible to advanced undergraduates as it will be important to scholars. Despite its centrality to philosophy in the English-speaking world, the analytic tradition in philosophy has had very few synthetic histories. This will be the benchmark against which all future accounts will be measured.
Note: This is a custom edition of Levin's full Discrete Mathematics text, arranged specifically for use in a discrete math course for future elementary and middle school teachers. (It is NOT a new and updated edition of the main text.)This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this.Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs.While there are many fine discrete math textbooks available, this text has the following advantages: - It is written to be used in an inquiry rich course.- It is written to be used in a course for future math teachers.- It is open source, with low cost print editions and free electronic editions.