Propositions, Functions, and Analysis


Book Description

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.




Real Analysis (Classic Version)


Book Description

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.




Analysis of Boolean Functions


Book Description

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.




Quine, New Foundations, and the Philosophy of Set Theory


Book Description

Quine's set theory, New Foundations, has often been treated as an anomaly in the history and philosophy of set theory. In this book, Sean Morris shows that it is in fact well-motivated, emerging in a natural way from the early development of set theory. Morris introduces and explores the notion of set theory as explication: the view that there is no single correct axiomatization of set theory, but rather that the various axiomatizations all serve to explicate the notion of set and are judged largely according to pragmatic criteria. Morris also brings out the important interplay between New Foundations, Quine's philosophy of set theory, and his philosophy more generally. We see that his early technical work in logic foreshadows his later famed naturalism, with his philosophy of set theory playing a crucial role in his primary philosophical project of clarifying our conceptual scheme and specifically its logical and mathematical components.




What Functions Explain


Book Description

This 2001 book offers an examination of functional explanation as it is used in biology and the social sciences, and focuses on the kinds of philosophical presuppositions that such explanations carry with them. It tackles such questions as: why are some things explained functionally while others are not? What do the functional explanations tell us about how these objects are conceptualized? What do we commit ourselves to when we give and take functional explanations in the life sciences and the social sciences? McLaughlin gives a critical review of the debate on functional explanation in the philosophy of science. He discusses the history of the philosophical question of teleology, and provides a comprehensive review of the post-war literature on functional explanation. What Functions Explain provides a sophisticated and detailed Aristotelian analysis of our concept of natural functions, and offers a positive contribution to the ongoing debate on the topic.




The Dawn of Analysis


Book Description

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.




Principia Mathematica


Book Description




Mathematical Analysis and Applications


Book Description

Offers an introduction to higher mathematics for students. Starting with a discussion of real numbers and functions, the text introduces standard topics of differential and integral calculus together with their applications such as differential equations, numerical analysis, and approximation methods.




The Cambridge Companion to Bertrand Russell


Book Description

Mathematics in and behind Russell's logicism, and its reception / I. Grattan-Guinness -- Russell's philosophical background / Nicholas Griffin -- Russell and Moore, 1898-1905 / Richard L. Cartwright -- Russell and Frege / Michael Beaney -- Bertrand Russell's logicism / Martin Godwyn and Andrew D. Irvine -- The theory of descriptions / Peter Hylton -- Russell's substitutional theory / Gregory Landini -- The theory of types / Alasdair Urquhart -- Russell's method of analysis / Paul Hager -- Russell's neutral monism / R.E. Tully -- The metaphysics of logical atomism / Bernard Linksy -- Russell's structuralism and the absolute description of the world / William Demopoulos -- From knowledge by acquaintance to knowledge by causation / Thomas Baldwin -- Russell, experience, and the roots of science / A.C. Grayling -- Bertrand Russell: moral philosopher or unphilosophical moralist? / Charles R. Pidgen.




Epistemology & Methodology I:


Book Description

In this Introduction we shall state the business of both descriptive and normative epistemology, and shall locate them in the map oflearning. This must be done because epistemology has been pronounced dead, and methodology nonexisting; and because, when acknowledged at all, they are often misplaced. 1. DESCRIPTIVE EPISTEMOLOGY The following problems are typical of classical epistemology: (i) What can we know? (ii) How do we know? (iii) What, if anything, does the subject contribute to his knowledge? (iv) What is truth? (v) How can we recognize truth? (vi) What is probable knowledge as opposed to certain knowledge? (vii) Is there a priori knowledge, and if so of what? (viii) How are knowledge and action related? (ix) How are knowledge and language related? (x) What is the status of concepts and propositions? In some guise or other all of these problems are still with us. To be sure, if construed as a demand for an inventory of knowledge the first problem is not a philosophical one any more than the question 'What is there?'. But it is a genuine philosophical problem if construed thus: 'What kinds of object are knowable-and which ones are not?' However, it is doubtful that philosophy can offer a correct answer to this problem without the help of science and technology. For example, only these disciplines can tell us whether man can know not only phenomena (appearances) but also noumena (things in themselves or self-existing objects).