_'Philosophy, from the earliest times, has made greater claims, and acheived fewer results than any other branch of learning... I believe that the time has now arrived when this unsatisfactory state of affairs can be brought to an end'_ - _Bertrand Russell_ So begins _Our Knowledge of the Eternal World_, Bertrand Russell's classic attempt to show by means of examples, the nature, capacity and limitations of the logico-analytical method in philosophy.

This book is an accessible introduction to the central themes of contemporary metaphysics. It carefully considers accounts of causation, freedom and determinism, laws of nature, personal identity, mental states, time, material objects, and properties, while inviting students to reflect on metaphysical problems. The philosophical questions discussed include: What makes it the case that one event causes another event? What are material objects? Given that material objects exist, do such things as properties exist? What makes it the case that a person (...) may exist at two different times? An Introduction to Metaphysics makes these tough questions tractable by presenting the features and flaws of current attempts to answer them. Intended primarily for students taking a first class in metaphysics, this lucid and well-written text would also provide an excellent introduction for anyone interested in knowing more about this important area of philosophy. (shrink)

In this book, Livingston develops the political implications of formal results obtained over the course of the twentieth century in set theory, metalogic, and computational theory. He argues that the results achieved by thinkers such as Cantor, Russell, Godel, Turing, and Cohen, even when they suggest inherent paradoxes and limitations to the structuring capacities of language or symbolic thought, have far-reaching implications for understanding the nature of political communities and their development and transformation. Alain Badiou's analysis of logical-mathematical structures forms (...) the backbone of his comprehensive and provocative theory of ontology, politics, and the possibilities of radical change. Through interpretive readings of Badiou's work as well as the texts of Giorgio Agamben, Jacques Lacan, Jacques Derrida, Gilles Deleuze, and Ludwig Wittgenstein, Livingston develops a formally based taxonomy of critical positions on the nature and structure of political communities. These readings, along with readings of Parmenides and Plato, show how the formal results can transfigure two interrelated and ancient problems of the One and the Many: the problem of the relationship of a Form or Idea to the many of its participants, and the problem of the relationship of a social whole to its many constituents. (shrink)

'Alain Badiou: Between Theology and Anti-theology' provides one of the first comprehensive analyses of the relationship between Badiou's philosophy and theology. Examining the full range of Badiou's writings, this provocative study explores how Badiou's philosophy relies on theology even if he claims otherwise and actively attempts to work against theology. Despite the complex questions discussed - ranging across ontology, the theory of truth and the subject, philosophy and its conditions, and anti-philosophy - this book presents a clear and accessible overview (...) of the theological, religious and biblical themes which animate Badiou's philosophy. (shrink)

I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel universes and (...) Gödel incompleteness. I hypothesize that only computable and decidable (in Gödel’s sense) structures exist, which alleviates the cosmological measure problem and may help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems. (shrink)

Structural realism is considered by many realists and antirealists alike as the most defensible form of scientific realism. There are now many forms of structural realism and an extensive literature about them. There are interesting connections with debates in metaphysics, philosophy of physics and philosophy of mathematics. This entry is intended to be a comprehensive survey of the field.

First published in 1971, Professor Putnam's essay concerns itself with the ontological problem in the philosophy of logic and mathematics - that is, the issue of whether the abstract entities spoken of in logic and mathematics really exist. He also deals with the question of whether or not reference to these abstract entities is really indispensible in logic and whether it is necessary in physical science in general.

This book offers a broad-based critical survey of recent anti-realist arguments in the philosophy of science, cultural theory, hermeneutics, the sociology of knowledge and the interpretation of quantum-mechanics.

The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox, a challenge to 'classical' mathematics from a world-famous mathematician, a new foundational school, and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection (...) brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field. (shrink)

This work stresses the illogical manner in which mathematics has developed, the question of applied mathematics as against 'pure' mathematics, and the challenges to the consistency of mathematics' logical structure that have occurred in the twentieth century.

"The Analysis of Matter" is one of the earliest and best philosophical studies of the new physics of relativity and quantum mechanics.

1929. The course of Gifford Lectures that Eddington delivered in the University of Edinburgh in January to March 1927.

How do we know what we "know"? How did we –as individuals and as a society – come to accept certain knowledge as fact? In _Human Knowledge,_ Bertrand Russell questions the reliability of our assumptions on knowledge. This brilliant and controversial work investigates the relationship between ‘individual’ and ‘scientific’ knowledge. First published in 1948, this provocative work contributed significantly to an explosive intellectual discourse that continues to this day.

This is a book that no one but Weyl could have written--and, indeed, no one has written anything quite like it since.

This edition provides texts from the full range of Berkeley's contributions to philosophy, and sets them in their historical and philosophical contexts.

"Entre la connaissance commune et la connaissance scientifique, la rupture nous paraît si nette que ces deux types de connaissance ne sauraient avoir la même philosophie. L'empirisme est la philosophie qui convient à la connaissance commune. Au contraire, la connaissance scientifique est solidaire du rationalisme et, qu'on le veuille ou non, le rationalisme est lié à la science, le rationalisme réclame des buts scientifiques. Par l'activité scientifique, le rationalisme connaît une activité dialectique qui enjoint une extension constante des méthodes". Voici (...) un livre sur l'activité rationaliste du chimiste contemporain. On y voit à l'oeuvre une "phénoménotechnique" qui construit ses multiples substances en éliminant progressivement l'irrationnel. Souligner l'engagement de pensée qui se manifeste dans cette activité, telle est la volonté de Bachelard inscrite dans son projet général d'attirer "l'attention des philosophes sur le caractère spécifique de la pensée et du travail de la science moderne". (shrink)

The selections contained in these volumes from the papers and letters of Leibniz are intended to serve the student in two ways: first, by providing a more adequate and balanced conception of the full range and penetration of Leibniz's creative intellectual powers; second, by inviting a fresher approach to his intellectual growth and a clearer perception of the internal strains in his thinking, through a chronological arrangement. Much confusion has arisen in the past through a neglect of the develop ment (...) of Leibniz's ideas, and Couturat's impressive plea, in his edition of the Opuscu/es et fragments (p. xii), for such an arrangement is valid even for incomplete editions. The beginning student will do well, however, to read the maturer writings of Parts II, III, and IV first, leaving Part I, from a period too largely neglected by Leibniz criticism, for a later study of the still obscure sources and motives of his thought. The Introduction aims primarily to provide cultural orientation and an exposition of the structure and the underlying assumptions of the philosophical system rather than a critical evaluation. I hope that together with the notes and the Index, it will provide those aids to the understanding which the originality of Leibniz's scientific, ethical, and metaphysical efforts deserve. (shrink)

Alexandre Koyré. of the fixed stars is infinite commit a contradiction in adjecto. In truth, an infinite body cannot be comprehended by thought. For the concepts of the mind concerning the infinite are either about the meaning oftheterm "infinite,"  ...

In this 1958 book, Professor Hanson turns to an equally important but comparatively neglected subject, the philosophical aspects of research and discovery.

An examination of the emergence of the phenomenon of deductive argument in classical Greek mathematics.

Originally published in 1989, Reclaiming Reality still provides the most accessible introduction to the increasingly influential multi-disciplinary and international body of thought, known as critical realism. It is designed to "underlabour" both for the sciences, especially the human sciences, and for the projects of human emancipation which such sciences may come to inform; and provides an enlightening intervention in current debates about realism and relativism, positivism and poststucturalism, modernism and postmodernism, etc. Elaborating his critical realist perspective on society, nature, science (...) and philosophy itself, Roy Bhaskar shows how this perspective can be used to undermine currently fashionable ideologies of the Right, and at the same time, to clear the ground for a reinvigorated Left. Reclaiming Reality contains powerful critiques of some of the most important schools of thought and thinkers of recent years—from Bachelard and Feyerabend to Rorty and Habermas; and it advances novel and convincing resolutions of many traditional philosophical problems. Now with a new introduction from Mervyn Hartwig, this book continues to provide a straightforward and stimulating introduction to current debates in philosophy and social theory for the interested lay reader and student alike. Reclaiming Reality will be of particular value not only for critical realists but for all those concerned with the revitalization of the socialist emancipatory project and the renaissance of the Marxist theoretical tradition. Roy Bhaskar is the originator of the philosophy of critical realism, and the author of many acclaimed and influential works including A Realist Theory of Science, The Possibility of Naturalism, Scientific Realism and Human Emancipation and Dialectic: The Pulse of Freedom. He is an editor of the recently published Critical Realism: Essential Readings and is currently chair of the Centre for Critical Realism. (shrink)

A collection of some of Sellars' lectures and articles from 1951 to 1962.

Even though mathematics and physics have been related for centuries and this relation appears to be unproblematic, there are many questions still open: Is mathematics really necessary for physics, or could physics exist without mathematics? Should we think physically and then add the mathematics apt to formalise our physical intuition, or should we think mathematically and then interpret physically the obtained results? Do we get mathematical objects by abstraction from real objects, or vice versa? Why is mathematics effective into physics? (...) These are all relevant questions, whose answers are necessary to fully understand the status of physics, particularly of contemporary physics. The aim of this book is to offer plausible answers to such questions through both historical analyses of relevant cases, and philosophical analyses of the relations between mathematics and physics. (shrink)

Quantum field theory provides the framework for many fundamental theories in modern physics, and over the last few years there has been growing interest in its historical and philosophical foundations. This anthology on the foundations of QFT brings together 15 essays by well-known researchers in physics, the philosophy of physics, and analytic philosophy.Many of these essays were first presented as papers at the conference?Ontological Aspects of Quantum Field Theory?, held at the Zentrum fr interdisziplin„re Forschung, Bielefeld, Germany. The essays contain (...) cutting-edge work on ontological aspects of QFT, including: the role of measurement and experimental evidence, corpuscular versus field-theoretic interpretations of QFT, the interpretation of gauge symmetry, and localization.This book is ideally suited to anyone with an interest in the foundations of quantum physics, including physicists, philosophers and historians of physics, as well as general readers interested in philosophy or science. (shrink)

No doubt my earlier paper has struck a sensitive nerve among existing and prospective constructive empiricists – hence their united reply.1 I shall, for brevity, introduce an imaginary single author of their critique and call him CE. In this rejoinder, I try to show, first, that CE’s counter-arguments do not refute my original arguments; and second, that a claim of CE’s paper is very close to the conclusion of my original paper. A central point of my original piece was that (...) there is a symmetry between scientific realism and constructive empiricism vis à vis van Fraassen’s arguments from the bad lot and from indifference. Scholastic charges of an ‘apparent misunderstanding’ of ‘empirical adequacy’ do not cast any light on the issues at stake. (However, the notion of empirical adequacy I employed, p. 41, is the standard one: ‘a theory is empirically adequate if and only if it saves all phenomena, past, present and future, and squares with all actual and possible observations’.) The issue between CE and myself is more substantive: CE relies on the thesis that for any theory there are ‘indefinitely many empirically equivalent rivals’ (p. 307), in order to infer that there are infinitely many empirically adequate theories, and then to argue that if realists.. (shrink)

The no-miracles argument for realism and the pessimistic meta-induction for anti-realism pull in opposite directions. Structural Realism---the position that the mathematical structure of mature science reflects reality---relieves this tension.

SummaryenThe main argument for scientific realism is that our present theories in science are so successful empirically that they can't have got that way by chance - instead they must somehow have latched onto the blueprint of the universe. The main argument against scientific realism is that there have been enormously successful theories which were once accepted but are now regarded as false. The central question addressed in this paper is whether there is some reasonable way to have the best (...) of both worlds: to give the argument from scientific revolutions its full weight and yet still adopt some sort of realist attitude towards presently accepted theories in physics and elsewhere. I argue that there is such a way - through structural realism, a position adopted by Poincare, and here elaborated and defended. (shrink)

Mark Wilson presents a highly original and broad-ranging investigation of the way we get to grips with the world conceptually, and the way that philosophical problems commonly arise from this. He combines traditional philosophical concerns about human conceptual thinking with illuminating data derived from a large variety of fields including physics and applied mathematics, cognitive psychology, and linguistics. Wandering Significance offers abundant new insights and perspectives for philosophers of language, mind, and science, and will also reward the interest of psychologists, (...) linguists, and anyone curious about the mysterious ways in which useful language obtains its practical applicability. (shrink)

Let us begin with the simple observation that applied mathematics can be very tough! It is a common occurrence that basic physical principle instructs us to construct some syntactically simple set of differential equations, but it then proves almost impossible to extract salient information from them. As Charles Peirce once remarked, you can’t get a set of such equations to divulge their secrets by simply tilting at them like Don Quixote. As a consequence, applied mathematicians are often forced to pursue (...) roundabout and shakily rationalized expedients if any useful progress is to be made. Often these provisional and quasi-empirical procedures within applied mathematics loom large in motivating the “anti-realist” or “anti-unificationist” conclusions of Nancy Cartwright and allied authors. (shrink)

This paper offers an explanation of how philosophy of science in the second half of the 20th century came to be so conspicuously silent on the problem of how to explain the applicability of mathematics. It examines the idea of the early logicists that the analyticity of mathematics accounts for its applicability, and how this idea was transformed during Carnap's efforts to establish a consistent and substantial philosophy of mathematics within the larger framework of Logical Empiricism. I argue that at (...) the end point of this development, philosophical discussion of the applicability problem was terminated although important aspects of the logicists' original response to the applicability problem had had to be sacrificed along the way. (shrink)

Hao Wang was one of the few confidants of the great mathematician and logician Kurt Gödel. _A Logical Journey_ is a continuation of Wang's _Reflections on Gödel_ and also elaborates on discussions contained in _From Mathematics to Philosophy_. A decade in preparation, it contains important and unfamiliar insights into Gödel's views on a wide range of issues, from Platonism and the nature of logic, to minds and machines, the existence of God, and positivism and phenomenology. The impact of Gödel's theorem (...) on twentieth-century thought is on par with that of Einstein's theory of relativity, Heisenberg's uncertainty principle, or Keynesian economics. These previously unpublished intimate and informal conversations, however, bring to light and amplify Gödel's other major contributions to logic and philosophy. They reveal that there is much more in Gödel's philosophy of mathematics than is commonly believed, and more in his philosophy than his philosophy of mathematics. Wang writes that "it is even possible that his quite informal and loosely structured conversations with me, which I am freely using in this book, will turn out to be the fullest existing expression of the diverse components of his inadequately articulated general philosophy." The first two chapters are devoted to Gödel's life and mental development. In the chapters that follow, Wang illustrates the quest for overarching solutions and grand unifications of knowledge and action in Gödel's written speculations on God and an afterlife. He gives the background and a chronological summary of the conversations, considers Gödel's comments on philosophies and philosophers, and his attempt to demonstrate the superiority of the mind's power over brains and machines. Three chapters are tied together by what Wang perceives to be Gödel's governing ideal of philosophy: an exact theory in which mathematics and Newtonian physics serve as a model for philosophy or metaphysics. Finally, in an epilog Wang sketches his own approach to philosophy in contrast to his interpretation of Gödel's outlook. (shrink)