This book argues against the view that mathematical knowledge is a priori,contending that mathematics is an empirical science and develops historically,just as ...

William P. Alston formulates and defends a realist conception of truth, which he calls alethic realism (from "aletheia", Greek for "truth").

In a late discussion of Kant’s essay, “Was ist Aufklärung?,” Foucault credits Kant with posing “the question of his own present” and positions himself as an inheritor of this Kantian legacy.1 Foucault has high praise for the critical tradition that emerges from Kant’s historical-political reflections on the Enlightenment and the French Revolution; Kant’s concern in these writings with “an ontology of the present, an ontology of ourselves” is, he says, characteristic of “a form of philosophy, from Hegel, through Nietzsche and (...) Max Weber, to the Frankfurt School,” a form of philosophy in which Foucault, perhaps surprisingly, situates his own work. (shrink)

Epistemic infinitism is the view that infinite series of inferential relations are productive of epistemic justification. Peirce is explicitly infinitist in his early work, namely his 1868 series of articles. Further, Peirce's semiotic categories of firsts, seconds, and thirds favors a mixed theory of justification. The conclusion is that Peirce was an infinitist, and particularly, what I will term an impure infinitist. However, the prospects for Peirce's infinitism depend entirely on the prospects for Peirce's early semantics, which are not good. (...) Peirce himself revised the semantic theory later, and in so doing, it seems also his epistemic infinitism. (shrink)

I will assume here the defenses of epistemic infinitism are adequate and inquire as to the variety standpoints within the view. I will argue that infinitism has three varieties depending on the strength of demandingness of the infinitist requirement and the purity of its conception of epistemic justification, each of which I will term strong pure, strong impure, and weak impure infinitisms. Further, I will argue that impure infinitisms have the dialectical advantage.

What is it to be scientific? Is there such a thing as scientific method? And if so, how might such methods be justified? Robert Nola and Howard Sankey seek to provide answers to these fundamental questions in their exploration of the major recent theories of scientific method. Although for many scientists their understanding of method is something they just pick up in the course of being trained, Nola and Sankey argue that it is possible to be explicit about what this (...) tacit understanding of method is, rather than leave it as some unfathomable mystery. They robustly defend the idea that there is such a thing as scientific method and show how this might be legitimated. This book begins with the question of what methodology might mean and explores the notions of values, rules and principles, before investigating how methodologists have sought to show that our scientific methods are rational. Part 2 of this book sets out some principles of inductive method and examines its alternatives including abduction, IBE, and hypothetico-deductivism. Part 3 introduces probabilistic modes of reasoning, particularly Bayesianism in its various guises, and shows how it is able to give an account of many of the values and rules of method. Part 4 considers the ideas of philosophers who have proposed distinctive theories of method such as Popper, Lakatos, Kuhn and Feyerabend and Part 5 continues this theme by considering philosophers who have proposed naturalised theories of method such as Quine, Laudan and Rescher. This book offers readers a comprehensive introduction to the idea of scientific method and a wide-ranging discussion of how historians of science, philosophers of science and scientists have grappled with the question over the last fifty years. (shrink)

This book is concerned with the history of metaphysics since Descartes. Taking as its definition of metaphysics 'the most general attempt to make sense of things', it charts the evolution of this enterprise through various competing conceptions of its possibility, scope, and limits. The book is divided into three parts, dealing respectively with the early modern period, the late modern period in the analytic tradition, and the late modern period in non-analytic traditions. In its unusually wide range, A. W. Moore's (...) study refutes the tired old cliché that there is some unbridgeable gulf between analytic philosophy and philosophy of other kinds. It also advances its own distinctive and compelling conception of what metaphysics is and why it matters. Moore explores how metaphysics can help us to cope with continually changing demands on our humanity by making sense of things in ways that are radically new. (shrink)

This book argues that the only kind of metaphysics that can contribute to objective knowledge is one based specifically on contemporary science as it really is, and not on philosophers' a priori intuitions, common sense, or simplifications of science. In addition to showing how recent metaphysics has drifted away from connection with all other serious scholarly inquiry as a result of not heeding this restriction, this book demonstrates how to build a metaphysics compatible with current fundamental physics, which, when combined (...) with metaphysics of the special sciences, can be used to unify physics with the other sciences without reducing these sciences to physics itself. Taking science metaphysically seriously, this book argues, means that metaphysicians must abandon the picture of the world as composed of self-subsistent individual objects, and the paradigm of causation as the collision of such objects. The text assesses the role of information theory and complex systems theory in attempts to explain the relationship between the special sciences and physics, treading a middle road between the grand synthesis of thermodynamics and information, and eliminativism about information. The consequences of the books' metaphysical theory for central issues in the philosophy of science are explored, including the implications for the realism versus empiricism debate, the role of causation in scientific explanations, the nature of causation and laws, the status of abstract and virtual objects, and the objective reality of natural kinds. (shrink)

_'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.

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)