Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a wider (...) audience. In addition to the new introduction by John Slater, this edition contains Russell's introduction to the 1937 edition in which he defends his position against his formalist and intuitionist critics. (shrink)

First published in 1903, _Principles of Mathematics_ was Bertrand Russell’s first major work in print. It was this title which saw him begin his ascent towards eminence. In this groundbreaking and important work, Bertrand Russell argues that mathematics and logic are, in fact, identical and what is commonly called mathematics is simply later deductions from logical premises. Highly influential and engaging, this important work led to Russell’s dominance of analytical logic on western philosophy in the twentieth century.

Craik published only one complete work of any length, this essay on The Nature of Explanation.

In the course of the discussion, Professor Quine pinpoints the difficulties involved in translation, brings to light the anomalies and conflicts implicit in our ...

This is the classic work upon which modern-day game theory is based. What began as a modest proposal that a mathematician and an economist write a short paper together blossomed, when Princeton University Press published Theory of Games and Economic Behavior. In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry (...) it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences. (shrink)

INTRODUCTION: TWO KINDS OF RLDUCTIONISM The man who laughs is the one who has not yet heard the terrible news. BERTHOLD BRECHT I propose, in this book, ...

Griinbaum's own article sets forth his views on the ontology of the curvature of empty space, especially in the geometrodynamics of Clifford and Wheeler. ...

In this book, Zalta attempts to lay the axiomatic foundations of metaphysics by developing and applying a (formal) theory of abstract objects. The cornerstones include a principle which presents precise conditions under which there are abstract objects and a principle which says when apparently distinct such objects are in fact identical. The principles are constructed out of a basic set of primitive notions, which are identified at the end of the Introduction, just before the theorizing begins. The main reason for (...) producing a theory which defines a logical space of abstract objects is that it may have a great deal of explanatory power. It is hoped that the data explained by means of the theory will be of interest to pure and applied metaphysicians, logicians and linguists, and pure and applied epistemologists. (shrink)

That laws of nature play a vital role in explanation, prediction, and inductive inference is far clearer than the nature of the laws themselves. My hope here is to shed some light on the nature of natural laws by developing and defending the view that they involve genuine relations between properties. Such a position is suggested by Plato, and more recent versions have been sketched by several writers.~ But I am not happy with any of these accounts, not so much (...) because they lack detail or engender minor difficulties, though they do, but because they share a quite fundamental defect. My goal here is to make this defect clear and, more importantly, to present a rather different version of this general conception of laws that avoids it. I begin by considering several features of natural laws and argue that these are best explained by the view that laws involve properties, that this involvement takes the form of a genuine relation between properties, and, finally, that the relation is a metaphysically necessary one. In the second section I start at the other end, and by reflecting on the nature of properties arrive at a similar account of natural laws. In the final section I develop this account in more detail, with emphasis on the nature of the relation between properties it invokes. Along the way several natural objections to the account are answered. (shrink)

This article is concerned to formulate some open problems in the philosophy of space and time that require methods characteristic of mathematical traditions in the foundations of geometry for their solution. In formulating the problems an effort has been made to fuse the separate traditions of the foundations of physics on the one hand and the foundations of geometry on the other. The first part of the paper deals with two classical problems in the geometry of space, that of giving (...) operationalism an exact foundation in the case of the measurement of spatial relations, and that of providing an adequate theory of approximation and error in a geometrical setting. The second part is concerned with physical space and space-time and deals mainly with topics concerning the axiomatic theory of bodies, the operational foundations of special relativity and the conceptual foundations of elementary physics. (shrink)

The subject of this paper is the philosophical problem of accounting for the relationship between mathematics and non-mathematical reality. The first section, devoted to the importance of the problem, suggests that many of the reasons for engaging in philosophy at all make an account of the relationship between mathematics and reality a priority, not only in philosophy of mathematics and philosophy of science, but also in general epistemology/metaphysics. This is followed by a (rather brief) survey of the major, traditional philosophies (...) of mathematics indicating how each is prepared to deal with the present problem. It is shown that (the standard formulations of) some views seem to deny outright that there is a relationship between mathematics and any non-mathematical reality; such philosophies are clearly unacceptable. Other views leave the relationship rather mysterious and, thus, are incomplete at best. The final, more speculative section provides the direction of a positive account. A structuralist philosophy of mathematics is outlined and it is proposed that mathematics applies to reality though the discovery of mathematical structures underlying the non-mathematical universe. (shrink)

This volume consists of the first of the John Dewey Lectures delivered under the auspices of Columbia University's Philosophy Department as well as other essays by the author. Intended to clarify the meaning of the philosophical doctrines propounded by Professor Quine in 'Word and Objects', the essays included herein both support and expand those doctrines.

A formal theory of quantity T Q is presented which is realist, Platonist, and syntactically second-order (while logically elementary), in contrast with the existing formal theories of quantity developed within the theory of measurement, which are empiricist, nominalist, and syntactically first-order (while logically non-elementary). T Q is shown to be formally and empirically adequate as a theory of quantity, and is argued to be scientifically superior to the existing first-order theories of quantity in that it does not depend upon empirically (...) unsupported assumptions concerning existence of physical objects (e.g. that any two actual objects have an actual sum). The theory T Q supports and illustrates a form of naturalistic Platonism, for which claims concerning the existence and properties of universals form part of natural science, and the distinction between accidental generalizations and laws of nature has a basis in the second-order structure of the world. (shrink)

The numerical representations of measurement, geometry and kinematics are here subsumed under a general theory of representation. The standard theories of meaningfulness of representational propositions in these three areas are shown to be special cases of two theories of meaningfulness for arbitrary representational propositions: the theories based on unstructured and on structured representation respectively. The foundations of the standard theories of meaningfulness are critically analyzed and two basic assumptions are isolated which do not seem to have received adequate justification: the (...) assumption that a proposition invariant under the appropriate group is therefore meaningful, and the assumption that representations should be unique up to a transformation of the appropriate group. A general theory of representational meaningfulness is offered, based on a semantic and syntactic analysis of representational propositions. Two neglected features of representational propositions are formalized and made use of: (a) that such propositions are induced by more general propositions defined for other structures than the one being represented, and (b) that the true purpose of representation is the application of the theory of the representing system to the represented system. On the basis of these developments, justifications are offered for the two problematic assumptions made by the existing theories. (shrink)

The formal methods of the representational theory of measurement (RTM) are applied to the extensive scales of physical science, with some modifications of interpretation and of formalism. The interpretative modification is in the direction of theoretical realism rather than the narrow empiricism which is characteristic of RTM. The formal issues concern the formal representational conditions which extensive scales should be assumed to satisfy; I argue in the physical case for conditions related to weak rather than strong extensive measurement, in the (...) sense of Holman 1969 and Colonius 1978. The problem of justifying representational conditions is addressed in more detail than is customary in the RTM literature; this continues the study of the foundations of RTM begun in an earlier paper. The most important formal consequence of the present interpretation of physical extensive scales is that the basic existence and uniqueness properties of scales (representation theorem) may be derived without appeal to an Archimedean axiom; this parallels a conclusion drawn by Narens for representations of qualitative probability. It is concluded that there is no physical basis for postulation of an Archimedean axiom. (shrink)

Actualism is the doctrine that the only things there are, that have being in any sense, are the things that actually exist. In particular, actualism eschews possibilism, the doctrine that there are merely possible objects. It is widely held that one cannot both be an actualist and at the same time take possible world semantics seriously — that is, take it as the basis for a genuine theory of truth for modal languages, or look to it for insight into the (...) modal structure of reality. For possible world semantics, it is supposed, commits one to possibilism. In this paper I take issue with this view. To the contrary, I argue that one can take possible world semantics seriously without any commitment to possible worlds or possibilism and hence remain in full compliance with actualist scruples. Moreover, one can do so without without invoking either "ersatz" worlds or haecceities. (shrink)

Actualists who believe in possible worlds typically regard them as "abstract" objects of some special sort. For example, Alvin Plantinga takes worlds to be maximal possible states-of-affairs, all of which "exist", as actualism requires, but only one of which "obtains". Views like Plantinga's run into difficulty in the interpretation of statements of "iterated" modality, statements about what is "possible" for individuals that "could" exist but that do not actually exist. These statements seem to require the existence of "singular" states-Of-affairs that (...) have nonactual individuals as constituents, a requirement that is incompatible with actualism. One can try to avoid the troublesome singular states-of-affairs by introducing "unexemplified individual essences" and maintaining that these are the true constituents of the required states-of-affairs, rather than the nonactual possibles themselves. However, serious arguments are raised against this employment of individual essences. (shrink)

Required reading at more than 100 colleges and universities throughout North America.

This study provides a unified theory of properties, relations, and propositions (PRPs). Two conceptions of PRPs have emerged in the history of philosophy. The author explores both of these traditional conceptions and shows how they can be captured by a single theory.

Modifications of current theories of ordinal, interval and extensive measurement are presented, which aim to accomodate the empirical fact that perfectly exact measurement is not possible (which is inconsistent with current theories). The modification consists in dropping the assumption that equality (in measure) is observable, but continuing to assume that inequality (greater or lesser) can be observed. The modifications are formulated mathematically, and the central problems of formal measurement theory--the existence and uniqueness of numerical measures consistent with data--are re-examined. Some (...) results also are given on a problem which does not arise in current theories: namely that of determining limits of accuracy attainable on the basis of observations. (shrink)

Nozick analyzes fundamental issues, such as the identity of the self, knowledge and skepticism, free will, the foundations of ethics, and the meaning of life.

The need for quantitative measurement represents a unifying bond that links all the physical, biological, and social sciences. Measurements of such disparate phenomena as subatomic masses, uncertainty, information, and human values share common features whose explication is central to the achievement of foundational work in any particular mathematical science as well as for the development of a coherent philosophy of science. This book presents a theory of measurement, one that is "abstract" in that it is concerned with highly general axiomatizations (...) of empirical and qualitative settings and how these can be represented quantitatively. It was inspired by, and represents a generalization and extension of, the last major research work in this field, Foundations of Measurement Vol. I, by Krantz, Luce, Suppes, and Tversky published in 1971. (shrink)

In this report I motivate and develop a type-free logic with predicate quantifiers within the general ontological framework of properties, relations, and propositions. In Part I, I present the major ideas of the system informally and discuss its philosophical significance, especially with regard to Russell's paradox. In Part II, I prove the soundness, consistency, and completeness of the logic.

This update to the award-winning first edition analyzes the pros and cons of different media and focuses on general guidelines and basic principles, making the ideas in this guide transferable to future technologies.

Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a wider (...) audience. In addition to the new introduction by John Slater, this edition contains Russell's introduction to the 1937 edition in which he defends his position against his formalist and intuitionist critics. (shrink)

Now in a new edition, this volume updates Davidson's exceptional Inquiries into Truth and Interpretation (1984), which set out his enormously influential philosophy of language. The original volume remains a central point of reference, and a focus of controversy, with its impact extending into linguistic theory, philosophy of mind, and epistemology. Addressing a central question--what it is for words to mean what they do--and featuring a previously uncollected, additional essay, this work will appeal to a wide audience of philosophers, linguists, (...) and psychologists. (shrink)

A wide-ranging study of the central concepts in epistemology - belief, truth and knowledge. Professor Armstrong offers a dispositional account of general beliefs and of knowledge of general propositions. Belief about particular matters of fact are described as structures in the mind of the believer which represent or 'map' reality, while general beliefs are dispositions to extend the 'map' or introduce casual relations between portions of the map according to general rules. 'Knowledge' denotes the reliability of such beliefs as representations (...) of reality. Within this framework Professor Armstrong offers a distinctive account of many of the main questions in general epistemology - the relations between beliefs and language, the notions of proposition, concept and idea, the analysis of truth, the varieties of knowledge, and the way in which beleifs and knowledge are supported by reasons. The book as a whole if offered as a contribution to a naturalistic account of man. (shrink)

My thesis is that there are good reasons for a philosophical account of measurement to deal primarily with the properties or magnitudes of objects measured, rather than with the objects themselves. The account I present here embodies both a realism about measurement and a realism about the existence of the properties involved in measurement. It thus provides an alternative to most current treatments of measurement, many of which are operationalistic or conventionalistic, and nearly all of which are nominalistic.1 This enables (...) the present account to give better explanations of a number of features of measurement and other aspects of science than competing accounts of measurement can, and to be more readily integrated into a realist account of natural laws and causation. It also illustrates a general strategy for combining a familiar and powerful approach to representation with intensional entities like properties, which I think can be useful for dealing with a number of philosophical problems. (shrink)