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)

This challenging study places fiction squarely at the centre of the discussion of metaphysics. Philosophers have traditionally treated fiction as involving a set of narrow problems in logic or the philosophy of language. By contrast Amie Thomasson argues that fiction has far-reaching implications for central problems of metaphysics. The book develops an 'artifactual' theory of fiction, whereby fictional characters are abstract artifacts as ordinary as laws or symphonies or works of literature. By understanding fictional characters we come to understand how (...) other cultural and social objects are established on the basis of the independent physical world and the mental states of human beings. (shrink)

_Metaphysics: A Contemporary Introduction_ is for students who have already completed an introductory philosophy course and need a fresh look at the central topics in the core subject of metaphysics. It is essential reading for any student of the subject. This Fourth Edition is revised and updated and includes two new chapters on Parts and Wholes, and Metaphysical Indeterminacy or vagueness. This new edition also keeps the user-friendly format, the chapter overviews summarizing the main topics, concrete examples to clarify difficult (...) concepts, annotated further reading at the end of each chapter, endnotes, and a full bibliography. Topics addressed include: the problem of universals the nature of abstract entities the problem of individuation the nature of modality identity through time the nature of time the nature of parts and wholes the problem of metaphysical indeterminacy the Realism/anti-Realism debate. Wherever possible, Michael J. Loux and Thomas M. Crisp relate contemporary views to their classical sources in the history of philosophy. As experienced teachers of philosophy and important contributors to recent debates, Loux and Crisp are uniquely qualified to write this book. (shrink)

Bernard Linsky and Edward Zalta have recently proposed a new form of actualism. I characterize the general form of their view and the motivations behind it. I argue that it is not quite new – it bears interesting similarities to Alvin Plantinga’s view – and that it definitely isn’t actualist.

This book is a defense of modal realism; the thesis that our world is but one of a plurality of worlds, and that the individuals that inhabit our world are only a few out of all the inhabitants of all the worlds. Lewis argues that the philosophical utility of modal realism is a good reason for believing that it is true.

This essay focuses on a recently prominent notion of ground which is distinctive for how it links metaphysics to explanation. Ground is supposed to serve both as the common factor in diverse in virtue of questions as well as the structuring relation in the project of explaining how some phenomena are “built” from more fundamental phenomena. My aim is to provide an opinionated synopsis of this notion of ground without engaging with others. Ground, so understood, generally resists illumination by appeal (...) to more familiar models of explanation. Nevertheless, its distinctive explanatory and metaphysical aspects guide us on characterizing its explanatory logic and its metaphysical features. Some issues concerning the meta-question of what grounds ground are explored, as well as some recent skeptical challenges to ground. (shrink)

Grounding is often glossed as metaphysical causation, yet no current theory of grounding looks remotely like a plausible treatment of causation. I propose to take the analogy between grounding and causation seriously, by providing an account of grounding in the image of causation, on the template of structural equation models for causation.

General discussion of grounding, including its formal features, relations to other notions, and applications. (Originally published 2014; revised 2021).

This paper argues that ground is irreducibly plural: a group of facts can be grounded together, as a collective, even though no member of the group has a ground on its own. This kind of plural grounding is applied to the metaphysics of individuals and quantities, yielding a “structuralist” view in each case. Some more general implications of plural grounding are also discussed.

Can there be grounding without necessitation? Can a fact obtain wholly in virtue of metaphysically more fundamental facts, even though there are possible worlds at which the latter facts obtain but not the former? It is an orthodoxy in recent literature about the nature of grounding, and in first-order philosophical disputes about what grounds what, that the answer is no. I will argue that the correct answer is yes. I present two novel arguments against grounding necessitarianism, and show that grounding (...) contingentism is fully compatible with the various explanatory roles that grounding is widely thought to play. (shrink)

The purpose of the book is to clarify the notion of existential dependence and cognate notions, such as supervenience and the notion of an internal relation. I defend the view that such notions are best understood in terms of the concept of metaphysical grounding, i.e. the concept of one fact obtaining in virtue of other facts, where ‘in virtue of’ has a distinctively metaphysical meaning.

Bertrand Russell is concerned in this book with the foundations of knowledge. He approaches his subject through a discussion of language, the relationships of truth to experience and an investigation into how knowledge of the structure of language helps our understanding of the structure of the world. This edition includes a new introduction by Thomas Baldwin, Clare College, Cambridge.

Timothy Williamson gives an original and provocative treatment of deep metaphysical questions about existence, contingency, and change, using the latest resources of quantified modal logic. Contrary to the widespread assumption that logic and metaphysics are disjoint, he argues that modal logic provides a structural core for metaphysics.

How does metaphysical grounding interact with the truth-functions? I argue that the answer varies according to whether one has a worldly conception or a conceptual conception of grounding. I then put forward a logic of worldly grounding and give it an adequate semantic characterisation.

Kit Fine, in "The Pure Logic of Ground", has made a seminal attempt at formalizing the notion of ground. Fine ties the formal treatment of grounding to the notion of a weak ground. Formalization of this sort is supposed to bring clarity and precision to our theorizing. Unfortunately, as I will argue, it's not clear what weak ground is. I review five alternative explanations of the idea, and argue that none of them are ultimately satisfactory. I close by outlining a (...) more complicated explanation of the notion that turns out to be more satisfactory. (shrink)

A number of philosophers have recently become receptive to the idea that, in addition to scientific or causal explanation, there may be a distinctive kind of metaphysical explanation, in which explanans and explanandum are connected, not through some sort of causal mechanism, but through some constitutive form of determination. I myself have long been sympathetic to this idea of constitutive determination or ‘ontological ground’; and it is the aim of the present paper to help put the idea on a firmer (...) footing - to explain how it is to be understood, how it relates to other ideas, and how it might be of use in philosophy. (shrink)

General discussion of grounding, including its formal features, relations to other notions, and applications.

A compelling idea holds that reality has a layered structure. We often disagree about what inhabits the bottom layer, but we agree that higher up we find chemical, biological, geological, psychological, sociological, economic, /etc./, entities: molecules, human beings, diamonds, mental states, cities, interest rates, and so on. How is this intuitive talk of a layered structure of entities to be understood? Traditionally, philosophers have proposed to understand layered structure in terms of either reduction or supervenience. But these traditional views face (...) well-known problems. A plausible alternative is that layered structure is to be explicated by appeal to explanations of a certain sort, termed / grounding explanations/. Grounding explanations tell us what obtains in virtue of what. Unfortunately, the use of grounding explanations to articulate the layered conception faces a problem, which I call /the collapse/. The collapse turns on the question of how to ground the facts stated by the explanations themselves. In this paper I make a suggestion about how to ground explanations that avoids the collapse. Briefly, the suggestion is that the fact stated by a grounding explanation is grounded in its /explanans/. (shrink)

In order to perfectly describe the world, it is not enough to speak truly. One must also use the right concepts - including the right logical concepts. One must use concepts that "carve at the joints", that give the world's "structure". There is an objectively correct way to "write the book of the world". Much of metaphysics, as traditionally conceived, is about the fundamental nature of reality; in the present terms, this is about the world's structure. Metametaphysics - inquiry into (...) the status of metaphysical questions - turns on structure. The question of whether ontological, causal, or modal questions are "substantive" is in large part a question of whether the world has ontological, causal, and modal structure - whether quantifiers, causal relations, and modal operators carve at the joints. (shrink)

Think of “locations” very abstractly, as positions in a space, any space. Temporal locations are positions in time; spatial locations are positions in (physical) space; particulars are locations in quality space. Should we reify locations? Are locations entities? Spatiotemporal relation- alists say there are no such things as spatiotemporal locations; the fundamental spatial and temporal facts involve no locations as objects, only the instantiation of spatial and temporal relations. The denial of locations in quality space is the bundle theory, according (...) to which particulars do not exist; facts apparently about particulars really concern relations between universals. A “space”, in our abstract sense, consists of a set of objects, together with properties and relations defined on those objects. The objects are the locations of the space, and the distribution of the properties and relations over the locations defines the space’s structure. All spaces are thus quality spaces; when the relations are thought of as spatiotemporal then the space is also a spatiotemporal space. By not reifying locations one denies that these abstract spaces isomorphically represent the real world. The real world does in some sense have a structure that can be non-isomorphically represented by a space (or, more likely, a class of spaces), but the locations in those spaces do not correspond to anything real. We will examine modal considerations on reifying locations. Denying the existence of spatiotemporal locations excludes certain possibilities for spatiotemporal reality. Denying the existence of qualitative locations excludes certain possibilities for qualitative space. In each case the excluded possibilities are pre-analytically possible. Some of the possibilities can be reinstated by modifying the locationless theories, but at the cost of an unattractive holism. Do these modal considerations mandate postulating locations? That depends on whether modal intuition can teach us about the actual world.. (shrink)

Consider a circle and a pair of its semicircles. Which is prior, the whole or its parts? Are the semicircles dependent abstractions from their whole, or is the circle a derivative construction from its parts? Now in place of the circle consider the entire cosmos (the ultimate concrete whole), and in place of the pair of semicircles consider the myriad particles (the ultimate concrete parts). Which if either is ultimately prior, the one ultimate whole or its many ultimate parts?

In this paper, I argue that there are universals. I begin (Sect. 1) by proposing a sufficient condition for a thing’s being a universal. I then argue (Sect. 2) that some truths exist necessarily. Finally, I argue (Sects. 3 and 4) that these truths are structured entities having constituents that meet the proposed sufficient condition for being universals.

A variety of relations widely invoked by philosophers—composition, constitution, realization, micro-basing, emergence, and many others—are species of what I call ‘building relations’. I argue that they are conceptually intertwined, articulate what it takes for a relation to count as a building relation, and argue that—contra appearances—it is an open possibility that these relations are all determinates of a common determinable, or even that there is really only one building relation.

This book tackles the issues that arise in connection with intensional logic -- a formal system for representing and explaining the apparent failures of certain important principles of inference such as the substitution of identicals and existential generalization -- and intentional states --mental states such as beliefs, hopes, and desires that are directed towards the world. The theory offers a unified explanation of the various kinds of inferential failures associated with intensional logic but also unifies the study of intensional contexts (...) and intentional states by grounding the explanation of both phenomena in a single theory. When an axiomatized realm of abstract entities is added to the metaphysical structure of the world, we can use them to identify and individuate the contents of directed mental states. The special abstract entities can be viewed as the objectified contents of mental files, and they play a crucial role in the analysis of truth conditions of the sentences involved in inferential failures. (shrink)

This is the 1991 (2nd) edition of the 1986 book (MIT Press), considered to be the classic defense of Millianism. The nature of the information content of declarative sentences is a central topic in the philosophy of language. The natural view that a sentence like "John loves Mary" contains information in which two individuals occur as constituents is termed the naive theory, and is one that has been abandoned by most contemporary scholars. This theory was refuted originally by philosopher Gottlob (...) Frege. His argument that the naive theory did not work is termed Frege's puzzle, and his rival account of information content is termed the orthodox theory. In this detailed study, Nathan Salmon defends a version of the naive theory and presents a proposal for its extension that provides a better picture of information content than the orthodox theory gives. He argues that a great deal of what has generally been taken for granted in the philosophy of language over the past few decades is either mistaken or unsupported, and consequently, much current research is focused on the wrong set of questions. Salmon dissolves Frege's puzzle as it is usually formulated and demonstrates how it can be reconstructed and strengthened to yield a more powerful objection to the naive theory. He then defends the naive theory against the new Frege puzzle by presenting an idea that yields both a surprisingly rich and powerful extension of the naive theory and a better picture of information content than that of the original orthodox theory. Nathan Salmon is Professor of Philosophy, University of California at Santa Barbara. (shrink)

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)

There is a long history of worrying about whether or not metaphysics is a legitimate philosophical discipline. Traditionally such worries center around issues of meaning and epistemological concerns. Do the metaphysical questions have any meaning? Can metaphysical methodology lead to knowledge? But these questions are, in my opinion, not as serious as they have sometimes (historically) been taken to be. What is much more concerning is another set of worries about metaphysics, which I take to the greatest threat to metaphysics (...) as a philosophical discipline. These worries, in effect, hold that the questions that metaphysics tries to answer have long been answered in other parts of inquiry, ones that have much greater authority. And if they haven’t been answered yet then one should not look to philosophy for an answer. What metaphysics tries to do has been or will be done by the sciences. There is nothing left to do for philosophy, or so the worry. Let me illustrate this with two examples, one of which is our main concern here. (shrink)

In this fascinating work, Scott Soames offers a new conception of the relationship between linguistic meaning and assertions made by utterances. He gives meanings of proper names and natural kind predicates and explains their use in attitude ascriptions. He also demonstrates the irrelevance of rigid designation in understanding why theoretical identities containing such predicates are necessary, if true.

This book, one of the first full-length studies of the modalities to emerge from the debate to which Saul Kripke, David Lewis, Ruth Marcus, and others are contributing, is an exploration and defense of the notion of modality de re, the idea that objects have both essential and accidental properties. Plantinga develops his argument by means of the notion of possible worlds and ranges over such key problems as the nature of essence, transworld identity, negative existential propositions, and the existence (...) of unactual objects in other possible worlds. He also applies his logical theories to the elucidation of two problems in the philosophy of religion: the problem of evil and the ontological argument. (shrink)

This anthology of essays on the work of David Kaplan, a leading contemporary philosopher of language, sprang from a conference, "Themes from Kaplan," organized by the Center for the Study of Language and Information at Stanford University.

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.

Frege's theory of indirect contexts and the shift of sense and reference in these contexts has puzzled many. What can the hierarchy of indirect senses, doubly indirect senses, and so on, be? Donald Davidson gave a well-known 'unlearnability' argument against Frege's theory. The present paper argues that the key to Frege's theory lies in the fact that whenever a reference is specified (even though many senses determine a single reference), it is specified in a particular way, so that giving a (...) reference implies giving a sense; and that one must be 'acquainted' with the sense. It is argued that an indirect sense must be 'immediately revelatory' of its reference. General principles for Frege's doctrine of sense and reference are sated, for both direct and indirect quotation, to be understood iteratively. I also discuss Frege's doctrine of tensed and first person statements in the light of my analysis. The views of various other authors are examined. The conclusion is to ascribe to Frege an implicit doctrine of acquaintance similar to that of Russell. (shrink)

It seems obvious that I could have failed to exist. My parents could easily never have met, in which case I should never have been conceived and born. The like applies to everyone. More generally, it seems plausible that whatever exists in space and time could have failed to exist. Events could have taken an utterly different course. Our existence, like most other aspects of our lives, appears frighteningly contingent. It is therefore surprising that there is a proof of my (...) necessary existence, a proof that generalizes to everything whatsoever. I will explain the proof and discuss what to make of it. A first reaction is that a ‘proof’ of such an outrageous conclusion must contain some dreadful fallacy. Yet the proof does not collapse under scrutiny. Further reflection suggests that, suitably interpreted, it may be sound. So interpreted, the conclusion is not outrageous, although it may not be the view you first thought of. (shrink)

On the now dominant Quinean view, metaphysics is about what there is. Metaphysics so conceived is concerned with such questions as whether properties exist, whether meanings exist, and whether numbers exist. I will argue for the revival of a more traditional Aristotelian view, on which metaphysics is about what grounds what. Metaphysics so revived does not bother asking whether properties, meanings, and numbers exist (of course they do!) The question is whether or not they are fundamental.

‘‘Thus I believe that there is no part of matter which is not—I do not say divisible—but actually divided; and consequently the least particle ought to be considered as a world full of an infinity of different creatures.’’ (Leibniz, letter to Foucher).

Something could be round even if it were the only thing in the universe, unaccompanied by anything distinct from itself. Jaegwon Kim once suggested that we define an intrinsic property as one that can belong to something unaccompanied. Wrong: unaccompaniment itself is not intrinsic, yet it can belong to something unaccompanied. But there is a better Kim-style definition. Say that P is independent of accompaniment iff four different cases are possible: something accompanied may have P or lack P, something unaccompanied (...) may have P or lack P. P is basic intrinsic iff (1) P and not-P are nondisjunctive and contingent, and (2) P is independent of accompaniment. Two things (actual or possible) are duplicates iff they have exactly the same basic intrinsic properties. P is intrinsic iff no two duplicates differ with respect to P. (shrink)

This paper distinguishes two kinds of realist issue -- the issue of whether the propositions of a given domain are factual and the issue of whether they are fundamental. It criticizes previous accounts of what these issues come to and suggests that they are to be understood in terms of a basic metaphysical concept of reality. This leaves open the question of how such issues are to be resolved; and it is argued that this may be done through consideration of (...) what grounds the facts of a given domain, when fundamentality is in question, and what grounds our engagement with the putative facts, when factuality is in question. (shrink)