If you’ve read the first five hundred pages of this book, you’ve read most of it (we assume that ‘most’ requires more than ‘more than half’). The set of natural numbers n such that the first n pages are most of this book is nonempty. Therefore, by the least number principle, it has a least member k. What is k? We do not know. We have no idea how to find out. The obstacle is something about the term ‘most’. It (...) is recognisably the same feature as the feature of ‘heap’ that prevents us from finding an answer to the question ‘How many grains make a heap?’ and the feature of many other expressions that prevents us from finding answers to similar questions involving them. Call this feature, whatever its underlying nature, vagueness. (shrink)

It has been maintained by such philosophers as Quine and Goodman that purely ‘extensional’ language suffices for all the purposes of properly formalized scientific discourse. Those entities that were traditionally called ‘universals’ — properties, concepts, forms, etc. — are rejected by these extensionalist philosophers on the ground that ‘the principle of individuation is not clear’. It is conceded that science requires that we allow something tantamount to quantification over non-particulars (or, anyway, over things that are not material objects, not space-time (...) points, not physical fields, etc.), but, the extensionalists contend, quantification over sets serves the purposes nicely. The ‘ontology’ of modern science, at least as Quine formalizes it, comprises material objects (or, alternatively, space-time points), sets of material objects, sets of sets of material objects,... but no properties, concepts,or forms. Let us thus examine the question: Can the principle of individuation for properties ever be made clear? (shrink)

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.

Philosophy, science, and common sense all refer to propositions--things we believe and say, and things which are true or false. But there is no consensus on what sorts of things these entities are. Jeffrey C. King, Scott Soames, and Jeff Speaks argue that commitment to propositions is indispensable, and each defend their own views on the debate.

Solutions to Russell’s paradox of propositions and to Kaplan’s paradox are proposed based on an extension of von Neumann’s method of avoiding paradox. It is shown that Russell’s ‘anti-Cantorian’ mappings can be preserved using this method, but Kaplan’s mapping cannot. In addition, several versions of the Epimenides paradox are discussed in light of von Neumann’s method.

Under what conditions are two utterances utterances of the same word? What are words? That these questions have not received much attention is rather surprising: after all, philosophers and linguists frequently appeal to considerations about word and sentence identity in connection with a variety of puzzles and problems that are foundational to the very subject matter of philosophy of language and linguistics.1 Kaplan’s attention to words is thus to be applauded. And there is no doubt that his discussion contains many (...) useful insights. Nevertheless, we find his picture deeply flawed for a variety of crosscutting reasons. Our aim in this paper is to further advance an understanding of the nature of words, both by remedying the problems with Kaplan’s account, and also by achieving a suitable perspective on what the metaphysical investigation of word identity can hope to achieve. Our discussion divides into four parts. In Part One, we examine and critique Kaplan’s discussion of a contrast integral to his own account: that between the type-token and the stage-continuant conceptions of words. In Part Two, we present three constraints on any account of words and two further themes in Kaplan’s discussion central to his conception of words – the role of repetition and the constitutive authority of intentions. While these ideas have laudable motivations, we argue they are far from the best way of making good on the insights that drive them. The final two sections take a skeptical turn. In Part Three, we express doubt about Kaplan’s presumption of the importance of what he calls ‘common currency names’, thus raising a suspicion that he may be in pursuit of chimera. Finally, in Part Four, we express pessimism about whether interesting answers to question above will be forthcoming, and suggest that the legitimacy of our word ontology need not depend on the availability of such answers. Along the way, we tease apart a number of metaphysical questions in the vicinity of the topic of word individuation – questions that are often not disentangled – and consider how the discussion of the previous parts bears on them.. (shrink)

§ i. After deserting for a time the old Euclidean standards of rigour, mathematics is now returning to them, and even making efforts to go beyond them. ...

In this paper, I discuss two concerns for pluralist truth theories: a concern about a key detail of these theories and a concern about their viability. The detail-related concern is that pluralists have relied heavily upon the notion of a domain, but it is not transparent what they take domains to be. Since the notion of a domain has been present in philosophy for some time, it is important for many theorists, not only truth pluralists, to be clear on what (...) domains are and what work they can do. The viability-related concern is that it’s not clear how a pluralist truth theory could explain the truth-conditions of mixed atomic propositions. To address this concern, truth pluralists should recognize something to which they have not been sufficiently attentive: that some atomic propositions belong to more than one domain. But, recognizing this requires rethinking the relationships between the nature of propositions, their membership in domains, and their truth. I address these issues and propose an understanding of them that is preferable to the best existing account of them, that offered by Michael Lynch. (shrink)

Lewis's notion of a "natural" property has proved divisive: some have taken to the notion with enthusiasm, while others have been sceptical. However, it is far from obvious what the enthusiasts and the sceptics are disagreeing about. This paper attempts to articulate what is at stake in this debate.

Paul Elbourne explores the complex nature of meaning in crystal clear language. He draws on approaches developed in linguistics, philosophy, and psychology - assuming a knowledge of none of them - in a manner that will appeal to everyone interested in this essential element of human psychology and culture.

In this paper, we do two things. First, we provide some support for adopting a version of the meaningless strategy with respect to the liar paradox, and, second, we extend that strategy, by providing, albeit tentatively, a solution to that paradox—one that is semantic, rather than logical.

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)

The renowned philosopher Jerry Fodor, a leading figure in the study of the mind for more than twenty years, presents a strikingly original theory on the basic constituents of thought. He suggests that the heart of cognitive science is its theory of concepts, and that cognitive scientists have gone badly wrong in many areas because their assumptions about concepts have been mistaken. Fodor argues compellingly for an atomistic theory of concepts, deals out witty and pugnacious demolitions of rival theories, and (...) suggests that future work on human cognition should build upon new foundations. This lively, conversational, and superbly accessible book is the first volume in the Oxford Cognitive Science Series, where the best original work in this field will be presented to a broad readership. Concepts will fascinate anyone interested in contemporary work on mind and language. Cognitive science will never be the same again. (shrink)

Kit Fine develops a Fregean theory of abstraction, and suggests that it may yield a new philosophical foundation for mathematics, one that can account for both our reference to various mathematical objects and our knowledge of various mathematical truths. The Limits ofion breaks new ground both technically and philosophically.

A selective background -- Broadly classical approaches -- Paracompleteness -- More on paracomplete solutions -- Paraconsistent dialetheism.

Essays discuss relativism, knowledge, creativity, progress, Aristotle, Galileo, cultural pluralism, and reason.

This paper is about the relationship between two questions: the question of what the objects of assertion are and the question of how best to theorise about ‘shifty’ phenomena like modality and tense. I argue that the relationship between these two questions is less direct than is often supposed. I then explore the consequences of this for a number of debates in the philosophy of language.

Timothy Williamson; VII*—Equivocation and Existence, Proceedings of the Aristotelian Society, Volume 88, Issue 1, 1 June 1988, Pages 109–128, https://doi.org/10.

Of course we all know now that mathematics has proved that logic doesn't really make sense, but Etchemendy (philosophy, Stanford Univ.) goes further and challenges the received view of the conceptual underpinnings of modern logic by arguing that Tarski's model-theoretic analysis of logical consequences is wrong. He may have found the soft underbelly of the dead horse. Annotation copyrighted by Book News, Inc., Portland, OR.

Science Without Numbers caused a stir in 1980, with its bold nominalist approach to the philosophy of mathematics and science. It has been unavailable for twenty years and is now reissued in a revised edition with a substantial new preface presenting the author's current views and responses to the issues raised in subsequent debate.

In these articles, I describe Cantor’s power-class theorem, as well as a number of logical and philosophical paradoxes that stem from it, many of which were discovered or considered (implicitly or explicitly) in Bertrand Russell’s work. These include Russell’s paradox of the class of all classes not members of themselves, as well as others involving properties, propositions, descriptive senses, class-intensions, and equivalence classes of coextensional properties. Part I focuses on Cantor’s theorem, its proof, how it can be used to manufacture (...) paradoxes, Frege’s diagnosis of the core difficulty, and several broad categories of strategies for offering solutions to these paradoxes. (shrink)

Sequel to Part I. In these articles, I describe Cantor’s power-class theorem, as well as a number of logical and philosophical paradoxes that stem from it, many of which were discovered or considered (implicitly or explicitly) in Bertrand Russell’s work. These include Russell’s paradox of the class of all classes not members of themselves, as well as others involving properties, propositions, descriptive senses, class-intensions and equivalence classes of coextensional properties. Part II addresses Russell’s own various attempts to solve these paradoxes, (...) including strategies that he considered and rejected (limitation of size, the zigzag theory, etc.), as well as his own final views whereupon many purported entities that, if reified, lead to these contradictions, must not be genuine entities, but ‘logical fictions’ or ‘logical constructions’ instead. (shrink)

The main objective of this paper is to examine how theories of truth and reference that are in a broad sense Fregean in character are threatened by antinomies; in particular by the Epimenides paradox and versions of the so-called Russell-Myhill antinomy, an intensional analogue of Russell’s more well-known paradox for extensions. Frege’s ontology of propositions and senses has recently received renewed interest in connection with minimalist theories that take propositions (thoughts) and senses (concepts) as the primary bearers of truth and (...) reference. In this paper, I will present a rigorous version of Frege’s theory of sense and denotation and show that it leads to antinomies. I am also going to discuss ways of modifying Frege’s semantical and ontological framework in order to avoid the paradoxes. In this connection, I explore the possibility of giving up the Fregean assumption of a universal domain of absolutely all objects, containing in addition to extensional objects also abstract intensional ones like propositions and singular concepts. I outline a cumulative hierarchy of Fregean propositions and senses, in analogy with Gödel’s hierarchy of constructible sets. In this hierarchy, there is no domain of all objects. Instead, every domain of objects is extendible with new objects that, on pain of contradiction, cannot belong to the given domain. According to this approach, there is no domain containing absolutely all propositions or absolutely all senses. (shrink)

Metaphysically possible worlds have many uses. Epistemically possible worlds promise to be similarly useful, especially in connection with propositions and propositional attitudes. However, I argue that there is a serious threat to the natural accounts of epistemically possible worlds, from a version of Russell’s paradox. I contrast this threat with David Kaplan’s problem for metaphysical possible world semantics: Kaplan’s problem can be straightforwardly rebutted, the problems I raise cannot. I argue that although there may be coherent accounts of epistemically possible (...) worlds with fruitful applications, any such an account must fundamentally compromise the basic idea behind epistemic possibility. (shrink)

Develops a structuralist understanding of mathematics, as an alternative to set- or type-theoretic foundations, that respects classical mathematical truth while ...

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)

am going to discuss some issues inspired by a well-known paper ofKeith Donnellan, "Reference and Definite Descriptions,”2 but the interest—to me—of the contrast mentioned in my title goes beyond Donnellan's paper: I think it is of considerable constructive as well as critical importance to the philosophy oflanguage. These applications, however, and even everything I might want to say relative to Donnellan’s paper, cannot be discussed in full here because of problems of length. Moreover, although I have a considerable interest in (...) the substantive issues raised by Donnellan’s paper, and by related literature, my own conclusions will be methodological, not substantive. I can put the matter this way: Donnellan’s paper claims to give decisive objections both to Russell’s theory of definite descriptions (taken as a theory about English) and to Strawson’s. My concem is not primarily with the question; is Donnellan right, or is Russell (or Strawson)? Rather, it is with the question: do the considerations in Donneilarfs paper refute Russell’s theory (or Strawson’s)? For definiteness, I will concentrate on Donnellan versus Russell, leaving Strawson aside. And about this issue I will draw a definite conclusion, one which I think will illuminate a few methodological maxims about language. Namely, I will conclude that the considerations in Donnellan’s paper, by themselves, do not refute Russell’s theory. Any conclusions about Russell’s views per se, or Donnellan’s, must be tentative, IfI were to be asked for a tentative stab about Russell, I would say that although his theory does a far better job of handling ordinary discourse than many have thought, and although many popular arguments against it are inconclusive, probably it ultimately fails. The considerations I have in mind have to do with the existence of “improper” definite descriptions, such as “the table," where uniquely specifying conditions are not contained in the description itself.. (shrink)

I propose that the meanings of vague expressions render the truth conditions of utterances of sentences containing them sensitive to our interests. For example, 'expensive' is analyzed as meaning 'costs a lot', which in turn is analyzed as meaning 'costs significantly greater than the norm'. Whether a difference is a significant difference depends on what our interests are. Appeal to the proposal is shown to provide an attractive resolution of the sorites paradox that is compatible with classical logic and semantics.

This book is collection of the the author’s previously published papers on the philosophy of modality and tense and it also includes three unpublished papers. The author provides an exposition and defence of certain positions for which he is well-known: the intelligibility of modality de re; the primitiveness of the modal; and the primacy of the actual over the possible. He also argues for some less familiar positions: the existence of distinctive forms of natural and normative necessity, not reducible to (...) any form of metaphysical necessity; the need to make a distinction between the worldly and unworldly, analogous to the distinction between the tensed and the tenseless; and the viability of a nonstandard form of realism about tense, which recognizes the tensed character of reality without conceding there is any privileged standpoint from which it is to be viewed. (shrink)

Divided into two parts, the first concentrates on the logical properties of propositions, their relation to facts and sentences, and the parallel objects of commands and questions. The second part examines theories of intentionality and discusses the relationship between different theories of naming and different accounts of belief.

Only human beings have a rich conceptual repertoire with concepts like tort, entropy, Abelian group, mannerism, icon and deconstruction. How have humans constructed these concepts? And once they have been constructed by adults, how do children acquire them? While primarily focusing on the second question, in The Origin of Concepts , Susan Carey shows that the answers to both overlap substantially. Carey begins by characterizing the innate starting point for conceptual development, namely systems of core cognition. Representations of core cognition (...) are the output of dedicated input analyzers, as with perceptual representations, but these core representations differ from perceptual representations in having more abstract contents and richer functional roles. Carey argues that the key to understanding cognitive development lies in recognizing conceptual discontinuities in which new representational systems emerge that have more expressive power than core cognition and are also incommensurate with core cognition and other earlier representational systems. Finally, Carey fleshes out Quinian bootstrapping, a learning mechanism that has been repeatedly sketched in the literature on the history and philosophy of science. She demonstrates that Quinian bootstrapping is a major mechanism in the construction of new representational resources over the course of childrens cognitive development. Carey shows how developmental cognitive science resolves aspects of long-standing philosophical debates about the existence, nature, content, and format of innate knowledge. She also shows that understanding the processes of conceptual development in children illuminates the historical process by which concepts are constructed, and transforms the way we think about philosophical problems about the nature of concepts and the relations between language and thought. (shrink)