Do non‐symmetric relations apply to the objects they relate in an order? According to the standard view of relations, the difference between aRb and bRa obtaining, where R is non‐symmetric, corresponds to a difference in the order in which the non‐symmetric relation R applies to a and b. Recently Kit Fine has challenged the standard view in his important paper ‘Neutral Relations’ arguing that non‐symmetric relations are neutral, lacking direction or order. In this paper I argue that Fine cannot account (...) for the application of non‐symmetric relations to their relata; so far from being neutral, these relations are inherently directional. (shrink)

The „Paradox of the Concept Horse" arises on the assumption of the Reference Principle: that co-referential expressions should be cross-substitutable salva veritate in extensional contexts and salva congruitate in all. Accordingly no singular term can co-refer with an unsaturated expression. The paper outlines a number of desiderata for a satisfactory response to the problem and argues that recent treatments by Dummett and Wiggins fall short by their lights. It is then pointed out that a more consistent perception of the requirements (...) of the Reference Principle leads not to the Paradox but to the result that Frege had no business extending the notion of Bedeutung to unsaturated expressions in the first place. Rather the relation between, e.g., predicates and the entities that comprise the range of higher-order logical variables must be logically unlike that between singular terms and their referents; the way is therefore opened for singular terms to refer to entities of the former kind after all. The Concept Horse is a concept (and a Fregean object too.). (shrink)

On reading the last sentence, did you interpret me as saying falsely that everything — everything in the entire universe — was packed into my carry-on baggage? Probably not. In ordinary language, ‘everything’ and other quantifiers (‘something’, ‘nothing’, ‘every dog’, ...) often carry a tacit restriction to a domain of contextually relevant objects, such as the things that I need to take with me on my journey. Thus a sentence of the form ‘Everything Fs’ is true as uttered in a (...) context C if and only if everything that is relevant in C satisfies the predicate ‘F’; ‘everything’ ranges just over the contextually relevant things. Such generality is restricted in a context-relative way. (shrink)

Timothy Williamson offers a proof of the counterintuitive claim that, if an object exists, then it exists necessarily. David Wiggins argues that this result reveals the philosophical disadvantage of a first level (or ‘ticking over’) view of the very ‘exists’ and the advantage of the second level account offered by Frege and Russell. The author seeks to show how, using an idea of G. Evans but without the use of the resources of ‘free logic’, all occurrences of ‘exist’, including its (...) occurrence in true, negative existential, singular statements, can be accommodated to the Frege–Russell view and accorded the intuitively required modal status. (shrink)

Ontological Pluralism is the view that there are different modes, ways, or kinds of being. In this paper, I characterize the view more fully (drawing on some recent work by Kris McDaniel) and then defend the view against a number of arguments. (All of the arguments I can think of against it, anyway.).

The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed description of higher-order logic, including a comprehensive discussion of its semantics. He goes on to demonstrate the prevalence of second-order concepts in mathematics and the extent to which mathematical ideas can be formulated in higher-order logic. He also shows how first-order languages are often insufficient to codify (...) many concepts in contemporary mathematics, and thus that both first- and higher-order logics are needed to fully reflect current work. Throughout, the emphasis is on discussing the associated philosophical and historical issues and the implications they have for foundational studies. For the most part, the author assumes little more than a familiarity with logic comparable to that provided in a beginning graduate course which includes the incompleteness of arithmetic and the Lowenheim-Skolem theorems. All those concerned with the foundations of mathematics will find this a thought-provoking discussion of some of the central issues in the field today. (shrink)

In this paper I discuss a certain kind of 'type confusion' which involves use of expressions of the wrong grammatical category, as in the string 'runs eats'. It is (nearly) universally accepted that such strings are meaningless. My purpose in this paper is to question this widespread assumption (or as I call it, 'the last dogma'). I discuss a range of putative reasons for accepting the last dogma: in §II, semantic and metaphysical reasons; in §III, logical reasons; and in §IV, (...) syntactic reasons. I argue that none of these reasons is conclusive, and that consequently we should be willing to question this last dogma of type confusions. (shrink)

Is the assumption of a fundamental distinction between particulars and universals another unsupported dogma of metaphysics? F. P. Ramsey famously rejected the particular – universal distinction but neglected to consider the many different conceptions of the distinction that have been advanced. As a contribution to the piecemeal investigation of this issue three interrelated conceptions of the particular – universal distinction are examined: universals, by contrast to particulars, are unigrade; particulars are related to universals by an asymmetric tie of exemplification; universals (...) are incomplete whereas particulars are complete. It is argued that these conceptions are wanting in several respects. Sometimes they fail to mark a significant division amongst entities. Sometimes they make substantial demands upon the shape of reality; once these demands are understood aright it is no longer obvious that the distinction merits our acceptance. The case is made via a discussion of the possibility of multigrade universals. (shrink)

Whether a predicate is a referential expression depends upon what reference is conceived to be. Even if it is granted that reference is a relation between words and worldly items, the referents of expressions being the items to which they are so related, this still leaves considerable scope for disagreement about whether predicates refer. One of Frege's great contributions to the philosophy of language was to introduce an especially liberal conception of reference relative to which it is unproblematic to suppose (...) that predicates are referring expressions. According to this liberal conception, each significant expression in a language has its own distinctive semantic role or power, a power to effect the truth-value of the sentences in which it occurs. (shrink)

This paper uses the resources of higher-order logic to articulate a Fregean conception of predicate reference, and of word-world relations more generally, that is immune to the concept horse problem. The paper then addresses a prominent style of expressibility problem for views of broadly this kind, versions of which are due to Linnebo, Hale, and Wright.

Keith Hossack's thesis is that knowledge is a conceptually primitive and metaphysically fundamental relation between a mind and a fact. He argues that in terms of the simple relation of knowledge we can analyze central notions of epistemology, of semantics, of modality and a priori knowledge, of psychology, and of linguistics. He does so in a framework that includes a fairly rich faculty psychology and that stresses causation: knowledge can be caused by belief, but because knowledge is simple, it is (...) not any kind of belief. He regards his enterprise as metaphysics, and he proceeds in a rather grand manner. The beginning of his Preface might remind one of the opening paragraphs of Leibniz's The Monadology.If knowledge is a simple relation between minds and facts, then we want to know a bit about facts. Hossack takes facts to consist in universals being instantiated among things. He favours a view of universals as respects in which things resemble each other, but his theory is at least officially silent about which universals exist, leaving that as a matter for scientific inquiry. But he takes metaphysics to be a science. Here he is being coy, and it is worth making out how. Hossack uses multigrade relations; these are relations of no fixed polyadicity that for any natural number n may be instantiated by n things. Vectors are bearers of such relations. The relation among working men of uniting to form a union is a multigrade relation, and the founders of the International Workers of the World are a vector bearing this relation. (shrink)

Translation of Frege's 'Über Begriff und Gegenstand' (1892). Translation by Peter Geach, revised by Max Black.

Plural logic is widely assumed to have two important virtues: ontological innocence and determinacy. It is claimed to be innocent in the sense that it incurs no ontological commitments beyond those already incurred by the first-order quantifiers. It is claimed to be determinate in the sense that it is immune to the threat of non-standard interpretations that confronts higher-order logics on their more traditional, set-based semantics. We challenge both claims. Our challenge is based on a Henkin-style semantics for plural logic (...) that does not resort to sets or set-like objects to interpret plural variables, but adopts the view that a plural variable has many objects as its values. Using this semantics, we also articulate a generalized notion of ontological commitment which enables us to develop some ideas of earlier critics of the alleged ontological innocence of plural logic. (shrink)

There is a standard view of relations, held by philosophers and logicians alike, according to which we may meaningfully talk of a relation holding of several objects in a given order. Thus it is supposed that we may meaningfully—indeed, correctly—talk of the relation loves holding of Anthony and Cleopatra or of the relation between holding of New York, Washington, and Boston. But innocuous as this view might appear to be, it cannot be accepted as applying to all relations whatever. For (...) there is an important class of metaphysical and linguistic contexts which call for an alternative conception of relation, one for which the order of the relata plays no role and in which the application of the relation to its relata is achieved by other means. (shrink)

In "nominalism and realism" armstrong carefully demolishes various nominalist responses to plato's "one over many" problem but simply dismissed the quinean response as "ostrich nominalism". The paper argues that plato's problem is pseudo. So to ignore it is not to behave like an ostrich. Rather to adopt realism because of this problem that isn't there is to be a "mirage realist." there are some good reasons that lead armstrong to realism but he is largely a mirage realist. Quine does not (...) ignore any real problem for nominalism and so is not an ostrich nominalist. (shrink)

Amie Thomasson and Eli Hirsch have both attempted to deflate metaphysics, by combining Carnapian ideas with an appeal to ordinary language. My main aim in this paper is to critique such deflationary appeals to ordinary language. Focussing on Thomasson, I draw two very general conclusions. First: ordinary language is a wildly complicated phenomenon. Its implicit ontological commitments can only be tackled by invoking a context principle; but this will mean that ordinary language ontology is not a trivial enterprise. Second: ordinary (...) language often points in different directions simultaneously, so that a wide variety of existence questions cannot be deflated merely by appealing to ordinary language. (shrink)

In this short text, a distinguished philosopher turns his attention to one of the oldest and most fundamental philosophical problems of all: How it is that we are able to sort and classify different things as being of the same natural class? Professor Armstrong carefully sets out six major theories—ancient, modern, and contemporary—and assesses the strengths and weaknesses of each. Recognizing that there are no final victories or defeats in metaphysics, Armstrong nonetheless defends a traditional account of universals as the (...) most satisfactory theory we have.This study is written for advanced students, but as Armstrong goes considerably beyond his earlier work on this topic, it will interest professional scholars as well. Carefully plotted and clearly written, Universals is both a paradigm of exposition and a case study on the value of careful analysis of fundamental issues in philosophy. (shrink)

This is a collection of twenty-five papers and reviews by the leading analytic philosopher of our time. It adds to the papers on metaphysics and epistemology to be found in his previous two-volume collection published by Oxford University Press. One previously unpublished paper—“Why Conditionalize?”—is included. Australasian philosophers may note with some pride that eleven of the pieces were first published in the Australasian Journal of Philosophy.

In my reply to michael devitt, It is argued, First, That quine fails to appreciate the force of plato's "one over many" argument for universals. It is argued, Second, That quine's failure springs in part at least from his doctrine of ontological commitment: from the view that predicates need not be treated with ontological seriousness. Finally, An attempt is made to blunt the force of devitt's contention that realists cannot give a coherent explanation of the way that universals stand to (...) particulars. (shrink)

Bob Hale presents a broadly Fregean approach to metaphysics, according to which ontology and modality are mutually dependent upon one another. He argues that facts about what kinds of things exist depend on facts about what is possible. Modal facts are fundamental, and have their basis in the essences of things--not in meanings or concepts.

Here, Bob Hale and Crispin Wright assemble the key writings that lead to their distinctive neo-Fregean approach to the philosophy of mathematics. In addition to fourteen previously published papers, the volume features a new paper on the Julius Caesar problem; a substantial new introduction mapping out the program and the contributions made to it by the various papers; a section explaining which issues most require further attention; and bibliographies of references and further useful sources. It will be recognized as the (...) most powerful presentation yet of a neo-Fregean program. (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.

Category mistakes are sentences such as 'Green ideas sleep furiously' or 'Saturday is in bed'. They strike us as highly infelicitous but it is hard to explain precisely why this is so. Ofra Magidor explores four approaches to category mistakes in philosophy of language and linguistics, and develops and defends an original, presuppositional account.

When we say a certain rose is red, we seem to be attributing a property, redness, to it. But are there really such properties? If so, what are they like, how do we know about them, and how are they related to the objects which have them and the linguistic devices which we use to talk about them? This collection presents these ancient problems in a modern light. In particular, it makes accessible for the first time the most important contributions (...) to the contemporary controversy about the nature of properties. Those new to the subject will find the clearly-written introduction, by two experts in the field, an invaluable guide to the intricacies of this debate. The volume illustrates very well the aims and methods of modern metaphysics and show how a thorough understanding of the metaphysics of properties is crucial to most of analytic philosophy. (shrink)

Suppose now that two philosophers, McX and I, differ over ontology. Suppose McX maintains there is something which I maintain there is not. McX can, quite consistently with his own point of view, describe our difference of opinion by saying that I refuse to recognize certain entities. I should protest of course that he is wrong in his formulation of our disagreement, for I maintain that there are no entities, of the kind which he alleges, for me to recognize; but (...) my finding him wrong in his formulation of our disagreement is unimportant, for I am committed to considering him wrong in his ontology anyway. When I try to formulate our difference of opinion, on the other hand, I seem to be in a predicament. I cannot admit that there are some things which McX countenances and I do not, for in admitting that there are such things I should be contradicting my own rejection of them. (shrink)

Call a quantifier unrestricted if it ranges over absolutely all things: not just over all physical things or all things relevant to some particular utterance or discourse but over absolutely everything there is. Prima facie, unrestricted quantification seems to be perfectly coherent. For such quantification appears to be involved in a variety of claims that all normal human beings are capable of understanding. For instance, some basic logical and mathematical truths appear to involve unrestricted quantification, such as the truth that (...) absolutely everything is self-identical and the truth that the empty set has absolutely no members. Various metaphysical views too appear to involve unrestricted quantification, such as the physicalist view that absolutely everything is physical. (shrink)

Gödel claimed that Zermelo-Fraenkel set theory is 'what becomes of the theory of types if certain superfluous restrictions are removed'. The aim of this paper is to develop a clearer understanding of Gödel's remark, and of the surrounding philosophical terrain. In connection with this, we discuss some technical issues concerning infinitary type theories and the programme of developing the semantics for higher-order languages in other higher-order languages.

This paper is about avoiding commitment to an ontology of possible worlds with two primitives: a hyperintensional connective like ‘in virtue of’, and primitive quantification into predicate position. I argue that these tools (which some believe can be independently motivated) render dispensable the ontology of possible worlds needed by traditional anaylses of modality. They also shed new light on the notion of truth-at-a-world.

Here is an account of logical consequence inspired by Bolzano and Tarski. Logical validity is a property of arguments. An argument is a pair of a set of interpreted sentences (the premises) and an interpreted sentence (the conclusion). Whether an argument is logically valid depends only on its logical form. The logical form of an argument is fixed by the syntax of its constituent sentences, the meanings of their logical constituents and the syntactic differences between their non-logical constituents, treated as (...) variables. A constituent of a sentence is logical just if it is formal in meaning, in the sense roughly that its application is invariant under permutations of individuals.1 Thus ‘=’ is a logical constant because no permutation maps two individuals to one or one to two; ‘∈’ is not a logical constant because some permutations interchange the null set and its singleton. Truth functions, the usual quantifiers and bound variables also count as logical constants. An argument is logically valid if and only if the conclusion is true under every assignment of semantic values to variables (including all non-logical expressions) under which all its premises are true. A sentence is logically true if and only if the argument with no premises of which it is the conclusion is logically valid, that is, if and only if the sentence is true under every assignment of semantic values to variables. An interpretation assigns values to all variables. (shrink)