The view that mathematical objects are indefinite in nature is presented and defended, hi the first section, Field's argument for fictionalism, given in response to Benacerraf's problem of identification, is closely examined, and it is contended that platonists can solve the problem equally well if they take the view that mathematical objects are indefinite. In the second section, two general arguments against the intelligibility of objectual indefiniteness are shown erroneous, hi the final section, the view is compared to mathematical structuralism, (...) and it is shown that a version of structuralism should be understood as embracing the same view. (shrink)

In this paper I argue that Gareth Evans’ famous proof of the impossibility of de re indeterminate identity fails on a counterpart-theoretic interpretation of the determinacy operators. I attempt to motivate a counterpart-theoretic reading of the determinacy operators and then show that, understood counterpart-theoretically, Evans’ argument is straightforwardly invalid.

We discuss arguments against the thesis that the world itself can be vague. The first section of the paper distinguishes dialectically effective from ineffective arguments against metaphysical vagueness. The second section constructs an argument against metaphysical vagueness that promises to be of the dialectically effective sort: an argument against objects with vague parts. Firstly, cases of vague parthood commit one to cases of vague identity. But we argue that Evans' famous argument against will not on its own enable one to (...) complete the reductio in the present context. We provide a metaphysical premise that would complete the reductio, but note that it seems deniable. We conclude by drawing general morals from our case study. (shrink)

Here is the paper that was attacked by George Rea in his “How many minds…?” paper. Has this issue been resolved? Can there be entities such that there is no definite answer to the question “Are there 13 minds at work here, or 14?” -/- .

Let the moral question of personal identity be the following: what is the nature of the entities we should focus our prudential concerns and ascriptions of responsibility around? (If indeed we should structure these things around any entities at all.) Let the semantic question of personal identity be the question of what is the nature of the entities that ‘person’ is true of. A naive (in the sense of simple and intuitive) view would have it that the two questions are (...) so intimately connected that the entities we should focus our concerns and ascriptions around are, pretty trivially, the persons. In part, my aim here is to evaluate this naive view. However, I will not actually attempt to give a definite verdict on it. Rather, I will identify the assumptions under which the naive view is true, and discuss how to go about evaluating those assumptions. (shrink)

This volume collects thirteen papers by one of the leading philosophers of his generation, who died prematurely in 1980.

This paper asks whether persistence can be a matter of convention. It argues that in a rather unexciting de dicto sense persistence is indeed a matter of convention, but it rejects the notion that persistence can be a matter of convention in a more substantial de re sense. However, scenarios can be imagined that appear to involve conventional persistence of the latter kind. Since there are strong reasons for thinking that such conventionality is impossible, it is desirable that our metaphysical-cum-semantic (...) theories of persistence be able to account for such scenarios in terms of conventions of the first kind. Later parts of the article therefore investigate whether three of the currently most influential metaphysical-cum-semantic theories of persistence—the endurance theory, the stage theory, and the perdurance theory—can do this. Fortunately, for them, it turns out that all can, though some philosophers have disputed this. However, when we ask how they account for a typical case of “conventional persistence” some problematic features of the theories—having to do with reference, persistence conditions, how they relate, and the epistemology of persistence—are revealed. (shrink)

In "Counting and Indeterminate Identity", N. Ángel Pinillos develops an argument that there can be no cases of `Split Indeterminate Identity'. Such a case would be one in which it was indeterminate whether a=b and indeterminate whether a=c, but determinately true that b≠c. The interest of the argument lies, in part, in the fact that it appears to appeal to none of the controversial claims to which similar arguments due to Gareth Evans and Nathan Salmon appeal. I argue for two (...) counter-claims. First, the formal argument fails to establish its conclusion, for essentially the same reason Evans's and Salmon's arguments fail to establish their conclusions. Second, the phenomena in which Pinillos is interested, which concern the cardinalities of sets of vague objects, manifest the existence of what Kit Fine called `penumbral connections', phenomena that the logics Pinillos considers are already known not to handle well. (shrink)

I argue that for those who follow Evans in finding indeterminacy of de re identity statements problematic, ontic vagueness within a three-dimensionalist metaphysics will raise some problems that are not faced by the four-dimensionalist. For the types of strategies used to avoid de re indeterminacy within the context of ontic vagueness at-at-time, that is, spatial vagueness, are problematic within a three-dimensionalist framework when put to use within the context of ontic vagueness across-time, that is temporal vagueness.

ABSOLUTE AND RELATIVE IDENTITY On the classical, or Fregean, view of identity it is an equivalence relation satisfying Leibniz's Law (so<alled), ...

Challenging, with several powerful arguments, some of our deepest beliefs about rationality, morality, and personal identity, Parfit claims that we have a false view about our own nature. It is often rational to act against our own best interersts, he argues, and most of us have moral views that are self-defeating. We often act wrongly, although we know there will be no one with serious grounds for complaint, and when we consider future generations it is very hard to avoid conclusions (...) that most of us will find very disturbing. (shrink)

Terence Parsons presents a lively and controversial study of philosophical questions about identity. Because many puzzles about identity remain unsolved, some people believe that they are questions that have no answers and that there is a problem with the language used to formulate them. Parsons explores a different possibility: that such puzzles lack answers because of the way the world is (or because of the way the world is not). He claims that there is genuine indeterminacy of identity in the (...) world. He articulates such a view in detail and defends it from a host of criticisms. (shrink)

Suppose that we repair a wooden ship by replacing its planks one by one with new ones while at the same time reconstructing it using the discarded planks. Some defenders of vague or indeterminate identity claim that: (1) although the reconstructed ship is distinct from the repaired ship, it is indeterminate whether the original ship is the reconstructed ship and indeterminate whether it is the repaired ship, and (2) the indeterminacy is due to the world and not just an imprecision (...) in the language used to describe the situation. I argue that such a description is incoherent. The argument has two features. First, it differs in spirit from Gareth Evans's more general famous proof against the possibility of indeterminate identity. This is because I rely on facts regarding counting and sets. Second, I focus on Terence Parsons's recent defence of indeterminate identity. I argue that his attempts at making sense of counting objects involving indeterminate identities fail on technical and philosophical grounds. (shrink)

Four-dimensionalism, the stage theory version in particular, has been defended as the best solution for avoiding vagueness in regards to composition, persistence and identity. Stage theory is highly problematic by itself, and the two views usually packed with it, unrestricted composition and counterpart theory, are a heavy burden. However, dispensing with these two views, four-dimensionalism could avoid vague persistence by issuing a criterion that would establish sharp temporal boundaries for the existence of genuine entities (simples, molecules and living organisms). This (...) would avoid vague existence and vague identity, but in a way that is still compatible with endurantism. Nevertheless, a minimal (substantialist) four-dimensionalism, a worm perdurantist ontology, would fit better with the unique way in which organisms persist: by retaining both identity and intrinsic change. (shrink)

What happens to a person in a case of fission? Does it survive? Does it go out of existence? Or is the outcome indeterminate? Since each description of fission based on the persistence conditions associated with our ordinary concept of a person seems to clash with one or more platitudes of common sense about the spatiotemporal profile of macroscopic objects, fission threatens the common-sense conception of persons with inconsistency. Standard responses to this paradox agree that the common-sense conception of persons (...) is unstable, differing over which part of the conception requires revision. I will show that this entrenched view of fission is not compulsory. I will develop a solution to the paradox that maintains the consistency of the common-sense conception of persons on the basis of an ontology of persons and other ordinary objects as double-layered compounds. Each of various descriptions of the outcome of personal fission is compatible with principles about the spatiotemporal profile of persons, because the descriptions and the principles manifest different perspectives on persons and are made true or false by different ontological components of the latter. What holds for the fission of persons, holds for the fission of other kinds of objects. (shrink)

There are well-known quasi-formal arguments that identity is a "strict" relation in at least the following three senses: (1) There is a single identity relation and a single distinctness relation; (2) There are no contingent cases of identity or distinctness; and (3) There are no vague or indeterminate cases of identity or distinctness. However, the situation is less clear cut than it at first may appear. There is a natural formal theory of identity that is very close to the standard (...) classical theory but which does not validate the formal analogues of (1)-(3). The core idea is simple: We weaken the Principle of the Indiscernibility of Identicals from a conditional to an entailment and we adopt a weakly classical logic. This paper investigates this weakly classical theory of identity (and related theories) and discusses its philosophical rami cations. It argues that we can accept a reasonable theory of identity without committing ourselves to the uniqueness, necessity, or determinacy of identity. (shrink)

In this paper I present a new argument against vague identity — one that is more fundamental than existing arguments — and I also try to explain why we find the idea of vague identity puzzling, in a way that will dispel the puzzlement. In brief, my argument is this: to make clear sense of something, one must at least model it set-theoretically; but due to the special place of identity in set-theoretic models, any vague relation that one does model (...) set-theoretically will not be identity, for real identity will already be there, built into the background of the model, and perfectly precise. (shrink)

Todd’s quip absurdly implies he knew that 30 carats is the threshold for vulgarity. But most philosophers think stopping here misses the root of the joke. They think there is a more fundamental absurdity; that it is even possible for a single carat to make the difference between a vulgar ring and a non-vulgar ring. We epistemicists defend the possibility.

The topic of personal identity has prompted some of the liveliest and most interesting debates in recent philosophy. In a fascinating new contribution to the discussion, Peter Unger presents a psychologically aimed, but physically based, account of our identity over time. While supporting the account, he explains why many influential contemporary philosophers have underrated the importance of physical continuity to our survival, casting a new light on the work of Lewis, Nagel, Nozick, Parfit, Perry, Shoemaker, and others. Deriving from his (...) discussion of our identity itself, Unger produces a novel but commonsensical theory of the relations between identity and some of our deepest concerns. In a conservative but flexible spirit, he explores the implications of his theory for questions of value and of the good life. (shrink)

The topic of this book is material objects. Like most interesting concepts, the concept of a material object is one without precise boundaries.

This paper asks whether persistence can be a matter of convention. It argues that in a rather unexciting de dicto sense persistence is indeed a matter of convention, but it rejects the notion that persistence can be a matter of convention in a more substantial de re sense. However, scenarios can be imagined that appear to involve conventional persistence of the latter kind. Since there are strong reasons for thinking that such conventionality is impossible, it is desirable that our metaphysical-cum-semantic (...) theories of persistence be able to account for such scenarios in terms of conventions of the first kind. Later parts of the article therefore investigate whether three of the currently most influential metaphysical-cum-semantic theories of persistence—the endurance theory, the stage theory, and the perdurance theory—can do this. Fortunately, for them, it turns out that all can, though some philosophers have disputed this. However, when we ask how they account for a typical case of “conventional persistence” some problematic features of the theories —having to do with reference, persistence conditions, how they relate, and the epistemology of persistence — are revealed. (shrink)

Gareth Evans’s argument against ontically vague identity has been picked over on many occasions. But extant proposals for blocking the argument do not meet well-motivated general constraints on a successful solution. Moreover, the pivotal position that defending ontically vague identity occupies vis a vis ontic vagueness more generally has not yet been fully appreciated. This paper advocates a way of resisting the Evans argument meeting all the mentioned constraints: if we can find referential indeterminacy in virtue of ontic vagueness, we (...) can get out of the Evans argument while still preserving genuinely ontically vague identity. To show how this approach can vindicate particular cases of ontically vague identity, I develop a framework for describing ontic vagueness in general in terms of multiple actualities. The effect, overall, is to provide a principled and attractive approach to ontically vague identity that is immune from Evansian worries. (shrink)

Might the world really be vague, as opposed to merely being vaguely represented? Arguments that it cannot be are in no short supply, but a notable feature of many such arguments is that they rely on assumptions that the defender of metaphysical vagueness either tacitly or explicitly rejects.

Digital pictures can be type-identical in respect of colours, shapes and sizes (allographic), but they are not tokens of notational systems, because the types under which they are identical have vague limits and do not meet the requirements for notational characters. Digital display devices are designed to instantiate only limited ranges of objective properties (light intensities, sizes and shapes). Those ranges keep differences in objective magnitudes below sensory discrimination thresholds, and thus define objective conditions sufficient, but not necessary, for the (...) phenomenal type-identity of pictures. The fact that digital pictures are types shows that pictures are not necessarily autographic. Moreover, the reasons why digital pictures are allographic (essentially, the consistent manipulation of sub-phenomenal information) could in principle also be made to apply to non-digital pictures. (shrink)

Definitions of phenomenal types (Nelson Goodman’s definition of qualia, Sydney Shoemaker’s phenomenal types, Austen Clark’s physicalist theory of qualia) imply that numerically distinct experiences can be type-identical in some sense. However, Goodman also argues that objects cannot be replicated in respect of continuous and densely ordered types. In that case, how can phenomenal types be defined for sizes, shapes and colours, which appear to be continuously ordered types? Concentrating on size, I will argue for the following points. (§2) We cannot (...) deny the possibility of replication in respect of dense types, because this would imply that particulars have determinable sizes, shapes and colours. (§3) Phenomenal sizes and shapes are determinable types; objective, or super-determinate, sizes and shapes are unknowable. (§4) We can define and know, prior to verification, groupings of objective sizes for which indiscriminability is transitive. (§5) Phenomenal identity has to be defined on the basis of these transitive groupings, because finer-grained criteria (such as Goodman’s) lead to definition of objective identity. The quality space of phenomenal types consists of overlapping but not dense types, and this prevents a collapse of phenomenal types. (shrink)