There is nothing to identity

Several have denied that there is, specifically, a criterion of identity for persons and some deny that there are, for any kind, diachronic criteria of identity. I argue, however, that there are no criteria of identity, either synchronic or diachronic, for any kind whatsoever (and could be none). I begin by elaborating the notion of a criterion of identity in order to clarify what exactly is being denied when I maintain there are none. I examine the motivation of those who qualify in some way the general claim that there are synchronic and diachronic criteria of identity for every kind, then present my direct and categorical argument against such criteria. I next evaluate the objections of those who argue that rejecting criteria of identity has untenable results. These objections are ineffective, each based on the incorrect assumption that if there is no criterion of identity for a kind, the identity of an instance of that kind is independent of its qualities. I conclude by considering some of the upshots of rejecting criteria of identity and the insight doing so provides into things in general and the limits of ontological inquiry.

On Non-Eliminative Structuralism. Unlabeled Graphs as a Case Study, Part A†

This is Part A of an article that defends non-eliminative structuralism about mathematics by means of a concrete case study: a theory of unlabeled graphs. Part A summarizes the general attractions of non-eliminative structuralism. Afterwards, it motivates an understanding of unlabeled graphs as structures sui generis and develops a corresponding axiomatic theory of unlabeled graphs. As the theory demonstrates, graph theory can be developed consistently without eliminating unlabeled graphs in favour of sets; and the usual structuralist criterion of identity can be applied successfully in graph-theoretic proofs. Part B will turn to the philosophical interpretation and assessment of the theory.

Absolutism and Relativism

Absolutism about quantifiers maintains, with a good deal of prima facie plausibility, that quantifiers like ‘everything’ sometimes range over an absolutely comprehensive domain. This view has been challenged on various grounds: some deny the availability of a universal nominal like ‘thing’ on the grounds that it lacks a non-trivial criterion of identity; others contend that absolutism is committed to objectionable views in metaontology. But the most compelling reason to support relativism about quantifiers as opposed to absolutism is bound up with the set-theoretic paradoxes. This introductory chapter offers an overview of the absolute generality debate, and sets the scene for the defence of relativism that follows in the rest of the book.

Stoics and Their Critics on Diachronic Identity

This article is a return to a theme I first tackled in “The Stoic criterion of identity” (1982): the Academics’ ‘Growing Argument’ (auxanomenos logos) and the Stoic response to its attack on diachronic identity. This time my aim is to separate out approximately five different stages of the debate between the two schools. This will be done by shifting more of the focus onto developments that seem likely to belong to the late second and/or early first century BC.

Unbearable Lightness of Being

This book defends an undemanding conception of objecthood according to which any acceptable criterion of identity suffices for the existence of objects governed by this criterion. Some even less demanding conceptions have been defended where not even criteria of identity are required. These ultra-thin conceptions are clarified and then criticized on two counts. First, they ascribe reference to terms that are semantically idle in the sense that their reference plays no role in the determination of the reference of more complex expressions. Second, the ultra-thin conceptions result in inexplicable relations of reference where a term is said to refer to an object although it is inexplicable why the term refers to this object rather than some other.

Thin Objects via Criteria of Identity

An approach to thin objects is developed by exploring and developing some Fregean ideas—regardless of whether Frege himself would have agreed with this development. This approach is structured around three concepts central to philosophical logic and metaphysics—object, reference, and criterion of identity. Frege sought to connect these three concepts. First, to be an object is just to be a possible referent of a singular term. An undemanding account of reference will thus ensure an undemanding form of existence, i.e. thin objects. Next, reference can be constituted by providing a criterion of identity for the would-be referent. This is an undemanding account of reference. In this way we obtain a Frege-inspired approach to thin objects.

Thin Objects

Are there objects that are “thin” in the sense that their existence does not make a substantial demand on the world? Frege famously thought so. He claimed that the equinumerosity of the knives and the forks suffices for there to be objects such as the number of knives and the number of forks, and for these objects to be identical. The idea of thin objects holds great philosophical promise but has proved hard to explicate. This book attempts to develop the needed explanations by drawing on some Fregean ideas. First, to be an object is to be a possible referent of a singular term. Second, singular reference can be achieved by providing a criterion of identity for the would-be referent. The second idea enables a form of easy reference and thus, via the first idea, also a form of easy being. Paradox is avoided by imposing a predicativity restriction on the criteria of identity. But the abstraction based on a criterion of identity may result in an expanded domain. By iterating such expansions, a powerful account of dynamic abstraction is developed.