The Necessity of Identity

The aim of this chapter is to explore to some extent the relationship between identity and necessity in logic and metaphysics. First, I provide a historically-based summary of proofs of the necessity of identity, highlighting the importance of the role that self-identity plays. Second, I introduce two examples of metaphysical topics where the necessity of identity has played a pivotal role: the necessary a posteriori, and the coincidence of material objects. I argue that important aspects of these debates rest on (...) how we represent identity. Third, I consider some recent work on generalized identity. This opens up new prospects for explaining why identity is necessary. (shrink)

This paper draws attention to a proof of the necessity of identity given by Arthur Prior. In its simplicity, it is comparable to a proof of Quine's, popularised by Kripke, but it is slightly different. Prior's Polish notation is transcribed into a more familiar idiom. Prior's proof is followed by a proof of the necessity of difference, possibly the first such proof in the literature, which is also repeated here and transcribed. The paper concludes with a brief discussion of Prior's (...) views on identity and difference over time. (shrink)

Philosophical Investigations, EarlyView.

Blum (Philosophical Investigations 46, 2023, 264) argues that Tarski's T‐schema and the thesis of the necessity of identity are mutually inconsistent. It is argued that his argument fails.

We show that the thesis that identity is necessary is equivalent to the thesis that everything is necessarily what it is. Hence the challenges facing either, faces them both.

Philosophical Investigations, EarlyView.

In a recent article forthcoming in *Mind*, Leech (2020) presents a challenge for essentialist accounts of metaphysical modality: why should it be that essences imply corresponding necessities? Leech’s main focus is to argue that one cannot overcome the challenge by utilizing an account of essence in terms of generalized identity due to Correia and Skiles (2019), on pain of circularity. In this reply, we will show how to use identity-based essentialism to bridge ‘epistemic’ and ‘explanatory’ understandings of this alleged essence-to-necessity (...) gap without circularity, Leech’s arguments notwithstanding. We do so by first presenting a novel proof that generalized identities imply corresponding necessities. We then propose several substantive identity-based explanations of how it is, exactly, that essences imply necessities. -/- . (shrink)

An essentialist theory of modality claims that the source of possibility and necessity lies in essence, where essence is then not to be defined in terms of necessity. Hence such theories owe us an account of why it is that the essences of things give rise to necessities in the way required. A new approach to understanding essence in terms of the notion of generalized identity promises to answer this challenge by appeal to the necessity of identity. I explore the (...) prospects for this approach, and argue that it fails. If one favours an account of essence in terms of generalized identity, then one will not, I argue, be able to satisfactorily defend an essentialist theory of modality against the challenge; if one wishes to defend an essentialist theory of modality, and thereby to give an explanation of how necessity arises from essence, one should not understand essence in terms of generalized identity. (shrink)

ABSTRACT The purpose of this paper is to bring out, by means of a simple thought experiment involving demonstratives, a discrepancy between what is expressed and what is believed, and to consider some consequences of this - most notably, whether we might hold, for example, that the ancients never believed that Hesperus is not Phosphorus. RESUMO O objetivo deste artigo é apresentar, por meio de um experimento mental simples envolvendo demonstrativos, uma discrepância entre o que é expresso e o que (...) se acredita, e considerar algumas consequências disso - principalmente se podemos sustentar, por exemplo, que os antigos nunca acreditaram que Hesperus não é Phosphorus. (shrink)

There is a certain argument against the principle of the indiscernibility of identicals, or the thesis that whatever is true of a thing is true of anything identical with that thing. In this argument, PInI is used together with the self-evident principle of the necessity of self-identity to reach the conclusion, which is held to be paradoxical and, thus, fatal to PInI. My purpose is to show that the argument in question does not have this consequence. Further, I argue that (...) PInI is a universally valid principle which can be used to prove the necessity of identity. (shrink)

ABSTRACT An apparent objection against my theory of instantiation as partial identity is that identity is necessary, yet instantiation is often contingent. To rebut the objection, I show how it can make sense that identity is contingent. I begin by showing how it can make sense that identity is temporary. I rely heavily on Andre Gallois’s formal theory of occasional identity, but argue that there is a gap in his explanation of how his formalisms make sense that needs to be (...) filled by appeal to my theory of Aspects. (shrink)

I show that intuitive and logical considerations do not justify introducing Leibniz’s Law of the Indiscernibility of Identicals in more than a limited form, as applying to atomic formulas. Once this is accepted, it follows that Leibniz’s Law generalises to all formulas of the first-order Predicate Calculus but not to modal formulas. Among other things, identity turns out to be logically contingent.

I argue that Fregeanism with respect to proper names—the view that modes of presentation are relevant to the contents of proper names—is able to account for the thesis that there are necessarily true a posteriori identity propositions such as the one expressed in “Hesperus is identical with Phosphorus”, whereas the Direct Reference Theory—according to which the semantic function of certain expressions, e.g., proper names, is only to pick out an object —is able to deal with only their necessary truth. Thus, (...) at least in so far as necessarily true a posteriori identity propositions are concerned, Fregeanism should be preferred to the Direct Reference Theory. (shrink)

There is a certain popular argument, deriving from Ruth Barcan and Saul Kripke, from the conjunction of the Principle of the Indiscernibility of Identicals (PInI, for short) and the Principle of the Necessity of Self-Identity to the Thesis of the Necessity of Identity. My purpose is to show that this argument does not work, not at least in the form it is often presented. I also give a correct formulation of the argument and point out that PInI is not even (...) needed in the argument for the necessity of identity. (shrink)

In this paper I show that a novel ontic reading of explanation, intending to capture the de re essential features of individuals, can support the qualitative view of individual essences. It is argued further that the putative harmful consequences of the Leibniz Principle and its converse for the qualitative view can be avoided, provided that individual essences are not construed in the style of the naïve bundle theory with set-theoretical identity- conditions. Adopting either the more sophisticated two-tier BT or, alternatively, (...) the neo-Aristotelian position of taking essences as natures in the Aristotelian sense, can help to evade these main charges against the qualitative view. The functional parallels with the alternative haecceitistic view of individuation and individual essence will also be considered. (shrink)

Composition as identity, as I understand it, is a theory of the composite structure of reality. The theory’s underlying logic is irreducibly plural; its fundamental primitive is a generalized identity relation that takes either plural or singular arguments. Strong versions of the theory that incorporate a generalized version of the indiscernibility of identicals are incompatible with the framework of plural logic, and should be rejected. Weak versions of the theory that are based on the idea that composition is merely analogous (...) to identity are too weak to be interesting, lacking in metaphysical consequence. I defend a moderate version according to which composition is a kind of identity, and argue that the difference is metaphysically substantial, not merely terminological. I then consider whether the notion of generalized identity, though fundamental, can be elucidated in modal terms by reverse engineering Hume’s Dictum. Unfortunately, for realists about possible worlds, such as myself,... (shrink)

The philosophy problem of identity and the related problem of change go back to the ancient Greek philosophers and fascinated later figures including Leibniz, Locke and Hume. Heraclitus argued that one could not swim in the same river twice because new waters were ever flowing in. When is a river not the same river? If one removes one plank at a time when is a ship no longer a ship? What is the basic nature of identity and persistence? This book (...) introduces and asseses the philosophical puzzles posed by things persisting through time. Beginning with essential historical background to the problem it explores the following key topics and debates: mereology and identity, including 'Leibniz's Law' the constitution view of identity the 'relative identity' argument concerning identity temporary identity four-dimensionalism, counterpart and mulitiple counterpart theory supervenience the problem of temporary intrinsics the necessity of identity presentism ontological and epistemological criteria for persistence and the difference between them. Including chapter summaries, annotated further reading and a glossary this book is essential reading for anyone seeking a clear and informative introduction to and assessement of the metaphysics of identity. (shrink)

This paper outlines a novel solution to the Ship of Theseus puzzle. The solution relies on situations, a philosophical tool used in natural language semantics among other places. The core idea is that what is true is always relative to the situation under consideration. I begin by outlining the problem before briefly introducing situations. I then present the solution: in smaller situations the candidate is identical to Theseus’s ship. But in larger situations containing both candidates these identities are neither true (...) nor false. Finally, I discuss some worries for the view that arise from the nature of identity, and suggest responses. It is concluded that the solution, and the theory that underpins it, are worth further investigation. (shrink)

Following insights from the New Theory of Reference, it has become widely accepted that theoretical identities like ‘water = H2O' are necessary. However, some have challenged this claim. I propose yet another challenge in the form of a sceptical argument. The argument is based on the contention that the necessity of theoretical identities is dependent upon criteria of identity. Thus, a theoretical identity is necessary given one criterion of identity but contingent given another. Since we do not know which criteria (...) of identity in fact obtain, it follows that, for all we know, theoretical identities may not be necessary. (shrink)

The purpose of this article is to introduce, interpret, and develop two incompatible process -ontological theories of personal identity that have received little attention in analytic metaphysics. The first theory derives from the notion of personal identity proposed in Alfred North Whitehead’s philosophy, but I interpret this notion differently from previous commentators. The Whiteheadian theory may appeal to those who believe that personal identity involves an entity or entities that are essentially dynamic, but has nothing to do with diachronic objectual (...) identity : the binary equivalence relation that every entity bears to itself, and only to itself, even after undergoing intrinsic change. The Whiteheadian theory may also find favor with those who, like Whitehead, reject the possibility of pure processes and hold that in every becoming, something—which need not be an object, thing, or individual substance—becomes. The second theory derives from the notion of recurrent dynamics presented in Johanna Seibt’s General Process Theory. The Seibtian theory may appeal to those who believe that personal identity involves not only an entity or entities that are essentially dynamic, but also the relation of diachronic objectual identity. The Seibtian theory may also find favor with those who, like Broad and Sellars, find reason to postulate pure processes. (shrink)

This paper establishes that the occasional identity relation and the contingent identity relation are both non-transitive and as such are not properly classified as identity relations. This is achieved by appealing to cases where multiple fissions and fusions occur simultaneously. These cases show that the contingent and occasional identity relations do not even satisfy the time-indexed and world-indexed versions of the transitivity requirement and hence are non-transitive relations.

I introduce and defend the semantic notion of counterfactual identity, distinguishing it from the metaphysical notion of transworld identity. After showing that Lewis's counterpart theory misconstrues counterfactual identity facts, I outline and motivate a ‘Leibnizian counterpart theory’ where the notion of counterfactual identity is adequately modelled. Finally, I show that counterfactual identity can be characterized without relying on some implausible features of Lewis's theory of conditionals.

In ‘Two Spheres, Twenty Spheres, and the Identity of Indiscernibles,’ Della Rocca argues that any counterexample to the PII would involve ‘a brute fact of non-identity [. . .] not grounded in any qualitative difference.’ I respond that Adams's so-called Continuity Argument against the PII does not postulate qualitatively inexplicable brute facts of identity or non-identity if understood in the context of Kripkean modality. One upshot is that if the PII is understood to quantify over modal as well as non-modal (...) properties, the qualitative explicability of numerical distinctness requires not the PII but a principle of the identity of necessary indiscernibles. (shrink)

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)

What George Spencer-Brown wants to rationalize out of existence is alternation itself – the prerequisite of his whole operation. By that he simplifies (identifies) more than he says. And he does not say all that is important.

Leibniz’s Law (or as it sometimes called, ‘the Indiscerniblity of Identicals’) is a widely accepted principle governing the notion of numerical identity. The principle states that if a is identical to b, then any property had by a is also had by b. Leibniz’s Law may seem like a trivial principle, but its apparent consequences are far from trivial. The law has been utilised in a wide range of arguments in metaphysics, many leading to substantive and controversial conclusions. This article (...) discusses the applications of Leibniz’s Law to arguments in metaphysics. It begins by presenting a variety of central arguments in metaphysics which appeal to the law. The article then proceeds to discuss a range of strategies that can be drawn upon in resisting an argument by Leibniz’s Law. These strategies divide into three categories: (i) denying Leibniz’s Law; (ii) denying that the argument in question involves a genuine application of the law; and (iii) denying that the argument’s premises are true. Strategies falling under each of these three categories are discussed in turn. (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 ramifications. It argues that we can accept a reasonable theory of identity without committing ourselves to the uniqueness, necessity, or determinacy of identity. (shrink)

Identity is a modally inflexible relation: two objects are necessarily identical or necessarily distinct. However, identity is not alone in this respect. We will look at the relation that one object bears to some objects if and only if it is one of them. In particular, we will consider the credentials of the thesis that no matter what some objects are, an object is necessarily one of them or necessarily not one of them.

Words and (Possible) Worlds is a study of the relation between language and reality; between words and world. It is a study of reference. Analysing reference often leads to addressing fundamental issues in semantics, metaphysics and epistemology, thus suggesting the close links of reference to these three realms. By utilising the powerful tool of possible-worlds analysis, Alik Pelman carefully explores these links, and elegantly integrates them into a clear and unified model of reference. In the course of his study, Pelman (...) addresses familiar philosophical puzzles (many of which are due to Kripke), for example, Could we discover that Queen Elizabeth was not the daughter of George VI, that is, would we be talking about Queen Elizabeth in this case? Could this table come into existence from a different hunk of wood than the one it was originally made of? Does the term "water" refer to the pink solid H2O on another possible world? (shrink)

In many African states, numerous different pre-colonial systems of power – such as kingships, sultanates or chieftaincies – which have a traditional legitimacy often confirmed in colonial and post-colonial times, have survived till our day. Their role in the contemporary republican state has been studied by many African intellectuals, and the views of Kwame Anthony Appiah, a thinker originating from Ghana, are of particular interest. He believes that in order to understand the significance of traditional authority and the phenomenon of (...) its continued existence in contemporary Africa, it is important to consider the source of its legitimacy. Appiah presents various sources – symbolic, religious and state – from which local African rulers derive the right to exert power and to exact obedience from their subjects. He minimizes the significance of most of these, however, and concludes that the basic source of legitimacy for traditional authority in the contemporary African state is the fact that this power, being a very important point of reference for the group over which it is wielded, reinforces its members’ sense of self-respect, and helps form their identity. He uses this idea to attempt to reconcile the continued existence of African power systems with liberal theory. Appiah, who is very unfavorably disposed towards most political and social hierarchies, views the political rights of individuals as the rights of citizens, not as the rights of persons who are the depositaries of some attributed or hereditary status. He enumerates the costs, in terms of liberal principles, of allowing traditional monarchy to persist. In his view, it is contrary to the liberal principle of public offices being open to persons of merit for the king of the Ashanti to be chosen from among persons of royal lineage. Such a perspective should generate a generally negative attitude towards the monarchy of the Ashanti, a people from whom Appiah originates, and yet he views Ashanti’s traditional monarchy as a source of pride. Published in "Africana Bulletin" 2010, No. 58, pp. 47-74. (shrink)

In his well-known 1952 dialogue Max Black describes a counterexample to the Principle of the Identity of Indiscernibles (PII). The counterexample is a world containing nothing but two purportedly indiscernible iron spheres. Reflecting on Black's example, Robert Adams uses the possibility of a world containing two almost indiscernible spheres to argue for the possibility of the indiscernible spheres world. One of Adams's almost indiscernible spheres has a small impurity, and, Adams writes, "Surely... the absence of the impurity would not make (...) such a universe impossible." The appeal to "surely" constitutes a gap in Adams's argument. This paper bridges the gap with a premise that exploits the counterfactual conditional and the related notion of causal independence. The paper then argues that causal independence bears in a similar way on an issue Nathan Salmon raises concerning Kripke's argument for the Essentiality of Origins. (shrink)

This paper challenges the Kripkean interpretation of a posteriori necessities. It will be demonstrated, by an analysis of classic examples, that the modal content of supposed a posteriori necessities is more complicated than the Kripkean line suggests. We will see that further research is needed concerning the a priori principles underlying all a posteriori necessities. In the course of this analysis it will emerge that the modal content of a posteriori necessities can be best described in terms of a Finean (...) conception of modality – by giving essences priority over modality. The upshot of this is that we might be able to establish the necessity of certain supposed a posteriori necessities by a priori means. (shrink)

In logic, the law (or principle) of identity states simply: 'A is A'. This article gives a concise account of identity.

Orthodox neural materialists think mental states are neural events or orthodox material properties of neutral events. Orthodox material properties are defining properties of the “physical”. A “defining property” of the physical is a type of property that provides a necessary condition for something’s being correctly termed “physical”. In this paper I give an argument against orthodox neural materialism. If successful, the argument would show at least some properties of some mental states are not orthodox material properties of neural events. Opposing (...) philosophical orthodoxy, I show there are no posteriori identities -- identities that cannot be known of a priori. (shrink)

Throughout his illustrious career, Roderick Chisholm was concerned with the nature of persons. On his view, persons are what he called ‘entia per se.’ They exist per se, in their own right. I too have developed an account of persons—I call it the ‘Constitution View’—an account that is different in important ways from Chisholm’s. Here, however, I want to focus on a thesis that Chisholm and I agree on: that persons have ontological significance in virtue of being persons. Although I’ll (...) make the notion of ontological significance more precise later, the rough idea is that Fs (persons, or whatever) have ontological significance just in case a new F is a new thing and not just a change in some already-existing thing. (shrink)

This dissertation is an investigation of the ontological status of identity . The preface is a discussion of how foundational and important metaphysical issues concerning identity are for philosophy in general, and of some of the problems that have plagued the study of identity historically. ;In chapter one various issues concerning identity are framed and the metaphysical issues are divided into two main genera: persistence problems and ontological problems. The primary attention of the dissertation is not given to persistence problems, (...) but to four major ontological problems of identity: what is the intension of 'identity'? what is the extension of 'identity'? how many of kinds of identity are there? and what is the ontological status of identity? ;In chapter two the relation of these four ontological problems to the most popular problems of identity in the contemporary literature is examined. The following contemporary discussions are covered: perdurance vs. endurance, contingent identity, vague identity, identity across possible worlds, and the criterion of identity. As a result, some ontic/epistemic confusions prevalent in the current literature are cleared up, and it is shown that we must study the relationship between identity and both individuality and unity to solve some of the problems concerning identity mentioned in chapter one. ;In chapter three a modified medieval schema of relations is used to give a detailed analysis of the intension of 'identity'. It is shown how identity cannot be understood as unity, individuality, or indiscernibility. It is later argued that identity is properly understood as lack of difference, where difference is understood broadly, and that ontological identity is properly understood as lack of difference in being. ;In chapter four a thorough analysis of the extension of 'identity' is given, concluding that 'identity' does not have universal extension or null extension, but rather partial extension . ;In chapter five the ontological status of identity is determined. It is argued that identity is a transcendental attribute of being, and that identity is only a relation in a secondary or derived sense, despite what many have held. (shrink)

The “scientific essentialist” doctrine asserts that the following are examples of a posteriori necessary identities: water is H2O; gold is the element with atomic number 79; and heat is the motion of molecules. Evidence in support of this assertion, however, is difficult to find. Both Hilary Putnam and Saul Kripke have argued convincingly for the existence of a posteriori necessities. Furthermore, Kripke has argued for the existence of a posteriori necessary identities in regard to a particular class of statements involving (...) proper names. Neither Kripke nor Putnam, however, has argued convincingly that sentences containing syntactically complex terms or descriptive phrases can express a posteriori necessary identities. I will argue by way of a hypothetical example that ‘water is H2O’ does not express a necessary identity. My argument is unique in that it attacks the relevant sufficiency claim needed to underwrite this putative necessary identity.1 That is, even if we grant that water is necessarily composed of H2O, we should not accept that H2O necessarily forms water. (shrink)

André Gallois (1998) attempts to defend the occasional identity thesis (OIT), the thesis that objects which are distinct at one time may nonetheless be identical at another time, in the face of two influential lines of argument against it. One argument involves Kripke’s (1971) notion of rigid designation and the other, Leibniz’s law (affirming the indiscernibility of identicals). It is reasonable for advocates of (OIT) to question the picture of rigid designation and the version of Leibniz’s law that these arguments (...) employ, but, the problem is, some form of rigidity is required for one to affirm the occasional identity of objects, and some (restricted) version of Leibniz’s law must be conceded if identity really is involved. Gallois accordingly recommends an account of rigidity and a version of Leibniz’s law to this end.1 We find Gallois’ proposals entirely inadequate to their task. We aim in this paper is to explicate and defend an alternative approach for occasional identity theorists. We do not seek to defend (OIT) per se; our aim, rather, is simply to show that the arguments from rigid designation and Leibniz’s law are inconclusive. Let’s begin with an outline of these arguments. (shrink)

An identity statement flanked on both sides with proper names is necessarily true, Saul Kripke thinks, if it's true at all. Thus, contrary to the received view – or at least what was, prior to Kripke, the received view – a statement like(A) Hesperus is Phosphorus.

Some relations - like supervenience and composition - can appear very much like identity. Sometimes, the relata differ only in modal, or modally-involved features. Yet, in some cases, we judge the pairs to be identical (water/H2O; Hesperus/Phosphorus), while in others, many judge one of the weaker relations to hold (c-fiber firing/pain; statues/lumps). Given the seemingly same actual properties these pairs have, what can justify us in sometimes believing identity is the relation, and sometimes something weaker? I argue that it can (...) only be knowledge of differences of individuative criteria that we know a priori because they are built into the meanings of the words/concepts involved. Possible metaphysical conclusions are considered. (shrink)