Relative Identity

Review of Andre Gallois,' Occasions of identity: The metaphysics of persistence, change, and sameness.

When the Necessity of Identity (NI) is combined with Composition as Identity (CAI), the contingency of composition (CC) is at risk. In the extant literature, either NI is seen as the basis for a refutation of CAI or CAI is associated with a theory of modality, such that: either NI is renounced (if counterpart theory is adopted); or CC is renounced (if the theory of modal parts is adopted). In this paper, we investigate the prospects of a new variety of (...) CAI, which aims to preserve both NI and CC. This new variety of CAI (CCAI, Contingent Composition as identity) is the quite natural product of the attempt to make sense of CAI on the background of a broadly Kripkean view of modality, such that one and the same entity is allowed to exist at more than one possible world. CCAI introduces a world-relative kind of identity, which is different from standard identity, and claims that composition is this kind of world-relative identity. CCAI manages to preserve NI and CC. We compare CCAI with Gibbard’s and Gallois’ doctrines of contingent identity and we show that CCAI can be sensibly interpreted as a form of Weak CAI, that is of the thesis that composition is not standard identity, yet is significantly similar to it. (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)

Numerical identity is the non-relational sameness of an object to itself. It is concerned with understanding how entities undergo change and maintain their identity. In substance metaphysics, an entity is considered a substance with an essence and such an essence is the source of its power. However, such a framework fails to explain the sense in which an entity is still the entity it was, amidst changes. Those who claim that essence is unaffected by existence are faced with challenge of (...) exploring the epistemic access to such an essence, which is questionable at best. Process metaphysics is a strong candidate for a theory that can ontologically explain regularity and change without appeal to essence. Process and its interactions is the main category. Every process is an emergent organization of constitutive interactions and is individuated on the basis of its interactive powers, that is, the ways in which it interacts with the world around it. Interactions are situated adaptation to changes. In this way, changes are crucial within process metaphysics and are included in the starting point of its investigation. What seems to the naked eyes as one-ness/singularity is a complex process where an organization of interactions is emerging from moment to moment by continually adapting to the changes around and within it. The question of numerical identity over time becomes valid only within substance metaphysics which has no space to accommodate change, due to its allegiance to essence. (shrink)

Reality is two-fold, composed of the lighted world as revealed in Genesis, and the darker primordiality which preceded it. The illuminated represents that which the human mind can comprehend, manipulate and re-order to its will: a “designed” and mechanical universe of parts. But behind it, in the backspace of reality, remains the darkness. A formless state of pre-creation, the darkness exists as an endless series of intertwining “signatures” – single possibilities waiting to be created in the illuminated forefront of reality. (...) Permitting each and every part of the lighted world to be connected to the rest, it possesses a “design” all of its own. The question is, if we are blind in the dark, how could we ever come to know it? (shrink)

Peter Geach famously holds that there is no such thing as absolute identity. There are rather, as Geach sees it, a variety of relative identity relations, each essentially connected with a particular monadic predicate. Though we can strictly and meaningfully say that an individual a is the same man as the individual b, or that a is the same statue as b, we cannot, on this view, strictly and meaningfully say that the individual a simply is b. It is difficult (...) to find anything like a persuasive argument for this doctrine in Geach's work. But one claim made by Geach is that his account of identity is the account most naturally aligned with Frege's widely admired treatment of cardinality. And though this claim of an affinity between Frege's and Geach's doctrines has been challenged, the challenge has been resisted. William Alston and Jonathan Bennett, indeed, go further than Geach to argue that Frege's doctrine implies Geach's. If Alston and Bennett are right, then those who favor a broadly Fregean treatment of cardinality have no choice but to adopt Geach's doctrine of relative identity. And because contemporary set-theoretic accounts of cardinality are essentially Fregean in all respects relevant to this issue (see §11 below), it follows from Alston and Bennett's claim that virtually every standard modern treatment of cardinality requires a 'relativized' treatment of identity. The purpose of this paper is to argue against the implication claimed by Alston and Bennett. Despite some superficial similarities between Frege's treatment of cardinality and Geach's treatment of identity, the two doctrines are fundamentally opposed. Frege's account of cardinality, and its set-theoretic descendants, are all inconsistent with the claim that identity is 'relative' in Geach's sense. (shrink)

We construct a Hilbert style system RPL for the notion of plausibility measure introduced by Halpern J, and we prove the soundness and completeness with respect to a neighborhood style semantics. Using the language of RPL, we demonstrate that it can define well-studied notions of necessity, conditionals and propositional identity.

Relativists maintain that identity is always relative to a general term. According to them, the notion of absolute identity has to be abandoned and replaced by a multiplicity of relative identity relations for which Leibniz’s Law does not hold. For relativists RI is at least as good as the Fregean cardinality thesis, which contends that an ascription of cardinality is always relative to a concept specifying what, in any specific case, counts as a unit. The same train of thought on (...) cardinality and identity is apparent among those – Artifactualists – who take relative identity sentences for artifacts as the norm. The aim of this paper is to criticize the thesis thatfrom FC it is possible to derive RI, and to explain why Artifactualists mistakenly believe that RI can be derived from FC. The misunderstanding derives from their assumption that the concept of artifact – like the concept of object – is not a sortal concept. (shrink)

P.T. Geach has maintained (see, e.g., Geach (1967/1968)) that identity (as well as dissimilarity) is always relative to a general term. According to him, the notion of absolute identity has to be abandoned and replaced by a multiplicity of relative identity relations for which Leibniz's Law - which says that if two objects are identical they have the same properties - does not hold. For Geach relative identity is at least as good as Frege's cardinality thesis which he takes to (...) be strictly connected with relative identity - according to which an ascription of cardinality is always relative to a concept which specifies what, in any particular case, counts as a unit. The idea that there is a close connection between relative identity and Frege's cardinality thesis has been issued again quite recently by Alston and Bennett in (1984). In their opinion, Frege's cardinality thesis is not only similar to relative identity - as Geach maintains - but it implies it. Moreover, they agree with Geach in claiming that a commitment to Frege's cardinality thesis forces a parallel commitment to relative identity. Against Geach, Alston and Bennett we will claim that (Tl): "Frege's cardinality thesis is similar to relative identity" is false and that therefore (T2) "Frege's cardinality thesis implies relative identity" is false as well. (shrink)

The problem of identity of being in Buddhist philosophy: The Buddhist philosophical school of Madhyamaka is famous for its statement that things do not have their own inherent nature, essence or self‑nature (svabhāva). As a result, it is said that there is no objective foundation of the identity of things. Thus, the identity of things is not grounded in things themselves but is solely imputed and externally imposed on them. Things are what they are only for us, whereas for themselves, (...) or from their ‘own side’ they are empty (śūnya). That is why Madhyamaka philosophy is often compared to the philosophical conceptions inspired by a linguistic reflection (from Ludwig Wittgenstein to Jacques Derrida) which defines the problem of identity in terms of cognitive subjectivism and constructivism. Starting the analysis from the Abhidharma Buddhist tradition I will show that this reading of Madhyamaka view is too narrow. I will demonstrate that it is a result of an assumption, shared by Parmenides and Plato and wrongly ascribed to this Buddhist school, that the identity of being must be grounded in the self‑existing, self‑defined and (relatively) permanent ontological foundation. This tacit assumption, if rejected, makes any identity a completely subjective and relative construct. The point I am going to argue for, however, is that the Madhyamaka school sticks to an alternative understanding of objectivity; the foundation of all things is nothing but pure relation that precedes, in the ontological sense, all co‑related elements (i.e. things). Therefore, the question comes up: how being‑in‑relationship or ‘relationality’ may be the foundation of identity and what kind of identity it endows. I will try to answer these questions. (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)

We construct a a system PLRI which is the classical propositional logic supplied with a ternary construction , interpreted as the intensional identity of statements and in the context . PLRI is a refinement of Roman Suszko’s sentential calculus with identity (SCI) whose identity connective is a binary one. We provide a Hilbert-style axiomatization of this logic and prove its soundness and completeness with respect to some algebraic models. We also show that PLRI can be used to give a partial (...) solution to the paradox of analysis. (shrink)

Goetz outlined legal models of identical entities that include natural persons who are identical to a coregency and natural persons who are identical to a general partnership. Those entities cohere with the formula logic of relative identity. This essay outlines the coexistence of relative identity and numerical identity in the models of identical legal entities, which is impure relative identity. These models support the synthesis of Relative Trinitarianism and Social Trinitarianism, which I call Relative-Social Trinitarianism.

Armstrong has loose identity be an equivalence relation, yet in cases of something becoming something else, loose identity is not transitive. My alternate account has an attribution of loose identity be really two: a true attribution of an underlying relation (perhaps not transitive) and a false attribution--a Humean feigning-of strict identity. The feigning may become less appropriate as the underlying relation grows more distant. What makes it appropriate initially is that the underlying relation supports a predictable change in some collective. (...) The importance of the predictably changing collective is signaled by regarding it as a single thing. (shrink)

I argue for the consistency of frege's treatments of identity and number. Specifically, I argue that geach is wrong in suggesting that frege's insights about number should have led him to the doctrine of relative identity.

Arc there cases in which an object x is thc same F as an object y but x is not the same G as y, cvcn though x is a G? A11 aihrmativc answer will have drastic repercussions 011 0ne’s account of identity and on one’s quantification theory. For suppose that the expression ‘x is the same F as y’ can be understood as ‘x is an F and y is an F and x is identical with y’, and that (...) ‘x is not the same G as y’ can be understood as ‘it is not the case that x is a G and y is a G and x is identical with y’. Then one may reason as follows. (shrink)

This paper examines a variety of contexts in metaphysics which employ a strategy I consider to be suspect. In each of these contexts, ‘The Suspect Strategy’ (TSS) aims at excluding a series of troublesome contexts from a general principle whose truth the philosopher in question wishes to preserve. We see (TSS) implemented with respect to Leibniz’s Law (LL) in the context of Gibbard’s defense of contingent identity, Myro and Gallois’ defense of temporary identity, as well as Terence Parsons’ defense of (...) indeterminate identity. Our example of (TSS) as implemented with respect to the Existence Principle (EP) is Terence Parsons’ defense of non-existent objects. Finally, the coincidence-theorist’s analysis of the problem of constitution as given by Baker, Fine and Yablo, as well as Deutsch’s recent defense of the relative-identity theory provide examples of (TSS) as implemented with respect to restricted indiscernibility principles of the form in (RI). While we of course cannot conclude from our exposure to extant versions of (TSS) that no exclusion-procedure could ever overcome the troubling features we encountered, my remarks in this paper should, I think, at least give us reasons to be skeptical that any strategy which proceeds by means of purely formal (e.g., syntactic) individuation-criteria could achieve its intended purpose; for we have seen that such strategies are in general too coarse-grained to individuate contexts correctly into those that should and those that should not be excluded from the reaches of the general principle under discussion. I suspect, moreover, though I do not argue for this stronger claim, that any strategy which does not proceed by means of purely formal criteria would in some way succumb to the charge of circularity. As a result, I recommend that we should learn to become accustomed to a universe populated with a surprising multitude of numerically distinct yet almost indiscernible objects, such as statues and the lumps of clay that constitute them. Given the large amounts of overlap among these almost indiscernible objects, such a densely populated universe is actually quite easy to live with, but that’s a story for a separate occasion. (shrink)

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)

Examples suggest that one and the same A may be different Bs, and hence that there is some sort of incompleteness in the unqualified statement that x and y are the same which needs to be eliminated by answering the question “the same what?” One way to make this more precise is by appeal to Geach's idea that identity is relative. In this paper I evaluate Geach's relative identity thesis.

My dissertation evaluates Peter Geach's theory of relative identity. Typically discussions of relative identity focus on predicative identity expressions of the form "is the same A as". My approach, following Geach, is broader: it also looks at how, if correct, the theory of relative identity must play into our accounts of proper names and quantifiers. ;Geach's theory is well known for denying the coherence of the concept of absolute identity, and for its espousal of a concept of identity allowing true (...) instances of "a is the same A as b and not -F and F". This position requires a positive theory of identity which does not covertly rely upon a Leibnizian understanding of identity to account for substitution, and does not covertly rely upon absolute identity to explain reference . I do not evaluate Geach's denial of absolute identity, but rather evaluate the positive theory of relative identity. ;To enable us to see more clearly what is involved in Geach's theory, I define several language structures which transparently embody aspects of the theory. I examine a series of examples in which one may be inclined to accept descriptions which require a non-Leibnizian understanding of the description's identity expressions. I then look at how the notion of individuating identity plays into truth conditions for ordinary predications of the form "F"; we consider what support this gives to Geach's view that proper names convey identity criteria as part of their sense. I address problems arising from temporal aspects of Geach's account of reference. Quantification is explained recursively in terms of sentences involving proper names. I consider consequences of Geach's views regarding what must be counted as a valid argument . A non-Leibnizian account of substitution is offered. Wiggins's thesis R is discussed. (shrink)

P. T. Geach, notoriously, holds the Relative Identity Thesis, according to which a meaningful judgment of identity is always, implicitly or explicitly, relative to some general term. ‘The same’ is a fragmentary expression, and has no significance unless we say or mean ‘the same X’, where ‘X’ represents a general term (what Frege calls a Begriffswort or Begriffsausdruck). (P. T. Geach, Mental Acts (London: Routledge and Kegan Paul, 1957), p. 69. I maintain that it makes no sense to judge whether (...) things are ‘the same’, or remain ‘the same’, unless we add or understand some general term - ‘the same F’. (P. T. Geach, Reference and Generality, third Edition (Ithaca, N.Y.: Cornell University Press, 1980), pp. 63f. I am arguing for the thesis that identity is relative. When one says ‘x is identical with y’, this, I hold, is an incomplete expression; it is short for ‘x is the same A as y’, where ‘A’ represents some count noun understood from the context of utterance - or else, it is just a vague expression of a half-formed thought. (P. T. Geach, ‘Identity,’ Review of Metaphysics 21 (1967-8), p. 3.) One of the ways Geach seeks to support this is by tying it to the well nigh universally admired Fregean thesis about cardinality. (shrink)

Much of the debate about identity in recent decades has been about personal identity, and specifically about personal identity over time, but identity generally, and the identity of things of other kinds, have also attracted attention. Various interrelated problems have been at the centre of discussion, but it is fair to say that recent work has focussed particularly on the following areas: the notion of a criterion of identity; the correct analysis of identity over time, and, in particular, the disagreement (...) between advocates of perdurance and advocates of endurance as analyses of identity over time; the notion of identity across possible worlds and the question of its relevance to the correct analysis of de re modal discourse; the notion of contingent identity; the question of whether the identity relation is, or is similar to, the composition relation; and the notion of vague identity. A radical position, advocated by Peter Geach, is that these debates, as usually conducted, are void for lack of a subject matter: the notion of absolute identity they presuppose has no application; there is only relative identity. Another increasingly popular view is the one advocated by Lewis: although the debates make sense they cannot genuinely be debates about identity, since there are no philosophical problems about identity. Identity is an utterly unproblematic notion. What there are, are genuine problems which can be stated using the language of identity. But since these can be restated without the language of identity they are not problems about identity. (For example, it is a puzzle, an aspect of the so-called “problem of personal identity”, whether the same person can have different bodies at different times. But this is just the puzzle whether a person can have different bodies at different times. So since it can be stated without the language of personal “identity”, it is not a problem about identity, but about personhood.) This article provides an overview of the topics indicated above, some assessment of the debates and suggestions for further reading. (shrink)

In order to avoid the problems faced by standard realist analyses of the “relation” of instantiation, Baxter and, following him, Armstrong each analyze the instantiation of a universal by a particular in terms of their partial identity. I introduce two related conceptions of partial identity, one mereological and one non-mereological, both of which require at least one of the relata of the partial identity “relation” to be complex. I then introduce a second non-mereological conception of partial identity, which allows for (...) both relata to be simple. I take these three conceptions to exhaust the plausible ways of construing two entities as being partially identical. I then argue that there is no analysis (including those offered by Baxter and Armstrong) of a universal and a particular as being partially identical consistent with any of these three conceptions that (i) is coherent, (ii) is consistently realist, (iii) does not lead to absurd consequences, and (iv) offers a “solution” to the problem of instantiation that avoids the problems with the other standard realist responses. In so arguing, I offer a criticism of the analysis of instantiation as partial identity that is independent of the standard criticism that it entails the necessity of predication. (shrink)

This essay proposes an ontological model in which a legal person such as a polity possesses natural unity from group properties that emerge in the self-organization of the human population. Also, analysis of customary legal persons and property indicates noncontradictory paradoxes that include Aristotelian essence of an entity, relative identity over time, ubiquitous authority, coinciding authorities, and identical entities. Mathematical modeling helps to explain the logic of the paradoxes.

Based on the notion of a trope, this paper gives a novel analysis of identificational sentences such as 'this is Mary','this is a beautiful woman', 'this looks like Mary', or 'this is the same lump of clay, but not the same statue as that'.