Relative Identity

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)

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)

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)

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)

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)

Relativists maintain that identity is always relative to a general term (RI). 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 (FC), 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 (i) to criticize the thesis (T1) thatfrom FC it is possible to derive RI, and (ii) 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)

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)

Traditionally, this puzzle has been solved in various ways. Aristotle, for example, distinguished between “accidental” and “essential” changes. Accidental changes are ones that don't result in a change in an objects' identity after the change, such as when a house is painted, or one's hair turns gray, etc. Aristotle thought of these as changes in the accidental properties of a thing. Essential changes, by contrast, are those which don't preserve the identity of the object when it changes, such as when (...) a house burns to the ground and becomes ashes, or when someone dies. Armed with these distinctions, Aristotle would then say that, in the case of accidental changes, (1) and (2) are both false—a changing thing can really change one of its “accidental properties” and yet literally remain one and the same thing before and after the change. (shrink)

This paper is a modification of Nicola Guarino and Christopher Welty's conception of the subsumption relation. Guarino and Welty require that that whether one property may subsume the other should depend on the modal metaproperties of those properties. I argue that the part of their account that concerns the metaproperty carrying a criterion of identity is essentially flawed. Subsequently, I propose to constrain the subsumption relation not, as Guarino and Welty require, by means of incompatible criteria of absolute identity but (...) by means of incompatible criteria of relative identity. After discussing the benefits of applying relative identity in ontological investigations I provide a formal framework in which to prove a counterpart of the identity criteria constraint. (shrink)

This paper is the first part of an exploration into the logical properties of relative identity. After providing the semantic grounds for various monadic logics of relative identity, I define the minimal system and its nine extensions. It is suggested that despite their purely formal origin at least some of them may contain nontrivial philosophical insights. All logics are axiomatized by means of sound and complete sequent calculi. I show their affinities with existing formalizations.

This paper briefly proposes a weak relative identity strategy for the doctrine of the Trinity called the general partnership model. This model develops a logically consistent metaphysical constitution for the orthodox Christian doctrines of one divine substance and three divine persons. Moreover, the model rejects the rigid use of absolute identity in Trinitarian doctrine while modeling relative identity with an analogy of general partnerships in the United States.

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.

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.

The author attacks the view that identity, Like largeness, Is a relative relation. The primary advocate of the view that identity is relative is p.T. Geach. It is argued that geach has not shown that the failure of the identity of indiscernibles principle, As a truth of logic, Forces us to stop taking indiscernibility within particular formal theories or languages as a sufficient condition for identity. The author also argues that the whole notion of relative identity, As explicated by geach, (...) Is very probably incoherent. (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)

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)

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)

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.

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)

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)

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'.

Philosophers who accept tropes generally agree that tropes act as the objects of reference of nominalizations of adjectives, such as 'Socrates’ wisdom' or 'the beauty of the landscape'. This paper argues that tropes play a further important role in the semantics of natural language, namely in the semantics of bare demonstratives like 'this' and 'that' in what in linguistics is called identificational sentences.

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.

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