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)

According to Zhiyi 智顗 (538–597), the founder of the Chinese Buddhist Tiantai school 天臺宗, “one object is all objects;” hence, all objects are profoundly interconnected. In this paper, I critically examine Zhiyi’s metaphysics of objects as presented in the historical Tiantai texts and subsequently develop a contemporary and accessible thesis of interconnectedness by integrating Zhiyi’s views with resources from contemporary analytic philosophy, particularly relative identity. By drawing on Zhiyi’s insights and incorporating contemporary philosophical ideas, I also illustrate how (...) historical Chinese Buddhism and contemporary analytic metaphysics can be mutually informing. (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.

This chapter considers Geach's claims solely as pertaining to the philosophy of language and philosophical logic, though much of the interest of the concept of relative identity concerns its applicability to other areas: the metaphysical controversy about personal identity and the debate in philosophical theology on the doctrine of the Trinity. It describes Geach's views under six headings: the non‐existence of absolute identity; the sortal relativity of identity; the derelativization thesis; the counting thesis; the thesis (...) of the irreducibility of restricted quantification; and the 'name for an A'/'name of an A' distinction. The sortal relativity thesis depends for its significance on the distinction between sortal terms and non‐sortal terms. An important component of Geach's position is his thesis that for any sortal term 'A' there is a distinction between restricted quantification over As and unrestricted quantification over things that are As. (shrink)

The doctrine of the Trinity maintains that there are exactly three divine Persons (Father, Son, and Holy Spirit) but only one God. The philosophical problem raised by this doctrine is well known. On the one hand, the doctrine seems clearly to imply that the divine Persons are numerically distinct. How else could they be ’three’ rather than one? On the other hand, it seems to imply that Father, Son, and Holy Spirit are identical. If each Person is divine, how else (...) could there be exactly ’one’ God? But the divine Persons can’t be both distinct and identical. Thus, the doctrine appears to be incoherent. Some try to solve this problem by appeal to the view that identity is sortal-relative. In this paper, I argue that this strategy is unsuccessful as a stand-alone solution to the problem of the Trinity. (shrink)

The indiscernibility of identicals is incompatible with geach's theory of 'relative' identity, But consistent with the view that x is identical with y iff x is the same a as y, For some count-Noun 'a'. 'x is the same a as y' expresses identity only if x is an a, Otherwise it is merely an equivalence relation.

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)

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.

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)

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.

In the October 1978 issue of Mind, Nicholas Griffin puts forward a criticism of one of my arguments in 'Wiggins on Identity'. Although I would not now wish to defend everything I said in that paper, the argument Griffin attacks still seems to me to be a good one. In what follows, I explain why I think his criticism fails to strike home.

I defend a slightly modified version of geach's rule r, I.E., That although both a and b are g, It is possible for a to be the same f as b and a different h than b, Provided that the question whether a and b are the same g is undecidable. Answering those who object to relative identity I claim that they tacitly adhere to a false fregean view, I.E., That one cannot use a singular term to denote (...) an entity x if it is not true that for every y, X=y or not x=y. I show, However, That such terms are, And must be, Used by every empirically oriented language with finite or infinite predicative arsenal, And hence relative identity is more handy than absolute identity. Finally I give a version of leibniz's law for relative identity. (shrink)

This article gives a holistic re-examination of the semantic content and syntactic structure of the concept of relative identity: it suggests and explains an expanded and enhanced dual-track characterization of relative identity. It is expanded in this sense: its due coverage is not narrowly restricted to the equal-status case of identity statements (the symmetric case for identity simplex) but also includes the category-assimilating case (the asymmetric case for identity complex), both of which are (...) unified by the shared semantic core content of relative identity. It is enhanced in this sense: it is intended to give a more refined characterization of relative identity for the sake of enhancing our understanding of the structure and content of real-life relative-identity statements in people’s basic employment of language in view of the relation between thought, language, and the world. (shrink)

LOCKE'S DISCUSSION OF ORGANISMS AND PERSONS IN "ESSAY" II.XXVI HAS LED GEACH AND OTHERS TO ATTRIBUTE THE THESIS OF RELATIVE IDENTITY TO HIM; THAT X IS NEVER IDENTICAL WITH Y "TOUT COURT" BUT ONLY RELATIVE TO SOME SORTAL PROPERTY F: X IS THE SAME F AS Y. I ARGUE THAT THIS ATTRIBUTION RESTS ON A MISUNDERSTANDING OF LOCKE'S POSITION. LOCKE INDEED HOLDS THAT AN OLD TREE MAY BE THE SAME OAK AS THE SEEDLING FROM WHICH IT GREW, (...) WHEREAS THE PARTICLES COMPOSING THE TREE AND THE SEEDLING ARE DIFFERENT MASSES OF MATTER. BUT HE ALSO HOLDS THAT PLANTS AND MASSES OF MATTER ARE DISTINCT ENTITIES TO START WITH, EVEN IF THEY OCCUPY THE SAME PLACE AT THE SAME TIME. AND SIMILARLY WITH PERSONS AND MEN. THE RESULT IS A COPIOUS ONTOLOGY, BUT THERE IS NO REASON TO THINK THAT LOCKE WOULD OR SHOULD HAVE BEEN BOTHERED BY THAT. (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 (...) class='Hi'>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)

It would seem that Geach's claim is that the relation expressed by 'is identical with' is like the relation expressed by 'is better than', at least in one respect. If x and y are people, it may turn out that x is a better golfer than y, while y is a better poet than x. If we merely say that x is better than y, we fail to specify the respect in which we hold x to be the better. Another (...) way to put this is to say that we have not made clear "in relation to what" x is the better. We can call the relation expressed by 'is better than' a "relative relation," since an ordered pair of things may stand in that relation relative to one thing but not relative to another thing. Geach seems to think that identity is a relative relation. (shrink)

Relative Identity contains a sustained attack on the classical or absolute theory of identity and a defense of a non-classical or relative theory of identity. According to the absolute theory of identity each thing is identical with itself and with nothing other than itself. The fundamental principle of this theory is Leibniz' Law:From a variety of characteristic principles about identity can be derived, including The Indiscernibility of Identicals, The Identity of Indiscernibles, and (...) the symmetry, reflexivity, and transitivity of identity. (shrink)

Borowski ("identity and personal identity," "mind", Volume lxxxv, Number 340, October 1976, Pages 481-502) claims that if x's brain were successfully transplanted into y's body, Our judgment of who the survivor z really is would be relative to our interest in z: for example, If the body y is that of an athlete or film actor, We would say it is y if we are athletic coaches or film directors. This view completely overlooks that acting talents and (...) athletic skills are also stored in the brain. If my brain controlled pele's body, Or laurence olivier's, I could not play football or act well. (shrink)

Since Geach did not give any account of what is to be considered the same form of relative identity, I assumed that 'x is the same A as y' expresses the same form of relative identity as 'x is the same B as y' if and only if 'A' means the same as 'B'. If this is an incorrect assumption, then I must ask what is the criterion of identity for forms of relative (...) class='Hi'>identity? (shrink)

This article defends my claim, first presented in "identity and trinity," "journal of religion" (1978), that the doctrine of the trinity is consistent. drawing upon tertullian's defense of the doctrine in "adversus praxean", i argue that the logic of the trinity is similar to the logic of emperorship. at various times, two persons, for example, diocletian and maximian, were the same emperor of the roman empire, just as three persons are the same god.

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)

In a recent paper M.R. Ayers attacks two widely held doctrines: Non-arbitary individuation requires principles of individuation and these are supplies only by sortal general terms. It is possible for an item a to be the same as b but not the same as b.I shall follow Ayers in calling a theory which includes both and ‘conceptualist’ or ‘sortalist’, but I shall not allow him to appropriate the honorific term ‘realist’ for his own theory, which I shall term ‘absolutist’. My (...) sole purpose here is to defend and in turn against Ayers’ attacks on them. Thus I shall ignore intermediate positions which accept but reject or vice-versa.Ayers’ paper is long and in many respects obscure; there are many points in it which require discussion but which can't receive it here for lack of space. In particular, I shall ignore his lengthy comments on the constitutive ‘is’, and also the wider metaphysical remarks in his conclusion and the postscript on Dummett. (shrink)

In the first twelve chapters of this book, I am concerned with the Fregean notion of an object (the reference of a proper name) and its connection with the notion of identity. The rest of the book is devoted to a discussion of the problem of personal identity.

I EXPLORE ONE WAY IN WHICH THE THEORY OF RELATIVE IDENTITY (DEVELOPED ALONG LINES SUGGESTED BY GEACH’S WRITINGS) CAN BE USED TO UNDERSTAND THE WAY LANGUAGE FUNCTIONS IN TRINITARIAN DOCTRINE. THIS INCLUDES A DISCUSSION OF REDUPLICATIVE PROPOSITIONS.

In this paper, I consider the philosophical consequences of one tradition in Trinitarian theology, which emphasizes that each of the persons of the Trinity is wholly God. I pay special attention to Leftow’s claim that the persons of the Godhead must be divine in the same sense of the word ‘divine’ as the Godhead itself. I argue that the existing philosophical account of the Trinity which best captures this view is what I have termed the ‘Strong Theory of Relative (...) Identity,’ first proposed Peter Geach. I then develop what I take to be the most pressing objection to this account of the Trinity, namely that it cannot be supplemented with a coherent model-theoretic semantics. I end with a suggestion for responding to this objection. (shrink)

The theorizing about the doctrine of the Trinity by contemporary analytic philosophers of religion has recently been imbued with an air of enthusiastic excitement and self-confidence. My intuition is that there’s room for saying something more in support to the embarrassment and puzzlement traditionally related to the predication of God’s onefoldness and threefoldness. My purpose is to deliver a general argument for (weak) trinitarian skepticism. My view is that the argument provides substantive reasons in support to the common sense intuition (...) that either God’s onefoldness and threefoldness aren’t actually compatible or God’s onefoldness and threefoldness aren’t robustly construed. (shrink)