It is widely held that counterfactuals, unlike attitude ascriptions, preserve the referential transparency of their constituents, i.e., that counterfactuals validate the substitution of identicals when their constituents do. The only putative counterexamples in the literature come from counterpossibles, i.e., counterfactuals with impossible antecedents. Advocates of counterpossibilism, i.e., the view that counterpossibles are not all vacuous, argue that counterpossibles can generate referential opacity. But in order to explain why most substitution inferences into counterfactuals seem valid, counterpossibilists also often (...) maintain that counterfactuals with possible antecedents are transparency‐preserving. I argue that if counterpossibles can generate opacity, then so can ordinary counterfactuals with possible antecedents. Utilizing an analogy between counterfactuals and attitude ascriptions, I provide a counterpossibilist‐friendly explanation for the apparent validity of substitution inferences into counterfactuals. I conclude by suggesting that the debate over counterpossibles is closely tied to questions concerning the extent to which counterfactuals are more like attitude ascriptions and epistemic operators than previously recognized. (shrink)

It is shown that typical arguments from intensionality against the Principle of Indiscernibility of Identicals (InI) misconstrue this principle, confusing it with the Principle of Substitution (PS). It has been proposed that Leibniz, in his statements like, "If A is the same as B, then A can be substituted for B, salva veritate, in any proposition", is not applying InI to objects nor PS to signs, but is talking about substitution of concepts in propositions, or applying InI (...) to concepts. It is shown in the paper that since Leibniz holds that there are exceptions to the principle thus stated, either the proposal in question is misguided, or else Leibniz is mistaken in thinking that there are such exceptions. (shrink)

This paper is concerned with notions of consequence. On the one hand, we study admissible consequence, specifically for substitutions of Σ 1 0 -sentences over Heyting arithmetic . On the other hand, we study preservativity relations. The notion of preservativity of sentences over a given theory is a dual of the notion of conservativity of formulas over a given theory. We show that admissible consequence for Σ 1 0 -substitutions over HA coincides with NNIL -preservativity over intuitionistic propositional logic . (...) Here NNIL is the class of propositional formulas with no nestings of implications to the left . The identical embedding of IPC -derivability into a consequence relation has in many cases a left adjoint. The main tool of the present paper will be an algorithm to compute this left adjoint in the case of NNIL -preservativity. In the last section, we employ the methods developed in the paper to give a characterization the closed fragment of the provability logic of HA. (shrink)

This paper is concerned with notions of consequence. On the one hand, we study admissible consequence, specifically for substitutions of Σ 1 0 -sentences over Heyting arithmetic . On the other hand, we study preservativity relations. The notion of preservativity of sentences over a given theory is a dual of the notion of conservativity of formulas over a given theory. We show that admissible consequence for Σ 1 0 -substitutions over HA coincides with NNIL -preservativity over intuitionistic propositional logic . (...) Here NNIL is the class of propositional formulas with no nestings of implications to the left . The identical embedding of IPC -derivability into a consequence relation has in many cases a left adjoint. The main tool of the present paper will be an algorithm to compute this left adjoint in the case of NNIL -preservativity. In the last section, we employ the methods developed in the paper to give a characterization the closed fragment of the provability logic of HA. (shrink)

According to one prominent strand of mainstream logic and metaphysics, identity is indistinguishability. Priest has recently argued that this permits counterexamples to the transitivity and substitutivity of identity within dialetheic metaphysics, even in paradigmatically extensional contexts. This paper investigates two alternative regimentations of indistinguishability. Although classically equivalent to the standard regimentation on which Priest focuses, these alternatives are strictly stronger than it in dialetheic settings. Both regimentations are transitive, and one satisfies substitutivity. It is argued that both regimentations provide better (...) candidates to occupy the core theoretical role of numerical identity than does the standard regimentation. (shrink)

In this paper we try to justify our way of looking for an alternative approach to quantum mechanics, which is based on a non-classical logic. We consider two specific questions related to quantum theory, namely, entanglement and the indiscernibility of quanta. We characterize individuals, and then explain in what sense entanglement is a concept which can be applied to individuals in a restricted sense only. Then, we turn to indiscernibility and, after realizing that this concept is of a fundamental importance, (...) we mention the ‘traditional’ theory of identity of standard logic and mathematics, which underly the basic formalism of quantum theory. Then we propose to call the Problem of Identity the question whether identity of objects can be justified, and under what conditions. As in the Hume’s celebrated Problem of Induction, we conclude that the attribution of transtemporal identity to an object has no logic justification, and must be considered as a metaphysical hypothesis. Numerical identity is also put aside for similar reasons. Then we guess that identity is just an useful concept, but which in certain fields, mainly in the quantum realm, could be substituted by a weaker concept of indiscernibility. This assumption motivates us to look for an interpretation of quantum mechanics based on a non-classical logic, termed non-reflexive, and the corresponding mechanics is called non-reflexive quantum mechanics. (shrink)

U.K. regulation of sexual identity within a marriage context has traditionally been linked to biological sex. In response to the European Court of Human Rights decisions in Goodwin and I.,2 and in order to address the question of whether a transsexual person can be treated as a “real” member of their adoptive sex, the U.K. has recently passed the Gender Recognition Act 2004. While the Act appears to signal a move away from biology and towards a conception of sexual identity (...) based on gender rather than sex, questions of sexual identity remain rooted in medico-legal assessments of the individual transsexual body/mind. In contrast, because transsexual people in some parts of Canada have been able to marry in their post-operative sex since 1990, contemporary debates on the sexual identity of transsexual people in British Columbia and Ontario do not focus on the validity of marriage, and more frequently centre upon the provision of goods and services, in human rights contexts where sex is said to matter. Currently in Canada this is prompting questions of what it means to be a woman in society, how the law should interpret sex and gender, and how, if at all, the parameters of sexual identity should be established in law. This article seeks to compare recent U.K. legal conceptualisations of transsexuality with Canadian law in this area. As human rights discourse begins to grow in the U.K., the question remains as to whether or not gender will become an adequate substitute for sex. (shrink)

One of the many important tasks of semantics is to provide an account of the substitution patterns of a language—that is, to furnish an explanation of the conditions under which semantic values of complexes are preserved when components are replaced. The importance of this issue is plain: we only have to recall the debates regarding substitutivity between proponents of direct reference theories and advocates of some version of Fregeanism, as well as the disagreements among different proponents of direct reference (...) theories as regards substitutivity in belief reports. This is why it is important to articulate an acceptable principle of substitution. A traditional statement of the principle of substitution holds that codesignative singular terms should be intersubtitutable salva veritate. In the past I have argued that such a principle is not connected properly to some pretheoretical data about the function of referring terms. In this chapter I argue that such a principle does not gain support either from other, more fundamental, laws. I end by defending the adequacy of a different principle of substitution. (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)

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 Propositional Attitudes, Mark Richard claims that some natural and formal language sentences of the form(∀ x)(∀ y)(x = y → α → α [y/x])are false. He suggests a substitution for α that is sensitive to certain ancillary features of the variable letter as well as the assignment, and then argues that this substitution generates a false instance of the above-mentioned schema. I reject Richard's argument and argue further that the sentence is not an instance of that schema. (...) I then argue that his putative natural language example fails as well. Finally, I suggest that although Richard's mistake here does not present any technical problem for his semantics for attitude ascriptions, it undermines his claim that his semantic theory is better able to respect the surface form of attitude ascriptions in natural languages than competing theories. (shrink)

Identity as traditionally conceived in mainstream Western thought is focused on theory, representation, knowledge, subjectivity and is centrally important in the works of Emmanuel Levinas. His critique of Western culture and corresponding notion of identity at its foundations typically raises the question of the other. Alterity in Levinas indicates existence of something on its own account, in itself independently of the subject’s will or consciousness. The objectivity of alterity tells of the impossible evasion of signs from their destiny, which is (...) the other. The implications involved in reading the signs of the other have contributed to reorienting semiotics in the direction of semioethics. In Levinas, the I-other relation is not reducible to abstract cognitive terms, to intellectual synthesis, to the subject-object relation, but rather tells of involvement among singularities whose distinctive feature is alterity, absolute alterity. Humanism of the other is a pivotal concept in Levinas overturning the sense of Western reason. It asserts human duties over human rights. Humanism of alterity privileges encounter with the other, responsibility for the other, over tendencies of the centripetal and egocentric orders that instead exclude the other. Responsibility allows for neither rest nor peace. The “properly human” is given in the capacity for absolute otherness, unlimited responsibility, dialogical intercorporeity among differences non-indifferent to each other, it tells of the condition of vulnerability before the other, exposition to the other. The State and its laws limit responsibility for the other. Levinas signals an essential contradiction between the primordial ethical orientation and the legal order. Justice involves comparing incomparables, comparison among singularities outside identity. Consequently, justice places limitations on responsibility, on unlimited responsibility which at the same time it presupposes as its very condition of possibility. The present essay is structured around the following themes: Premiss; Justice, uniqueness, and love; Sign and language; Dialogue and alterity; Semiotic materiality; Globalization and the trap of identity; Human rights and rights of the other: for a new humanism; Ethics; The World; Outside the subject; Responsibility and Substitution; The face; Fear of the other; Alterity and justice; Justice and proximity; Literary writing; Unjust justice; Caring for the other. (shrink)

The first principle of Fichte’s philosophy, the Wissenschaftslehre, is “I am,” whereas the logical principle of identity is “A is A.” The relationship of Fichte’s philosophy to logic helps us understand the relation between the principles of these two disciplines. The first principle of the Wissenschaftslehre as an Act (Thathandlung) is the ground of consciousness and therefore renders logic possible as a science. Even though logic is grounded on the Wissenschaftslehre, the form of logic is used by the latter to (...) comprehend itself. The difference between logic and the Wissenschaftslehre consists in the fact that the former merely supplies a form and the latter contains both the form and the content. Logic arises from the Wissenschaftslehre through the free acts termed “abstraction” and “reflection.” In the Wissenschaftslehre, the form of logical propositions as equality, affirmation and substitution, are derived from the primordial act of the self-positing of the I. (shrink)

The particular problem which will concern us here is raised by "Leibniz's Rule": Eadem sunt quorum unum in alterius locum substitui potest, salva veritate. The puzzle arises from the following inference.

The paper argues that philosophers commonly misidentify the substitutivity principle involved in Russell’s puzzle about substitutivity in “On Denoting”. This matters because when that principle is properly identified the puzzle becomes considerably sharper and more interesting than it is often taken to be. This article describes both the puzzle itself and Russell's solution to it, which involves resources beyond the theory of descriptions. It then explores the epistemological and metaphysical consequences of that solution. One such consequence, it argues, is that (...) Russell must abandon his commitment to propositions. (shrink)

Raymond Kelly’s widely cited _Warless Societies and the Origin of War_ (University of Michigan Press, 2000) seeks to explain the origins of two central signatures of human society: war and segmented—i.e., multilevel—societies. Both, he argues, arose with the emergence of a social-substitutability principle, a rule that establishes a collective identity among a set of individuals such that any one member becomes equivalent to, and responsible for the actions of, the others. This principle emerged during the Holocene, when population increase gave (...) rise to the first lethal ambushes. By its nature, ambush obscures attackers’ identities. Those attempting to retaliate for the ambush were therefore obliged to target members of the ambushers’ group indiscriminately—i.e., based on a social-substitutability principle. Kelly’s proposals draw welcome attention to a widespread, deeply influential, and unsettling human behavior, the disposition to hold everyone in a group culpable for the actions of a few, a proclivity that all too often results in mass slaughter. His general argument, however, is logically and empirically deficient, and cross-cultural evidence on ambush in contact-era New Guinea undermines his anonymity-of-ambush hypothesis. What then accounts for war and multilevel society? The New Guinea evidence strongly supports a contention that social-substitutability behavior arose not from offensive military action (i.e., ambush) but from the defensive military response to ambush. These findings render the social-substitutability argument’s unconventional definition of war superfluous, undermine its chronology for the emergence of war, and underwrite an alternative scenario for the origins of multilevel, segmented society. (shrink)

I trace the principles known as the indiscernibility of identicals, "Leibniz's Law", and the principle of substitutivity, beginning with Aristotle, through Leibniz, Frege, and Russell, and culminating in Quine. I argue that the indiscernibility of identicals is an ontological principle and the principle of substitutivity is a linguistic principle. I discuss the relations and conflations of the principles and various attempts to defend the principle of substitutivity from apparent counter-examples, focussing on Quine's attempt to use the principle as (...) a criterion for referential and non-referential occurrences of singular terms. I find Quine's acount ambivalent and counter-intuitive, yet I think his insight that pronouns or variables are paradigmatic of reference is significant. With that as a cue, I suggest an analysis of all singular terms into a counting device and an identifying component. I argue, finally, that the principle of substitutivity holds fundamentally for the counting element, and only "by courtesy" for unanalyzed singular terms. (shrink)

How to interpret singular terms in fiction? In this paper, we address this semantic question from the perspective of the Artifactual Theory of Fiction (ATF). According to the ATF, fictional characters exist as abstract artifacts created by their author, and preserved through the existence of copies of an original work and a competent readership. We pretend that a well-suited semantics for the ATF can be defined with respect to a modal framework by means of Hintikka’s world lines semantics. The question (...) of the interpretation of proper names is asked in relation to two inference rules, problematic when applied in intensional contexts: the Substitution of Identicals and Existential Generalization. The former fails because identity is contingent. The latter because proper names are not necessarily linked to well-identified individuals. This motivates a non-rigid interpretation of proper names in fiction, although cross-fictional reference (e.g. to real entities) is made possible by the interpretative efforts of the reader. (shrink)

In this paper a principle of substitutivity of logical equivalents salve veritate and a version of Leibniz’s law are formulated and each is shown to cause problems when combined with naive truth theories.

The Identity of Indiscernibles is the principle that objects cannot differ only numerically. It is widely held that one interpretation of this principle is trivially true: the claim that objects that bear all of the same properties are identical. This triviality ostensibly arises from haecceities (properties like \textit{is identical to a}). I argue that this is not the case; we do not trivialize the Identity of Indiscernibles with haecceities, because it is impossible to express the haecceities of indiscernible objects. I (...) then argue that this inexpressibility generalizes to all of their trivializing properties. Whether the Identity of Indiscernibles is trivially true ultimately turns on whether we can quantify over properties that we cannot express. (shrink)

Logical consequence in first-order predicate logic is defined substitutionally in set theory augmented with a primitive satisfaction predicate: an argument is defined to be logically valid if and only if there is no substitution instance with true premises and a false conclusion. Substitution instances are permitted to contain parameters. Variants of this definition of logical consequence are given: logical validity can be defined with or without identity as a logical constant, and quantifiers can be relativized in substitution (...) instances or not. It is shown that the resulting notions of logical consequence are extensionally equivalent to versions of first-order provability and model-theoretic consequence. Every model-theoretic interpretation has a substitutional counterpart, but not vice versa. In particular, in contrast to the model-theoretic account, there is a trivial intended interpretation on the substitutional account, namely, the homophonic interpretation that does not substitute anything. Applications to free logic, and theories and languages other than set theory are sketched. (shrink)

The paper deals with Leibniz’s ontology and the metaphysics of the aggregate. Concerning the ontology of aggregates, the main aim is to provide _a new argument_ in favor of the claim that an aggregate and its constituents have the same ontological import. This argument takes the form of a weakening of a principle known in the contemporary literature of mereology as ‘composition as identity’ (CAI). The paper shows that Leibniz’s nominalism toward aggregates is a direct consequence of two elements: the (...) way in which he considers the relationship between aggregates and their constituents in his logical calculus; and his theory of identity (and more generally, equivalence relations) as providing us with the ground for substitution _salva veritate_. It is concluded that Leibniz is committed to a principle that the author dubs Ontological-CAI: the aggregate/whole is _ontologically identical_ (i.e. it has the same ontological import) as its constituents/parts. Concerning the metaphysics of aggregates, the paper outlines in what sense aggregates are grounded on their constituents: arguing that Leibniz is committed to a further principle that the author calls Metaphysical-CAI: the aggregate/whole is _metaphysically grounded_ on its constituents/parts. From this it can be understood in which sense Leibniz could be considered a mereological nihilist, and in which sense not. The paper also sets out two different and competing readings of Metaphysical-CAI, and argues that Leibniz accepted both of them by interpreting them as different levels of explanation of the nature of aggregates. (shrink)

The standard Leibnizian view of identity allows for substitutivity of identicals and validates transitivity of identity within classical semantics. However, in a series of works, Graham Priest argues that Leibnizian identity invalidates both principles when formalized in paraconsistent semantics. This paper aims to show the Leibnizian view of identity validates substitutivity of identicals and transitivity of identity whether the logic is classical or paraconsistent. After presenting Priest's semantics of identity, I show what a semantic expression of Leibnizian identity (...) does amount to. Then, I argue that Priest's semantic definition of identity is not Leibnizian. Finally, I offer a semantics characterization of identity in paraconsistent logic that is truly Leibnizian. I demonstrate that the correct formalization of Leibnizian identity in paraconsistent logic also validates substitutivity of identicals and transitivity of identity. (shrink)

The presence of increasing percentages of immigrants in the European social landscape is not only a quantitative fact, with consequences on several social and cultural dynamics and indicators. It produces an important qualitative change. From being a pathology, plurality is becoming physiology. Religion is a key factor in this process. There is a synchronic pluralization going on: the level of pluralization of the religious and cultural offer is increasing, making society a kaleidoscope of cultures, whose pieces are in constant movement. (...) Islam – and in particular Islam in Europe – is often considered the most problematic and ‘problematized’ expression of this process. It is what we could call exceptionalism: the tendency to see Islam and Muslims as an exceptional rather than standard case. Even the mediatic perception of Islam in conflictual terms can be considered a form of exceptionalism and conflict a specific way of understanding Islam. Islamophobia is part of this phenomenon. Exceptionalism explains why Islam has become a discursive substitute of the main transformation, which is the much higher degree of cultural and religious pluralization of European societies. (shrink)

This book is a rationalist critique of the identity theory, oriented by a discussion of Feigl’s significance-reference distinction. Large chapters on the impossibility of identity, on both methodological and empirical grounds, are filled with helpful quotes and clear interpretations of contemporary theories. For Polten dualism is not resolved by language clarification. "Morning star" and "evening star" do not have the same sense, nor do they refer to the same extension. They could not be substituted for one another. "X = Y (...) if and only if X and Y have every property in common.... If I only show one property which is not common between mind and body, the identity theory is disconfirmed," logically. Empirically there are grounds for a dualist position because "... mind and brain are observed to be different." Epistemologically, "... what we do perceive is mind-dependent without exception;" the basis of experience is personal and a pure ego enables us to account for this privileged access. Polten tends to collapse distinctions between logic, epistemology, and ontology to provide a metaphysical overview in the pure ego. "... Object and subject merge, and the experience is one of self-illumination and transparence." His arguments do not justify this metaphysics, but he does make a case, in terms of his criticisms of attempts at reduction, for linguistic and epistemological dualism.—P.S. (shrink)

This essay discusses rules and semantic clauses relating to Substitution—Leibniz’s law in the conjunctive-implicational form s=t ∧ A(s) → A(t)—as these are put forward in Priest’s books "In Contradiction" and "An Introduction to Non-Classical Logic: From If to Is." The stated rules and clauses are shown to be too weak in some cases and too strong in others. New ones are presented and shown to be correct. Justification for the various rules are probed and it is argued that (...) class='Hi'>Substitution ought to fail. (shrink)

This dissertation examines critically the assumptions of extensionalism and the traditional doctrine of substitutivity, according to which codesignativeness or coextensionality of terms should be a sufficient condition to guarantee intersubstitution of expression salva veritate. First, the discussion focuses on the traditional justifications of the extensionalist principles of substitutivity. The following alleged sources of support for extensionalism are examined: the claim that the extensionalist approach to substitutivity relies on fundamental principles outside the domain of semantics, like the Law of Indiscernibility of (...) Identicals and Leibniz's Law of Substitutivity; the assumption that all sentences that exhibit failures of substitutivity have in common a certain structure, that they include explicit or implicit intensional operators, which cause failures of substitutivity; the presumption that the extensionalist principles of substitutivity follow from a thesis of compositionality of meaning,according to which the meaning of a complex expression is determined by the meanings of its components and the mode of composition. Second, the intuitive foundations of a theory about the contributions of terms to the assertions expressed by uses of sentences are explored. I claim that this theory provides strong reasons to reject the extensionalist approach to substitutivity. (shrink)

Competing theories on the semantics of group pejorative terms (also known as‘slurs’)comprise both advocates and opponents to the Identity Thesis (IT), according to whichthese terms and their neutral counterparts do not differ in semantic value. In the oppo-nents’camp, Christopher Hom has offered an argument based on substitution of slurs andneutral counterparts that both supports his semanticist approach and cast doubts on all IT-based approaches to slurs. We aim to point to a dilemma triggered by this argument based on evidence (...) showing that substitution of some words (including but not restricted to slurs)for non-problematically co-referential pairs may fail to preserve truth-values in some linguistics contexts. (shrink)

We show that, contrary to conventional wisdom, Frege’s distinction between sense and reference does not reconcile a classical logic of identity with apparent counterexamples to it involving proper names embedded under propositional attitude verbs.

One way to theorize about we-identities—the identities that individual subjects have as ‘one of us’—is in terms of the uniformity, interchangeability, and prototypicality of group members. The social-psychological theory of self-categorization epitomizes this approach, which has strongly influenced contemporary phenomenological research on the we. This paper argues that this approach has one important and largely overlooked limitation: the we-identities tied to close personal relationships—exemplified by long-term friendships and romantic partnerships—are based on patterns of interpersonal interaction and integration through which individuals (...) tend to grasp their non-substitutability and complementarity. This limitation suggests that another approach is needed to tackle the we-identities characteristic of close personal relationships. I outline such an approach, by combining resources from classical phenomenology and ongoing research on the socially extended mind. (shrink)

ABSTRACT Recently, in a series of papers, Joshua Spencer has introduced, defended, and developed a modified version of Neo-Russellianism, namely Plenitudinous Russellianism, according to which there are structurally identical but numerically distinct singular Russellian propositions. PR claims to provide novel semantic solutions to all the major problems that NR faces with no radical revision in NR. In this paper, I introduce a semantic puzzle for PR: the view leads to the violation of the principle of substitutivity of co-referential proper names (...) within simple ‘that’-clauses. I consider different responses to my argument, and show that none of them is fully satisfactory for the Russellian. I conclude that PR needs to depart from NR more radically. RÉSUMÉ Récemment, Joshua Spencer a publié une série d'articles où il expose, défend et développe une version modifiée du Néo-Russellianisme, appelée Russellianisme de plénitude, selon laquelle il y a des propositions Russelliennes singulières structurellement identiques mais numériquement distinctes. Ce Russellianisme de plénitude prétend apporter de nouvelles solutions sémantiques à tous les problèmes majeurs auxquels le NR se confronte, sans pour autant procéder à une révision radicale du NR. Dans cet article, je mettrai le PR face à un casse-tête : cette vision mène à la violation du principe de substitution des noms propres co-référentiels au sein des subordonnées complétives simples. Je tâcherai de considérer différentes réponses à mon argument et de montrer qu'aucune d'entre elles n'est pleinement satisfaisante pour un Russellien. Je vais conclure que le PR devrait s’écarter plus radicalement du NR. (shrink)

The paper presents an alternative substitutional semantics for first-order modal logic which, in contrast to traditional substitutional (or truth-value) semantics, allows for a fine-grained explanation of the semantical behavior of the terms from which atomic formulae are composed. In contrast to denotational semantics, which is inherently reference-guided, this semantics supports a non-referential conception of modal truth and does not give rise to the problems which pertain to the philosophical interpretation of objectual domains (concerning, e.g., possibilia or trans-world identity). The paper (...) also proposes the notion of modality de nomine as an alternative to the denotational notion of modality de re. (shrink)

At some step in proving the Liar Paradox in natural language, a sentence is derived that seems overdetermined with respect to its semantic value. This is complemented by Tarski’s Theorem that a formal language cannot consistently contain a naive truth predicate given the laws of logic used in proving the Liar paradox. I argue that proofs of the Eubulidean Liar either use a principle of truth with non-canonical names in a fallacious way or make a fallacious use of substitution (...) of identicals. Tarski never committed the first fallacy and may have himself considered it fallacious. Nevertheless, I clarify that it is fallacious. I then argue substitution of identicals needs to be restricted within the scope of the truth predicate. A logic for truth implementing this restriction is a monotonic extension of a classical first order logic, or indeed a formalizable fragment of natural language. Proofs of Tarski’s Indefinability of Truth theorem are invalid in this logic. This approach generalizes to invalidate proofs of Liar-like paradoxes, particularly the predicate form of the Knower paradox. Consequently, such a logic can be further extended in a way that avoids Montague’s theorem for such a system. Yet, the semantic status of a Liar sentence is not fully resolved. It is no longer overdetermined; it is now underdetermined. (shrink)

John Damascene, one of the most productive Greek theologians of the Middle Byzantine era, also composed a treatise on the Trisagion hymn, or how it should be sung correctly and why; a text that has been little discussed in contemporary scholarship. The present paper provides an overview of the work – with special reference to the notion of identity in John’s description of the Trinitarian doctrine. It also examines the treatise especially in the context of anti-heretical polemics. The author argues (...) that John’s approach to the question of the correct way of singing the hymn is gentle: instead of using pejorative language, he even praises the object of his reproach. (shrink)

In this series of four lectures a scientist examines some philosophical implications of what one might loosely call "the modern scientific view of life". Bronowski has produced numerous books and articles on everything from the poetry of Blake to the clock paradox of relativity theory. It is therefore to be regretted that his latest work suffers from an annoying amount of oversimplification, and a tendency to substitute rhapsodizing for reasoning. Those concerned with the "two cultures" debate and related matters will (...) nevertheless find this book valuable and enjoyable, especially for the author's argument—which is convincing—that science and the arts need not be antithetical either in subject-matter or in spirit.—H. P. K. (shrink)

It seems that the Truth-teller is either true or false, but there is no accepted principle determining which it is. From this point of view, the Truth-teller is a hypodox. A hypodox is a conundrum like a paradox, but consistent. Sometimes, accepting an additional principle will convert a hypodox into a paradox. Conversely, in some cases, retracting or restricting a principle will convert a paradox to a hypodox. This last point suggests a new method of avoiding inconsistency. This article provides (...) a significant example. The Liar paradox can be defused to a hypodox by relatively minimally restricting three principles: the T-schema, substitution of identicals and universal instantiation. These restrictions are not arbitrary. For each, I identify the source of a contradiction given some presumptions. Then I propose each restriction as a reasonable way to deal with that source of contradiction. (shrink)

Composition as Identity is the view that an object is identical to its parts taken collectively. I elaborate and defend a theory based on this idea: composition is a kind of identity. Since this claim is best presented within a plural logic, I develop a formal system of plural logic. The principles of this system differ from the standard views on plural logic because one of my central claims is that identity is a relation which comes in a variety of (...) forms and only one of them obeys substitution unrestrictedly. I justify this departure from orthodoxy by showing some problems which result from attempts to avoid inconsistencies within plural logic by means of postulating other non-singular terms besides plural terms. Thereby, some of the main criticisms raised against Composition as Identity can be addressed. Further, I argue that the way objects are arranged is relevant with respect to the question which object they compose, i.e. to which object they are identical to. This helps to meet a second group of arguments against Composition as Identity. These arguments aim to show that identifying composite objects on the basis of the identity of their parts entails, contrary to our common sense view, that rearranging the parts of a composite object does not leave us with a different object. Moreover, it allows us to carve out the intensional aspects of Composition as Identity and to defend mereological universalism, the claim that any objects compose some object. Much of the pressure put on the latter view can be avoided by distinguishing the question whether some objects compose an object from the question what object they compose. Eventually, I conclude that Composition as Identity is a coherent and plausible position, as long as we take identity to be a more complex relation than commonly assumed. (shrink)

Trinitarians are charged with at least two contradictions. First, the Father is God and the Son is God, so it seems to follow that the Father is the Son. Trinitarians affirm the premises but deny the conclusion, which seems contradictory. Second, the Father is a God, the Son is a God, and the Holy Spirit is a God, but the Father is not the Son, the Father is not the Holy Spirit, and the Son is not the Holy Spirit. This (...) argument seems to entail that there are three Gods. Again, Trinitarians affirm the premises but deny the conclusion. In this article, I present a novel Trinitarian solution to these alleged contradictions. The solution allows one to maintain that the premises in the above arguments are absolute identity statements, forestalls the need to develop a new way of counting (e.g. by sortals or numerical sameness), and is compatible with divine simplicity. (shrink)

Equality and identity. Bulletin of Symbolic Logic. 19 (2013) 255-6. (Coauthor: Anthony Ramnauth) Also see https://www.academia.edu/s/a6bf02aaab This article uses ‘equals’ [‘is equal to’] and ‘is’ [‘is identical to’, ‘is one and the same as’] as they are used in ordinary exact English. In a logically perfect language the oxymoron ‘the numbers 3 and 2+1 are the same number’ could not be said. Likewise, ‘the number 3 and the number 2+1 are one number’ is just as bad from a logical point (...) of view. In normal English these two sentences are idiomatically taken to express the true proposition that ‘the number 3 is the number 2+1’. Another idiomatic convention that interferes with clarity about equality and identity occurs in discussion of numbers: it is usual to write ‘3 equals 2+1’ when “3 is 2+1” is meant. When ‘3 equals 2+1’ is written there is a suggestion that 3 is not exactly the same number as 2+1 but that they merely have the same value. This becomes clear when we say that two of the sides of a triangle are equal if the two angles they subtend are equal or have the same measure. -/- Acknowledgements: Robert Barnes, Mark Brown, Jack Foran, Ivor Grattan-Guinness, Forest Hansen, David Hitchcock, Spaulding Hoffman, Calvin Jongsma, Justin Legault, Joaquin Miller, Tania Miller, and Wyman Park. -/- ► JOHN CORCORAN AND ANTHONY RAMNAUTH, Equality and identity. Philosophy, University at Buffalo, Buffalo, NY 14260-4150, USA E-mail: [email protected] The two halves of one line are equal but not identical [one and the same]. Otherwise the line would have only one half! Every line equals infinitely many other lines, but no line is [identical to] any other line—taking ‘identical’ strictly here and below. Knowing that two lines equaling a third are equal is useful; the condition “two lines equaling a third” often holds. In fact any two sides of an equilateral triangle is equal to the remaining side! But could knowing that two lines being [identical to] a third are identical be useful? The antecedent condition “two things identical to a third” never holds, nor does the consequent condition “two things being identical”. If two things were identical to a third, they would be the third and thus not be two things but only one. The plural predicate ‘are equal’ as in ‘All diameters of a given circle are equal’ is useful and natural. ‘Are identical’ as in ‘All centers of a given circle are identical’ is awkward or worse; it suggests that a circle has multiple centers. Substituting equals for equals [replacing one of two equals by the other] makes sense. Substituting identicals for identicals is empty—a thing is identical only to itself; substituting one thing for itself leaves that thing alone, does nothing. There are as many types of equality as magnitudes: angles, lines, planes, solids, times, etc. Each admits unit magnitudes. And each such equality analyzes as identity of magnitude: two lines are equal [in length] if the one’s length is identical to the other’s. Tarski [1] hardly mentioned equality-identity distinctions (pp. 54-63). His discussion begins: -/- Among the logical concepts […], the concept of IDENTITY or EQUALITY […] has the greatest importance. -/- Not until page 62 is there an equality-identity distinction. His only “notion of equality”, if such it is, is geometrical congruence—having the same size and shape—an equivalence relation not admitting any unit. Does anyone but Tarski ever say ‘this triangle is equal to that’ to mean that the first is congruent to that? What would motivate him to say such a thing? This lecture treats the history and philosophy of equality-identity distinctions. [1] ALFRED TARSKI, Introduction to Logic, Dover, New York, 1995. [This is expanded from the printed abstract.] . (shrink)

Property-identical divine-command theory (PDCT) is the view that being obligatory is identical to being commanded by God in just the way that being water is identical to being H2O. If these identity statements are true, then they express necessary a posteriori truths. PDCT has been defended in Robert M. Adams (1987) and William Alston (1990). More recently Mark C. Murphy (2002) has argued that property-identical divine-command theory is inconsistent with two well-known and well-received theses: the free-command thesis and the supervenience (...) thesis. I show that Murphy's argument is vitiated by mistaken assumptions about the substitutivity of metaphysical identicals in contexts of supervenience. The free-command thesis and the supervenience thesis therefore pose no serious threat to PDCT. (Published Online August 11 2004). (shrink)

Mares and Goldblatt, 163–187, 2006) provided an alternative frame semantics for two quantified extensions of the relevant logic R. In this paper, I show how to extend the Mares-Goldblatt frames to accommodate identity. Simpler frames are provided for two zero-order logics en route to the full logic in order to clarify what is needed for identity and substitution, as opposed to quantification. I close with a comparison of this work with the Fine-Mares models for relevant logics with identity and (...) a discussion of constant and variable domains. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Convention for Protection of Human Rights and Dignity of the Human Being with Regard to the Application of Biology and Biomedicine: Convention on Human Rights and BiomedicineCouncil of EuropePreambleThe Member States of the Council of Europe, the other States and the European Community signatories hereto,Bearing in mind the Universal Declaration of Human Rights proclaimed by the General Assembly of the United Nations on 10 December 1948;Bearing in mind the (...) Convention for the Protection of Human Rights and Fundamental Freedoms of 4 November 1950;Bearing in mind the European Social Charter of 18 October 1961;Bearing in mind the International Covenant on Civil and Political Rights and the International Covenant on Economic, Social and Cultural Rights of 16 December 1966;Bearing in mind the Convention for the Protection of Individuals with Regard to Automatic Processing of Personal Data of 28 January 1981;Bearing also in mind the Convention on the Rights of the Child of 20 November 1989;Considering that the aim of the Council of Europe is the achievement of a greater unity between its members and that one of the methods by which that aim is to be pursued is the maintenance and further realisation of human rights and fundamental freedoms;Conscious of the accelerating developments in biology and medicine;Convinced of the need to respect the human being both as an individual and as a member of the human species and recognising the importance of ensuring the dignity of the human being; [End Page 277]Conscious that the misuse of biology and medicine may lead to acts endangering human dignity;Affirming that progress in biology and medicine should be used for the benefit of present and future generations;Stressing the need for international co-operation so that all humanity may enjoy the benefits of biology and medicine;Recognising the importance of promoting a public debate on the questions posed by the application of biology and medicine and the responses to be given thereto;Wishing to remind all members of society of their rights and responsibilities;Taking account of the work of the Parliamentary Assembly in this field, including Recommendation 1160 (1991) on the preparation of a Convention on bioethics;Resolving to take such measures as are necessary to safeguard human dignity and the fundamental rights and freedoms of the individual with regard to the application of biology and medicine;Have agreed as follows:Chapter IGeneral provisionsArticle 1. (Purpose and object)Parties to this Convention shall protect the dignity and identity of all human beings and guarantee everyone, without discrimination, respect for their integrity and other rights and fundamental freedoms with regard to the application of biology and medicine.Each Party shall take in its internal law the necessary measures to give effect to the provisions of this Convention.Article 2. (Primacy of the human being)The interests and welfare of the human being shall prevail over the sole interest of society or science.Article 3. (Equitable access to health care)Parties, taking into account health needs and available resources, shall take appropriate measures with a view to providing, within their jurisdiction, equitable access to health care of appropriate quality. [End Page 278]Article 4. (Professional standards)Any intervention in the health field, including research, must be carried out in accordance with relevant professional obligations and standards.Chapter IIConsentArticle 5. (General rule)An intervention in the health field may only be carried out after the person concerned has given free and informed consent to it.This person shall beforehand be given appropriate information as to the purpose and nature of the intervention as well as on its consequences and risks.The person concerned may freely withdraw consent at any time.Article 6. (Protection of persons not able to consent)1. Subject to Articles 17 and 20 below, an intervention may only be carried out on a person who does not have the capacity to consent, for his or her direct benefit.2. Where, according to law, a minor does not have the capacity to consent to an intervention, the intervention may only be carried out with the authorisation of his or her representative or an authority or a person or... (shrink)

Many competent speakers initially judge that (i) is true and (ii) isfalse, though they know that (iii) is true. (i) Superman leaps more tallbuildings than Clark Kent. (ii) Superman leaps more tall buildings thanSuperman. (iii) Superman is identical with Clark Kent. Semanticexplanations of these intuitions say that (i) and (ii) really can differin truth-value. Pragmatic explanations deny this, and say that theintuitions are due to misleading implicatures. This paper argues thatboth explanations are incorrect. (i) and (ii) cannot differ intruth-value, yet (...) the intuitions are not due to implicatures, but ratherto mistakes in evaluating (i) and (ii). (shrink)