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Identity Statements

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lightbulbAbout this topic
Identity statements are declarative sentences that assert the equivalence or sameness of two entities, often expressed in the form 'A is B.' They are fundamental in logic, philosophy, and linguistics, serving to clarify relationships between concepts, objects, or individuals within various theoretical frameworks.
lightbulbAbout this topic
Identity statements are declarative sentences that assert the equivalence or sameness of two entities, often expressed in the form 'A is B.' They are fundamental in logic, philosophy, and linguistics, serving to clarify relationships between concepts, objects, or individuals within various theoretical frameworks.

Key research themes

1. How do philosophical and logical accounts characterize the nature and semantics of identity statements?

This theme investigates various conceptual and logical frameworks developed to understand the semantics, meaning, and logical properties of identity statements. It explores objections to classical treatments, introduces novel logical systems, and debates the adequacy of identity criteria from metaphysical and formal viewpoints.

Key finding: The paper argues against the traditional relational analyses of identity statements (object-view and name-view), positing that identity statements are sui generis and do not ascribe a relation. Through diagrammatic models, it... Read more
Key finding: This work proposes a non-classical, extensionalist semantics where singular terms denote structured individuals ('complexes') rather than atomic particulars. It distinguishes between formal and material identity by... Read more
Key finding: The paper introduces three formal logical systems (IL1, IL2, IL3) centered on identity and in-identity, demonstrating completeness results. It advocates for identity logics as pedagogically superior to propositional and... Read more
Key finding: This study identifies that candidate relations intended as identity criteria often fail logical requirements, particularly transitivity, undermining their adequacy. It systematically evaluates methods to approximate such... Read more
Key finding: The paper proves that any finitely axiomatized first-order theory incorporating identity criteria can be reformulated as a conjunction of a non-triviality statement and a weakened criterion of identity. It highlights that... Read more

2. What are the philosophical, theological, and ethical implications of identity concepts in personal, social, and religious contexts?

This theme focuses on identity beyond formal logic, investigating how identity shapes social-political theories, religious doctrines (especially Trinitarian identity), and individual self-understanding. It evaluates influential notions of identity in liberal political theory, analyzes identity challenges at the state level, and discusses how religious identity statements intersect with logic and metaphysics.

Key finding: This article critically examines Akeel Bilgrami's philosophical notion of identity as fundamentally tied to sustained commitments that individuals 'tie themselves to the mast' to preserve against change. It identifies the... Read more
Key finding: The paper addresses logical incoherence challenges to Classical Trinitarianism arising from interpreting the statement 'the Son is God' as numerical identity. It proposes a nuanced semantic framework that distinguishes a... Read more

3. How can alternative logical frameworks and semantic theories enhance the modeling and understanding of identity and equivalence in mathematics and computer science?

This theme explores novel logical systems and semantic frameworks that attempt to overcome classical logic's limitations in effectively capturing identity's conceptual and applied nuances. It involves introducing new equivalence notions, like descriptive equivalence, alternative logics grounded on identity relations, and approximate satisfaction of identity equations in topological and metric contexts.

Key finding: The paper introduces a new formal logic (LD), based on descriptive equivalence rather than classical truth-functional equivalence. It constructs a semantics using novel algebras, proving soundness and completeness results.... Read more
Key finding: The paper develops harmonious introduction and elimination rules for the identity operator within an inferentialist logical framework, responding to challenges that standard identity rules lack harmony (logical coherence). It... Read more
Key finding: This work investigates the compatibility of topological spaces with sets of equations via approximate satisfaction metrics. It introduces a measure λ_A(Σ) quantifying how closely a space A with metric d can satisfy equations... Read more

All papers in Identity Statements

Resumen: En "¿Puede Frege formular el puzzle de Frege?", Stavroula Glezakos argumenta que Frege no puede formular su puzzle sin apelar a algo como la noción teórica de Sinn y, así, el denominado puzzle no afecta a los no-fregeanos, y los... more
Classical Trinitarians claim that Jesus—the Son of God—is truly God and that there is only one God and the Father is God, the Spirit is God, and the Father, Son, and Spirit are distinct. However, if the identity statement that ‘the Son is... more
an anonymous referee, and audiences at Simon Fraser University, the Society for Exact Philosophy, the Western Canadian Philosophical Association, and the Russell vs. Meinong Conference for helpful comments on various aspects of this... more
In this chapter I chart the history of the different English translations of ‘Bedeutung’ in Frege’s writings, setting them in context, explaining their rationale, and exploring some of the philosophical issues raised.
an anonymous referee, and audiences at Simon Fraser University, the Society for Exact Philosophy, the Western Canadian Philosophical Association, and the Russell vs. Meinong Conference for helpful comments on various aspects of this... more
an anonymous referee, and audiences at Simon Fraser University, the Society for Exact Philosophy, the Western Canadian Philosophical Association, and the Russell vs. Meinong Conference for helpful comments on various aspects of this... more
In “On Denoting” and to some extent in “Review of Meinong and Others, Untersuchungen zur Gegenstandstheorie und Psychologie” published in the same issue of Mind in 1905, Russell presents not only his famous elimination (or contextual... more
This paper is about the meaning and function of identity statements involving proper names. There are two prominent views on this topic, according to which identity statements ascribe a relation: the object-view, on which identity... more
Francaises sg aussi architectural ;i) et de plus, il n'est pas vrai qu'il n'ajamais employe la comparaison entre la musique et 1'architecture : par exemple, en 1888 dans " Scolie }> faisant suite 5 sa traduction des Pob'mes d'Ecigar... more
Le medecin Gaultier et le courant cache du materialisme emergentiste du XVIIIC siecle Je veudrais, tout d'abord, defifiir le terme d'timergence. T. S. Hall en rend remarquablement compte
un emploi pronominal inconnu ou mal connu du verbe laissier et de son equivalent occitan laissar La Chanson de Guillaume, ceuvre du milieu du 12e sieclei), conservee dans un seul rnanuscrit posterieur d'un sibcle (British Museum Add.... more
Nous pouvons consid6rer cette possibilit6 de d6velopper un paradigme comme un aspect permettant une formation productive. Parmi Ies compos6s de ce type, certains d'entre eux sont inscrits comme tels dans le dictionnaire, mais la plupart... more
Saison en linfor a 6t6 vouee cemme par une sorte de fatalit6 b des modes particuliers de lecture. D'un c6t6, il y a sa logique interne, son intention de rupture, que semble venir confirmer le mythe d'un abandon immediat de la litt6rature,... more
In “On Denoting” and to some extent in “Review of Meinong and Others, Untersuchungen zur Gegenstandstheorie und Psychologie” published in the same issue of Mind in 1905, Russell presents not only his famous elimination (or contextual... more
Diderot aimait conter : tout Ie monde le dit. Diderot causeur, bavard, au point d'exceder la tsarine : on 1'a maintes fois rep6t6. Mais qu'est-ce que conter, lorsqu'il s'agit d'un 6crivain comme Diderot ? La SocieteJaponaise deLangue et... more
My aim in the following observations is simply to remind Frege’s motivations for introducing the Sinn, and some important facts about his use of ‘=’. I think they are relevant at the time of scrutinizing what has been called “Frege’s... more
For Russell, a denoting phrase is any phrase (other than a proper name) that can stand as the grammatical subject of a sentence – e.g., "the author of Waverley," "the King of France," "a man," "some... more
In 'On Denoting' and to some extent in 'Review of Meinong and Others, Untersuchungen zur Gegenstandstheorie und Psychologie', published in the same issue of Mind (Russell, 1905a,b), Russell presents not only his famous... more
In the case of an actual proper name such as 'Aristotle' opinions as to the Sinn may differ. It might, for instance, be taken to be the following: the pupil of Plato and teacher of Alexander the Great. Anybody who does this will... more
The opening passage of Frege's best-known paper is hard to understand. On a straightforward reading what Frege does in the passage is this. He first details an argument which had once convinced him that 'a=b' does not express a relation... more
How proper names refer to objects" and "Do proper names have senses", and the most important problem "How non referring names work" have always been problems in the philosophy of language. There are two important philosophical approaches... more
The story we've been telling has it that a name denotes an individual and an open sentence represents a property, and the sentence obtained by substituting a name for free occurrences of a variable in an open sentence is true if and only... more
In "Practical Knowledge of Language", C.-h. Tsai criticizes the arguments in "Swimming and Speaking Spanish" (this issue, pp. 331-341), on the grounds that its account of knowledge of language as knowledge-how is mistaken. In its place,... more
In 'On Denoting' and to some extent in 'Review of Meinong and Others, Untersuchungen zur Gegenstandstheorie und Psychologie', published in the same issue of Mind (Russell, 1905a,b), Russell presents not only his famous... more
At the beginning of the article “Der Gedanke”, Frege disposes of a long-standing philosophical doctrine in less than a paragraph. The discarded doctrine is nothing less than the so-called classical definition of truth, which makes it... more
In classical identity theory, variables range over simple units, devoid of ontological structure, with no bearing on the logical dimensions of identity. In this paper, the ontology-free thematizations of identity in vogue among... more
La SocieteJaponaise deLangue et Mtterature Francaises V6nigme des 6nonc6s d'identit6 de type K a = b )> : Une solution grammaticale 1. V6nigme des 6nonc6s d'identit6 de type K a = b )
A detailed interpretation is provided of the 'Gray's Elegy' passage in Russell's 'On Denoting' . The passage is sufficiently obscure that its principal lessons have been independently rediscovered. Russell attempts to demonstrate that the... more
Call a semantics for singular terms extensionalist if it embraces (1) and classical if it embraces (2). 1. The meaning of a singular term is its reference. 2. The reference of a singular term is logically simple. Call such a... more
It is argued that the semantic difference between sentences of the form “a = a” and “a = b” reflects a difference in their truth-makers. My account of these truth-makers combines a referential semantics--singular terms contribute nothing but... more
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