A central problem within an influential strand of recent philosophy of mind has been to explain the “conformity of mind to thing” that characterizes knowledge. John Haldane has argued that this problem can be best addressed by a development of Thomas Aquinas’s account of the “formal identity” of the knowing subject with the object known. However, such a development is difficult to present in a manner perspicuous to a contemporary audience. This paper seeks to present a persuasive account (...) of formal identity, taking sensory cognition of the individual object as the primary case for examination. Formal identity is initially explored usingthe notion of encoding, or the systematic transfer of information reflecting efficient and formal causal processes. The mathematical notion of “isomorphism” is thenemployed to describe precisely the features of encoding needed for formal identity. Forms are defined as formally identical if and only if they are isomorphic. (shrink)

In De Anima Book III, Aristotle subscribed to a theory of formal identity between the human mind and the extra-mental objects of our understanding. This has been one of the most controversial featu...

In the so-called modern age, a transition can be observed in Western thought regarding this issue of tolerance. A perceptible shift can be seen in the understanding of tolerance as mere endurance to attempts to conceive of tolerance as a kind of well-grounded acceptance. It is regrettable, however, that this change in thinking has often remained hypothetical rather than heuristic. This certainly has to do with the fact that most of the time only large-scale theological, philosophical, or political projects were (...) negotiated. In this case, as is often happens, the directly concerned individual, the concrete person in the course of the demonstration efforts, was lost. We want to counter this loss with our study. In our investigation, which is based on a phenomenological reflection, we want to examine tolerance and respect as an existential problem couched within an individual. We wish to consider a person who desires to be tolerant and respectful; a person who accepts tolerance and respect as an existential task. (shrink)

Steven French and Decio Krause examine the metaphysical foundations of quantum physics. They draw together historical, logical, and philosophical perspectives on the fundamental nature of quantum particles and offer new insights on a range of important issues. Focusing on the concepts of identity and individuality, the authors explore two alternative metaphysical views; according to one, quantum particles are no different from books, tables, and people in this respect; according to the other, they most certainly are. Each view comes with (...) certain costs attached and after describing their origins in the history of quantum theory, the authors carefully consider whether these costs are worth bearing. Recent contributions to these discussions are analyzed in detail and the authors present their own original perspective on the issues. The final chapter suggests how this perspective can be taken forward in the context of quantum field theory. (shrink)

We propose a novel, ontological approach to studying mathematical propositions and proofs. By “ontological approach” we refer to the study of the categories of beings or concepts that, in their practice, mathematicians isolate as fruitful for the advancement of their scientific activity (like discovering and proving theorems, formulating conjectures, and providing explanations). We do so by developing what we call a “formal ontology” of proofs using semantic modeling tools (like RDF and OWL) developed by the computer science community. In (...) this article, (i) we describe this new approach and, (ii) to provide an example, we apply it to the problem of the identity of proofs. We also describe open issues and further applications of this approach (for example, the study of purity of methods). We lay some foundations to investigate rigorously and at large scale intellectual moves and attitudes that underpin the advancement of mathematics through cognitive means (carving out investigationally valuable concepts and techniques) and social means (like communication, collaboration, revision, and criticism of specific categories, inferential patterns, and levels of analysis). Our approach complements other types of analysis of proofs such as reconstruction in a deductive system and examination through a proof-assistant. (shrink)

Following the global financial crisis, banks have become more regulated to advance ethical sales cultures throughout the sector. Based on case studies of three retail banks, we find that they construct the ‘appropriate advisor’ in different ways. Inspired by Bakhtin’s work on ethics, we propose a vocabulary of relational ethics centered on the ‘answerable self.’ We argue that this vocabulary is apt for studying and discussing how organizations advance ethical sales cultures in ways that instead of encouraging value congruence and (...) alignment allow for ethical openness. In such cultures, employees—as moral agents—are morally questioning, critically self-reflexive, and answerable for their own actions toward others in their social relationships. Our paper makes three theoretical contributions, namely, problematizing the idea of cultural alignment and value congruence, demonstrating that identity regulation can both comprise and support the ‘answerable self,’ and advancing our understanding of the interdependence of ethical openness and ethical closure in fostering ethical sales cultures. (shrink)

Review of Steven French, Décio Krause: 'Identity in Physics: A Historical, Philosophical and Formal Analysis', Oxford: Oxford University Press, 2006.

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 first quodlibetal question by William of Alnwick is a reply to John Duns Scotus' Quaestio de Formalitatibus, where the latter clarified his understanding of the formal distinction: ‘formal non-identity’ of the personal properties in God (and of the divine attributes) does not preclude a formal distinction if the latter is conceived as a distinction weakened by the modifier ‘formal’. Whereas Scotus' Quaestio has been subjected to a detailed analysis by Stephen Dumont, “Duns Scotus’ Parisian (...) Question”, there is as yet no such analysis of Alnwick's response. In the present paper his position is explained in detail. Alnwick rejects Scotus' view of ‘formal’ as a weakening modifier; he argues that the formal distinction necessarily is unqualified and may still import too much of unwanted realism in the matter at hand. Both Scotus and Alnwick acknowledge that the formal non-identity reflects the nature of things without falling back to a real distinction. But for Alnwick the right kind of distinction is a qualified distinction that is not a formal distinction. (shrink)

Formalizing Euclid’s first axiom. Bulletin of Symbolic Logic. 20 (2014) 404–5. (Coauthor: Daniel Novotný) -/- Euclid [fl. 300 BCE] divides his basic principles into what came to be called ‘postulates’ and ‘axioms’—two words that are synonyms today but which are commonly used to translate Greek words meant by Euclid as contrasting terms. -/- Euclid’s postulates are specifically geometric: they concern geometric magnitudes, shapes, figures, etc.—nothing else. The first: “to draw a line from any point to any point”; the last: the (...) parallel postulate. -/- Euclid’s axioms are general principles of magnitude: they concern geometric magnitudes and magnitudes of other kinds as well even numbers. The first is often translated “Things that equal the same thing equal one another”. -/- There are other differences that are or might become important. -/- Aristotle [fl. 350 BCE] meticulously separated his basic principles [archai, singular archê] according to subject matter: geometrical, arithmetic, astronomical, etc. However, he made no distinction that can be assimilated to Euclid’s postulate/axiom distinction. -/- Today we divide basic principles into non-logical [topic-specific] and logical [topic-neutral] but this too is not the same as Euclid’s. In this regard it is important to be cognizant of the difference between equality and identity—a distinction often crudely ignored by modern logicians. Tarski is a rare exception. The four angles of a rectangle are equal to—not identical to—one another; the size of one angle of a rectangle is identical to the size of any other of its angles. No two angles are identical to each other. -/- The sentence ‘Things that equal the same thing equal one another’ contains no occurrence of the word ‘magnitude’. This paper considers the problem of formalizing the proposition Euclid intended as a principle of magnitudes while being faithful to the logical form and to its information content. (shrink)

The paper is an extended version of a talk given to the XXXth Conference on the History of Logic devoted to the work of Professor Roman Suszko . Its aim is to present Sentential Calculus with Identity in comparison with other formalizations of propositional identity.

This is a short review of Identity in Physics, by Steven French and Decio Krause. (Tip: if you’re only going to read one chapter, make it chapter 4, where the philosophical juice is especially concentrated.).

The physics and metaphysics of identity and individuality Content Type Journal Article DOI 10.1007/s11016-010-9463-7 Authors Don Howard, Department of Philosophy and Graduate Program in History and Philosophy of Science, University of Notre Dame, Notre Dame, IN 46556, USA Bas C. van Fraassen, Philosophy Department, San Francisco State University, 1600 Holloway Avenue, San Francisco, CA 94132, USA Otávio Bueno, Department of Philosophy, University of Miami, Coral Gables, FL 33124, USA Elena Castellani, Department of Philosophy, University of Florence, Via Bolognese 52, (...) 50139 Florence, Italy Laura Crosilla, Department of Pure Mathematics, School of Mathematics, University of Leeds, Leeds, LS2 9JT UK Steven French, Department of Philosophy, University of Leeds, Leeds, UK Décio Krause, Department of Philosophy, Federal University of Santa Catarina, 88040-900 Campus Trindade, Florianópolis, SC Brazil Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796. (shrink)

In the past years, the relevance of Thomas Aquinas's theory of cognition for contemporary debates on epistemology has been widely discussed. That theory claims that mind and world are formally identical and that this relationship overcomes various problems associated with scepticism concerning mental representation. The proposal, however, is grounded on the idea that the world can act on the mind through a relation of formal causation. This thesis attempts to develop a Thomistic theory of formal causation which may (...) be suitable for a realist account of mental representation and which may meet the requirements prompted by current discussions. The suggested view is grounded on Aquinas's metaphysics, according to which the world is constituted of substances. The claim that change is possible since substances are hylomorphically constituted is defended. Aquinas's claim that some substances have forms which may act independently of matter is also supported. The paradigmatic examples are human souls, i.e. the forms of human beings, whose higher cognitive capacity, i.e. thinking, can be in principle carried on without the need of any material organ. A Thomistic theory of causation is subsequently proposed. It is argued that hylomorphism explains the distinction among four species of causes. Aquinas's attempt to explain causal relations conditionally is developed along the lines suggested by John Mackie's INUS conditional analysis. Jaegwon Kim's implementation of Mackie's proposal through an object-based metaphysics of events is then adapted to the hylomorphical account of substances. On these grounds, a theory of formal causation can be proposed and applied to Aquinas's theory of mental representation. The ensuing proposal is offered not in the spirit of historical exegesis but as a substantive philosophical account and it is Thomistic only in the broad sense that it is built on Aquinas's metaphysics and is consistent with his claims on causation. (shrink)

Multi-national corporations (MNCs) have been criticised for not behaving ethically in some situations, which could have a negative effect on their reputation. This study examines the ethics of a large MNC in its relationship with its suppliers. A brief literature review of corporate identity, business ethics and buyer–supplier relationships is undertaken. The views and perceptions of the buying staff and the suppliers to a large South African MNC are obtained and discussed. The results indicate that this MNC has a (...) good corporate reputation among both its suppliers (an important stakeholder) and its own buying department. The existence and implementation of formal codes of ethics was found to be a necessary, but not sufficient condition for good ethical practice. Candid relationships with suppliers emerged as a second and important factor. Ethical perceptions of buyers by suppliers are driven by the management of corporate identity, through the elements of ethical standards and candid relationships. We present a model of corporate identity/reputation in Buyer–Supplier Relationships. (shrink)

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)

Absolute identity seems at first sight to be presupposed in the branch of formal logic called identity theory. Classical identity theory may be obtained by adjoining a single schema to ordinary quantification theory.

Questions about the relation between identity and discernibility are important both in philosophy and in model theory. We show how a philosophical question about identity and dis- cernibility can be ‘factorized’ into a philosophical question about the adequacy of a formal language to the description of the world, and a mathematical question about discernibility in this language. We provide formal definitions of various notions of discernibility and offer a complete classification of their logical relations. Some new (...) and surprising facts are proved; for instance, that weak dis- cernibility corresponds to discernibility in a language with constants for every object, and that weak discernibility is the most discerning nontrivial discernibility relation. (shrink)

Steven French and Décio Krause have written what bids fair to be, for years to come, the definitive philosophical treatment of the problem of the individuality of elementary particles in quantum mechanics and quantum field theory. The book begins with a long and dense argument for the view that elementary particles are most helpfully regarded as non-individuals, and it concludes with an earnest attempt to develop a formal apparatus for describing such non-individual entities better suited to the task than (...) our customary set theory. Along the way one is treated to a compendious philosophical history of quantum statistics and a well-nigh exhaustive (I’m tempted to say, “exhausting”) analytical history of philosophical responses to the quantum theory’s prima facie challenge to classical notions of particle individuality. The book is also a salvo from the headquarters artillery company of the “pro” side in the contemporary structuralism wars, and an essay in metaphysical naturalism. Whew! There are too many places where the friendly critic wants to engage the argument, and few where the authors have not already anticipated such engagement. I take this as my excuse, then, for offering not any systematic response to the whole project, but just some questions and observations about several points that caught my attention. (shrink)

Completed in 1983, this work culminates nearly half a century of the late Alfred Tarski's foundational studies in logic, mathematics, and the philosophy of science. Written in collaboration with Steven Givant, the book appeals to a very broad audience, and requires only a familiarity with first-order logic. It is of great interest to logicians and mathematicians interested in the foundations of mathematics, but also to philosophers interested in logic, semantics, algebraic logic, or the methodology of the deductive sciences, and to (...) computer scientists interested in developing very simple computer languages rich enough for mathematical and scientific applications. The authors show that set theory and number theory can be developed within the framework of a new, different, and simple equational formalism, closely related to the formalism of the theory of relation algebras. There are no variables, quantifiers, or sentential connectives. Predicates are constructed from two atomic binary predicates (which denote the relations of identity and set-theoretic membership) by repeated applications of four operators that are analogues of the well-known operations of relative product, conversion, Boolean addition, and complementation. All mathematical statements are expressed as equations between predicates. There are ten logical axiom schemata and just one rule of inference: the one of replacing equals by equals, familiar from high school algebra. Though such a simple formalism may appear limited in its powers of expression and proof, this book proves quite the opposite. The authors show that it provides a framework for the formalization of practically all known systems of set theory, and hence for the development of all classical mathematics. The book contains numerous applications of the main results to diverse areas of foundational research: propositional logic; semantics; first-order logics with finitely many variables; definability and axiomatizability questions in set theory, Peano arithmetic, and real number theory; representation and decision problems in the theory of relation algebras; and decision problems in equational logic. (shrink)

Identity criteria are used to confer ontological respectability: Only entities with clearly determined identity criteria are ontologically acceptable. From a logical point of view, identity criteria should mirror the identity relation in being reflexive, symmetrical, and transitive. However, this logical constraint is only rarely met. More precisely, in some cases, the relation representing the identity condition fails to be transitive. We consider the proposals given so far to give logical adequacy to inadequate identity conditions. (...) We focus on the most refined proposal and expand its formal framework by taking into account two further aspects that we consider essential in the application of identity criteria to obtain logical adequacy: contexts and granular levels. (shrink)

In this paper I try to answer four basic questions: (1) How the concept of God is to be represented? (2) Are there any logical principles governing it? (3) If so, what kind of logic lies behind them? (4) Can there be a logic of the concept of God? I address them by presenting a formal-logical account to the concept of God. I take it as a methodological desideratum that this should be done within the simplest existing logical formalism. (...) I start with first-order logic (FOL) with identity, and then show that its simplest modal extension (SQML, or the simplest quantified modal logic) is enough for us to formalize a minimally satisfactory theory of the concept of God. I focus exclusively on the monotheistic concept of God. (shrink)

Identity is a transitive relation, according to all standard accounts. Necessarily, if x = y and y = z, then x = z. However, people sometimes say that two objects, x and z, are the same as a third, y, even when x and z have different properties (thus, x = y and y = z, but x ≠ z). In the present experiments, participants read stories about an iceberg that breaks into two icebergs, one to the east and (...) the other to the west. Many participants (32–54%, in baseline conditions across experiments) decided that both successors were the original iceberg, despite the different spatial locations of the successors. Experiment 1 shows that this tendency is not due to participants failing to understand both to mean both are simultaneously the original. Similarly, Experiment 2 demonstrates that the tendency is not solely due to their interpreting the question to be about properties of the icebergs rather than about the icebergs themselves. Experiments 3 and 4 suggest, instead, that participants may understand Which is the original? to mean Which, in its own right, is entitled to be the original? Emphasizing entitlement increases the number of seemingly intransitive responses, whereas emphasizing the formal properties of identity decreases them. (shrink)

Agency and identity -- Necessitation -- Acts and actions -- Aristotle and Kant -- Agency and practical identity -- The metaphysics of normativity -- Constitutive standards -- The constitution of life -- In defense of teleology -- The paradox of self-constitution -- Formal and substantive principles of reason -- Formal versus substantive -- Testing versus weighing -- Maximizing and prudence -- Practical reason and the unity of the will -- The empiricist account of normativity -- The (...) rationalist account of normativity -- Kant on the hypothetical imperative -- Against particularistic willing -- Deciding and predicting -- Autonomy and efficacy -- The function of action -- The possibility of agency -- Non-rational action -- Action -- Attribution -- The psychology of action -- Expulsion from the garden : the transition to humanity -- Instinct, emotion, intelligence, and reason -- The parts of the soul -- Inside or outside -- Pull yourself together -- The constitutional model -- Models of the soul -- The city and the soul -- Platonic virtues -- Justice : substantive, procedural, and platonic -- Kant and the constitutional model -- Defective action -- The problem of bad action -- Being governed by the wrong law -- Or five bad constitutions -- Conceptions of evil -- Degrees of action -- Integrity and interaction -- Deciding to be bad -- The ordinary cases -- Dealing with the disunified -- Kant's theory of interaction -- My reasons -- Deciding to treat someone as an end in himself -- Interacting with yourself -- How to be a person -- What's left of me? (shrink)

Review: French, Steven& Krause, Décio. Identity in Physics: a Historical, Philosophical, and Formal Analysis.

The key to understanding self-identity is identifying the transcendental structures that make a temporally extended, continuous, and unified experiential life possible. Self-identity is rooted in the formal, temporalizing structure of intentional experience that underlies psychological continuity. Personal identity, by contrast, is rooted in the content of the particular flow of experience, in particular and primarily, in the convictions adopted passively or actively in reflection by a self-identical subject in the light of her social and traditional inheritances. (...) Secondarily, a person’s identity is rooted in others’ characterizations of that person in the light of the social conventions and constructs of the cultures and traditions that have shaped the personal identity of the ones who make the attributions. Personal identity, on this view, is fundamentally rooted in beliefs, traits—especially character traits—sentiments, and moods, that is, in the subject’s convictions about the true, the good, and the right—and in the commitments to the pursuit of (apparently) worthwhile goods and to the practical identities rooted in those convictions. (shrink)

A recurrent issue in linguistic theory and psychology concerns the cognitive status of memorized lists and their internal structure. In morphological theory, the collections of inflected forms of a given noun, verb, or adjective into inflectional paradigms are thought to constitute one such type of list. This book focuses on the question of which elements in a paradigm can stand in a relation of partial or total phonological identity. Leading scholars consider inflectional identity from a variety of theoretical (...) perspectives, with an emphasis on both case studies and predictive theories of where syncretism and other "paradigmatic pressures" will occur in natural language. The authors consider phenomena such as allomorphy and syncretism while exploring questions of underlying representations, the formal properties of markedness, and the featural representation of conjugation and declension classes. They do so from the perspective of contemporary theories of morphology and phonology, including Distributed Morphology and Optimality Theory, and in the context of a wide range of languages, among them Amharic, Greek, Romanian, Russian, Saami, and Yiddish. The subjects addressed in the book include the role of featural decomposition of morphosyntactic features, the status of paradigms as the unit of syncretism, asymmetric effects in identity-dependence, and the selection of a base-of-derivation. The Bases of Inflectional Identity will interest linguists and cognitive scientists, especially students and scholars of phonological theory and the phonology-morphology and mind-language interfaces at graduate level and above. (shrink)

The field of iterated belief change has focused mainly on revision, with the other main operator of AGM belief change theory, i.e. contraction, receiving relatively little attention. In this paper we extend the Harper Identity from single-step change to define iterated contraction in terms of iterated revision. Specifically, just as the Harper Identity provides a recipe for defining the belief set resulting from contracting A in terms of (i) the initial belief set and (ii) the belief set resulting (...) from revision by ¬A, we look at ways to define the plausibility ordering over worlds resulting from contracting A in terms of (iii) the initial plausibility ordering, and (iv) the plausibility ordering resulting from revision by ¬A. After noting that the most straightforward such extension leads to a trivialisation of the space of permissible orderings, we provide a family of operators for combining plausibility orderings that avoid such a result. These operators are characterised in our domain of interest by a pair of intuitively compelling properties, which turn out to enable the derivation of a number of iterated contraction postulates from postulates for iterated revision. We finish by observing that a salient member of this family allows for the derivation of counterparts for contraction of some well known iterated revision operators, as well as for defining new iterated contraction operators. (shrink)

U radu se nudi opis konteksta unutar kojeg je formuliran poznati dokaz za nužnost identiteta. Iznosi se formalni prikaz ovog dokaza kako ga je formulirao poznati filozof i logičar Saul Kripke. Također se razmatra gledište filozofa Allana Gibbarda koji nasuprot Kripkeu brani tvrdnju da neki iskazi identiteta mogu biti kontingentni. Osnovni cilj rada je upoznati domaćeg čitatelja s formalnim aspektom rasprave o nužnosti identiteta te dati kratki pregled konteksta unutar kojeg su formulirani argumenti za nužnost identiteta. In the paper, we (...) offer an overview of the context within which the well-known proof of the necessity of identity is formulated. A formal account of this proof is presented as formulated by the renowned philosopher and logician Saul Kripke. Furthermore, we discuss the account of the philosopher Allan Gibbard, who defends the claim that some statements of identity can be contingent. The main goal of the paper is to acquaint the readers who understand the Croatian language with the formal aspect of the discussion on the necessity of identity and to give a brief overview of the context within which the arguments for the necessity of identity are formulated. (shrink)

Axel Honneth draws a distinction between three types of recognition: (1) love, (2) respect and (3) social esteem. In his The Struggle for Recognition, the recognition of cultural particularity is situated in the third sphere. It will here be argued that the logic of recognition of cultural identity also demands a non-evaluative recognition, namely a respect for difference. Difference-respect is formal because it is a recognition of the value of a particular culture not "for society" or "as such", (...) but for the social group involved. Yet, although it is formal, difference-respect cannot be reduced to respect for personal autonomy and its preconditions, as Honneth wrongly suggests in Redistribution or Recognition? It is argued here that difference-respect is oriented towards another dimension of the person, namely social attachments. This kind of respect entails a separate register of formal recognition with a corresponding concept of personal identity and a parallel category of social disrespect. What morally justifies difference-respect from a recognition-theoretic approach is the practical relation-to-self that thus becomes possible, namely self-respect as a sense of belonging. The formal conception of the good life that Honneth articulates should include the insight that this sense of belonging is as much a necessary condition for the good life as is personal autonomy. (shrink)

In this paper we analyse the connection between the contested ethno-cultural labelling of Gipsy-Travellers in Wales and their position of social marginalisation, with special reference to spatial issues, such as the provision of campsites and public housing. Our main aim is to show how the formal and informal (mis)labelling of minority groups leads to a number of morally and politically questionable outcomes in their treatment on the part of political authorities. Our approach combines a close reading of official policy (...) documents, government-commissioned and independent empirical research with a theoretical framework drawn mainly from contemporary political philosophy, and especially from the debate on redistribution and recognition. (shrink)

It is usually stated that quantum mechanics presents problems with the identity of particles, the most radical position—supported by E. Schrödinger—asserting that elementary particles are not individuals. But the subject goes deeper, and it is even possible to obtain states with an undefined particle number. In this work we present a set theoretical framework for the description of undefined particle number states in quantum mechanics which provides a precise logical meaning for this notion. This construction goes in the line (...) of solving a problem posed by Y. Manin, namely, to incorporate quantum mechanical notions at the foundations of mathematics. We also show that our system is capable of representing quantum superpositions. (shrink)

In contemporary society, identities—culture; race; ethnicity; gender; and lesbian, gay, bisexual, and transgender —are at the heart of discourses of belonging and related collectivist constructions of meaning. As distinct social markers, they clearly demarcate the society in ways that also have political implications. The discussion of identity politics below takes a nominally genealogical approach beginning with modern philosophy’s individualistic account. It then decenters this narrative and posits that the field has been ill-equipped to grapple with the power of (...) class='Hi'>identity as a source of belonging, a moral critique, and as a site of political conflict. Education is the primary context of the discussion, which is framed as the quest for cultural and social pluralism. Although the term identity has roots in Western philosophy and more recently in psychology, identity politics is a highly contested expression in education, political theory and in philosophy. Bernstein :47–74, 2005) traced its origin as a formal term to 1979, where social science scholars coined the phrase as a label for a type of activism. Its initial iteration pertained to persons with disabilities who challenged prevailing societal perceptions. Over the next two decades, scholars broadened its use to mean a category of collective action that included violent ethnic conflict and activist nationalism. Below, the discussion of the term begins with its semantic and philosophical provenance and explores its discursive engagement with the ever modifying meanings of gender, race or ethnicity and sexual orientation in society and education. It is association with these categories as forms of joint group membership that ipso facto gives rise to political activism to advance beliefs, bring about change or to promote a given worldview. (shrink)

The paper takes off from the problem of finding a proper content for the relation of identity as it holds or fails to hold among ordinary things or substances. The necessary conditions of identity are familiar, the sufficient conditions less so. The search is for conditions at once better usable than the Leibnizian Identity of Indiscernibles (independently suspect) and strong enough to underwrite all the formal properties of the relation.It is contended that the key to this (...) problem rests at the level of metaphysics and epistemology alike with a sortalist position. Sortalism is the position which insists that, if the question is whether a and b are the same, it has to be asked what are they? Any sufficiently specific answer to that question will bring with it a principle of activity or functioning and a mode of behaviour characteristic of some particular kind of thing by reference to which questions of persistence or non-persistence through change can be adjudicated.These contentions are illustrated by reference to familiar examples such as the human zygote, the Ship of Theseus and Shoemaker's Brown-Brownson. The first example is hostage for a mass of unproblematical cases. The problems presented by the second and third sort of examples arise chiefly (it is claimed) from an incompleteness in our conceptions of the relevant sort—the what the thing in question is. That incompleteness need not prevent us from knowing perfectly well which thing we are referring to. In the concluding section, sortalism is defended against various accusations of anthropocentrism.The paper touches on the interpretation of Heraclitus, Leibniz's theory of clear indistinct ideas, the difficulties of David Lewis's ‘perdurantist’ or stroboscopic view of persistence, four-dimensionalism, and the relation of personal identity both to experiential memory and to the particular bodily physiognomy of a subject. At some points—as in connection with the so-called Only a and b rule—the paper corrects, supplements or extends certain theses or formulations proposed in the author's Sameness and Substance Renewed (2001). (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)

Among the most interesting features of Homotopy Type Theory is the way it treats identity, which has various unusual characteristics. We examine the formal features of “identity types” in HoTT, and how they relate to its other features including intensionality, constructive logic, the interpretation of types as concepts, and the Univalence Axiom. The unusual behaviour of identity types might suggest that they be reinterpreted as representing indiscernibility. We explore this by defining indiscernibility in HoTT and examine (...) its relationship with identity. We argue that identity types are a primitive component of HoTT and cannot be reduced to indiscernibility. (shrink)

It is usually stated that quantum mechanics presents problems with the identity of particles, the most radical position—supported by E. Schrödinger—asserting that elementary particles are not individuals. But the subject goes deeper, and it is even possible to obtain states with an undefined particle number. In this work we present a set theoretical framework for the description of undefined particle number states in quantum mechanics which provides a precise logical meaning for this notion. This construction goes in the line (...) of solving a problem posed by Y. Manin, namely, to incorporate quantum mechanical notions at the foundations of mathematics. We also show that our system is capable of representing quantum superpositions. (shrink)

Stephen Read presented harmonious inference rules for identity in classical predicate logic. I demonstrate here how this approach can be generalised to a setting where predicate logic has been extended with epistemic modals. In such a setting, identity has two uses. A rigid one, where the identity of two referents is preserved under epistemic possibility, and a non-rigid one where two identical referents may differ under epistemic modality. I give rules for both uses. Formally, I extend Quantified (...) Epistemic Multilateral Logic with two identity signs. I argue that a uniform meaning for identity tout court can be given by adopting Maria Aloni’s account of reference using conceptual covers. We obtain a harmonious set of rules for identity that is sound and complete for Aloni’s model theory. (shrink)