Quillen [17] introduced model categories as an abstract framework for homotopy theory which would apply to a wide range of mathematical settings. By all accounts this program has been a success and—as, e.g., the work of Voevodsky on the homotopy theory of schemes [15] or the work of Joyal [11, 12] and Lurie [13] on quasicategories seem to indicate—it will likely continue to facilitate mathematical advances. In this paper we present a novel connection between model categories and mathematical logic, inspired (...) by the groupoid model of (intensional) Martin–Löf type theory [14] due to Hofmann and Streicher [9]. In particular, we show that a form of Martin–Löf type theory can be soundly modelled in any model category. This result indicates moreover that any model category has an associated “internal language” which is itself a form of Martin-Löf type theory. This suggests applications both to type theory and to homotopy theory. Because Martin–Löf type theory is, in one form or another, the theoretical basis for many of the computer proof assistants currently in use, such as Coq and Agda (cf. [3] and [5]), this promise of applications is of a practical, as well as theoretical, nature. This paper provides a precise indication of this connection between homotopy theory and logic; a more detailed discussion of these and further results will be given in [20]. (shrink)

Homotopy Type Theory is a proposed new language and foundation for mathematics, combining algebraic topology with logic. An important rule for the treatment of identity in HoTT is path induction, which is commonly explained by appeal to the homotopy interpretation of the theory's types, tokens, and identities as spaces, points, and paths. However, if HoTT is to be an autonomous foundation then such an interpretation cannot play a fundamental role. In this paper we give a derivation of path (...) induction, motivated from pre-mathematical considerations, without recourse to homotopy theory. (shrink)

Philosophy Compass, Volume 17, Issue 2, February 2022.

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)

In this essay I shall argue that the crucial assumptions of Kripke's argument, i.e. the collapse of the appearance/reality distinction in the case of phenomenal states and the idea of a qualitatively identical epistemic situation, imply an objective principle of identity for mental-state types. This principle, I shall argue, rather than being at odds with physicalism, is actually compatible with both the type-identity theory of the mind and Kripke's semantics and metaphysics. Finally, I shall sketch a version (...) of the type-identity theory. (shrink)

It is commonly believed that there is a fundamental incompatibility between multiple realization and type identity in the philosophy of mind. This claim can be challenged, however, since a single neural type may be realized by different microphysical types. In this case, the identity statement would connect the psychological and the neural type, while the neural type, in turn, could be multiply realized by different microphysical types. Such a multiple realization of higher level types (...) occurs quite frequently even within physics and it should be acceptable for physicalism in general. (shrink)

Although it seems plausible to say that the same story can be retold in different media, it is difficult to say exactly what this would entail. The primary difficulty is in coming up with an acceptable theory of story identity. In this article I present several theories of story identity and explore their weaknesses. I argue that in the end we are left with two unattractive options: a strict theory that implies that the same story can almost never (...) be retold and a lenient theory that has trouble differentiating between a general story type and the same story. (shrink)

The type identity theory, according to which types of mental state are identical to types of physical state, fell out of favour for some years but is now being considered with renewed interest. Many philosophers are critically re-examining the arguments which were marshalled against it, finding in the type identity theory both resources to strengthen a comprehensive, physicalistic metaphysics and a useful tool in understanding the relationship between developments in psychology and new results in neuroscience. This (...) volume brings together leading philosophers of mind, whose essays challenge in new ways the standard objections to type identity theory, such as the multiple realizability objection and the modal argument. Other essays show how cognitive science and neuroscience are lending new support to type identity theory and still others provide, extend and improve traditional arguments concerning the theory's explanatory power. (shrink)

This paper presents the results of empirical research that explores the links between types of social participation and identity. The author availed herself of the neo-eriksonian approach to identity by Luyckx et al. and the concept of social participation types. The study involved 1,665 students from six types of schools: lower secondary school, general upper secondary school, technical upper secondary school, specialized upper secondary school, university, and post-secondary school. The results of the research, conducted with the use of (...) Dimensions of Identity Development Scale and Social Participation Questionnaire, indicate that transitive orientation increases with age and that, consequently, the frequency of assimilation and integration types of social participation tends to be higher in emerging adulthood in comparison with adolescence. The study showed that general upper secondary school students, contrary to their colleagues from technical and specialized upper secondary schools, did not differ in terms of transitive and moratorium orientation levels from lower secondary school students. The hypothesis about the relationship between transitive orientation and commitment scales was confirmed, whereas the hypotheses concerning the links between exploration scales and both dimensions of social participation were not validated. (shrink)

In his "Materialism without Reductionism: What Materialism Does not Entail," Richard Boyd answers Kripke's challenge to materialists to come up with a way to explain away the apparent contingency of mind-brain identities. Boyd accuses Kripke of an imaginative myopia manifesting itself as a failure to realize that the more theoretical term in the identity is fixed by contingent descriptions - descriptions that might pick out otherworldly kinds of neural events where C-fibres are absent. If this is something we can (...) confuse in the imagination with actual C-fibre firings, then we have an explanation of the apparent contingency of the necessary identity 'Pain=C-fiber firings.' However, for this to succeed it must be the case that the reference of 'C-fiber firings'€™ is fixed by some contingent description, which is false. Boyd, I submit, has failed to answer Kripke'€™s challenge after all. (shrink)

The logic of identity contains riches not seen through the coarse lens of predicate logic. This is one of several lessons to draw from the subtle treatment of identity in Martin‐Löf type theory, to which the reader will be introduced in this article. After a brief general introduction we shall mainly be concerned with the distinction between identity propositions and identity judgements. These differ from each other both in logical form and in logical strength. Along (...) the way, connections to philosophical debates concerning identity are noted. Some use of logical symbolism is inevitable in any serious discussion of type theory, but the emphasis here is on basic ideas rather than technicalities. (shrink)

This paper challenges a popular thesis which we call the explanatory primitiveness thesis (for short, EPT), namely, the thesis that identities leave no logical space wherein explanatory questions may be formulated and explanatory gaps may reside. We argue that while EPT is, in all likelihood, flawless when the relevant domain consists of identity statements flanked by proper names of individuals it is a mistake to hold that the thesis generalizes to cover all identity statements. In particular, we argue (...) that EPT fails decisively with respect to an important class of identity statements, viz., those in which natural kinds are identified across different theoretical levels (i.e., the so-called inter-level type-identities). If correct, our result shows EPT to be much more limited in scope than is usually supposed. Moreover, and perhaps more significantly, it shows that there is no inherent absurdity in the idea that certain type-identity statements, in particular psychophysical type-identity statements, suffer from an explanatory gap. (shrink)

The multiplicity of Islamic interpretations is reflected in the heterogeneous nature of the Romanian Muslim communities. The internal fragmentation and disunity of Muslim communities, intra-Islamic difficulties, ideological and sectarian rivalry, success of Salafism among certain groups, the absence of stronger and more visible Islamic alternative discourses and the lack of interest in finding adequate mechanisms to facilitate the integration of the new Muslims in society are some of the general problems of the Romanian Muslims. Local Islamic revival has an ethno-cultural (...) dimension, a religious and even a political one as external disputes are imported in the Romanian context and affects the way Muslims define and practice Islam. Some Rroma and indigenous Tatar-Turkish adopted the neo-traditionalism consolidated in the second half of the last century and promoted by the most active Sunni NGOs in Romania. Some converts emancipated from the ideological control by conservative and neoconservative Islamic currents and are in search of progressive or mystical interpretations; other new Muslims found safety in the Salafi’s certitudes and rigid rules. Case study findings presented in this article may suggest that the more it depends on formal rituals, external behavior and rigid canonical displays of religiosity, the more fragile the Muslim identity becomes. A vulnerable constructed Self conceives differences and alterity as an attack against personal identity, hence the increasing aggressive and intolerant, superior Salafi attitudes. The more it is built on universal values, inner experience, ethical convictions, the more open and capable of integrating alterity and fostering positive relations with people of different religions becomes Muslim identity. (shrink)

This is a paper, aimed at students, which sets out some issues regarding personal identity over time.

Modern analytical metaphysics contains many theories and approaches regarding the problem of personal identity. This diversity inevitably leads to the emergence of various classifications, the authors of which are trying to develop a compact way of typologizing existing views. Most of the classifications involve a significant simplification of the theories and approaches under consideration, and some of them are not taken into account at all. As such global classifications, one can single out an approach based on the identity (...) criterion used in the theory (psychological, biological, narrative views). However, numerous local classifications allow one to point out potential differences in theories, even if formally they use a common criterion of identity. Other possible classifications are the division into endurantism and perdurantism, as well as simple (non-reductionist) and complex (reductionist) theories of identity. Special attention is paid to M. Shechtman‘s approach, which offers a local classification of narrative theories. Its main classification is the presentation of the views of researchers in the form of a possible spectrum. The place of a particular philosopher on this spectrum characterizes his views in relation to other supporters of the narrative approach. The purpose of this article is, based on the classification of narrative theories proposed by Shechtman, to propose a classification option for all theories and approaches to the problem of personal identity, which would be sensitive to conceptual details and differences that are important to them. (shrink)

Nonreductive physicalists have a causal exclusion problem. Given certain theses all physicalists accept, including psychophysical supervenience and the causal closure of the physical realm, it is difficult to see how irreducible mental phenomena could make a causal difference to the world. The upshot, according to those who push the problem, is that we must embrace reductive physicalism. Only then is mental causation saved. -/- Grant the argument, at least provisionally. Here our focus is the conditional question: What form should one's (...) reductionism take if it is motivated in part by the exclusion problem? Must one be a type identity theorist, or are alternative reductive views available, as Jaegwon Kim has suggested more than once? (shrink)

On the basis of Martin-Löf’s meaning explanations for his type theory a detailed justification is offered of the rule of identity elimination. Brief discussions are thereafter offered of how the univalence axiom fares with respect to these meaning explanations and of some recent work on identity in type theory by Ladyman and Presnell.

In this paper I will develop a lambda-term calculus, lambda-2Int, for a bi-intuitionistic logic and discuss its implications for the notions of sense and denotation of derivations in a bilateralist setting. Thus, I will use the Curry-Howard correspondence, which has been well-established between the simply typed lambda-calculus and natural deduction systems for intuitionistic logic, and apply it to a bilateralist proof system displaying two derivability relations, one for proving and one for refuting. The basis will be the natural deduction system (...) of Wansing's bi-intuitionistic logic 2Int, which I will turn into a term-annotated form. Therefore, we need a type theory that extends to a two-sorted typed lambda-calculus. I will present such a term-annotated proof system for 2Int and prove a Dualization Theorem relating proofs and refutations in this system. On the basis of these formal results I will argue that this gives us interesting insights into questions about sense and denotation as well as synonymy and identity of proofs from a bilateralist point of view. (shrink)

Families of types are fundamental objects in Martin-Löf type theory. When extending the notion of setoid (type with an equivalence relation) to families of setoids, a choice between proof-relevant or proof-irrelevant indexing appears. It is shown that a family of types may be canonically extended to a proof-relevant family of setoids via the identity types, but that such a family is in general proof-irrelevant if, and only if, the proof-objects of identity types are unique. A similar (...) result is shown for fibre representations of families. The ubiquitous role of proof-irrelevant families is discussed. (shrink)

I argue, first, that there is a problem for his account of reduction as it stands; second, that the change that needs to be made is relatively clear ; but, third, that when the needed change is made, his claim that the best form of physicalism is a reductive one amounts to the claim that the best form of physicalism is the ‘Australian’ type-type identity version. I do not see this as an objection—far from it.

Charles S. Peirce introduces the distinction between a token and a type into semiotics and philosophy by using as an example two ways of individuating words:(P1) A common mode of estimating the amount of matter in a MS. or printed book is to count the number of words. There will ordinarily be about twenty the's on a page, and of course they count as twenty words. In another sense of the word "word," however, there is but one word "the" (...) in the English language; and it is impossible that this word should lie visibly on a page or be heard in any voice, for the reason that it is not a Single thing or Single event. It does not exist; it only determines things that do exist. Such a definitely significant Form, I propose.. (shrink)

An algebra A = ⟨A, ∨, ∧, →, 0, 1⟩ is a semi-Heyting algebra if ⟨A, ∨, ∧, 0, 1⟩ is a bounded lattice, and it satisfies the identities: x ∧ ≈ x ∧ y, x ∧ ≈ x ∧ [ → ], and x → x ≈ 1.

Departing from the model suggested by Luyckx, Schwarz, Berzonsky et al., the relationships between identity and educational context, social participation, and identity information processing style were investigated. Participants were 972 students from six vocational schools in Poznań. The students, within these six schools, attended Grades I-III of three types of vocational schools: basic vocational schools, technical upper secondary schools, and specialized upper secondary schools. Three questionnaires were used: The Dimensions of Identity Development Scale, which measures five (...) class='Hi'>identity dimensions according to the concept of Luyckx, Schwarz, Berzonsky et al., Social Participation Questionnaire, developed by Brzezińska, Rękosiewicz and Hejmanowski, enabling identification of the type of social participation, and the Polish adaptation of M. Berzonsky’s Identity Style Inventory 4 authored by A. Senejko, to examine identity styles. The results showed that the students from basic vocational schools and technical upper secondary schools were more often characterized by the normative identity style, whereas the students from specialized upper secondary schools manifested a greater tendency to engage themselves in exploration, both adaptive and ruminative. (shrink)

This paper addresses ethical challenges posed by a robot acting as both a general type of system and a discrete, particular machine. Using the philosophical distinction between “type” and “token,” we locate type-token ambiguity within a larger field of indefinite robotic identity, which can include networked systems or multiple bodies under a single control system. The paper explores three specific areas where the type-token tension might affect human–robot interaction, including how a robot demonstrates the highly (...) personalized recounting of information, how a robot makes moral appeals and justifies its decisions, and how the possible need for replacement of a particular robot shapes its ongoing role. We also consider how a robot might regard itself as a replaceable token of a general robotic type and take extraordinary actions on that basis. For human–robot interaction robotic type-token identity is not an ontological problem that has a single solution, but a range of possible interactions that responsible design must take into account, given how people stand to gain and lose from the shifting identities social robots will present. (shrink)

I argue, first, that there is a problem for his account of reduction as it stands; second, that the change that needs to be made is relatively clear ; but, third, that when the needed change is made, his claim that the best form of physicalism is a reductive one amounts to the claim that the best form of physicalism is the ‘Australian’ type-type identity version. I do not see this as an objection—far from it.

_Purpose._ This article aims at outlining the consider Ukrainian identity in the context of European collective action through the prism of value orientations/approaches. _Theoretical basis._ The following methods were used in order to cover the problem as objectively as possible: historical, analytical, comparative, socio-geographical, behavioral, and dialectical. The use of these methods contributed to tracing the peculiarities of identity and collective action in the dynamics of the historical process and social development. _Originality._ The role of identity in (...) collective action formation is considered. It was established that identity determines the socio-species structure and projects social development. After all, identification for a person in the formation process is a basic need that determines a person’s belonging, not identity. During the formation of "I" there is a combination of "I1" + "I2" + "Other" = "WE". This process is complex and long-term, but it is precisely the process that gives you the opportunity to clearly understand your "I" and know yourself. It was found that identity as a social phenomenon, which is related to the formation of the "I", is determined by certain circumstances, which can be conditionally divided into objective and subjective. After analyzing the scientific literature, a generalization was made that identity is not a new phenomenon, but it has certain features at each stage of social development. This became most noticeable in the conditions of globalization, when countries that are actually different perceive the "Other", unite around certain problems, and then this union forms a system of mutual relations. It is thanks to this approach that alliances, multicultural associations, etc. are formed, and an example of this is the heterogeneous European identity. Special attention is drawn to the role of values, which are the landmarks in the process of identity and the formation of collective action. Based on political, social, economic, historical processes and ontological features, it was established that identity is a dynamic process, since values during a person’s life, the existence of the state, etc. are variables. This is confirmed by the value orientation and various socio-political processes aimed at the formation of Homo in countries that have the status of "between". _Conclusions._ The article illustrates and justifies the existence of several forms of identity according to which the types of identity are formed. The fact proves that identity is not a constant process and varies due to multiple factors: social, political, economic, and religious as well as due to formations – regional, local, civilizational, etc. As practice shows, the problem of identity mostly has situational nature and arises due to the need for unification. The socio-historical process manifests the significance of the values in the formation of a collective European heterogeneous identity. These processes are influenced by many factors: geographical, historical, mythological, etc. (shrink)

When philosophers address personal identity, they usually explore numerical identity: what are the criteria for a person's continuing existence? When non-philosophers address personal identity, they often have in mind narrative identity: Which characteristics of a particular person are salient to her self-conception? This book develops accounts of both senses of identity, arguing that both are normatively important, and is unique in its exploration of a range of issues in bioethics through the lens of identity. (...) Defending a biological view of our numerical identity and a framework for understanding narrative identity, DeGrazia investigates various issues for which considerations of identity prove critical: the definition of death; the authority of advance directives in cases of severe dementia; the use of enhancement technologies; prenatal genetic interventions; and certain types of reproductive choices. He demonstrates the power of personal identity theory to illuminate issues in bioethics as they bring philosophical theory to life. (shrink)

In this paper, I present a two-pronged argument devoted to defending the type-identity theory of mind against the argument presented by Kripke in _Naming and Necessity_. In the first part, the interpersonal case, I show that since it is not possible to establish the metaphysical conditions for phenomenal identity, it is not possible to argue that there can be physical differences between two subjects despite their phenomenal identity. In the second part, the intrapersonal case, I consider (...) the possibility of imagining one and the same individual having the same phenomenal state while counterfactually being in very different physical states. I argue that this case should respect Kripke’s implicit theory of personal identity—but this proves to be a very difficult task to accomplish, thus preventing the argument from getting off the ground. Therefore, I maintain, that the type-identity theory is still the better option to solve the mind–body problem. (shrink)

I argue that different argumentative practices require participants to categorize themselves in different modes. Accordingly, I distinguish four types of argumentation: _rational argumentation,_ _intergroup argumentation_, _intragroup argumentation_, and, finally, _personal argumentation_. An inescapable implication of my approach to deliberation is that deliberation presupposes the self-categorization of participants in the same ingroup. Deliberation does not require, however, the group to antecede the deliberation process, and a distinctive feature of successful public deliberation is its capacity to produce social identification with the deliberative (...) group. Thus, identity negotiation is an important part of deliberative processes. (shrink)

The author argues that uploading does preserve personal identity, at least identity of a certain sort. The fact that we are assuming that computers are capable of embodying all the same type of properties necessary for personal identity means that we can make use of the equivalency thesis. There are two reasons for invoking the equivalency thesis. The first is so that we are not misled by a new form of racism: substratism. The second is that (...) it makes directly relevant an enormous amount of philosophical effort that has gone into exploring the possibility of carbonto‐ carbon transfers. He examines an alternative explanation to somaticism for why people might be reluctant to use Parfit's Teletransporter, namely, fear of the unknown. Finally, the author talks about the type/token (TT) account of personal identity and then see whether the no‐branching argument has any traction against it. (shrink)

Positive public perceptions of academic quality and professional ethics are critical to the long-term legitimacy of American colleges and universities. Faculty codes of conduct are one mechanism whereby the professoriate can define acceptable practice, exercise social control, and maintain public confidence in higher education, yet the drivers of their adoption are not well understood. Building upon previous research into such organizational behavior by institutional type, this study examined the prevalence and content of publicly posted faculty codes of conduct within (...) an organizational field of institutions that share a common religious identity but differ in their institutional types and employment structures. Faculty handbooks from American member institutions of the Council for Christian Colleges & Universities, an international association of faith-based institutions, were gathered and analyzed. Although only 27% of CCCU member institutions in the U.S. publicly posted faculty codes of conduct, the average number of tenets present in each code was higher than suggested by previous research. Study findings also revealed that membership category, institutional type, and employment structures influence the content of faculty codes of conduct, indicating that isomorphic pressures operate within this particular organizational field. The piece concludes by commending publicly posted codes of conduct as an affirmation of the personal responsibility, fairness, and care exercised by ethical professionals in the academy. (shrink)

Type materialism is a theory of the place of states of phenomenal consciousness in nature. It is the theory that qualitative mental states are type identical with certain neuroscientific states. This chapter examines this theory and discusses some required background details. There are currently a number of scientific projects that are aimed at finding the neural correlates of states of phenomenal consciousness. Whether any of these projects will succeed is of course an empirical issue. Type materialism for (...) phenomenal consciousness is the view that types of states of phenomenal consciousness are identical with their strict neuroscientific correlates. If type materialism is true, then states of phenomenal consciousness are causally efficacious; for they are neuroscientific states with causal effects. Type materialism allows that there can be phenomenal consciousness in actual “absent folk role” cases. The chapter distinguishes type materialism from representationalism and psychofunctionalism. (shrink)

This book examines the conception of the person at work in John Rawls's writings from Theory of Justice to Justice as Fairness: A Restatement. The book aims to show that objections to Rawls's political conception of the person fail and that a Rawlsian conception of political identity is defensible. The book shows that the debate between liberals and communitarians is relevant to the current debate regarding perfectionism and neutrality in politics, and clarifies the debate between Rawls and communitarians in (...) a way that will promote fruitful discussion on the issue of political identity. It does this by providing a clearer account of a conception of personal identity according to which persons are socially constituted, including the intuitions and assumptions underlying the communitarians' conception of persons as "socially constituted." It examines the communitarian objections to liberal political theory and to the liberal conception of persons, the "unencumbered self." The book differentiates between two types of objection to the liberal conception of persons: the metaphysical and normative. It explains Rawls's political conception of persons, and the metaphysical and normative commitments Rawls incurs-and does not incur-in virtue of that conception. It shows that both kind of objection to Rawls's political conception of the person fail. Finally, modifying Rawls's political conception of the person, a Rawlsian conception of political identity is explained and defended. (shrink)

This volume explores the concepts of reference and identity in public discourses. Its contributions study discourse-specific reference and labelling patterns, both from a historical and present-day perspective, and discuss their impact on self- and other-representation in the construction of identity. They combine multiple methodological approaches, including corpus-based quantitative as well as qualitative approaches, and apply them to a range of text types that are or were (intended to be) public, such as letters, newspapers, parliamentary debates, and online communication (...) in the form of reader comments, discussion pages and tweets. In addition to English, the languages studied include Polish as well as European and Latin American Spanish. The volume is aimed at researchers from different research paradigms in linguistics and related disciplines, such as media communication or the social and cultural sciences, who are interested in the interplay of reference and identity. (shrink)