Truth, Proof and Gödelian Arguments : A Defence of Tarskian Truth in Mathematics

One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established to be true once we expand the formal system with Alfred Tarski s semantical theory of truth, as shown by Stewart Shapiro and Jeffrey Ketland in their semantical arguments for the substantiality of truth. According to them, in Gödel sentences we have an explicit case of true but unprovable sentences, and hence deflationism is refuted. Against that, Neil Tennant has shown that instead of Tarskian truth we can expand the formal system with a soundness principle, according to which all provable sentences are assertable, and the assertability of Gödel sentences follows. This way, the relevant question is not whether we can establish the truth of Gödel sentences, but whether Tarskian truth is a more plausible expansion than a soundness principle. In this work I will argue that this problem is best approached once we think of mathematics as the full human phenomenon, and not just consisting of formal systems. When pre-formal mathematical thinking is included in our account, we see that Tarskian truth is in fact not an expansion at all. I claim that what proof is to formal mathematics, truth is to pre-formal thinking, and the Tarskian account of semantical truth mirrors this relation accurately. However, the introduction of pre-formal mathematics is vulnerable to the deflationist counterargument that while existing in practice, pre-formal thinking could still be philosophically superfluous if it does not refer to anything objective. Against this, I argue that all truly deflationist philosophical theories lead to arbitrariness of mathematics. In all other philosophical accounts of mathematics there is room for a reference of the pre-formal mathematics, and the expansion of Tarkian truth can be made naturally. Hence, if we reject the arbitrariness of mathematics, I argue in this work, we must accept the substantiality of truth. Related subjects such as neo-Fregeanism will also be covered, and shown not to change the need for Tarskian truth. The only remaining route for the deflationist is to change the underlying logic so that our formal languages can include their own truth predicates, which Tarski showed to be impossible for classical first-order languages. With such logics we would have no need to expand the formal systems, and the above argument would fail. From the alternative approaches, in this work I focus mostly on the Independence Friendly (IF) logic of Jaakko Hintikka and Gabriel Sandu. Hintikka has claimed that an IF language can include its own adequate truth predicate. I argue that while this is indeed the case, we cannot recognize the truth predicate as such within the same IF language, and the need for Tarskian truth remains. In addition to IF logic, also second-order logic and Saul Kripke s approach using Kleenean logic will be shown to fail in a similar fashion.

Pathet : Musiikin symboliikka jaavalaisessa varjoteatterissa

The aim of this study is to define and analyse the symbolism hidden in the gamelan music of the Central Javanese, especially in the Yogyakartanese wayang kulit shadow theatre. This dissertation is divided into two parts. The first part deals with the theory, history and practice of Central Javanese shadow theatre. It also presents the tone symbol theory on which this study is based of B. Y. H. Sastrapustaka, the court servant and musician of the sultan s palace of Yogyakarta. For historical comparison, other theories and phenomena that seem to have some connections with the previously mentioned tone symbol theory are presented here as well as the equipment of the shadow theatre, its music, musical instruments and the shadow theatre in general in literature. The theoretic-methodological basis of the study is an enlarged model of research of cultural music, in which a person in the centre of the model with his/her concepts and by his/her behaviour creates a work of art and receives criticism through feedback, while the process of reciprocal action dynamically affects the whole development of the culture in question. In connection with the concepts of the work of art, the manner of approach of this study is also semiotic as the tone symbol theory gives a particular meaning to each musical note. Thus the purpose of this study is to find answers to how the tone symbol theory manifests itself in practical music making, what its origin is, if it is well known or not, and whether shadow theatre music supports this theory. The second part of this dissertation deals with material collected through interviews and observations as well as representative samples of musical pieces for shadow theatre and their analyses. In relation to this a special tool for analysing gamelan music, developed for the purpose of this study, is also presented. Sufficiently versatile material on the essence and meaning of the shadow theatre collected from many puppet masters of an older generation, many of whom are no longer with us, constitutes an important part of this study. This study proves that the tone symbol theory of Sastrapustaka is of tantristic tradition from the Hindu-Javanese period before the 16th century and before the appearance of Islam in Java. The variants of the previously mentioned theory can be found also in other fields of Javanese advanced civilization, such as architecture and dance. But it seems that knowledge about the tone symbolism connected to the shadow theatre especially has only been preserved in the sultan s palace of Yogyakarta and its intimate circles. The outsider puppet masters surely follow the theory, but they do not necessarily know its origin. As a result of the musical analysis, it is obvious that the musical pieces used for the shadow theatre bear different kinds of symbolic meanings which only an initiated person can feel and understand. These meanings are closely related to the plot of the play at the moment.

Changes in Beer Labels and their Meaning : A Holistic Approach to the Semiosic Process

The purpose of this study is to find a framework for a holistic approach to, and form a conceptual toolbox for, investigating changes in signs and in their interpretation. Charles S. Peirce s theory of signs in a communicative perspective is taken as a basis for the framework. The concern directing the study is the problem of a missing framework in analysing signs of visual artefacts from a holistic perspective as well as that of the missing conceptual tools. To discover the possibility of such a holistic approach to semiosic processes and to form a conceptual toolbox the following issues are discussed: i) how the many Objects with two aspects involved in Peirce s definition of sign-action, promote multiple semiosis arising from the same sign by the same Interpretant depending on the domination of the Objects; ii) in which way can the relation of the individual and society or group be made more apparent in the construction of the self since this construction is intertwined with the process of meaning-creation and interpretation; iii) how to account for the fundamental role of emotions in semiosis, and the relation of emotions with the often neglected topic of embodiment; iv) how to take into account the dynamic, mediating and processual nature of sign-action in analysing and understanding the changes in signs and in the interpretation of signs. An interdisciplinary approach is chosen for this dissertation. Concepts that developed within social psychology, developmental psychology, neurosciences and semiotics, are discussed. The common aspect of the approaches is that they in one way or another concentrate on mediation provided by signs in explaining human activity and cognition. The holistic approach and conceptual toolbox found are employed in a case study. This consists of an analysis of beer brands including a comparison of brands from two different cultures. It becomes clear that different theories and approaches have mutual affinities and do complement each other. In addition, the affinities in different disciplines somewhat provide credence to the various views. From the combined approach described, it becomes apparent that by the semiosic process, the emerging semiotic self intertwined with the Umwelt, including emotions, can be described. Seeing the interpretation and meaning-making through semiosis allows for the analysis of groups, taking into account the embodied and emotional component. It is concluded that emotions have a crucial role in all human activity, including so-called reflective thinking, and that emotions and embodiment should be consciously taken into account in analysing signs, the interpretation, and in changes of signs and interpretations from both the social and individual level. The analysis of the beer labels expresses well the intertwined nature of the relationship between signs, individual consumers and society. Many direct influences from society on the label design are found, and also some indirect attitude changes that become apparent from magazines, company reports, etc. In addition, the analysis brings up the issues of the unifying tendency of the visual artefacts of different cultures, but also demonstrates that the visual artefacts are able to hold the local signs and meanings, and sometimes are able to represent the local meanings although the signs have changed in the unifying process.

Questions to Artificial Nature: A Philosophical Study of Interdisciplinary Models and their Functions in Scientific Practice

This thesis presents an interdisciplinary analysis of how models and simulations function in the production of scientific knowledge. The work is informed by three scholarly traditions: studies on models and simulations in philosophy of science, so-called micro-sociological laboratory studies within science and technology studies, and cultural-historical activity theory. Methodologically, I adopt a naturalist epistemology and combine philosophical analysis with a qualitative, empirical case study of infectious-disease modelling. This study has a dual perspective throughout the analysis: it specifies the modelling practices and examines the models as objects of research. The research questions addressed in this study are: 1) How are models constructed and what functions do they have in the production of scientific knowledge? 2) What is interdisciplinarity in model construction? 3) How do models become a general research tool and why is this process problematic? The core argument is that the mediating models as investigative instruments (cf. Morgan and Morrison 1999) take questions as a starting point, and hence their construction is intentionally guided. This argument applies the interrogative model of inquiry (e.g., Sintonen 2005; Hintikka 1981), which conceives of all knowledge acquisition as process of seeking answers to questions. The first question addresses simulation models as Artificial Nature, which is manipulated in order to answer questions that initiated the model building. This account develops further the "epistemology of simulation" (cf. Winsberg 2003) by showing the interrelatedness of researchers and their objects in the process of modelling. The second question clarifies why interdisciplinary research collaboration is demanding and difficult to maintain. The nature of the impediments to disciplinary interaction are examined by introducing the idea of object-oriented interdisciplinarity, which provides an analytical framework to study the changes in the degree of interdisciplinarity, the tools and research practices developed to support the collaboration, and the mode of collaboration in relation to the historically mutable object of research. As my interest is in the models as interdisciplinary objects, the third research problem seeks to answer my question of how we might characterise these objects, what is typical for them, and what kind of changes happen in the process of modelling. Here I examine the tension between specified, question-oriented models and more general models, and suggest that the specified models form a group of their own. I call these Tailor-made models, in opposition to the process of building a simulation platform that aims at generalisability and utility for health-policy. This tension also underlines the challenge of applying research results (or methods and tools) to discuss and solve problems in decision-making processes.

Luce Irigaray's Philosophy of Feminine Being : Body, Desire and Wisdom

Luce Irigaray is a Belgian-born philosopher, psychoanalyst and linguist. Irigaray s concept of woman is crucial for understanding her own work but also for examining and developing the theoretical and methodological basis of feminist theory. This thesis argues that, ultimately, Irigaray s exploration of woman s being challenges our traditional notion of philosophy as a neutral discourse and the traditional notion of ourselves as philosophizing persons or human beings. However, despite its crucial role, Irigaray s idea of woman still lacks a comprehensive explication. This is because the discourse of sexual difference is blurred by the ideas of essentialism and biologism. --- Irigaray s concept of woman has been interpreted and criticized from the perspectives of metaphysical essentialism, strategic essentialism, realist essentialism and deconstructionism. This thesis argues that a reinterpretation is necessary to account for Irigaray s claims about the the traditional woman , mimesis, the specificity of the feminine body, feminine expression and sexual difference. Moreover, any reading should account for the differences between women and avoid giving a prescriptive function to the essence of woman. --- My thesis develops a new interpretation of Irigaray s concept of woman on the basis of the phenomenology of the body. It argues that Irigaray s discourse on woman can and must be understood by an idea of existential style. Existential style is embodied, affective and spiritual and it is constituted in relation to oneself, to others and to the world. It is temporal, it evolves and changes but preserves its open unity in its transformations. Stylistic unities, such as femininity or philosophy, are constituted in and by the singulars. -- This study discusses and analyses feminine existential style as a central theme and topic of Irigaray s works and shows how her work operates as a primary and paradigmatic example of the feminine style. These tasks are performed by studying the mimetic positions available for women and by explicating the phenomenological background of Irigaray s conceptions of the philosophical method, and the lived, expressive and affective body. The critical occupation and transformation of these mimetic positions, the inquiry into the first-person pre-discursive experience, and the cultivation of feminine expressivity open up the possibility of becoming a woman writer, a woman lover and a woman philosopher. The appearance of these new feminine figures is a precondition for the realization of sexual difference. So Irigaray opens up the possibility of sexual difference by instituting and constituting a feminine subject of love and wisdom, and by problematizing the idea of a neutral and absolute subject.

Aristotle on the Perception of Perception : Seeing, Remembering, and Sleeping

This study is an inquiry into three related topics in Aristotle’s psychology: the perception of seeing, the perception of past perception, and the perception of sleeping. Over the past decades, Aristotle’s account of the perception of perception has been studied in numerous articles and chapters of books. However, there is no monograph that attempts to give a comprehensive analysis of this account and to assess its relation and significance to Aristotle’s psychological theory in general as well as to other theories pertaining to the topics (e.g. theories of consciousness), be they ancient, medieval, modern, or contemporary. This study intends to fill this gap and to further the research into Aristotle’s philosophy and into the philosophy of mind. The present study is based on an accurate analysis of the sources, on their Platonic background, and on later interpretations within the commentary tradition up to the present. From a methodological point of view, this study represents systematically orientated research into the history of philosophy, in which special attention is paid to the philosophical problems inherent in the sources, to the distinctions drawn, and to the arguments put forward as well as to their philosophical assessment. In addition to contributing many new findings concerning the topics under discussion, this study shows that Aristotle’s account of the perception of perception substantially differs from many later theories of consciousness. This study also suggests that Aristotle be regarded as a consistent direct realist, not only in respect of sense perception, but also in respect of memory.

Musiikki ahdistuksen taitona : Filosofinen tutkimus musiikin eksistentiaalis-ontologisesta merkityksestä

Music as the Art of Anxiety: A Philosophical Approach to the Existential-Ontological Meaning of Music. The present research studies music as an art of anxiety from the points of view of both Martin Heidegger s thought and phenomenological philosophy in general. In the Heideggerian perspective, anxiety is understood as a fundamental mode of being (Grundbefindlichkeit) in human existence. Taken as an existential-ontological concept, anxiety is conceived philosophically and not psychologically. The central research questions are: what is the relationship between music and existential-ontological anxiety? In what way can music be considered as an art of anxiety? In thinking of music as a channel and manifestation of anxiety, what makes it a special case? What are the possible applications of phenomenology and Heideggerian thought in musicology? The main aim of the research is to develop a theory of music as an art of existential-ontological anxiety and to apply this theory to musicologically relevant phenomena. Furthermore, the research will contribute to contemporary musicological debates and research as it aims to outline the phenomenological study of music as a field of its own; the development of a specific methodology is implicit in these aims. The main subject of the study, a theory of music as an art of anxiety, integrates Heideggerian and phenomenological philosophies with critical and cultural theories concerning violence, social sacrifice, and mimetic desire (René Girard), music, noise and society (Jacques Attali), and the affect-based charme of music (Vladimir Jankélévitch). Thus, in addition to the subjective mood (Stimmung) of emptiness and meaninglessness, the philosophical concept of anxiety also refers to a state of disorder and chaos in general; for instance, to noise in the realm of sound and total (social) violence at the level of society. In this study, music is approached as conveying the existentially crucial human compulsion for signifying i.e., organizing chaos. In music, this happens primarily at the immediate level of experience, i.e. in affectivity, and also in relation to all of the aforementioned dimensions (sound, society, consciousness, and so on). Thus, music s existential-ontological meaning in human existence, Dasein, is in its ability to reveal different orders of existence as such. Indeed, this makes music the art of anxiety: more precisely, music can be existentially significant at the level of moods. The study proceeds from outlining the relevance of phenomenology and Heidegger s philosophy in musicology to the philosophical development of a theory of music as the art of anxiety. The theory is developed further through the study of three selected specific musical phenomena: the concept of a musical work, guitar smashing in the performance tradition of rock music, and Erik Bergman s orchestral work Colori ed improvvisazioni. The first example illustrates the level of individual human-subject in music as the art of anxiety, as a means of signifying chaos, while the second example focuses on the collective need to socio-culturally channel violence. The third example, being music-analytical, studies contemporary music s ability to mirror the structures of anxiety at the level of a specific musical text. The selected examples illustrate that, in addition to the philosophical orientation, the research also contributes to music analysis, popular music studies, and the cultural-critical study of music. Key words: music, anxiety, phenomenology, Martin Heidegger, ontology, guitar smashing, Erik Bergman, musical work, affectivity, Stimmung, René Girard

Ruumiinkuvia! : Suomalainen performanssi- ja kehotaide 1980- ja1990-luvulla psykoanalyysin valossa

My PhD-thesis Body Images! Psychoanalytical Analysis of Finnish Performance and Body Art in the 1980s and 1990s considers Finnish performance and body art performed mainly by visual artists. In Part I, I chart the historical construction of performance art and its extension since the beginning of the 21st century. There are several wievs of the historical background of performance art. I introduce three different genealogies of performance art. One is Rose-Lee Goldberg s view. She connects performance art with the European avant-garde already at the beginning of the 20th century from futurists and dadaists to Russian avant-garde and the Bauhaus. I prefer to present performance art as contemporary art, which began to take shape in connection with visual arts in the 1950s and 1960s. The focus on the body is apparent in nearly all performance art. Nevertheless, throug the concept of body art I want to empasize the artist s body as the place of art. Body art (as part of performance art) functions as thematic and interpretive concept, which allows me to focus on performances where the questions of body image, narcissism, desire, language and pleasure are incorporated in particular intensive ways. In Part II, I explore the arrival of performance art in Finnish visual arts in the 1980s. I study the new generation s relation to earlier Finnish happenings (1960s) and performative actions in 1970 s. I briefly introduce performance groups of the 1980s art scene and consider their reception in media. The main focus is on the group Jack Helen Brut, in which I see many similarities to the so- called Theatre of Images. The goal of this part II is to provide historical context for the performance analysis that follows. In Part III, I develop the concept of body image which is my main theoretical term. The concept of body image is used according to Lacanian psychoanalytical theory, especially his considerations of mirror stages. My first mapping of body image, which I call imaginary body image, is based on Lacan s famous mirror stage article (1949). According to my reading, body image is narcistic and aggressive. The important concepts here are ego, imaginary, méconnaisance and alienation. In 1953 Lacan began to develop different version on mirror stage, in which he emphasized the primacy of symbolic dimension. It is not image, but language which constructs the foundations of body image. Central concepts in this chater are Other as language, ego-ideal, demand and desire. In the last chapter I connect the third version of the mirror stage to concepts of gaze, phantasy, real, jouissance and object a. In previous chapters I had considered body image in relation to ego. Now I explore it in relation to subject. In my reading the body image is fragile phenomen, which oscillates between yearning for coherence and phantasies of fragmented images. Part IV of the thesis begins with an introduction to the central concepts and debates in performace studies over the last few decades. Important concepts are presence, performativity and theatricality. The main substance of my thesis, however, is the performance analysis, which focuses on works by three Finnish artists and one Finnish group. The first analysis concerns the performance (1992) of Kimmo Schroderus. I discuss the relationship between narcissism and body art and the changes in demands projected on body images of men in recent decades in a Euro-American context. I also explore this performance in relation to the myth of Narcissus, which I reinterpret through Narcissus s aggression against his own body. The group Homo S is the main subject of the next analysis. I discuss the relationship between feminist art and performance art, especially in the United States in the 1960s and 1970s. Homo S is different from this early performance art because of its anarchism, humor and rejection of all ideals. Homo S characterizes its performance Body Body (1983) as liberating vulgar feminism . Sociality and performance of erotic relations between women are central in Body Body. Pia Lindman s performances are the subjects of my third analysis. I study three of her performances: Olen muoto (1993), 17 and in love (1994) and Arranged views (1995). I interpret these performances as efforts to disperse the imaginary and symbolic structures of the body image. She constructs the peculiar object a and phantasy space of her own. In the last analysis I move from questions of image and gaze to a study of language, sound and jouissance. I discuss at a general level the performance of orality and helplesness (Hilflosigkeit) in body art. The central elements in Pentti Otto Koskinen s performances are the ear, listening and receptive gestures and postions. Perseveraatio (1998) can be understood representing as submission to the super-ego s power, which compels one to enjoy. I examine particularly closely the performance Maissi on hyvää ei missään nimessä maissia (1995), which I interpret as the return of a baby s body image to the liminal site of choice: language or jouissance?

Patterns in tropical seagrass photosynthesis in relation to light, depth and habitat

Seagrass meadows across north-eastern Australia, survive a range of environmental conditions in coastal bays, reefs, estuarine and deepwater habitats through adaptation of a range of structural, morphological and physiological features. The aim of this study was to investigate the influence of spatial features (habitat type, site and depth) and photon flux on the photosynthetic performance of 11 tropical seagrass species. Pulse amplitude modulated (PAM) fluorometry was used to generate rapid light curves from which measures of maximal electron transport rate (ETRmax), photosynthetic efficiency (?), saturating irradiance (Ek) and effective quantum yield (?F/Fm?) were derived. The amount of light absorbed by leaves (absorption factor) was also determined for each population. In intertidal habitats many seagrass species exhibited typical sun-type responses with a close coupling of both ETRmax and Ek with photon flux. Photosynthetic performance ranged from minima in Thalassodendron ciliatum to maxima in Syringodium isoetifolium. The absence of a coupling between photosynthetic performance and photon flux in subtidal populations was most likely due to highly variable light climates and possible light attenuation, and hence the photo-biology of estuarine and deepwater seagrasses exhibited photosynthetic responses indicative of light limitation. In contrast seagrass species from shallow reef and coastal habitats for the most part exhibited light saturation characteristics. Of all the variables examined ETRmax, Ek and ?F/Fm? were most responsive to changing light climates and provide reliable physiological indicators of real-time photosynthetic performance of tropical seagrasses under different light conditions.

Vikuroivia vilkaisuja : Ruumis, sukupuoli, seksuaalisuus ja visuaalisen kulttuurin tutkimus

The PhD dissertation "Bucking Glances: On Body, Gender, Sexuality and Visual Culture Research" consists of theoretical introduction and five articles published between 2002-2005. The articles analyze the position of visual representations in the processes of knowledge production on acceptable genders, bodies, and sexualities in contemporary Wes¬tern societies. The research material is heterogeneous, consisting of representations of contemporary art, advertisements, and fashion images. The ideological starting point of the PhD dissertation is the politics of the gaze and the methods used to expose this are the concepts of oppositional gaze, close reading, and resisting reading. The study situates visual representations in dialogue with the concepts of the grotesque and androgyny, as well as with queer-theory and theories of the gaze. The research challenges normative meanings of visual representations and opens up space for more non-conventional readings attached to femininity and masculinity. The visual material is read as troubling the prevailing heteronormative gender system. The dissertation also indicates how visual culture research utilizing the approach of queer theory can be fruitful in opposing and re-visioning changes in the repressive gender system. The article "A Heroic Male and A Beautiful Woman. Teemu Mäki, Orlan and the Ambivalence of the Grotesque Body" problematizes the concept of heroic masculinity through the analysis of the Finnish artist Teemu Mäki's masochistic performance The Good Friday (1989). It also analyzes cosmetic surgery, undertaken by the French artist Orlan, as a cultural tool in constructing and visualizing the contemporary, com¬mercial ideals of female beauty. The article "Boys Will Be Girls Will Be Boys Will Be Girls. The Ambivalence of Androgyny in Calvin Klein' Advertisements" is a close reading of the Calvin Klein perfume advertisement One (1998) in reference to the concept of androgyny. The critical point of the article is that androgynous male bodies allow the extension of the categorical boundaries of masculinity and homosexuality, whereas representations of androgynous women feed into the prevailing stereotypes of femininity, namely the fear of fat. The article "See-through Closet: Female Androgyny in the 1990s Fashion Images, New Woman and Lesbian Chic" analyzes the late 1990s fashion advertisements through the concept of female androgyny. The article argues that the figures of the masculine female androgynes in the late 1990s fashion magazines do not problematize the dichotomous gender binary. The women do not pass as men but produce a variation of heterosexual desirability. At the same time, the representations open up space for lesbian gazing and desiring. The article "Why are there no lesbian advertisements?" addresses the issue of femme gaze and desire in relation to heterosexual fashion advertisements from the British edition of the mainstream fashion magazine Vogue. The article considers possibilities for resistant femme visibility, identification, and desire. The article "Woman, Food, Home. Pirjetta Brander's and Heidi Romo's Works as Bucking Representations of Femininity" analyses the production and queering of heteronormative femininity and family through the analysis of art works. The article discusses how the term queer has been translated into Finnish. The article also introduces a new translation for the term queer: the noun vikuuri, i.e. faulty form and the verb vikuroida, i.e. to buck. In Finnish, the term vikuuri is the vernacular or broken form of the term figure, i.e. figuuri. Vikuuri represents all forms situated outside the norm and the normative.

The development of a guideline of care for patients with a Sengstaken-Blakemore Tube insitu in a general Intensive Care Unit using translational change theory

Aims & Objectives - identify and diagnose the current problems associated with patient care with regard to the nursing management of patients with Sengstaken-Blakemore tubes insitu; - Identify current nursing practice currently in place within the ICU and the hospital; identify the method by which the assessment and provision of nursing care is delivered in the ICU

Theory For The Anomalous Hall Constant Of Mixed-Valence Systems

We show that the large anomalous Hall constants of mixed-valence and Kondo-lattice systems can be understood in terms of a simple resonant-level Fermi-liquid model. Splitting of a narrow, orbitally unquenched, spin-orbit split, f resonance in a magnetic field leads to strong skew scattering of band electrons. We interpret both the anomalous signs and the strong temperature dependence of Hall mobilities in CeCu2Si2, SmB6, and CePd3 in terms of this theory.

Gauge theory of a group of diffeomorphisms. I. General principles

Any (N+M)-parameter Lie group G with an N-parameter subgroup H can be realized as a global group of diffeomorphisms on an M-dimensional base space B, with representations in terms of transformation laws of fields on B belonging to linear representations of H. The gauged generalization of the global diffeomorphisms consists of general diffeomorphisms (or coordinate transformations) on a base space together with a local action of H on the fields. The particular applications of the scheme to space-time symmetries is discussed in terms of Lagrangians, field equations, currents, and source identities. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.