Este trabalho discute o emprego da topologia como ramo da matemática nos desenvolvimentos teóricos de Jacques Lacan. O ponto de partida é a crítica apresentada por Sokal quanto à falta de fundamento deste recurso em seu uso pela psicanálise, em contraposição às afirmações lacanianas quanto a ser a topologia a própria estrutura. O objetivo central é defender a idéia de que o recurso metodológico à topologia, às matemáticas e à lógica é compatível com o conceito de significante, oriundo do estruturalismo saussuriano e este pode ser fundamentado na noção lógica de conjunto tal como a matemática, após Cantor o concebeu. Discute-se três argumentos contrários a uma possível formalização nas ciências do homem: o da qualidade, o do sentido e o da singularidade. Realiza-se em seguida: (1) uma análise das relações entre o conceito de significante e o de conjunto a partir dos axiomas da teoria de Zermelo-Fraenkel, (2) a apresentação de uma possível lógica para o significante tomado em suas relações de significação tal como a psicanálise lacaniana as concebe, e (3) a proposição do emprego do conceito matemático de modelo, como o que reúne o conceito de conjunto à lógica. Os três resultados obtidos baseiam-se nos desenvolvimentos do filósofo francês Alain Badiou em seu esforço de discutir filosofia através do mesmo recurso à matemática. Conclui-se que nos limites da fundamentação da lógica e da matemática encontra-se os problemas que também norteiam as investigações psicanalíticas a respeito da subjetividade e de suas possíveis transformações / The present study discusses the use of topology as a branch in mathematics in Jacques Lacans theoretical developments. The starting point is the criticism presented by Sokal concerning a supposed lack of fundament of such an appeal in its use within psychoanalysis, contrary to lacanians assertions of topology as its proper structure. Our central objective is to defend the idea that the methodological appeal to topology, to mathematics and to logic is indeed compatible with the concept of significant, as brought by saussurian structuralism, and that the former concept can be grounded on the logical concept of set, as mathematics after Cantor conceived it. Three arguments that oppose to a possible formalization within human sciences are discussed: one concerning quality, one regarding meaning and one that affirms singularity. The following are developed in the sequence: (1) an analysis of the relations between the concept of significant and that of set, according to the axioms of Zermelo- Fraenkel theory, (2) a presentation of a possible logic for the significant taken in its signifying relations, as lacanian psychoanalysis conceives it, and (3) a proposition of adoption of the mathematical concept of model, as one that unites the concept of set and logic. These three results are based on Alain Badious developments and effort to discuss philosophy through this same appeal to mathematics. One concludes that in the very limits of mathematical and logic fundaments one finds the same problems that guide psychoanalytical research regarding subjectivity and its possible transformation

Este trabalho discute o emprego da topologia como ramo da matemática nos desenvolvimentos teóricos de Jacques Lacan. O ponto de partida é a crítica apresentada por Sokal quanto à falta de fundamento deste recurso em seu uso pela psicanálise, em contraposição às afirmações lacanianas quanto a ser a topologia a própria estrutura. O objetivo central é defender a idéia de que o recurso metodológico à topologia, às matemáticas e à lógica é compatível com o conceito de significante, oriundo do estruturalismo saussuriano e este pode ser fundamentado na noção lógica de conjunto tal como a matemática, após Cantor o concebeu. Discute-se três argumentos contrários a uma possível formalização nas ciências do homem: o da qualidade, o do sentido e o da singularidade. Realiza-se em seguida: (1) uma análise das relações entre o conceito de significante e o de conjunto a partir dos axiomas da teoria de Zermelo-Fraenkel, (2) a apresentação de uma possível lógica para o significante tomado em suas relações de significação tal como a psicanálise lacaniana as concebe, e (3) a proposição do emprego do conceito matemático de modelo, como o que reúne o conceito de conjunto à lógica. Os três resultados obtidos baseiam-se nos desenvolvimentos do filósofo francês Alain Badiou em seu esforço de discutir filosofia através do mesmo recurso à matemática. Conclui-se que nos limites da fundamentação da lógica e da matemática encontra-se os problemas que também norteiam as investigações psicanalíticas a respeito da subjetividade e de suas possíveis transformações / The present study discusses the use of topology as a branch in mathematics in Jacques Lacans theoretical developments. The starting point is the criticism presented by Sokal concerning a supposed lack of fundament of such an appeal in its use within psychoanalysis, contrary to lacanians assertions of topology as its proper structure. Our central objective is to defend the idea that the methodological appeal to topology, to mathematics and to logic is indeed compatible with the concept of significant, as brought by saussurian structuralism, and that the former concept can be grounded on the logical concept of set, as mathematics after Cantor conceived it. Three arguments that oppose to a possible formalization within human sciences are discussed: one concerning quality, one regarding meaning and one that affirms singularity. The following are developed in the sequence: (1) an analysis of the relations between the concept of significant and that of set, according to the axioms of Zermelo- Fraenkel theory, (2) a presentation of a possible logic for the significant taken in its signifying relations, as lacanian psychoanalysis conceives it, and (3) a proposition of adoption of the mathematical concept of model, as one that unites the concept of set and logic. These three results are based on Alain Badious developments and effort to discuss philosophy through this same appeal to mathematics. One concludes that in the very limits of mathematical and logic fundaments one finds the same problems that guide psychoanalytical research regarding subjectivity and its possible transformation

Thesis (PhD)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: The primary concern of this dissertation will be to understand under what conditions novelty arises within a system. In classical philosophy, the notion of novelty is usually said to arise out of an event. However, the notion of an event often carries with it metaphysical and conservative implications. Therefore, part of the concern of this dissertation is to begin to develop an approach to novelty which is not dependent upon the event. This approach is developed through the insights offered by Critical Complexity and post‐structuralist philosophy. In social science the model of the frame has dominated how to think about the limitations to the context specific nature of knowledge. Instead of the analogy of a frame, this dissertation argues that it is better to adopt the notion of an ‘economy’. This is due to the fact that the notion of an economy allows social scientists to better theorize the relationships which constitute the models they create. The argument for an economy is made by exploring the connections between the work of Jacques Derrida, the complexity theorist Edgar Morin and Georges Bataille. However, when using the notion of an economy, one must always take the excess of this economy into consideration. This excess always feeds back to disrupt the economy from which it is excluded. Using terms developed in complexity theory, this dissertation illustrates how a system adapts to the environment by using this excess. Due to this there can never be a comprehensively modelled complex system because there are always facets of this system which remain hidden to the observer. The work of Alain Badiou, whose central concern is the notion of novelty arising out of an event, is introduced. The implications of depending on the event for novelty to arise are drawn out by discussing the affinities between the work of Derrida and Badiou. In this regard, Derrida’s use of the term ‘event’ much more readily agrees with a complexity informed understanding of the term in contrast to the quasi‐religious definition which Badiou uses. This complexity‐informed understanding of the event illustrates that what the event reveals is simultaneously a dearth and wealth of possibilities yet to be realized. Therefore the event cannot be depended upon to produce novelty. However, the notion of the event must not be discarded too quickly; classical science has traditionally discarded this idea due to its reductive approach. The idea of process opens up an understanding of the radical novelties produced in history to the possibility of the event and to a new understanding of ontology. This dissertation proposes that one can begin to think about radical forms of novelty without the event through the notion of experimentation. This approach allows one to engage with what exists rather than relying upon an event to produce novelty. This argument is made by following Bataille, who argues that through an engagement with non‐utilitarian forms of action, by expending for the sake of expenditure, the world is opened up to possibilities which remain unrealized under the current hegemony. In this light, this dissertation begins to develop a definition of novelty as that which forces a rereading of the system’s history. / AFRIKAANSE OPSOMMING: Hierdie proefskrif onderneem hoofsaaklik om die omstandighede waaronder nuwigheid binne ʼn stelsel ontstaan te verstaan. Daar word in die klassieke filosofie voorgehou dat nuwigheid gewoonlik vanuit ʼn gebeurtenis ontstaan. Die idee van ʼn gebeurtenis hou egter dikwels ongewenste metafisiese en konserwatiewe implikasies in. Hierdie proefskrif onderneem dus om, deels, ʼn benadering tot nuwigheid te ontwikkel wat onafhanklik van die gebeurtenis staan. Hierdie benadering word verder uitgebrei met behulp van insigte vanuit die Kritiese Kompleksiteits‐ en Post‐Strukturalistiese filosofie. Tot onlangs het die model van die raamwerk die wyse waarop daar oor die beperkinge van die konteks‐spesifieke aard van kennis in die sosiale wetenskappe gedink word oorheers. In hierdie proefskrif word voorgehou dat die idee van ʼn ‘ekonomie’ in plaas van die analogie van ʼn raamwerk hier gebruik behoort te word, omdat dit ons sal toelaat om die verhoudings binne die modelle wat deur sosiale wetenskaplikes gebruik word beter te verken. Verder word die moontlike verbande tussen Jacques Derrida , die kompleksiteitsfilosoof Edgar Morin en Georges Bataille teen hierdie agtergrond verken. Wanneer daar van ʼn ekonomie gepraat word, moet die oormaat van die ekonomie altyd in ag geneem word. Hierdie oormaat ontwrig altyd die ekonomie waarby dit uitgesluit word. Om te wys hoe die stelsel van so ʼn oormaat gebruik maak om by sy omgewing aan te pas, sal terminologie wat in die konteks van kompleksiteitsteorie ontwikkel is gebruik word. As gevolg van die oorvloed binne ʼn stelsel sal daar nooit ʼn volledige model van die stelsel ontwikkel kan word nie ‐‐ fasette van die stelsel sal altyd vir die waarnemer verborge bly. Verder sal die werk van Alain Badiou, wie se filosofie rondom die idee van nuwigheid wat uit ʼn gebeurtenis ontstaan gesentreed is, in hierdie verhandeling bespreek word. Die implikasies van die idee dat nuwigheid van die gebeurtenis afhanklik is word uitgelig deur die verwantskappe tussen die werke van Derrida en Badiou te bespreek. Derrida se gebruik van die term ‘gebeurtenis’ dra ʼn noue verwantskap met kompleksiteitsteorie, en dit word teenoor Badiou se amper‐godsdienstige gebruik van die term gestel. Daar word aangevoer dat daar binne ʼn kompleksiteits‐ingeligte verstaan van ʼn gebeurtenis beide ʼn skaarste en ʼn oorvloed van moontlikhede bestaan wat vervul kan word. Daarom kan daar juis nié op die gebeurtenis staatgemaak word om nuwigheid te skep nie. Die idee van die gebeurtenis moet egter nie te gou verwerp word nie. As gevolg van die klassieke wetenskap se reduksionisme is die idee van ʼn gebeurtenis tradisioneel ontken. Daarteenoor ontsluit die idee van ʼn proses die moontlikheid van radikale nuwighede in die geskiedenis as gevolg van ʼn verstaan van die gebeurtenis wat tot ʼn nuwe verstaan van die ontologie lei. Hierdie proefskrif stel dus voor dat ons voortaan aan radikale nuwigheid dink in terme van die denkbeeld van eksperimentering eerder as in terme van die gebeurtenis. Eksperimentering laat ons toe om te werk met wat ons het, eerder as om op ʼn gebeurtenis te moet wag. Na aanleiding van Bataille is die voorstel dat daar deur om te gaan met nieutilitaristiese vorms van optrede nuwe geleenthede vir die wêreld oopgemaak word; geleenthede wat onder die huidige hegemonie ongerealiseerd sal bly. In hierdie verband stel die proefskrif ʼn definisie van nuwigheid voor as dít wat mens dwing om die geskiedenis van ʼn stelsel te herformuleer.

Cette recherche a pour objectif principal de mener à bien une étude théorique originale d'inspiration marxienne sur la théorie révolutionnaire d'Alain Badiou et de Toni Negri. Nous avons fait une généalogie de la pensée politique révolutionnaire ce qui nous permit de situer le marxisme dans cette tradition. Par la suite, nous avons procédé à la définition des principaux concepts théoriques utilisés par Negri et Badiou. Cette étude conceptuelle a été menée parallèlement à une recherche historico-politique sur le parcours des deux auteurs. Chacun des concepts a été placé en lien avec une période spécifique de leur vie militante. Enfin, nous avons établi le lien entre leur travail théorique actuel et leur engagement politique. ______________________________________________________________________________

This thesis argues that it is both necessary and possible to change the world. Changing the world requires engaging with, to try to understand it from the basis of lived reality, and then acting. Our ability to do this is, however, affected by hegemony, which attempts to convince us that the way things are is either normal and natural and the only possible way they could be, or that it is impossible to change them. Nevertheless, there is always resistance to this, and I suggest that we might learn something useful by examining how this happens. The thesis thus explores Gramsci’s theory of hegemony, and its applicability to our current world; and also considers resistance to this. I argue that the nature of capitalism has shifted, and discuss how this shift has impacted on hegemony, identifying three current interlocking hegemonic ideologies. I consider current resistance to this hegemony, including the role of social movements. Much resistance, and many social movements, I argued, cannot properly be called counter-hegemonic in that, although it/they may critique the dominant economic system, it/they remain trapped within hegemonic logic. However, it is clear that there is existing truly counter-hegemonic resistance, including some social movements, and I argue that Abahlali baseMjondolo is one such counter-hegemonic movement. Thus it is possible that those who join/align themselves with this movement might be considered to have ‘unlearned’ hegemony and be useful subjects for this study. I thus consider the life stories of seven people who have aligned themselves to this movement, in order to determine whether they have indeed ‘unlearned’ hegemony, and if so, how. I discuss relevant and appropriate theory for examining this phenomenon, including experiential learning, transformative learning and Freirean emancipatory learning. I argue that whilst these theories of learning are helpful, they cannot entirely account for unlearning. I then turn to the theory of the event of Alain Badiou as a possible complementary or alternative way into thinking about unlearning. I apply both the learning theories and Badiou’s theory of the event to the stories, all of which show strong evidence of unlearning,, and consider how useful the theories are in understanding this. I conclude that all of the theories help to some extent in understanding the unlearning in stories. There are, however, fundamental differences between the learning theories on the one hand and Badiou’s theory on the other. I construct a model showing that the basis of the difference between the adult learning theories and Badiou’s theory of the event rests on the locus of the trigger for transformation. I argue that Badiou’s theory provides a very useful additional perspective to adult learning theory; but that it cannot be considered to have replaced existing theories in understanding how people learn informally to think and act in counter-hegemonic ways. / Thesis (Ph.D.)-University of KwaZulu-Natal, Pietermaritzburg, 2012.

Submitted by Setor de Tratamento da Informa??o - BC/PUCRS (tede2@pucrs.br) on 2016-05-10T13:24:07Z No. of bitstreams: 1 TES_ALMERINDO_ANTONIO_BOFF_COMPLETO.pdf: 1424543 bytes, checksum: c5fc6845e6654e6a216e1767b6bd2718 (MD5) / Made available in DSpace on 2016-05-10T13:24:07Z (GMT). No. of bitstreams: 1 TES_ALMERINDO_ANTONIO_BOFF_COMPLETO.pdf: 1424543 bytes, checksum: c5fc6845e6654e6a216e1767b6bd2718 (MD5) Previous issue date: 2016-03-03 / In creating psychoanalysis, at the end of the 19th century, Freud dedicated himself to explain the epistemological foundations in which he grounds his assumption of having created a new science, a new branch of natural sciences, with which it shared these epistemological foundations as well as its Weltanschauung. In mid-twentieth century, originating at the critique of psychoanalytical scientificity that came especially from neopositivist epistemology, it fell to Jacques Lacan to resume the question of psychoanalytical epistemology and to consolidate it over new foundations. The present thesis seeks to highlight the fact that, after the lacanian approach to the issue, an original way of conceiving psychoanalysis comes from outside of the psychoanalytical field, more precisely from Jacques Derrida?s philosophy. According to Derrida, psychoanalysis not only doesn?t fit in its entirety within the limits of a regional science, but it also comes to constitute, in harmony with derridean graphemathics, an original way of viewing the constitution of reality in general. The thesis follows the path of derridian critique to freudian epistemology and to lacanian structuralist psychoanalysis of the 1950?s, regarding the contemporary thought that seeks, in the last Lacan through the psychoanalytical field, and in Alain Badiou through the field of philosophy, the foundations of both in the fields of mathematical formalisation. Other than allowing to conceive a new psychoanalytical epistemology consolidated in his philosophy, the thesis follows Derrida in pointing at the challenging paths of a psychoanalysis to come. / Ao criar a psican?lise, a partir do final do s?culo XIX, Freud dedicou-se a explicitar os fundamentos epistemol?gicos em que alicer?ava sua pretens?o de haver criado uma nova ci?ncia, um novo ramo das ci?ncias naturais, com as quais ela compartilhava, portanto, tanto estes fundamentos epistemol?gicos quanto sua Weltanschauung. Em meados do s?culo XX, e agora a partir da cr?tica ? cientificidade da psican?lise provinda especialmente da epistemologia neopositivista, coube a Jacques Lacan retomar a quest?o da epistemologia da psican?lise para alicer??-la sobre outros fundamentos. A presente tese procura evidenciar que, ap?s a abordagem lacaniana do problema, vem de fora da psican?lise, mais precisamente da filosofia de Jacques Derrida, uma maneira original de conceber a psican?lise. Para Derrida, a psican?lise n?o apenas n?o cabe toda dentro dos limites de uma ci?ncia regional, como vem a constituir, em harmonia com a grafem?tica derridiana, uma maneira original de pensar a constitui??o da realidade em geral. A tese percorre os caminhos da cr?tica derridiana ? epistemologia freudiana e ? psican?lise estruturalista lacaniana dos anos 50 do s?culo XX, at? encontrar-se com o pensamento contempor?neo que busca, no ?ltimo Lacan pelo campo da psican?lise, e em Alain Badiou pelo campo da filosofia, a fundamenta??o destas no campo da formaliza??o matem?tica. Al?m de permitir pensar uma nova epistemologia da psican?lise alicer?ada em sua filosofia, a tese acompanha Derrida ao apontar para os desafiadores rumos de uma psican?lise por vir.

Gilles Deleuze’s ontology is often understood to ground a kind of radical pluralism, the political defense of which is thought to be articulated most strongly in the Capitalism and Schizophrenia books. It is clear, however, that this “politics” is defined in a wholly negative way, and that the revolutionary dimension of these books is animated by a strictly ethical logic. In my view, if there is a politics in Deleuze it must be understood in relation to the central problem of his ontology: namely, the problem of understanding how Being is produced. To grasp politics as a singularity, as a mode of ontological production, has a number of radical consequences – consequences, however, that Deleuze himself did not embrace. Ultimately, Deleuze’s conception of ontological production appears marked by an apolitics, in that any effective mobilization of Being’s transformative potential requires that we stand posed to sacrifice anything of the integrity and organizational capacity of political existence that limits the expression of Being itself.

Gilles Deleuze’s ontology is often understood to ground a kind of radical pluralism, the political defense of which is thought to be articulated most strongly in the Capitalism and Schizophrenia books. It is clear, however, that this “politics” is defined in a wholly negative way, and that the revolutionary dimension of these books is animated by a strictly ethical logic. In my view, if there is a politics in Deleuze it must be understood in relation to the central problem of his ontology: namely, the problem of understanding how Being is produced. To grasp politics as a singularity, as a mode of ontological production, has a number of radical consequences – consequences, however, that Deleuze himself did not embrace. Ultimately, Deleuze’s conception of ontological production appears marked by an apolitics, in that any effective mobilization of Being’s transformative potential requires that we stand posed to sacrifice anything of the integrity and organizational capacity of political existence that limits the expression of Being itself.