yes / Thomas S. Kuhn is famous both for his work on the Copernican Revolution and his ‘paradigm’ view of scientific revolutions. But Kuhn later abandoned the notion of paradigm (and related notions) in favour of a more ‘evolutionary’ view of the history of science. Kuhn’s position therefore moved closer to ‘continuity’ models of scientific progress, for instance ‘chain-of-reasoning’ models, originally championed by D. Shapere. The purpose of this paper is to contribute to the debate around Kuhn’s new ‘developmental’ view and to evaluate these competing models with reference to some major innovations in the history of cosmology, from Copernicanism to modern cosmology. This evaluation is made possible through some unexpected overlap between Kuhn’s earlier discontinuity model and various versions of the later continuity models. It is the thesis of this paper that the ‘chain-of-reasoning’ model accounts better for the cosmological evidence than both Kuhn’s early paradigm model and his later developmental view of the history of science.

The problem of historical explanation consists in how historical facts are put together. No mere collection of facts constitutes an explanation: there must be some underlying explanation for why those facts occurred in the way they did. Many competing theories of historical explanation have thus been offered, from the highly technical D-N or covering law model, to narrative-based explanations. This paper exposes the flaws in the covering law model proposed by Carl Hempel, and offers a justification for narrative-based explanations by appealing to the notion of language games as used by Ludwig Wittgenstein, as well as the narrative and paradigm models of Arthur Danto and Thomas Kuhn for explaining historical events. / Master of Arts / The problem of historical explanation consists in how historical facts are put together. No mere collection of facts constitutes an explanation: there must be some underlying explanation for why those facts occurred in the way they did. Many competing theories of historical explanation have thus been offered, from the highly technical D-N or covering law model, which imitates the methods of explanation in “hard” scientific inquiry through a careful description of initial conditions and relevant laws and formulas, to narrative-based explanations, or explanations that use a story with a beginning, a middle, and an end. This paper exposes the flaws in the covering law model proposed by Carl Hempel, and offers a justification for narrative-based explanations by appealing to the notion of language games as used by Ludwig Wittgenstein, as well as the narrative and paradigm models of Arthur Danto and Thomas Kuhn for explaining historical events. The aim of this project is to prevent scientific analysis being incorrectly applied to non-scientific entities, such as persons (e.g. Napoleon Bonaparte) and places (e.g. Russia) which are referenced in ordinary language, and which are in principle irreducible to the primary entities of the so-called “hard” sciences, such as subatomic particles and fundamental forces.

This work is concerned with the construction of preconditioners for indefinite linear systems. The systems under investigation arise in the numerical solution of quadratic programming problems, for example in the form of Karush--Kuhn--Tucker (KKT) optimality conditions or in interior--point methods. Therefore, the system matrix is referred to as a KKT matrix. It is not the purpose of this thesis to investigate systems arising from general quadratic programming problems, but to study systems arising in linear quadratic control problems governed by partial differential equations. The KKT matrix is symmetric, nonsingular, and indefinite. For the solution of the linear systems generalizations of the conjugate gradient method, MINRES and SYMMLQ, are used. The performance of these iterative solution methods depends on the eigenvalue distribution of the matrix and of the cost of the multiplication of the system matrix with a vector. To increase the performance of these methods, one tries to transform the system to favorably change its eigenvalue distribution. This is called preconditioning and the nonsingular transformation matrices are called preconditioners. Since the overall performance of the iterative methods also depends on the cost of matrix--vector multiplications, the preconditioner has to be constructed so that it can be applied efficiently. The preconditioners designed in this thesis are positive definite and they maintain the symmetry of the system. For the construction of the preconditioners we strongly exploit the structure of the underlying system. The preconditioners are composed of preconditioners for the submatrices in the KKT system. Therefore, known efficient preconditioners can be readily adapted to this context. The derivation of the preconditioners is motivated by the properties of the KKT matrices arising in optimal control problems. An analysis of the preconditioners is given and various cases which are important for interior point methods are treated separately. The preconditioners are tested on a typical problem, a Neumann boundary control for an elliptic equation. In many important situations the preconditioners substantially reduce the number of iterations needed by the solvers. In some cases, it can even be shown that the number of iterations for the preconditioned system is independent of the refinement of the discretization of the partial differential equation. / Master of Science

La presente investigación constituye un acercamiento crítico a la noción de inconmensurabilidad propuesta por Kuhn en 1962. Consideramos que es una noción insostenible tanto en su versión radical como en la moderada. Así, en primera instancia, realizaremos una revisión histórica del concepto en sus versiones ontológicas, epistemológicas y, sobre todo, semánticas. Nuestras críticas iniciales reposan sobre los alcances que Davidson, Putnam y Coseriu han hecho sobre el tema: el primero con su crítica a la idea de esquema conceptual, el segundo sobre la teoría de la referencia y, el tercero, sobre las posibilidades y condiciones de la traducción. Asumimos que el elemento vinculante entre estas críticas es el realismo que subyace a sus propuestas. Una vez realizada la revisión histórica y la recopilación de argumentos en contra de la noción en cuestión presentaremos nuestra propuesta. Esta defiende que la experiencia es el eje para poner en cuestión nuestro lenguaje y nuestro paradigma. Para llevar a cabo este trabajo, primero presentaremos los alcances centrales de Kuhn sobre esta noción. Luego presentaremos las perspectivas críticas a este concepto desde los tres autores mencionados. En un tercer momento reformularemos las críticas planteadas y presentaremos nuestra hipótesis sobre el tema: esta establece que la experiencia está por encima de las palabras y por encima de los paradigmas. Asimismo, propondremos que hay una salida práctica para los casos de inconmensurabilidad parcial: el uso de ―enunciados básicos‖ ya descritos por Popper y que equiparamos con la idea de ―teorías al paso‖ de Davidson. Cerraremos el trabajo con la revisión de las conclusiones alcanzadas en el desarrollo.

The foundations of deep learning are supported by the seemingly opposing perspectives of approximation or learning theory. The former advocates for large/expressive models that need not generalize, while the latter considers classes that generalize but may be too small/constrained to be universal approximators. Motivated by real−world deep learning implementations that are both expressive and statistically reliable, we ask: "Is there a class of neural networks that is both large enough to be universal but structured enough to generalize?" This paper constructively provides a positive answer to this question by identifying a highly structured class of ReLU multilayer perceptions (MLPs), which are optimal function approximators and are statistically well−behaved. We show that any L−Lipschitz function from [0,1]ᵈ to [−n,n] can be approximated to a uniform Ld/(2n) error on [0,1]ᵈ with a sparsely connected L−Lipschitz ReLU MLP of width 𝒪(dnᵈ), depth 𝒪(łog(d)), with 𝒪(dnᵈ) nonzero parameters, and whose weights and biases take values in {0,± 1/2} except in the first and last layers which instead have magnitude at−most $n$. Unlike previously known "large" classes of universal ReLU MLPs, the empirical Rademacher complexity of our class remains bounded even when its depth and width become arbitrarily large. Further, our class of MLPs achieves a near−optimal sample complexity of 𝒪(łog(N)/√{N}) when given N i.i.d. normalized sub−Gaussian training samples. We achieve this by avoiding the standard approach to constructing optimal ReLU approximators, which sacrifices regularity by relying on small spikes. Instead, we introduce a new construction that perfectly fits together linear pieces using Kuhn triangulations and avoids these small spikes. / Thesis / Master of Science (MSc)

This qualitative research is a contribution to the ongoing debate among marketing researchers regarding if there is a dominant paradigm and viewpoint of marketing and which one is the most appropriate. In this study current views of marketing are identified and then compared against the older Goods-Dominant Logic of Marketing and Vargos’ and Luschs’ alternative Service-Dominant Logic of Marketing. The trends that have been observed are situated in the framework of Thomas S. Kuhn’s philosophy of science. The aim has been to make an analysis about which stage marketing is in its scientific revolution today. Kuhn’s philosophy has, as far as we know, never been examined with the chosen methodology. Further it has not been applied onto a social science either. The conclusion that has been drawn in the thesis is that marketing is dealing with anomalies at this moment. Therefore it is in a stage of crisis in its scientific revolution. Hence there is not a dominant paradigm in marketing currently. / Bakgrunden till uppsatsen är den debatt vilken pågått under snart 20 år fram till dags dato mellan marknadsföringsforskare gällande vilket grundläggande synsätt som vetenskapen bör ha. Forskning visar på att marknadsföringsdisciplinen under lång tid präglats av ett varucentrerat synsätt som har sitt ursprung i nationalekonomin. I debatten tydliggör forskarna för de brister som de finner med det varucentrerade synsättet och särskilt gällande det förhållningssätt synsättet har till service och tjänster. Undersökningen har sin utgångspunkt i den fråga några forskare ställer sig gällande om ett paradigmskifte kan vara på gång inom marknadsföringsdisciplinen. Frågan ställer vi mot det alternativa synsätt Stephen Vargo och Robert Lusch utvecklat. De är inte de enda forskare som utvecklat alternativa synsätt men deras utmärker sig på två sätt. Dels genom att service istället för varor är grundstenen i synsättet dels den aggregerade nivån på deras resonemang. Vi ställer oss frågan vilket som är det rådande paradigmet inom marknadsföringsdisciplinen idag. Är det Vargos och Luschs nya servicecentrerade synsätt Service-Dominant (S-D) Logic of Marketing, eller det äldre varucentrerade som de benämner Goods-Dominant (G-D) Logic of Marketing? Eller kanske något annat? Frågeställningen ställs utifrån Thomas S. Kuhns vetenskapsfilosofi vari paradigm är det mest centrala begreppet. Vidare syftar vi till att påvisa i vilken av faserna i den vetenskapliga revolution som marknadsföringsdisciplinen är i idag. Undersökningen har främst en deduktiv ansats, där grunden utgörs av en omfattande litteraturstudie. Kuhns vetenskapsfilosofi och alla de faser som ingår i den vetenskapliga utvecklingen som han kallar för vetenskapliga revolutioner fungerar som en metateori. Vidare redogörs det även för de karakteristiska dragen i G-D Logic och S-D Logic. Metodvalet är kvalitativt då vi syftar till att ge en ögonblicksbild av rådande synsätt vilket stämmer väl överens med kvalitativa metoders styrkor. Tio informanter inom urvalet intervjuades rörande deras synsätt kring områden som marknadsföringsämnet består av. Analysen byggs sedan upp i två steg. Informanternas svar analyseras utifrån G-D Logic och S-D Logic för att se om informanternas synsätt omfattas av dem eller om något annat synsätt är tydligt. De tendenser vi finner i informanternas synsätt analyserar vi sedan utifrån Kuhns vetenskapsfilosofi. Därefter var det möjligt att dra slutsatsen att marknadsföringsdisciplinen idag befinner sig i den vetenskapliga fasen kris som karakteriseras av anomalier. Vidare är inget synsätt dominant idag. Undersökningen har främst två målgrupper. Dels forskare inom marknadsföringsämnet där vi bidrar till den rådande debatten. Dels till andra samhällsvetenskapliga discipliner. Vi har inte kunnat finna att Kuhns filosofi har testas inom samhällsvetenskapen tidigare. Därigenom kommer undersökningen också med ett metodologiskt bidrag.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / e recent literature in philosophy of science has been reassessing the positivist legacy. One of the items on the agenda is the alleged opposition between the theses put forth by positivists such as Carnap and the so-called post-positivists , such as Kuhn. Although the laer came to be viewed as a critic of several important positivist theses, more recent authors such as Friedman, Reisch, Earman, Irzik and Grünberg, maintain that several of the most characteristic theses of the Kuhnian view of science were already present in Carnap s philosophy. Against this kind of reading, authors such as Oliveira and Psillos argue that within Carnap s philosophy there is no place for Kuhnian theses like incommensurability, holism or the theoryladenness of observations. e first article of this dissertation presents the reasons for each of those readings and assesses them having in view the perspectives from which they are offered. It argues that it is possible to show that some aspects of Kuhn s thesis have a counterpart in the works of Carnap, although those theses vary in importance for Carnap and Kuhn. e second article presents aspects that can be seen as antagonistic in the two views, namely, the conceptions that relate to that distinction made famous by Reichenbach between contexts of discovery and justification. / A literatura recente em filosofia da ciência vêm reavaliando o legado positivista. Um dos itens dessa reavaliação é a suposta oposição entre as teses defendidas por positivistas como Carnap e os chamados pós-positivistas , como Kuhn. Embora este último tenha sido percebido como um crítico de diversas teses positivistas importantes, autores mais recentes como Friedman, Reisch, Earman, Irzik e Grünberg, sustentam que várias das teses mais características da concepção kuhniana da ciência já estariam presentes na filosofia positivista. Contra esse tipo de leitura, autores como Oliveira e Psillos argumentam que não há na filosofia de Carnap e outros positivistas lugar para teses como a da incomensurabilidade, do holismo ou da impregnação teórica das observações, características das concepções kuhnianas. O primeiro artigo desta dissertação apresenta as razões para cada uma dessas leituras e avalia cada uma tendo em vista a perspectiva a partir da qual elas são oferecidas. Defende que é possível mostrar que algumas teses kuhnianas têm uma contraparte já nos trabalhos de Carnap, muito embora tais teses ocupem posições e importâncias diferenciadas em Carnap e Kuhn. O segundo artigo apresenta aspectos que podem ser vistos como antagônicos nas filosofias de ambos, a saber, as concepções que dizem respeito àquela distinção feita famosa por Reichenbach entre contextos de descoberta e justificação.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this work some classical methods for constrained nonlinear optimization are studied. The mathematical formulations for the optimization problem with equality and inequality constrained, convergence properties and algorithms are presented. Furthermore, optimality conditions of rst order (Karush-Kuhn-Tucker conditions) and of second order. These conditions are essential for the demonstration of many results. Among the methods studied, some techniques transform the original problem into an unconstrained problem (Penalty Methods, Augmented Lagrange Multipliers Method). In others methods, the original problem is modeled as one or as a sequence of quadratic subproblems subject to linear constraints (Quadratic Programming Method, Sequential Quadratic Programming Method). In order to illustrate and compare the performance of the methods studied, two nonlinear optimization problems are considered: a bi-dimensional problem and a problem of mass minimization of a coil spring. The obtained results are analyzed and confronted with each other. / Neste trabalho são estudados alguns métodos clássicos de otimização restrita não linear. São abordadas a formulação matemática para o problema de otimização com restrições de igualdade e desigualdade, propriedades de convergência e algoritmos. Além disso, são relatadas as condições de otimalidade de primeira ordem (condições de Karush-Kuhn-Tucker) e de segunda ordem. Estas condições são essenciais para a demonstração de muitos resultados. Dentre os métodos estudados, algumas técnicas transformam o problema original em um problema irrestrito (Métodos de Penalidade, Método dos Multiplicadores de Lagrange Aumentado). Em outros métodos, o problema original é modelado como um ou uma seqüência de subproblemas quadráticos sujeito _a restrições lineares (Método de Programação Quadrática, Método de Programação Quadrática Seqüencial). A fim de ilustrar e comparar o desempenho dos métodos estudados são considerados dois problemas de otimização não linear: um problema bidimensional e o problema de minimização da massa de uma mola helicoidal. Os resultados obtidos são examinados e confrontados entre si. / Mestre em Matemática

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The publication of Thomas Kuhn s The structure of scientific revolutions is considered a watershed in the philosophy of science for having presented scientific knowledge as produced by a dynamic and historically situated process. Many of the concepts introduced by the author sparked controversy in the initial reception of this work. We highlight in this dissertation Kuhn s theses on scientific revolutions, incommensurability, and scientific choice between rival hypothesis, which were interpreted by authors such as Popper, Lakatos, Laudan and Putnam as introducing elements of irrationality and relativism into Kuhn s analysis of scientific practice. In the first paper of this dissertation, we investigate passages from Structure that led to those interpretations, and track down Kuhn s later reformulations of the three controversial theses, which attempted to avoid or respond the criticisms of irrationality and relativism. We highlight the linguistic emphasis given by Kuhn in his later works to the concepts of incommensurability and scientific revolution, and show that his thesis about scientific choices remained nearly unchanged. We claim that in Kuhn s later works his theses became more precisely formulated and narrower in scope, and that they manifest a realist inclination by the author. The second paper of this dissertation develops in more detail the issue of the rationality of scientific choice. It presents briefly three theories of scientific rationality due to Kuhn, Lakatos and Laudan, and then shows some of the problems that Lakatos and Laudan s theories face due to focusing their notion of rationality on univocal rules of choice. We then indicate that there are advantages in understanding as Kuhn did the notion of rationality in terms of values that influence objectively the choices to be made without determining them univocally. / A publicação de A estrutura das revoluções científicas, de Thomas Kuhn, é considerada um divisor de águas na filosofia da ciência por apresentar o conhecimento científico como sendo gerado por um processo dinâmico e historicamente situado. Muitos dos conceitos introduzidos pelo autor foram motivos de controvérsia na recepção inicial da obra. Destacamos na presente dissertação as teses de Kuhn sobre revoluções científicas, incomensurabilidade e escolhas científicas entre hipóteses rivais, que foram interpretadas por autores como Popper, Lakatos, Laudan e Putnam, como introduzindo elementos de irracionalidade e relativismo na análise kuhniana da atividade científica. No primeiro artigo desta dissertação, investigamos as passagens na Estrutura que levaram a essas interpretações, e rastreamos as reformulações kuhnianas posteriores para as três teses controversas com vistas a evitar ou responder as críticas de irracionalidade e relativismo. Destacamos a ênfase linguística dada por Kuhn aos conceitos de incomensurabilidade e revolução científica, e mostramos que a tese acerca das escolhas científicas permanece quase inalterada nos textos tardios. Defendemos que na obra tardia de Kuhn suas teses tornaram-se mais precisas e menos abrangentes e evidenciam uma inclinação realista do autor. O segundo artigo desta dissertação desenvolve de maneira mais detalhada a questão da racionalidade das escolhas científicas, apresentando as propostas de três teorias historicistas da racionalidade científica, devidas a Kuhn, Lakatos e Laudan. Apresentamos alguns dos problemas que as teorias de Lakatos e Laudan enfrentam ao concentrar a noção de racionalidade em regras unívocas de escolha e indicamos que há vantagens em se compreender a noção de racionalidade em termos de valores que influenciam objetivamente as escolhas sem determiná-las univocamente, como propôs Kuhn.

Numerous studies have attempted to measure scientists' influence by measuring the quantity of citations to their works. The problem with "citation counting," as it is called, is that it assumes that each listing of an author in a citation index is equal to another without bothering to explore the substantive uses of citations in the source article. The present study attempts to alleviate this problem by content analysis of citations in a limited sphere: reference to major philosophers of science by sociologists. In just over 100 sociology journals, citations to Thomas Kuhn, Karl Popper, Ernst Nagel, and Carl Hempel (overall, the most frequently cited philosophers of science) from 1971-1982 were randomly sampled. Each citation was classified according to the following criteria: 1) philosopher cited; 2) work cited, 3) exclusivity (whether cited with others); 4) multiplicity (number of citations by the philosopher in the same article); 5) type of article; and 6) purpose of citation. Purposes of citation included seven categories: 1) listing as relevant literature; 2) definition of a concept; 3) modification or extension of a philosopher's theory; 4) formulation of a research problem; 5) interpretation of results; 6) critical of philosopher's work; and 7) other. Analysis of these data revealed the following conclusions: 1) the major use of philosophy was the furnishing of concepts and their definitions; 2) philosophy of science played little or no role in directing research or interpreting results; 3) the use of citations differed greatly among the philosophers; 4) simple citation counting would have severely distorted the relative influences of each philosopher; and 5) the dialogue between sociology and the philosophy of science has, in the last decade, been dominated by Kuhn's theory of scientific revolutions.