Rozprawy doktorskie na temat „Incommensurability”

In the dissertation, I propose to consider the vicissitudes of Thomas Kuhn's historical approach to science with an eye to clarifying his controversial notion of incommensurability. Although the notion of incommensurability, one of the most significant results of Kuhn's The Structure of Scientific Revolutions, has been much criticized in recent Anglo-American philosophy, I argue that it incorporates insights that are still worth reviving and defending. Moreover, since these insights derived from Kuhn's syntheses of the ideas of thinkers such as L. Fleck, A. Koyre, L. Wittgenstein, N. Hanson, M. Polanyi, H. Gadamer and P. Feyerabend, my defence of Kuhn's concept of incommensurability provides a review of some profound issues in recent Anglo-American philosophy. Also in this connection, I assume that the"Kuhnian Revolution" in philosophy of science in the 1960s did not occur by chance in the avenue of contemporary American philosophy. Rather, the appearance, the reception and the subsequent criticism of The Structure of Scientific Revolutions, including Kuhn's later conversion to the "analytical tradition", must be interpreted in their respective philosophical contexts. I maintain that the debate between the Kuhnian school and its opponents should be examined historically in the light of the deeper and broader cultural and philosophical issues involved, issues that even Kuhn seems not to have fully appreciated. Through investigating the debate, I argue that the critiques of Kuhn's original ideas, including his own later objections to the ideas, presuppose as well as impose the analytical standard of legitimatization that underlies present-day Anglo-American ways of reasoning. It is this standard, however, that presupposes the very requirement whose feasibility Kuhn's notions of paradigms and incommensurability put into question. More specifically, I defend Kuhn's historical approach to philosophy of science in 1962 against those criticisms which are guided merely by ahistorical and linguistic requirements of analyzability, and criticize Kuhn's acceptance of the precepts of the analytical tradition since 1969. Central to this research is the view that there are phenomena of incommensurability in the process of communication and understanding and that no account of rationality is valid unless it recognizes the development of reason in history. In light of this, I hold, the analytical approach should always allow a historically-oriented vision in order to detect the real picture of our everyday thinking. To understand different rationalities in history and culture, philosophy must go to the history of sciences and to the real process of our everyday thinking. Methodologically, I approach the vicissitudes of Thomas Kuhn's notion of incommensurability in two ways: in Part I by historical case studies of Kuhn's changing views, and in Part II by philosophical reflections on those consequences of the historical case studies. (Abstract shortened by UMI.)

Kuhn's incommensurability thesis is the claim that successive scientific theories often conflict not only logically but also normatively: i.e. they differ both about nature and also about the use of common apparatus, concepts and experimental results, and what are proper scientific goals and methods. Critics commonly object that Kuhn's thesis attacks such traditional scientific values as objectivity and rationality. But their strongest response can be expressed as a dilemma: either, if taken literally, the incommensurability thesis is self-contradictory; or, if that literal reading is rejected, this thesis has no philosophical Import. Kuhn claims his critics have misinterpreted his thesis and he maintains both its intelligibility and relevance. The problem is whether his position can be sustained. In support of Kuhn, I argue that his critics' reading of his thesis is based on a mistaken Identification of logic with formal logic and, more generally, of comparability with commensurabil-lty. I argue that logical comparison of theories that lack common concepts is possible if one can compare theories directly, as whole to whole, and that such direct logical comparison is actually commonplace in natural languages. I also argue more generally that Kuhn's critics' identification of comparison with com-mensuration leads to a vicious regress. My attempt at resolving the dispute between Kuhn and his critics is informed by a simple "hermeneutic" principle: If one view seems either unintelligible or irrelevant to the other, then both sides probably disagree on the Interpretation of shared concepts. Once the focus of the dispute is located, arguments can often be given for preferring one interpretation over another. Thus if I am right that Kuhn's critics' view wrongly equates comparability with commensurability and logic with formal logic, that view clearly must be replaced by one that distinguishes them. I argue that if those distinctions are made, incommensurability can be seen to represent no essential threat to scientific rationality and objectivity. In this light, I suggest Kuhn's major analytic concepts be viewed as Improvements on more traditional notions drawn from formal logic. I also use a historical case study of the original discovery of geometrical incommensurability to illustrate further Kuhn's concepts and to develop a more general notion of a proof of incommensurability that is applicable to scientific theories.<br>Arts, Faculty of<br>Philosophy, Department of<br>Graduate

This dissertation investigates the possible implications of incommensurability of values for practical reason and distributive justice. Under certain conditions incommensurability of values causes incomplete comparability' of options.

This dissertation proposes a theory of reference for the language of scientific theories. This theory of reference looks at the nature of postulation in scientific theories, and shows that mental posits are metaphorical in nature. It is a hybrid of internalist and extensive reference theories. This, allied with the competing epistemological assumptions of competing schools of linguistics, can account for the existence of incommensurability across two paradigms of linguistics. The relationship between transformational generative grammar and socio- linguistics is vexed. Both claim the same object of study, but with radi- cally different methods and aims. This dissertation shows that the meta- phorical nature of the posits used in each leads to incommensurable vo- cabularies. Thomas Kuhn's notions of paradigms and incommensurability are used to elucidate this relationship. Chapter one proposes and explains the theory of reference. Chapter two defines the major areas of the thesis. Chapter three explores the history of linguists claiming that a particular area of linguistics instantiates a Kuhnian paradigm, and looks at arguments concerning the possibilities for studying language scientifically. Chapter four explores the epistemological bases of TGG and sociolinguistics, starting from Chomsky's claims to do 'Cartesian linguistics', and concludes that opposing epistemological commitments lead to incommensurability. Chapter five demonstrates the inc- ornmensurable concepts and vocabulary items, and shows how my theory of reference can account for that incommensurability, while maintaining a certain amount of the traditional natural science - social science distinction. Because postulation is free and metaphorical. terms borrowed from natural languages into scientific theories can end up with overlapping, but incommensurable, references. Incommensurability is shown to be local and surmountable, through 'language-learning' rather than through 'translation'.

As it is discussed in philosophy, economics, and some other social sciences, well-being is very commonly conceived of and treated in quantificational terms. However, it is difficult, if not impossible to make room in the quantificational conception of well-being for any notion of sufficiency––of having enough in a sense that it is especially ethically significant that people attain. This difficulty with sufficiency is encapsulated by the Threshold Problem: that of non-arbitrarily specifying a sufficiency level on a scale of well-being. This thesis takes this difficulty and this problem as an opportunity to investigate deeper problems with the quantifying approach. One line of inquiry pursued is whether a theory of needs could solve the Threshold Problem. To this end existing theories of needs are surveyed, but found wanting. The central element of the thesis, however, is a critique of the quantifying account of well-being emerging from a discussion of value incommensurability––which in turn provides resources for the development of an account of the structure of well-being. This account presents a new theory of needs, and analyses well-being in terms of needs. It avoids the Threshold Problem, because well-being is no longer a level at which a person is, nor an amount of anything they have. Rather, both having enough and being well are to have everything one needs.

This study focuses on the erasure of the black woman from the mainstream theatre space of South Africa as a provocation towards the creation of a dramaturgical process that pivots around the notion of 'deliberate incommensurability' as a catalyst for exploration. 'deliberate incommensurability' is a term I have coined myself as it suggests an agency in the black woman as subject and object of study. I suggest the requirement for an autoethnographic inquest in carrying out the research, as the methodology used in the creation of the processes and products of the study was Practice as Research (PaR). The methodology uses the modes of translation and literary studies in order to unpack the myriad ways in which the representation of the black female has effectively been an erasure of her presence. I detail four points of origin for the study drawn primarily from Gayatri C. Spivak and Toni Morrison. In addition, the study interrogates the processes towards creating O Kae? - a performance installation that evaluates the importance of opacity towards the self-representation of the Other in an attempt to discover an alternative aesthetic and creative praxis for myself.

This thesis assesses the legal doctrine res ipsa loquitur ('the thing speaks for itself) in the context of delictual claims for compensation for medical negligence in South African law. The thesis accepts that the doctrine is defensible in principle: a civil court may justifiably draw an inference that a defendant's negligent conduct was a factual cause of the harm suffered in simple cases where there is uncontradicted evidence sufficient to establish a prima facie case. However, it is argued that the South Africa Appellate Division's rejection of the doctrine in the context of medical negligence in 1924 remains justified. It is sometimes thought that the doctrine would assist plaintiffs in complex medical cases by easing the difficulty of establishing a cause of action on a balance of probabilities. However, the thesis argues to the contrary that applying the doctrine in the context of medical negligence claims in South Africa is potentially unjust to claimants and defendants alike. Judgments of medical negligence cannot be made soundly without a proper appreciation of the relevant medical facts. The availability of the doctrine, in the South African context, provides a motivation for plaintiffs to advance insufficiently-prepared evidence, sometimes without the views of experts. This results in the oversimplification of complex medical realities, which increases the risk that courts may reach conclusions regarding negligence and factual causation for reasons that are unjustifiable from a medical perspective. Insufficiently-prepared evidence is also vulnerable to rebuttal by defendant-doctors on 'exotic' or inadequate grounds from a medical perspective, resulting in the unjust rejection of negligence claims. By enabling a superficial approach to deciding questions of medical negligence in the South African context, the doctrine may promote the erroneous assumption that bad medical outcomes typically result from medical wrongdoing. To make its case, the thesis draws on case studies of a variety of medical procedures and contrasts the operation of res ipsa loquitur in South Africa against English legal experience. Differences between the two systems of medical negligence cast doubt on the notion that the English approach should be transplanted to South Africa. Rather than relying on the res ipsa loquitur doctrine to bolster claims made without medical expert evidence, the South African plaintiff should instead rely on constitutional arguments, appealing to basic rights to bodily integrity and dignity, to justify the injection of a degree of flexibility into the common-law elements of a delictual claim.

This thesis examines postmodern challenges to the modern understanding of subjectivity, reality, rationality and morality and uses the work of Hans Magnus Enzensberger to exemplify and comment on the debates between modern and postmodern thought. The modern and the postmodern are presented as modes of thought (rather than as specific theories) that are defined by the way their respective discourses are conducted. This thesis shows how modern and postmodern ways of thinking approach the concepts of the subject and the Self, the notions of reality, truth and representation, the problem of morality and justice, and the question of what it means to be rational. The impetus behind postmodern thought is its dissatisfaction - on both cognitive and moral grounds with the universalising and commensurating strategies of modern discourse. To ensure the heterogeneity of individual paradigms, as well as to safeguard their autonomy and "purity" (Lyotard), postmodern thought promotes incommensurability and advances a type of discourse that is suspicious of metanarratives and resists methodological constraints. The postmodern insistence on incommensurability and plurality, however, becomes especially problematic where the issue of morality is concerned. This thesis argues that the very notion of morality depends on an intersubjective "we" to distinguish it from the self-interest of moral relativism. From the postmodern perspective, however, the notion of community threatens the inviolability of the individual and brings about the spectre of coercion. This thesis examines the different ways postmodern thought approaches the problem of incommensurability and morality, while maintaining its opposition to relativism. The above themes are discussed with reference to Enzensberger's writing through which he raises his concerns about both modes of thinking. This thesis contends that although Enzensberger generally supports the open-ended, pluralistic discourse of postmodern thought and disputes the validity of the either/or approach of modern thought, his writing nevertheless retains a critical awareness of the limitations of both modem and postmodern attitudes.

Problem-solving courts appear to achieve outcomes that are not common in mainstream courts. There are increasing calls for the adoption of more therapeutic and problem-solving practices by mainstream judges in civil and criminal courts in a number of jurisdictions, most notably in the United States and Australia. Currently, a judge who sets out to exercise a significant therapeutic function is likely to be doing so in a specialist court or jurisdiction, outside the mainstream court system, and arguably, outside the adversarial paradigm itself. To some extent, this work is tolerated but marginalised. However, do therapeutic and problem-solving functions have the potential to help define, rather than simply complement, the role of judicial officers? The core question addressed in this thesis is whether the judicial role could evolve to be not just less adversarial, but fundamentally non-adversarial. In other words, could we see—or are we seeing—a juristic paradigm shift not just in the colloquial, casual sense of the word, but in the strong, worldview changing sense meant by Thomas Kuhn? This thesis examines the current relationship between adversarialism and therapeutic jurisprudence in the context of Kuhn’s conception of the transition from periods of ‘normal science’, through periods of anomaly and disciplinary crises to paradigm shifts. It considers whether therapeutic jurisprudence and adversarialism are incommensurable in the Kuhnian sense, and if so, what this means for the relationship between the two, and for the agenda to mainstream therapeutic jurisprudence. The thesis asserts that Kuhnian incommensurability is, in fact, a characteristic of the relationship between adversarialism and therapeutic jurisprudence, but that the possibility of a therapeutic paradigm shift in law can be reconciled with many adversarial and due process principles by relating this incommensurability to a broader disciplinary matrix.

Thesis advisor: Arthur Madigan<br>Since at least Galileo, not only the technological abilities of natural science but the meaning of science's claims have been shaken to their very foundations, according to Edmund Husserl. We know what scientists say, but we do not know what they mean. Nor, Husserl claims, do they know what they mean. They do what works. They measure, they tabulate, they calculate. But they do not thereby really know the world. And since they are the standing authorities of knowledge in our culture, we do not have a reliable referent to which we can turn for an appropriate standard of meaning. At some level we realize that this piece of paper in my hand is not precisely a geometrical rectangle, in which all four angles are exactly ninety degrees and both sets of sides are exactly parallel to each other, but for the most part we simply identify it as a rectangle and move on. In our everyday experience, Husserl would say, we tend to conflate geometrical space and experiential space. We do not, however, have any real idea why we can do so effectively, even if we are engineers or physicists. Geometrical shapes are categorically different from the shapes we daily experience in our interactions with the world. No matter how carefully I draw lines or cut edges, I can never make a piece of paper (or, for that matter, a cow) that exactly meets the requirements of a geometrical rectangle. Even the fact that geometrical rectangles are, by definition, plane figures, which means they only have two dimensions, rather than the (at least) three that structure any perceptible thing, prevents perceptible things from ever meeting the strict requirements of geometrical figures. Given this basic disparity, what is it that justifies our using these geometrical figures to describe the perceptible world in which we live? If we want to know the world, Husserl tells us, we need to know what our scientific claims mean. This, he claims, is the only way we can meaningfully ground our increasingly science-governed lives. Plan of the Dissertation In this dissertation, then, I undertake the project of identifying more precisely what this problem is and offering some solution to it. My argument will have three steps. I shall argue first that to solve the problem Husserl so helpfully lays out, we need to go back to Aristotle's Metaphysics; second, that although Aristotle proposes a solution for the metaphysical problems implied by using mathematics to know perceptible things, this solution fails to answer the questions as he presents them, even if it is broadly interpreted; and, finally, that there are within Aristotle's metaphysical thought implicit resources for constructing this missing metaphysical justification, and that these can be found explicitly in his way of thinking about the distinction between actuality and potency, in his discussion of the metaphysical implications of knowing, and in his discussion of material causality. The basic problem is that mathematical objects and perceptible things are different kinds of things. We would not say that `Joe's idea is hungry' in anything other than a very metaphorical way, because we recognize that ideas are not the kinds of things that get hungry. Hunger is the province of animals. Ideas are not animals. Ideas, then, cannot be hungry. Mathematical objects and perceptible things, though, while also different kinds of things, are regularly combined. We do say, `This piece of paper is rectangular', although it would seem that pieces of paper (or cows) are not the kinds of things that could be rectangles. In this dissertation, I begin in chapter one with a careful recapitulation of Husserl's articulation of this problem of thoughtlessly conflating mathematical and experiential things. Husserl takes this to be the root of the crisis, not only of the meaning of the sciences, but also of all human meaning. I use Husserl's articulation, rather than simply explaining the problem as I understand it and moving directly to Aristotle's Metaphysics, where I see the roots of its solution, in part because Husserl's work was so influential in shaping my own understanding of the problem. More importantly, though not unrelatedly, Husserl helpfully contextualizes the problem both culturally and historically. He tells us why this matters, and he tells us how it seems to have happened. Both of these seem to me to be crucial to any ultimately successful resolution to the problem. In Husserl's articulation of the problem, he identifies Galileo as responsible for taking it as `obvious' that the `universally valid' shapes of geometry constituted the objectively real component of all things. He argues that Galileo inherits a tradition in which our approximations to `limit shapes' and the increased precision in replicating these made possible by technological advances gradually meld together, such that we learn to take the world to be fundamentally a mathematical manifold. In taking over this tradition, Galileo simply presumes that the world is fundamentally mathematizable and sets about developing methods by which even the concrete sensory plena through which any experienced shape is necessarily presented can be mathematized. Since we take as `given' these assumptions, whose origin Husserl attributes to Galileo, and which remain unjustified metaphysically, Husserl's tracing of the development of these assumptions can help us notice and evaluate them. This will be helpful in recovering the meaning of our mathematical scientific claims, and, ultimately, in recovering the meaning of our non-scientific claims. While Husserl helpfully identifies the problem and begins the historical tracing he proposes with his analysis of Galileo's assumptions, he does not complete the latter project, in part because he died so soon after beginning it. His project in the Crisis, as with many of the projects he undertook as a scholar, gets developed in many different directions, without any of these being completed. He proposes a philosophical-historical retracing of the assumptions of geometry, from its earliest inception through the present. He proposes a simultaneous careful consideration of the metaphysical assumptions at work in mathematical science and the justification necessary for it. He proposes transcendental phenomenology as the way to correctly understand the correlation between mathematical claims and the perceptible world they describe. While the development of transcendental phenomenology and the ways that it can help us come to understand more correctly our interaction with the world are fascinating, in this dissertation I want to focus on Husserl's other proposals toward a solution, namely the philosophical-historical retracing of assumptions and the metaphysical analysis. Specifically, I want to focus on the metaphysical analysis that Aristotle performs on the problems generated by presuming that one can use mathematical objects to know perceptible things. In chapter two, then, I explain more thoroughly the first two proposals toward a solution that Husserl proposes, and defend my claim that this metaphysical analysis in Aristotle is an appropriate continuation of Husserl's project. For completeness, Husserl's project needs, in addition to his tracing of the historical sources of lazy assumptions, an Aristotelian metaphysical analysis of what material and mathematical things are, to clarify whether and how mathematics could be appropriately (or inappropriately) applied to material things. In chapter three, I turn to Aristotle's Metaphysics and cull from its pages, primarily from Books III and XIII, the basic metaphysical questions and problems that arise in Aristotle's discussion of the use of mathematical objects to know perceptible things. I organize these into six central questions: 1) What exactly are the mathematical objects Aristotle discusses? 2) Are these mathematical objects substances? 3) Are these mathematical objects separable from perceptible things? 4) Are these mathematical objects constituents of perceptible things? 5) Are these mathematical objects principles or causes of perceptible things? 6) Is knowledge of these mathematical objects somehow knowledge of perceptible things? From these six questions, the basic problem that emerges is that knowledge of mathematical objects requires these objects to be exact, unchangeable, and indivisible, whereas the perceptible things of which they are supposed to provide knowledge are less determinate, changeable, and divisible. It seems like the mathematical objects would have to be separate from these perceptible things to be objects of mathematical knowledge, but if they were so, it is unclear how knowledge of them could be taken to also be knowledge of the perceptible things. These mathematical objects would have to somehow be part of the causal structure of these perceptible things for knowledge of them to be knowledge of these perceptible things. In chapter four, I take up the solution that Aristotle proposes for these difficulties, the `insofar as'/ `qua' (hêi) structure of knowing. Various attributes belong to a given perceptible thing in virtue of various ways of its being. Being green belongs to a plant, for example, insofar as it is a surface. The method of abstraction (aphairesis) allows us to separate out in thought the relevant way of being of the thing, so as to make the appropriate attribution to it. We can know a thing as something, even if that `something' is not itself actually separable. This proposal of Aristotle's begins to resolve some of the metaphysical problems that chapter three articulated. It is not itself, however, metaphysically justified. While it seems that we do regularly make these kinds of claims about perceptible things, it is not clear what justifies us in separating in thought what is not separate in fact, nor just how these various ways of being belong to the unified perceptible thing such that knowledge of them provides knowledge of the thing. This difficulty in giving a metaphysically coherent account of Aristotle's model of abstraction pervades the scholarly literature. Aristotle, it seems, does not have a satisfactory solution to the troubling metaphysical problems he raises about using mathematical objects to know perceptible things. In my fifth, and final, chapter, I undertake to construct from other texts in Aristotle's corpus a metaphysical justification for his model of abstraction that can, in fact, resolve the metaphysical problems that he and Husserl have raised. I find this metaphysical justification in an implicit claim of Aristotle's, to be found in the same section where he proposes his model of abstraction as a solution (Met XIII.3): the claim that mathematical objects are potential substances. I examine what these potential substances are, how they are related to their own actualizations and how they are related to the perceptible things of which they are supposed to provide knowledge, relying primarily on Metaphysics VIII and IX. I consider how knowledge of these could be possible, using texts from De Anima III, and then explore a connection between these potencies and the material cause of perceptible things in Physics II.9. I conclude at last that we are, in fact, justified in using mathematical objects to describe perceptible things. These objects, however, are mathematically describable only insofar as they are material, by which Aristotle means, insofar as they are potential, rather than actual<br>Thesis (PhD) — Boston College, 2010<br>Submitted to: Boston College. Graduate School of Arts and Sciences<br>Discipline: Philosophy

This thesis is focused on the intersections of ontology and politics in the work of Michel Foucault and Jacques Derrida. In particular it concerns the ways in which these two thinkers offer accounts of (ethical, social, political) relations which exceed a traditional dichotomy between transcendentalism and empiricism. Both Derrida and Foucault show universal foundations to originate in an anterior play of differences 'between' the transcendental and empirical. However, as this thesis shows, each thinks this anterior 'medium' of relations in radically incommensurable ways: as differance or aporia in Derrida and as power and problematization in Foucault. As such, each necessarily views the other as failing to account for the ‘true medium’ of relationality and so of its violent effacement and disavowal. This incommensurability, it is argued, results in a polemic between them which is explicit in their competing accounts of Descartes’ Meditations and implicit throughout all of their work. This thesis traces the polemic between Derrida and Foucault across their accounts of subjectivity, ethics and politics. It is argued that in their engagements with each of these fields they employ parallel politicizing strategies which are nevertheless wholly exclusive of one another. The incommensurability between Derrida and Foucault reflects a broader problematic which any political thought affirming its own finitude cannot explicitly recognize. Postfoundational accounts of relationality, it is claimed, violently exclude competing philosophical strategies without the capacity of accounting for this exclusion.

Submitted by Andrea Hayashi (deachan@gmail.com) on 2016-06-23T19:27:58Z No. of bitstreams: 1 dissertacao-caio-sievers-sperandio.pdf: 854209 bytes, checksum: 2b792c063fb149e03dbd294127cb0ac1 (MD5)<br>Approved for entry into archive by Andrea Hayashi (deachan@gmail.com) on 2016-06-23T19:28:39Z (GMT) No. of bitstreams: 1 dissertacao-caio-sievers-sperandio.pdf: 854209 bytes, checksum: 2b792c063fb149e03dbd294127cb0ac1 (MD5)<br>Made available in DSpace on 2016-06-23T19:28:39Z (GMT). No. of bitstreams: 1 dissertacao-caio-sievers-sperandio.pdf: 854209 bytes, checksum: 2b792c063fb149e03dbd294127cb0ac1 (MD5) Previous issue date: 2014-03<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)<br>O debate sobre o progresso linear do conhecimento toma um grande papel na filosofia da ciência, tendo como uma de suas principais figuras Thomas S. Kuhn com sua tese de incomensurabilidade. Porém, a incomensurabilidade é o tema mais polêmico dos trabalhos de Kuhn, geradora de criticas de relativismo e irracionalismos. Devido a essas críticas, ou por uma evolução natural do pensamento de Kuhn, a tese da incomensurabilidade encontra dois momentos, segundo comentadores como Robson Guitarrari. Em sua primeira formulação ela possui um patamar mais amplo, porém, posteriormente, Kuhn defende uma incomensurabilidade local, dando uma maior ênfase para a linguagem. A presente dissertação analisa três questões referentes à incomensurabilidade: é possível manter a tese da incomensurabilidade? As causas que levaram a essa mudança de perspectiva da incomensurabilidade? e se é possível não cairmos em um relativismo? Para tanto, apresentamos, brevemente, a dinâmica científica defendida por Kuhn, passando pelo período pré-paradigmático, paradigmático e de revolução cientifica para, só então, tratar propriamente da questão da incomensurabilidade. Para essa empreitada, utilizaremos dos textos de Thomas Kuhn, deixando claro os dois momentos da incomensurabilidade e, partindo da análise de comentadores, apresentaremos as críticas e defesas a essa tese.<br>The debate on the linear progress of knowledge takes a big role in the philosophy of science, having as one of its leading figures Thomas S. Kuhn with his thesis of incommensurability. However, the incommensurability is the most polemical theme of the works of Kuhn, generating criticism of relativism and irrationalism. Because of these criticisms or a natural evolution of the thought of Kuhn's thesis of incommensurability meets two times, according to commentators as Robson Guitarrari. In its initial formulation it has a broader level, however, later, Kuhn maintains a local incommensurability, giving greater emphasis to the language. This dissertation analyses three issues incommensurability, it is possible to maintain the thesis of incommensurability, the question that led to this change of perspective of incommensurability, and if you can not fall into relativism. Therefore, we present briefly the scientific dynamics advocated by Kuhn, through pre - paradigmatic, paradigmatic and scientific revolution then properly approach the incommensurability issue. For this work will use the texts of Thomas Kuhn, making clear the two moments of incommensurability and, starting from the analyses commentators, and present the critics and defences to this thesis.

Made available in DSpace on 2015-03-04T21:01:07Z (GMT). No. of bitstreams: 0 Previous issue date: 24<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>O cenário geral da filosofia da ciência no século XX foi principalmente desenhado pelos traços epistemológicos do Positivismo Lógico e seu verificacionismo, pelo falsificacionismo popperiano, pelos programas de pesquisa lakatianos, pelo anarquismo epistemológico de Paul Feyerabend e pela filosofia da ciência de Thomas Kuhn. A partir desse cenário geral, esta dissertação analisa os aspectos principais da filosofia da ciência de Thomas Kuhn, o espectro das críticas que recebeu, as respostas que ofereceu e as mudanças que se seguiram na epistemologia kuhniana. Kuhn envolveu-se em um frutífero debate com alguns dos mais proeminentes filósofos da ciência do século XX, sobre suas idéias de revolução científica, ciência normal e incomensurabilidade. Esse debate, discutido nesta dissertação, contribuiu para as mudanças que Kuhn fez em sua proposta original tal como exposta em seu mais famoso trabalho, The Structure of Scientific Revolutions. Essas modificações e sua abrangência são o tema principal do presente estudo<br>The general scenario of the philosophy of science in the 20th century was mainly determined by the epistemological traits of Logical Positivism and its verificationism, Popperian falsificationism, the Lakatian research programs, Paul Feyrebend’s epistemological anarchism, and Thomas Kuhn’s philosophy of science. Starting from this general scenario, this dissertation analyzes the main aspects of Thomas Kuhn’s philosophy of science, the spectrum of its critique by other thinkers, Kuhn’s response to that critique and the subsequent changes in Kuhn’s epistemology. Kuhn was involved in a fruitful debate on his ideas about scientific revolutions, normal science, paradigms, and incommensurability with some of the most important philosophers of the 20th century. This debate, which is discussed in the dissertation, prompted Kuhn to make changes in his original proposal as expounded in his most famous work, The Structure of Scientific Revolutions. These modifications and their scope are the main topic of the present

Submitted by AROLDO FERREIRA LEÃO null (aroldoleao@gmail.com) on 2017-10-03T15:04:30Z No. of bitstreams: 1 TESE - VERSÃO FINAL PDF.pdf: 3579912 bytes, checksum: 7de711208698b6061ca5c67c58f31a03 (MD5)<br>Rejected by Monique Sasaki (sayumi_sasaki@hotmail.com), reason: Solicitamos que realize uma nova submissão seguindo a orientação abaixo: O arquivo submetido está sem a ficha catalográfica. A versão submetida por você é considerada a versão final da dissertação/tese, portanto não poderá ocorrer qualquer alteração em seu conteúdo após a aprovação. Corrija esta informação e realize uma nova submissão contendo o arquivo correto. Agradecemos a compreensão. on 2017-10-03T16:41:14Z (GMT)<br>Submitted by AROLDO FERREIRA LEÃO null (aroldoleao@gmail.com) on 2017-10-03T18:08:00Z No. of bitstreams: 1 TESE - VERSÃO FINAL - AROLDO LEÃO - PDF.pdf: 5642125 bytes, checksum: 51c18cae874835a9fab0d6ea37a5e748 (MD5)<br>Approved for entry into archive by Monique Sasaki (sayumi_sasaki@hotmail.com) on 2017-10-03T18:21:34Z (GMT) No. of bitstreams: 1 leao_af_dr_rcla.pdf: 5642125 bytes, checksum: 51c18cae874835a9fab0d6ea37a5e748 (MD5)<br>Made available in DSpace on 2017-10-03T18:21:34Z (GMT). No. of bitstreams: 1 leao_af_dr_rcla.pdf: 5642125 bytes, checksum: 51c18cae874835a9fab0d6ea37a5e748 (MD5) Previous issue date: 2017-09-29<br>Esta Tese tem como objetivo contribuir para um maior entendimento e aprofundamento da incomensurabilidade exposta no Livro X, da obra Os Elementos, de Euclides. As pesquisas relacionadas, ao estudo específico sobre o Livro X, em toda a sua expansão e complexidade, são ainda insuficientes e carecem de um maior compêndio de buscas e norteamentos, que possibilitem trazer à tona, todo o esplendor deste livro singular. Então, fez-se necessário uma análise completa do Livro X, um mergulho nas suas engrenagens e desmembramentos. Tal livro, o maior e mais intenso de Os Elementos, além de ser considerado o mais difícil, ocupando mais de um quarto do mesmo, tido como “a cruz dos matemáticos”, “um beco sem saída”, evidencia, de forma categórica, um dos temas mais sutis, não só da matemática da antiga Grécia, como também dos dias atuais, ao se dedicar ao estudo dos segmentos retilíneos que são incomensuráveis com respeito a um segmento retilíneo dado, ou seja, ao estudo dos números irracionais. Os vínculos com a Educação Matemática foram realçados e possibilitaram a escrita de um texto, que ampliando inúmeros enfoques, consolidou a importância do Livro X no relacionamento com outros livros de Os Elementos, como também a sua característica particular de tratar, fundamentalmente, do tema da incomensurabilidade.<br>This thesis aims to contribute to a greater understanding and deepening of the incommensurability exposed in Book X, of the work The Elements, by Euclid. The researches related to the specific study of Book X, in all its expansion and complexity, are still insufficient and lack a greater compendium of searches and guidelines, that make possible to bring to the surface, all the splendor of this singular book. Then it took a full analysis of Book X, a dip in its gears and dismemberments. Such a book, the largest and most intense of The Elements, in addition to being considered the most difficult, occupying more than a quarter of it, considered as "the cross of mathematicians", "a dead end", shows categorically one of the subtler themes not only of the mathematics of ancient Greece but also of the present day, when it is devoted to the study of rectilinear segments which are incommensurable with respect to a given rectilinear segment, that is, to the study of irrational numbers. The links with Mathematics Education were emphasized and made possible the writing of a text, which enlarged numerous approaches, consolidated the importance of Book X in the relationship with other books of The Elements, as well as its particular characteristic of dealing, fundamentally, with the theme of Incommensurability.

Paradigmos sąvokos išklaida chronologiškai sekant T. Kuhno minties raidą. Aptariami trys paradigmos sąvokos raidos etapai ir kai kurios implikacijos, pavyzdžiui nebendramatiškumas ir sąntykis su Karlo Popperio kritiniu racionalizmu.<br>Thomas Kuhn's concept of paradigm is expounded by chronologically following his publications. Three different stages of development of the concept are analysed and then compared to Karl Popper's critical rationalism.

A presente dissertação tem por objetivo analisar o desenvolvimento da proposta fleckiana de uma teoria comparativa do conhecimento, seu estatuto epistemológico, bem como o diagnóstico de algumas de suas dificuldades teóricas. Defenderemos o caráter potencialmente científico de sua teoria e indicaremos que a incomensurabilidade entre estilos de pensamento constitui o problema mais imediato para sua efetivação. Nesse ínterim, sintetizaremos as principais diretrizes metodológicas esboçadas em sua teoria, entendida como um programa de pesquisa aberto, e indicaremos possíveis desdobramentos futuros. Esta dissertação terá início, em sua Introdução, com uma sucinta análise das principais fases de recepção da obra de Fleck, tendo em vista a compreensão de suas tradições de leitura e do significado atual de seus escritos. No Capítulo I, reconstituiremos o quadro conceitual da teoria comparativa de Ludwik Fleck a partir da análise de suas principais linhas e dimensões de desenvolvimento: médico-imunológica, sociológica, de crítica ao positivismo lógico e histórica. O Capítulo II será dedicado à análise dos processos comunicativos de sua teoria tanto ao nível diacrônico como ao nível sincrônico, bem como do fenômeno da incomensurabilidade. Estabeleceremos paralelos sobre a manifestação desse fenômeno com as formulações de Thomas Kuhn e Paul Feyerabend. No Capítulo III, abordaremos a tese do relacionismo cognitivo defendido por Fleck, indicando que sua teoria comparativa do conhecimento não possui um estatuto epistemológico privilegiado, sendo, portanto, um saber também relacional. Diante disso, defenderemos seu caráter científico, em conformidade, em linhas gerais, com as demais ciências naturais. Por fim, em nossas Considerações finais indicaremos, a partir das diretrizes lançadas pelo filósofo, algumas das possíveis linhas metodológicas que o programa da teoria comparativa deve seguir diante do problema da incomensurabilidade e da necessidade de um desenvolvimento metodológico mais preciso.<br>This dissertation aims to analyze the development of Fleck\'s proposal of a comparative theory of knowledge, its epistemological status and the diagnosis of some of its theoretical difficulties. We will defend the potentially scientific status of its theory and indicate that the incommensurability between thinking styles constitutes the most immediate problem for its effectiveness. Meanwhile, we intend to synthesize the main methodological guidelines outlined in his theory, understood as an open research program, and indicate possible future developments. This dissertation will start in its Introduction with a brief analysis of the main stages of reception of Fleck\'s work, so as to understand its traditions of readings and the current meaning of his writings. In Chapter I, we will reconstitute the conceptual framework of Fleck\'s comparative theory from the analysis of its main lines and dimensions of development: medical and immunological, sociological, as well as his criticism of historical and logical positivisms. Chapter II is devoted to the analysis of his theory of communicative processes at both the diachronic and synchronous level, as well as the phenomenon of incommensurability. We will establish parallels with Thomas Kuhn and Paul Feyerabend\'s formulations of this phenomenon. In Chapter III, we discuss the thesis of cognitive relationalism defended by Fleck, indicating that his comparative theory of knowledge does not have a privileged epistemological status, being, by its turn, also a relational knowledge. In the face of it, we will defend its scientific character, in accordance, in general, with the other natural sciences. Finally, in our final considerations we indicate, from guidelines released by the philosopher, some of the possible methodological lines that the program of comparative theory must follow regarding the problem of incommensurability and the need for a more precise methodological development.

O debate atual sobre a racionalidade científica tem envolvido uma tomada de posição quanto ao relativismo epistemológico. Um dos focos do debate consiste na superação do relativismo presente em pronunciamentos de Thomas Kuhn sobre a escolha científica. Procurando libertar-se de um relativismo kuhniano nas justificações de escolhas científicas, Hilary Putnam e Larry Laudan apresentam estratégias bastante distintas. Putnam vê incoerências autodestrutivas em tal relativismo, especialmente por duas razões: sua formulação seria auto-refutante e, quanto aos atributos cognitivos, essa posição não permitiria distinguir o homem de qualquer outro ser. Laudan procurou desmistificar os efeitos que a incomensurabilidade kuhniana teria causado para uma visão de racionalidade dirigida por regras metodológicas e, além disso, buscou mostrar a falta de poder explicativo do relativismo decorrente dela. O presente trabalho investiga se ainda há razão para considerar que o relativismo gerado pela incomensurabilidade kuhniana constitui uma ameaça à racionalidade científica. Apresentamos um modelo kuhniano de racionalidade, com base em uma análise dos textos de Kuhn sobre a escolha de paradigmas, que ressalta o papel da incomensurabilidade de problemas e padrões científicos. Procuramos mostrar que duas das principais acusações de incoerência, elaboradas por Putnam, não atingem tal modelo. Por fim, defendemos que esse modelo kuhniano de racionalidade apresenta várias restrições para o efetivo estabelecimento das críticas que Laudan lhe dirige.<br>The current debate on scientific rationality has involved taking sides regarding the question of epistemological relativism. The debate is focused, among other things, in overcoming the relativism present in Thomas Kuhns statements about scientific choice. Hilary Putnam and Larry Laudan, aiming at dispensing with a Kuhnian relativism in the justification of scientific choices, propose quite different strategies. Putnam sees self-destructive incoherencies in such relativism, mainly for two reasons: first, its formulation would be self-defeating and, second, this position wouldnt allow one to distinguish man from any other being as regards cognitive attributes. Laudan attempted to demystify the effects that Kuhnian incommensurability could cause to a vision of rationality governed by methodological rules, and, furthermore, attempted to show the lack of explanatory power of the relativism that follows from it. The present work inquires whether there is still reason to consider that the relativism originated by Kuhnian incommensurability constitutes a menace to scientific rationality. We present a Kuhnian model of rationality, based on an analysis of Kuhns texts on paradigm choice, which highlights the role of incommensurability as regards scientific problems and standards. We aim to show that two of the main charges of incoherence, formulated by Putnam, arent able to affect the model. Lastly, we maintain that this Kuhnian model of rationality poses various constraints on the actual establishment of the criticisms directed against it by Laudan.

The aim of this dissertation is to provide a critical understanding of a Rural Territorial Development (RTD) intervention in a context of conflict dynamics, by looking at the case of the Programme for Development and Peace in Middle Magdalena (PDPMM) - Colombia. To accomplish this task the research process discussed both theoretical and empirical inputs. Firstly, a theoretical framework was developed to understand the dynamics of the development-conflict nexus in rural territories. Secondly, supported by the examination of a case-study, systematic empirical information was collected, incorporating quantitative and qualitative evidence in order to explore the explicit conflict dynamics, namely the practical and theoretical incommensurability between opposite views of rural development taking place in the Middle Magdalena region. Such analysis was further elaborated in three steps: first, the research characterized the main visions of rural development that are being pursued in Middle Magdalena; second, a comparative analysis was carried out in order to identify incommensurabilities and contradictions among those views of development; and third, the study focused on the PDPMM in order to examine how its rural territorial development strategy influences the course of conflict dynamics. On the basis of this methodology, the study shows that rural territorial interventions should focus on building pragmatic articulations among opposite views of development to establish a common development proposal that overcomes conflict and poverty in rural territories.

Human induced climate change poses a series of ethical challenges to the current political economy, although it has often be regarded by economists as only an ethical issue for those concerned about future generations. The central debate in economics has then concerned the rate at which future costs and benefits should be discounted. Indeed the full range of ethical aspects of climate change are rarely even discussed. Despite recent high profile and lengthy academic papers on the topic the ethical remains at best superficial within climate change economics. Recognising the necessary role of ethical judgment poses a problem for economists who conduct exercises in cost-benefit analysis and deductive climate modelling under the presumption of an objectivity that excludes values. Priority is frequently given to orthodox economic methodology, but that this entails a consequentialist utilitarian philosophy is forgotten while the terms of the debate and understanding is simultaneously restricted. We set out to raise the relevance of a broader range of ethical issues including: intergenerational ethics as the basis for the discount rate, interregional distribution of harm, equity and justice issues concerning the allocation of carbon budgets, incommensurability in the context of compensation, and the relationship of climate ethics to economic growth. We argue that the pervasiveness of strong uncertainty in climate science, incommensurability of values and nonutilitarian ethics are inherent features of the climate policy debate. That mainstream economics is ill-equipped to address these issues relegates it to the category of misplaced concreteness and its policy prescriptions are then highly misleading misrepresentations of what constitutes ethical action. (authors' abstract)<br>Series: SRE - Discussion Papers

Thomas Kuhn foi um dos mais importantes filósofos da ciência do século XX. Entre suas principais contribuições, destaca-se a tese da incomensurabilidade das teorias científicas. O presente trabalho visa mostrar como tal tese, apresentada originalmente no livro A estrutura das revoluções, de 1962, foi modificada por Kuhn ao longo dos anos, com foco em seus últimos artigos, escritos entre as décadas de 1980 e 1990. A incomensurabilidade é reduzida então a uma relação semântica restrita a certos pontos da linguagem (incomensurabilidade local). A fim de explicar como isso é possível, Kuhn é levado a pensar, em primeiro lugar, no aprendizado e funcionamento dos conceitos, e como se organizam em estruturas taxonômicas. Em seguida, elabora outros aspectos de uma filosofia da linguagem, como significado e verdade, que lhe permitem responder às principais críticas que haviam sido dirigidas à noção de incomensurabilidade originalmente exposta.<br>Thomas Kuhn was one of the most important philosophers of science of the twentieth century. Among his major contributions, there is the thesis of incommensurability of scientific theories. This work aims to show how this theory, originally presented in the book The Structure of Revolutions, from 1962, was modified by Kuhn over the years, focusing on his last articles, written between the 1980s and 1990s. The incommensurability is then reduced to a semantic relation restricted to certain portions of language (local incommensurability). To explain how this is possible, Kuhn is led to think, firstly, in the learning and operation of the concepts, and how they are organized in taxonomic structures. After that he elaborates other aspects of a philosophy of language, as meaning and truth, which allow him to answer the main criticisms which had been directed to the notion of incommensurability originally exposed.

Made available in DSpace on 2016-04-27T16:57:07Z (GMT). No. of bitstreams: 1 Walkiria Correa dos Santos.pdf: 2202936 bytes, checksum: 0b47cf76b6ab7f2053830abc5b6950c9 (MD5) Previous issue date: 2011-05-13<br>Secretaria da Educação do Estado de São Paulo<br>This paper seeks to contribute to the study of the main ideas that involve the Fundamental Theorem of Calculus (FTC) from the Mathematics in Ancient Greece to contributions of Newton (1642 - 1727) and Leibniz (1646 - 1716), the seventeenth century. Given the scope of this theme, we focus our attention on the question of Incommensurability and in consequence, the definition of Proportion of Eudoxus (390 a.C. - 320 a.C.). Such a definition, results in the 'geometrization' of translating the mathematical ideas that culminated in the concepts of derivative and integral, in quadrature issues and calculation of volumes, through method of exhaustion and method Mechanic Archimedes (287 a.C. - 212 a.C.), and the method of tracing the tangent of Apollonius (262 a.C.) - 190 a.C.). The searches tangent to a curve and the problem of quadrature were a predecessor motive for the work of Newton (1642 - 1727) and Leibniz (1646 - 1716) could establish "Infinitesimal Calculus". The revival of mathematical activity in the fifteenth century, with the need for new routes of commerce and navigation, covering arithmetic, algebra and trigonometry and the sixteenth century, were of great importance, forming the basis of all algebraic development. In the seventeenth century, an important area has been established: the Analytic Geometry, which contributed greatly to the achievements of Newton (1642 - 1727), and Leibniz (1646 - 1716), by establishing, in definitive, that the process of integration and differentiation are inverse operations of one another. The result is now known as the Fundamental Theorem of Calculus. The product of the research conducted is a text, drafted with didactic concern, which aims to facilitate understanding of the interconnection of ideas that have contributed, through centuries, to the result that we now know as the Fundamental Theorem of calculus<br>Esse trabalho busca contribuir com o estudo das principais ideias que envolvem o Teorema Fundamental do Cálculo (TFC), desde a Matemática na Grécia Antiga até as contribuições de Newton (1642 - 1727) e Leibniz (1646 - 1716), no século XVII. Dada a abrangência de tal tema, focamos nossa atenção na questão da Incomensurabilidade e em decorrência, na definição de Proporção de Eudoxo (390 a.C. - 320 a.C.). Tal definição traz como consequência a &#8215;geometrização da matemática traduzindo as ideias que culminaram nos conceitos de derivada e integral, nas questões de quadratura e cálculo de volumes, por meio dos métodos de Exaustão e o método Mecânico de Arquimedes (287 a.C. - 212 a.C.), e no método do traçado de tangente de Apolônio (262 a.C. - 190 a.C.) . As buscas da tangente a uma curva e a questão da quadratura foram a mola precursora para que os trabalhos de Newton (1642 - 1727) e Leibniz (1646 - 1716) pudessem estabelecer o Cálculo Infinitesimal. O renascimento da atividade matemática no século XV, pela necessidade de novas rotas de comércios e navegação, abordando a aritmética, a álgebra e a trigonometria e o século XVI, foram de grande importância, constituindo a base de todo desenvolvimento algébrico. No século XVII, uma importante área foi estabelecida: a Geometria Analítica que muito contribuiu para os resultados alcançados por Newton (1642 - 1727) e Leibniz (1646 - 1716), estabelecendo, em definitivo, que o processo de integração e derivação são operações uma inversa da outra. O resultado é hoje conhecido como Teorema Fundamental do Cálculo. O produto da pesquisa realizada é um texto, redigido com preocupação didática, que pretende facilitar o entendimento da interligação das ideias que contribuíram, através de séculos, para o resultado que hoje conhecemos como o Teorema Fundamental do Cálculo

John Finnis is one of the seminal contemporary jurisprudential thinkers working within the natural law tradition. His Natural Law and Natural Rights, first published in 1980, has had a significant impact and stands as a centerpiece of modern natural law theory. It is at once a work of ethics, political philosophy as well as jurisprudence. The starting point of his theory of natural law con­sists in concepts such as basic human goods, practical reasonableness and the common good. These concepts provide the foundation for his analysis of communities and society as well as the legal system. This thesis sets out to expound on his theory of natural law by exploring Finnis’ understanding of the basic human goods, practical reasonableness and the common good and the way they interact with his ideas of law and justice. Some of the more controversial or contentious aspects of his theory will also be addressed; such as the supposed self-evident nature of the basic goods and their incommensurable status. Some critics allege that his theory is lacking some of the defining characteristics of a natural law theory and that it thus fails as a theory of natural law, while others have claimed that his theory lends itself to the justification of an authoritarian society. Some of these criticisms carry more strength than others and I conclude by granting that Finnis’ theory contains some weaknesses. However, these should not weaken our appreciation of his vision of the good that law can do and the interrelatedness of law and morality.

Scopo della presente tesi è quello di descrivere i momenti fondamentali che hanno caratterizzato lo sviluppo del concetto di numero reale. A partire dalla scoperta delle grandezze incommensurabili, e passando attraverso la risoluzione di tale "trauma" grazie alla teoria delle proporzioni sviluppata da Eudosso di Cnido nella prima metà del secolo IV a. C. - pervenutaci attraverso il Libro V degli Elementi di Euclide - si arriverà alla data simbolica del 1872, anno a cui risalgono le fondamentali pubblicazioni di Cantor e Dedekind, che daranno una sistemazione teorica definitiva al campo dei numeri reali. Verranno presentate in dettaglio le rispettive costruzioni, che saranno sviluppate utilizzando notazioni e concetti moderni, tenendo però conto degli articoli originali, al fine di evidenziare le idee presenti in essi, soprattutto in considerazione del fatto che esse fossero già contenute, in nuce, nella trattazione euclidea. Infine, verrà dimostrata l'equivalenza del modello di Cantor e di quello di Dedekind, e più in generale l'unicità, a meno di isomorfismi, del campo dei numeri reali, conseguenza, com'è noto, di un importante teorema dovuto a Hilbert. Inoltre, verrà presentata la definizione assiomatica storica data da Hilbert, che definisce i numeri reali come costituenti un campo ordinato archimedeo che goda del cosiddetto "Axiom der Vollständigkeit", e verrà dimostrata l'equivalenza di tale nozione con quelle che emergono dai lavori di Cantor e Dedekind.

Made available in DSpace on 2016-04-27T16:56:59Z (GMT). No. of bitstreams: 1 dissertacao_olga_corbo.pdf: 11888785 bytes, checksum: 9fd54776e71e1d194c1bd940375f91fc (MD5) Previous issue date: 2005-08-16<br>We have conducted this study to contribute to education of future teachers, by proposing the use of golden section as a context to explore the notion of incommensurable magnitudes. We have based our study on the notion of jeux de cadres , introduced by Douady (1986) in Mathematics Didactic, and used the Didactic Engineering research methodology. Our research was developed on the following hypothesis: a teaching sequence about the golden section which favors an interaction among different knowledge domains can advance the comprehension and/or development of the notion of incommensurability of straight line segments . For this study, we have attempted to determine if the process of successive divisions based on Euclids algorithm helped foster the development of the notion of incommensurability of straight line segments in the future teachers. Furthermore, we verified whether they used the jeux de cadres to solve some problems presented in the sequence and how it contributed to develop the notion of golden rectangle and the notion of incommensurable straight line segments. Finally, we determined if they have established a relationship between the golden rectangle characteristics and the notion of incommensurability of straight line segments, by offering a proof of the incommensurability of the sides of the golden rectangle. The results seem to indicate some progress in relation to the answers provided in the pre-test, which allows us to conclude that the golden section can be a favorable context for the comprehension and/or development of the notion of incommensurable straight line segments. The examination of the students performance have also shown that the sequence can promote an interaction among different knowledge domains, allowing a connection between certain geometric constructions and irrational numbers. At the end, we discuss some limitations observed during the development of this study, whose analysis can serve as a starting point for new investigations on the same theme.<br>O presente estudo foi realizado com o objetivo de contribuir para a formação inicial de professores de Matemática, propondo a utilização da seção áurea como contexto para explorar a noção de incomensurabilidade de segmentos de reta. Tomando como referencial teórico a noção de jogos de quadros , introduzida por Douady (1986) na Didática da Matemática e usando a metodologia de pesquisa denominada Engenharia Didática, desenvolvemos nosso trabalho com base na hipótese de que uma seqüência de ensino sobre a seção áurea, cuja realização favoreça a articulação entre quadros distintos de conhecimentos, pode propiciar a compreensão e/ou desenvolvimento da noção de incomensurabilidade de segmentos de reta . Por este estudo, examinamos se o processo das divisões sucessivas baseado no algoritmo de Euclides propiciou aos sujeitos de nossa pesquisa o desenvolvimento da noção de incomensurabilidade de segmentos de reta. Analisamos, ainda se os participantes recorriam à mudança de quadros para a resolução de algumas das situações apresentadas na seqüência e de que forma essa estratégia contribuiu para introduzir a noção de retângulo áureo e a noção de incomensurabilidade de segmentos de reta. Finalmente, examinamos se estabeleciam uma relação entre as características do retângulo áureo e a noção de incomensurabilidade de segmentos de reta, por meio da elaboração de uma justificativa de que os lados do retângulo áureo são segmentos incomensuráveis entre si. Os resultados indicam que houve um avanço em relação às respostas apresentadas no pré-teste, permitindo-nos concluir que a seção áurea pode ser um contexto favorável à compreensão e/ou desenvolvimento da noção de segmentos incomensuráveis. O exame do desempenho dos estudantes revelou também que a seqüência desenvolvida pode favorecer a inter-relação entre quadros distintos de conhecimentos, possibilitando que seja estabelecido um elo de ligação entre determinadas construções geométricas e números irracionais. Nas considerações finais, são discutidas as limitações observadas durante a realização deste trabalho, cuja análise poderá servir como ponto de partida para novas investigações sobre o mesmo tema.

Ce travail concerne la recherche de nouveaux matériaux à base de bismuth à propriétés spécifiques plus performantes, ou l'amélioration de propriétés de matériaux connus telles que la conduction ionique pour leur intérêt, en particulier dans le domaine énergétique. Dans le système Bi2O3-PbO-V2O5, notre travail a porté tout d'abord sur le domaine riche en bismuth. La structure du composé PbBi6V2O15 a été déterminée. Le problème de discernement par diffraction X de Bi3+ et de Pb2+ a été abordé par le remplacement du plomb par d'autres cations M2+ tels que Sr2+, Ca2+ et Cd2+. Les déterminations structurales sur monocristaux ont révélé des solutions solides. Partant de la structure connue Pb5Bi18V4O42, le remplacement du Pb par Sr, Ca et Cd a abouti à de nouvelles phases cristallines non stoechiométriques. Il s'agit dans ces différents cas de surstructures dérivées de Bi2O3-δ.<br /> L'étude s'est prolongée au sein du binaire BiVO4-nPbO. Une transition de phase α→β a été caractérisée pour le terme n=1, PbBiVO5. Les structures des cristaux «maclés» ont été résolues à l'ambiante et à 530°C. PbBiPO5 subit une transition analogue. PbBiAsO5 cristallise dès l'ambiante dans la forme β.<br /> Pb2BiVO6 (n=2) subit plusieurs transitions structurales α, β et δ. Les structures des formes α et β ont été déterminées sur monocristal ; la résolution de la structure de β a nécessité l'emploi d'un formalisme 4D. Deux nouvelles formes α' et δ' ont été obtenues par substitution du V par Mn ou P. Leurs structures découlent des phases α à l'ambiante, et δ à 680°C. La conductivité électrique des matériaux a été étudiée et des corrélations propriétés de conduction - caractéristiques structurales proposées.

Ce travail concerne la recherche de nouveaux matériaux à base de bismuth à propriétés spécifiques plus performantes, ou l'amélioration de propriétés de matériaux connus telles que la conduction ionique pour son intérêt en particulier dans le domaine énergétique. Dans le système Bi2O3-PbO-V2O5, notre travail a porté tout d'abord sur le domaine riche en bismuth. La structure du composé PbBi6V2O15 a été déterminée. Le problème de discernement par diffraction X de Bi3+ et de Pb2+ a été abordé par le remplacement du plomb par d'autres cations M2+ tels que Sr2+, Ca2+ et Cd2+. Les déterminations structurales sur monocristaux ont révélé des solutions solides. Partant de la structure connue Pb5Bi18V4O42. Le remplacement du Pb par Sr. Ca et Cd a abouti à de nouvelles phases cristallines non stoechiométriques. Il s'agit dans ces différents cas de surstructures dérivées de Bi2O3-ð[delta]. L'étude s'est prolongée au sein du binaire Bi VO4-nPbO. Une transition de phase α→β a été caractérisée pour Ie terme n=1, PbBiVO5. Les structures des cristaux «macIés» ont été résolues à l'ambiante et à 530°c. PbBiPO5 subit une transition analogue. PbBiAsO5 cristallise dès l'ambiante dans la forme β. Pb2BiVO6, (n=2) subit plusieurs transitions structurales α β et ð. Les structures des formes α et β ont été déterminées sur monocristal : la résolution de la struture de β a nécessité l'emploi d'un formalisme 4D. Deux nouvelles formes α' et ð' ont été obtenues par substitution du V par Mn ou P. Leurs structures découlent des phases α à l'ambiante, et ð à 680°C. La conductivité électrique des matériaux a été étudiée et des corrélations propriétés de conduction - caractéristiques structurales proposées.

Le problème de fusion d’informations survient dès qu’il faut prendre en compte des bases de données distribuées, des systèmes multi-agents ou des informations distribuées en général. La plupart des approches de fusion proposées dans la littérature reposent sur des opérateurs d'agrégation : ceux-ci combinent les degrés de cohérence des différentes interprétations vis-à-vis des sources à fusionner, eux-même fortement dépendants des poids que ces sources accordent à leurs propres croyances. Mais lorsque les sources ne partagent pas une signification commune des poids qu'elles utilisent, quel sens cela a-t-il de comparer ou d'agréger ces mêmes poids ? Ainsi, nous étudions dans cette thèse différentes approches de fusion de croyances en l'absence de commensurabilité des échelles utilisées. Nous proposons tout d'abord une première méthode, reposant sur la notion d'échelle compatible, que nous appliquons à des opérateurs basés sur la somme et sur le maximum. Les opérateurs résultants peuvent être caractérisés au moyen d’un ensemble infini d’échelles compatibles, mais également au moyen de relations de type Pareto sur l’ensemble des mondes possibles. Puis nous étudions plus particulièrement certaines familles d’échelles compatibles afin de caractériser des opérateurs moins prudents et prenant en compte l'intensité des poids. Nous fournissons une analyse complète de la production des inférences et de la rationalité des opérateurs de fusion définis. En particulier, nous proposons la notion de consensus, souhaitable en l'absence de l'hypothèse de commensurabilité et vérifiée par la plupart de nos opérateurs<br>The problem of merging multiple-source information is crucial for many applications, in particular when one requires to take into account several potentially conflicting pieces of information, such as distributed databases frameworks, multi-agent systems, or distributed information in general. The relevant pieces of information are provided by different sources and all existing pieces of information have to be confronted to obtain a global and coherent point of view. This problem is well-known as the data fusion problem. Most of existing merging methods are based on the following assumption: ranks associated with beliefs are commensurable from one source to another. This commensurability assumption can be too strong for several applications: comparing or combining ranks does not make sense if sources do not share the same meaning of scales. This thesis proposes different solutions to the problem of incommensurability for ranked beliefs merging. Our first main contribution consists of proposing a natural way to restore commensurability relying on the notion of compatible scales. The second one directly defines a partial pre-order between interpretations in a way similar to the one based on the Pareto criterion. Moreover, this thesis introduces several inference relations based on some selection functions of compatible scales. We analyze the impact of these selection functions on the satisfaction of rational postulates, and on the prudence of merging operators. In particular we introduce a stronger version of the fairness postulate, called the consensus postulate. We show that most of our defined merging operators constitute consensual approaches

L'etude des composes rga#2 et ra1ga (r=ho et dy) par differentes methodes experimentales a montre la richesse des proprietes magnetiques macroscopiques et microscopiques resultant de la frustration des interactions d'echange. Les structures magnetiques, modulees en amplitude juste en dessous de t#n, deviennent toutes antiferromagnetiques simples a basse temperature. Cette evolution est soit progressive soit brutale avec une transition incommensurable-commensurable du vecteur de propagation. Des processus metamagnetiques a sauts multiples sont observes a basse temperature. Il en resulte des diagrammes de phases h-t complexes dont les aspects microscopiques mis en evidence sont caracterises par des retournements partiels des moments, des changements de vecteur de propagation, l'existence de phases chaotiques et de point critique. Un modele de champ moleculaire periodique, n'utilisant que des parametres determines au-dessus et a t#n, a permis d'effectuer une analyse quantitative tout a fait satisfaisante des proprietes magnetiques complexes observees dans le domaine ordonne telles que les processus metamagnetiques, les structures induites par le champ, la susceptibilite et la chaleur specifique

La thèse porte sur le statut scientifique de la psychanalyse sur la transformation du principe d'inertie sur l'incommensurabilité entre psychanalyse et neurosciences. Elle se compose de trois parties : 1° explication du projet Freudien de 1895 2° situation du projet Freudien de 1895 dans l'histoire des sciences (HELMHOLTZ) 3° critique et incommensurabilité entre psychanalyse et neurosciences<br>This thesis deals with the scientific status of psychanalysis of the transformation of the principe of inertia. It is composed in three parts : 1° exploration of the Freudian project of 1895 2° situation of the Freudian project into the history of sciences (HELMHOLTZ) 3° critics and incommensurability between psychanalysis and neurosciences

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>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.<br>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.

La connaissance, parce qu'elle est le résultat de l'interprétation par un individu d'une information, ne peut pas toujours être manipulée comme un objet. C'est en filtrant au travers de nos schémas d'interprétation les informations qui nous parviennent que nous créons des connaissances. La commensurabilité des schémas d'interprétation est un concept abstrait se basant sur une règle assez floue : plus il est probable que la même information prenne le même sens pour plusieurs individus, plus leurs schémas d'interprétation sont commensurables ; moins il est probable que la même information prenne le même sens pour plusieurs individus, moins leurs schémas d'interprétation sont commensurables. L'objet de cette thèse est de proposer des approches pour déterminer dans quelle mesure deux individus donnent le même sens à la même information.

La determination des structures cristallographiques des surfaces de semiconducteurs joue un role preponderant dans la comprehension de leurs proprietes physiques. Lors de la croissance par jets moleculaires de l'alliage ternaire (in,ga)as contraint sur gaas(001), un phenomene de segregation de l'indium en surface se produit. La diffraction des rayons x en incidence rasante (dxir) s'est averee une methode experimentale puissante pour etudier les alliages de surface formes. Des mesures de dxir ont permis de reveler un ordre chimique des cations dans la maille unite de la surface reconstruite (2 3) caracteristique de ce systeme. Des surfaces incommensurables reconstruites (2 n), avec n<3 ou n>3 ont pu etre stabilisees en deposant une fraction de monocouche d'inas sur une surface de gaas reconstruite (2 4) ou (c4 4). L'ecart a la commensurabilite est decrit en introduisant une distribution statistique de fautes dans l'arrangement structural de reference (2 3) et peut etre ainsi relie a la concentration de surface de l'indium. Pour rendre compte de l'intensite diffusee par ces modeles structuraux desordonnes, nous avons applique une approche theorique qui traite l'enchainement aleatoire d'objets decrivant les surfaces (in,ga)as reconstruites (2 n). Le desordre structural unidimensionnel est bien decrit par des sequences de blocs reconstruits constituants de la maille de surface (2 3) in 2 / 3ga 1 / 3as/gaas(001) et rend compte de la forme des profils d'intensite mesures. Dans le cas de l'alliage in 0 , 5 3ga 0 , 4 7as adapte sur inp(001), le modele structural de la surface reconstruite (2 4) a aussi ete determine. Il presente des elements structuraux communs aux surfaces (2 n) commensurables ou non. Toutefois, l'ordre chimique decele en surface est different de celui deja observe : le dernier plan de cations, ordonne, n'est pas enrichi en indium par rapport au volume alors que l'avant dernier l'est.

De nombreux composes, tant naturels que synthetiques, presentent une organisation structurale bidimensionnelle sous forme de feuillets, qui peuvent etre uniques, intercales, ou bien differents dans des materiaux composites. Le manuscrit presente les resultats d'etudes realisees sur plusieurs familles de ces materiaux, a savoir des chalcogenures et oxychalcogenures de terres rares et metaux de transition, d'un point de vue cristallochimique et magnetique. Les etudes magnetiques au squid indiquent de tres fortes interactions dans le cas des composes 2d-misfit (une couche magnetique separee par cinq couches non magnetiques). Les etudes cristallographiques etant rendues difficiles, soit en raison de l'incommensurabilite de ces materiaux, soit d'une repartition statistique de certains atomes, nous nous sommes aides, en plus de la diffraction des rayons x, d'etudes en microscopie electronique ainsi qu'en spectroscopies mossbauer et d'absorption x. Nous avons egalement utilise la diffraction des neutrons afin de reveler les structures magnetiques de deux autres familles de composes : * c'est le cas de la solution solide licrs2-litis2, pour laquelle nous pouvions attendre des surstructures magnetiques ; on observe une diminution des frustrations magnetiques et de la temperature d'ordre au fur et a mesure de la dilution magnetique (cr(iii) par ti(iii)). * pour le compose tb2ti2s2o5, on observe une transition magnetique incommensurable-commensurable a 2,6 k, avec un changement de direction du vecteur de propagation ((0,44;0;0)-(1/2;0;1/2)). Ces materiaux bidimensionnels presentent donc des phenomenes magnetiques tres varies pour lesquels nous proposons un modele.

Dans l’état d’onde de densité de spin (ODS) des conducteurs organiques (TMTSF)₂ClO₄ et (TMTSF)₂PF₆, l’amplitude du paramètre d’ordre et le vecteur de nesting Q̅ sont déterminés à partir d’une analyse détaillée de la forme de raie R. M. N. Des protons des groupes méthyles, pour diverses orientations du champ. Dans l’état métallique (paramagnétique), la rotation rapide par effet tunnel de deux groupes méthyles inéquivalents donne une raie centrale et deux paires de satellites avec des déplacements variables suivant l’orientation du champ magnétique, en bon accord avec la théorie. Dans l’état onde de densité de spin, les champs locaux dus à la structure magnétique ordonnée entrainent un élargissement important de la raie. Par une étude approfondie de la forme de raie et de son évolution en fonction de l’orientation du champ, nous prouvons que, pour ces deux composés, l’ODS est incommensurable ; nous déterminons les champs locaux correspondant à chaque groupe méthyle et séparons la contribution dipolaire du terme de contact hyperfin ; nous déduisons l’amplitude δ et le vecteur d’onde Q̅ de l’ODS. L’amplitude δ = 8% +̠ 2% (en unité μB par molécule) pour PF₆ est très supérieure à certaines estimations antérieures. La composante du vecteur de nesting suivant le vecteur de base b̅* pour PF₆ est en contradiction avec les modèles théoriques simples conduisant à Q̅b = 0 ou Q̅b = 0. 5 b̅*, mais correspond aux résultats d’un calcul de bande réaliste, dans l’approximation des liaisons fortes. Le vecteur Q̅ est différent dans (TMTSF)₂ClO₄, en accord avec les prédictions théoriques suivant lesquelles Q̅ dépend de la nature de l’anion et des conditions expérimentales (pression)<br>For the first time, in the S. D. W. State of the organic conductors (TMTSF)₂ClO₄ and (TMTSF)₂PF₆, the amplitude δ f the order parameter and the nesting vector Q̅ are determined, from a detailed analysis of the methyl proton N. M. R. Line-shape for various magnetic field orientations. In the paramagnetic metallic state, the fast rotational tunneling of the two inequivalent methyl groups splits the line into one central line and two pairs of satellites with shifts depending on field orientation, in good agreement with theory. In the S. D. W. State, the local fields due to the ordered magnetic structure lead to an important broadening of the line. By a careful analysis of the lineshape and its evolution in terms of field orientation, we prove, for both compounds, that the S. D. W. Is incommensurate; we are able to determine the local fields at each methyl site and separate the dipolar contribution from the hyperfine contact term; we deduce both the amplitude δ and wave vector Q̅ of the S. D. W. The amplitude δ = 8% +̠ 2% (in unit μB per molecule) for PF₆ is much larger than previous estimates from N. M. R. Broadening. The b* component of the nesting vector Q̅b = (0. 20 + 0. 05) b̅* (b̅* reciprocal lattice basis vector) for PF₆ is in contradiction with simple theories leading to Q̅b = 0 or Q̅b = 0. 5 b̅* but agrees with the consequences of realistic tight binding band calculations. The Q̅ vector is different in (TMTSF)₂ClO₄, in agreement with the theoretical prediction that Q̅ depends on the nature of anion and experimental conditions like pressure

Le présent travail a permis d'une part d'aborder une analyse structurale des phases température ambiante (TA)et basse température (BT) du composé d'insertion du graphite C8Br (stade 2)et d'autre part d'étudier la transition de phase incommensurable (TA)- commensurable (BT)des couches de brome ainsi que l'évolution des corrélations intercouches. Cette étude a été réalisée en mesurant et caractérisant les réflexions (hkl) de la structure de brome obtenues par deux méthodes de diffraction des rayons X : la méthode de précession et L'utilisation d'un diffractomètre. A température ambiante (TA), les couches de brome présentent une structure incommensurable fortement modulée par le graphite comme indiqué par L'importance de l'intensité des satellites de diffraction. D'autre part, ces couches sont partiellement corrélées comme le montre les modulations des Lignes diffuses relatives aux réflexions caractéristiques de cette phase. Les corrélations évoluent avec la température et varient brutalement aux alentours de 296 K et 286 K. Les couches de brome subissent à environ T≃275 K une transition de phase du premier ordre incommensurable-commensurable. La phase BT bidimensionnelle est caractérisée par une maille rectangulaire de grande taille. L'ordre commensurable au sein des couches s'accompagne d'une façon surprenante par une perte totale des correlations intercouches. Nous sommes donc en présence d'une transition entre une phase incommensurable (I) tridimensionnelle (3D) à température ambiante (TA) et une phase commensurable (C) bidimensionnelle (2D) à basse température (BT)<br>The object of this thesis was on the one hand a structural analysis of the room temperature (RT) and low temperature (LT) phases of the saturated bromine-intercalated graphite compound : C8Br (stage 2) and on the other hand the study of the in-plane incommensurate (RT) - commensurate (LT) phase transition and of the interlayer correlations. This study was performed by measuring and analysing the (hkl) reflections of the intercalate structure using precession and diffractometer X ray techniques. At room temperature (RT) the intercalate bromine layers are found to present an incommensurate in-plane structure strongly modulated by the graphite host as revealed by the large intensity of the modulation satellites. A partial correlation between layers exists as evidenced by the modulations of the diffuse rods passing through the in-plane RT reflections. These correlations evolve with temperature and exhibit a sudden change around 296 K and 286 K. At about T ≃ 275 K the intercalate layer exhibits a first order incommensurate-commensurate phase transition. The 2D low temperature phase is characterized by a large rectangular unit cell. Surprisingly this in-plane commensurate ordering is accompanied by a loss of the interlayer correlations. We have therefore a transition from an incommensurate (I) three-dimensional (3D) phase at room temperature (RT) to a commensurate (C) two-dimensional (2D) phase at low temperature (LT)

Ce travail est consacré à l'analyse structurale de l'onde de polarisation dans un composé isolant incommensurable la thiourée. La forme microscopique de la modulation et son anharmonicité reflètent de façon intime les interactions existant dans le système. L'onde de modulation est décrite à l'aide d'un modèle de Landau displacif. Le paramètre d'ordre comprend une onde de distorsion primaire, et une série d'harmoniques de distorsion. A partir de sa symétrie, on peut discuter la symétrie et la stabilité des différentes phases accrochées possibles. Ce modèle a permis d'affiner la structure de la phase longue-période "1/9", à partir d'une collection de données de diffraction de neutrons faite sur un monocristal deutérié.

Ce travail est consacré à l'étude de "l'effet mémoire" se dans la phase modulée incommensurable d'un isolant : Cet effet est la signature d'un réseau de défauts mobiles capables de s'ordonner selon la périodicité spatiale de la modulation (par couplage défauts-modulation). En retour un tel réseau de défauts, une fois, ordonné, peut provoquer un blocage de la périodicité de la modulation. Cet effet de mémoire parait être une propriété générale de toutes les structures modulées. La susceptibilité électrique et la biréfringence linéaire optique sont des grandeurs couplées au paramètre d'ordre de la modulation, et permettent donc d'étudier les effets mémoire dans la thiourée. Nous nous sommes particulièrement attachés aux processus d'inscription et de relaxation de l'effet mémoire<br>This is a study of the "memory effect" which is found in the modulated, incommensurate phase of the insulator thiourea. This effect is the sign of a set of mobile defects, which can become ordered according to the spatial period of the modulation (via defect-modulation coupling). In return, the set of defects, once ordered, can lock in the modulation period. This memory effect appears to be a general property of all modulated structures. The dielectric susceptibility and linear, optic, birefringency are coupled to the modulation order parameter, and enable one to study the memory effect in thiourea. We paid particular attention to the marking and relaxation processes of the memory effect

L’impiego della storia della matematica è auspicato oggi più di ieri dalle attuali Indicazioni nazionali per i Licei ed è supportato da numerosi quadri teorici,che traghettano la storia della matematica dalle rive dell’essere artefatto all’essere conoscenza. In particolare nel secondo paragrafo del primo capitolo di questa tesi vengono presentati gli ostacoli epistemologici di Guy Brousseau, l’approccio socio-culturale di Louis Radford, l’approccio ”voci ed echi” di Paolo Boero ed infine lo spaesamento di Barbin. Nel terzo paragrafo vengono analizzati quei contributi che mirano a rendere più operativo l’entusiasmo suscitato dall’uso della storia nell’insegnamento della matematica. Quindi il primo capitolo ha l’obiettivo di porre le basi teoriche all’uso della storia nella trasmissione del sapere matematico; pertanto ho deciso di mettere a punto una sperimentazione da condurre in una classe seconda di Liceo Scientifico avente come oggetto una fonte storica. Come argomento è stato scelto l’irrazionalità, introdotto in tale trattazione nel secondo capitolo: nel primo paragrafo viene trattato il problema della nascita dell’incommensurabilità, mentre nel secondo vengono analizzate le numerose dimostrazioni che sono state proposte nel corso dei secoli in merito all’incommensurabilità di lato e diagonale di un quadrato partendo da Aristotele ed Euclide, passando per Alessandro d’Aforisia e Platone, attraversando le dimostrazioni geometriche e quelle che sfruttano il metodo dell’anthyphairesis, per giungere ad una dimostrazione moderna che non presta il fianco alle critiche aristoteliche proposte da Salomon Ofman. Nel terzo capitolo viene presentata la sperimentazione che ho condotto, anteponendo a ciò i criteri adottati per la scelta del brano, ossia le lezione di Geometria tratta dal Menone di Platone ed un breve tributo alla figura di Platone e alla sua opera da cui è tratto il brano scelto come fonte storica. Tale capitolo è articolato in tre paragrafi: nel terzo vengono descritte dettagliatamente tutte le attività condotte in classe e vengono presentati i lavori e le risposte degli studenti. Infine, nel quarto capitolo, vengono esaminati dettagliatamente i risultati dei ragazzi alla luce dei quadri teorici precedentemente introdotti e vengono messe in luce le peculiarità dell’attività dell’argomentare e le doti e mancanze relative a ciò degli studenti.

La birnessite est un oxyde de manganèse lamellaire dont les feuillets sont composés d'octaèdres MnO6. La présence dans ces feuillets de cations Mn hétérovalents ou de lacunes induit un déficit de charge compensé par la présence de cations hydratés dans l'espace interfoliaire. Les oxydes de manganèse jouent un rôle fondamental pour le devenir de nombreux polluants organiques ou métalliques dans l'environnement, mais la connaissance imparfaite de leur structure limite la modélisation de cet impact. Le but de ce travail était de recenser et de classifier les différentes variétés de birnessites obtenues selon deux critères pertinents (symétrie du feuillet et mode d'empilement) et de déterminer la structure de plusieurs variétés essentielles par diffraction des rayons X et des électrons. La birnessite hydrothermale est caractérisée par un feuillet lacunaire de symétrie hexagonale et un empilement rhomboédrique 3R. Dans l'empilement des feuillets de la birnessite haute-température, les octaèdres des feuillets successifs présentent une orientation inverse induisant un polytype à deux feuillets. La symétrie de ces feuillets, liée à l'origine du déficit de charge, dépend de la température de synthèse. A 800°C, le feuillet lacunaire possède une symétrie hexagonale (polytype 2H). A 1000°C, le déficit de charge est dû à la présence de Mn3+ dans le feuillet. L'allongement systématique de ces octaèdres selon l'axe a induit une symétrie orthogonale du feuillet (polytype 2O). Diverses hétérogénéités chimiques et structurales ont également été décrites dans ces échantillons, ainsi que l'occurrence originale d'un nouveau type de désordre structural. Nous avons enfin illustré le lien fondamental entre l'origine de la charge foliaire et la symétrie du feuillet, ainsi que l'influence des paramètres physico-chimiques lors de la synthèse (température, degré d'oxydation du manganèse, nature du cation) sur la structure du composé obtenu, et comparé leurs stabilités chimiques et thermiques.

Ce manuscrit présente l’étude expérimentale des propriétés structurales et physiques d’une série de composés à chaînes de spins Sr4−xCaxCoMn2O9, appartenant à la famille d’oxydes A1+X(A’XB1−X)O3. Dans cette série, les chaînes 1D sont constituées des octaèdres MnO6 et prismes trigonaux CoO6 reliés par les faces, et réparties sur un réseau triangulaire avec un couplage antiferromagnétique entre elles. Ces chaînes présentent une forte anisotropie magnétique de type Ising provenant du cation Co2+ (HS, 3d7, S = 3/2). D’abord, l'étude structurale de ces chaînes révèle qu’elles peuvent être incommensurables, à cause d’un changement de degré d'oxydation du cobalt en fonction des conditions de synthèse. Ensuite, nous nous sommes intéressés à l'étude des deux composés Sr4CoMn2O9 (x=0) et Sr2Ca2CoMn2O9 (x=2). Le composé x=0 commensurable a montré l'absence de mise en ordre magnétique à longue distance (LRO) et des réponses dynamiques de relaxation de spins, typiques des Single-Ion Magnet (SIM) et Single-Chain Magnet (SCM) dont l'amplitude de leurs pics caractéristiques dépendde la (in)commensurabilité. En revanche, dans x=2, seule la réponse SIM a été observée à basse température, et qui coexiste avec le LRO à TN ~ 28 K. Les données de diffraction des neutrons montrent que cet LRO est compatible avec un état antiferromagnétique partiellement désordonné (PDA). Un régime pré-transitionnel particulier a été aussi observé entre TN et T* (~ 32.5 K), qui a été considéré comme un effet précurseur de LRO. D'un autre côté, un couplage magnéto-électrique a été également mis en évidence au sein de ce composé, dont l'origine a été interprétée par un phénomène de striction d’échange. Finalement, nous avons étudié l'anisotropie magnétique dans des échantillons orientés, dont la morphologie des grains a été optimisée par différents traitements thermiques<br>This manuscript presents the experimental study of structural and physical properties of a spin chain compounds Sr4-xCaxCoMn2O9, belonging to the large oxides family A1+XA'XB1-XO3. In this series, the 1D chains are made up of the octahedra MnO6 (Mn4+) and trigonal prisms CoO6 (Co2+) connected by the faces, and distributed over a triangular lattice with an antiferromagnetic coupling between them. These chains exhibit a strong Ising-type magnetic anisotropy, originating from the cation Co2+ (HS, 3d7, S = 3/2). First of all, the structural study of these chains reveals that they can be immcommensurate, due to a change in the degree of oxidation of cobalt depending on the synthesis conditions. Then, we were interested in the study of the two compounds Sr4CoMn2O9 (x=0) and Sr2Ca2CoMn2O9 (x=2). The x=0 compound showed the absence of long-range magnetic ordering (LRO) and dynamic spin relaxation responses, typical of Single-Ion Magnet (SIM) and Single-Chain Magnet (SCM), of which the amplitude of their characteristic peaks depends on the (in)commensurability. On the other hand, in x = 2, only the SIM response was observed at low temperature, and which coexists with the LRO at TN ~ 28 K. The neutron diffraction data show that this LRO is compatible with a partially disordered antiferromagnetic state (PDA). A particular pre-transitional regime was also observed between TN and T* (~ 32.5 K), which was considered to be a precursor effect of LRO. Furthermore, a magneto-electric (ME) coupling has also been demonstrated within this compound. The mechanism of this ME coupling has been discussed as a result of exchange-striction phenomenon. Finally, we studied the magnetic anisotropy in oriented samples, whose grain morphology was optimized by different heat treatments