Made available in DSpace on 2015-09-17T15:24:35Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-11-25. Added 1 bitstream(s) on 2015-09-17T15:47:36Z : No. of bitstreams: 1 000847337.pdf: 1291940 bytes, checksum: e8ff06439aa8fa7f8228c7d0e48fa739 (MD5) / Nesta pesquisa o objetivo é expor a compreensão do que é a abdução para Peirce, a partir de uma análise hermenêutica tal qual ela é tratada por pesquisadores da UNESP/RC vinculados ao Programa de Pós-Graduação em Educação Matemática e das ideias de Hans Georg Gadamer (1999). Para tanto, a pergunta que norteou a pesquisa é: o que é abdução? O estudo hermenêutico dos textos de Peirce, especialmente no The Collected Papers of Charles Sanders Peirce composto de oito volumes, é apresentado em dois quadros que trazem Ideias Nucleares (I.N.) que, mediante análise, levam-nos as categorias: característica, procedimento e definição. A interpretação dessas categorias nos permite dizer que a abdução, em Peirce, é um raciocínio lógico, um ato inferencial que tem origem na ação de questionar sendo um tipo de raciocínio que difere da lógica clássica pelo modo como abre possibilidades de uma nova inteligibilidade do que se vê, do que se pode expressar quando é elaborada uma explicação do visto. Entendendo as características da abdução pode-se ver que ela abre possibilidades para a produção do conhecimento matemático dando forma ao conceito, que é expresso por meio de uma linguagem que expõem o sentido do produzido / In this research the goal is to expose the understanding of what is the abduction for Peirce, from a hermeneutic analysis such as it is treated by researchers from UNESP/RC bound to Mathematic Education Post-Graduation Program and to ideas of Hans Georg Gadamer (1999). For that, the question that guided the research is: What is abduction?. The hermeneutic study of Peirce's texts, especially at The Collected Papers of Charles Sanders Peirce compound of eight volumes, is presented in two boards which bring Nuclear Ideas (I.N.) that, by analysis, take us to the categories: feature, procedure and definition. The interpretation of these features allow us to say the abduction, in Peirce, is a logic reasoning, an inferential act which origin at action of question being a type of reasoning that differs from classic logic by the way how it opens possibilities of a new intelligibility of what it's seen, from what it can express when is developed a new explanation of seen. Perceiving the features of abduction it can see how it opens possibilities for a production of the mathematic knowledge giving shape to the concept, that is expressed by a language that expose the direction of produced

Made available in DSpace on 2014-11-10T11:09:47Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-05-06Bitstream added on 2014-11-10T11:58:04Z : No. of bitstreams: 1 000789882.pdf: 2892998 bytes, checksum: cd8c3f24ece89e5fe38a56b25c7412e4 (MD5) / O primeiro movimento desta pesquisa visa cartografar os processos: educador/educando e as possibilidades da relação dialógica entre estes, em situação de sala de aula. Como elemento constitutivo, deste movimento, foram utilizadas estratégias didáticas que enfatizaram o argumento e a construção conjunta de conhecimento incentivando, assim, ambientes criativos e heurísticos de aprendizagem. Desenharam-se oficinas em Geometria, olhando-as como um dispositivo acionador e de intervenção dentro da sala de aula para trabalhar com estudantes da Educação de Jovens e Adultos (EJA). Analisaram-se, assim, os processos, inerentes na relação dialógica, contextualizados nos estudos de Paulo Freire e nas relações de poder, como propostas por Michel Foucault. Foram exploradas situações problemáticas do entorno que conseguiram corresponder aos aspectos criativos como: a arte, a música e a exploração do meio. Espera-se que os resultados da investigação iluminem o tipo de relação argumentativa que ocorre em sala de aula. Ao utilizar estratégias didáticas, previamente desenhadas, como disparadoras do desenvolvimento das oficinas espera-se alterar, ao menos localmente, as relações de poder que travam as possibilidades dialógicas em sala de aula / The first movement of this research aims to map the processes: teacher / student relationship and the possibilities of dialogue between them in the classroom situation. As a constitutive element, this movement used teaching strategies that emphasize the argument and the joint construction of knowledge by encouraging thus creative environments and heuristic learning. Were designed and conducted geometry workshops, that were observed as a driver and intervention device within the classroom to work with students of Youth and Adults (EJA). We analyzed the inherent processes in the dialogic relationship, contextualized in the studies of Paulo Freire and power relationships, as proposed by Michel Foucault. Surrounding situation issues that can match the creative aspects such as art, music and exploration of the environment were explored. The research findings elucidated the argumentative type of relationship that occur in the classroom. By using teaching strategies, previously designed as triggering of the development of the workshops, there was a change, at least locally, in the relations of power that keep dialogical possibilities in the classroom

Orientador: Fátima Regina Rodrigues Évora / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências Humanas / Made available in DSpace on 2018-08-25T13:29:44Z (GMT). No. of bitstreams: 1 Calazans_Alex_D.pdf: 1884458 bytes, checksum: e130faa10a7b5bed837ce429d5d12c5d (MD5) Previous issue date: 2014 / Resumo: O objetivo desta tese é estabelecer um estudo de como Berkeley concebeu os objetos matemáticos. Interessa saber se há, em seu pensamento, uma unidade no critério de inteligibilidade desses objetos. Busca-se, para isso, reconstruir alguns de seus argumentos quanto ao que ele considera como objetos legítimos não só da aritmética, álgebra e geometria, como também do cálculo infinitesimal. A partir disso, serão avaliadas as consequências interpretativas de seus textos de maturidade - como é o caso do texto O Analista (1734), conhecido pela crítica ao cálculo infinitesimal - sobre se há primazia de tais objetos no processo de avaliação da cientificidade das matemáticas. Não se almeja, portanto, adotar como porta de entrada a macro questão sobre o que é ciência matemática, para Berkeley, mas a questão de como a noção de objeto matemático apresenta-se, ou não, como um dos elementos importantes para o esclarecimento desse problema mais geral / Abstract: The aim of this thesis is to establish a study of how Berkeley devised mathematical objects. It is of interest to know whether there is, in his thinking, a unit in the criterion of intelligibility of these objects. To do this, we try to reconstruct some of his arguments about what he considers as legitimate objects, not only in arithmetic, algebra and geometry, but also in the infinitesimal calculus. From this, the interpretive consequences of his maturity texts are evaluated - such as the text The Analyst (1734), which is known for the criticism of the infinitesimal calculus - on whether there is primacy of such objects in the process of evaluating the scientific character of mathematics. Therefore, we don¿t want to adopt as an entrance the more general question of what is mathematical science, to Berkeley, but the question of how the notion of mathematical object is presented, or not, as one of the important elements to enlighten this more general problem / Doutorado / Filosofia / Doutor em Filosofia

Orientador: Walter Alexandre Carnielli / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências Humanas / Made available in DSpace on 2018-08-25T21:09:00Z (GMT). No. of bitstreams: 1 Almeida_HenriqueAntunes_M.pdf: 1516387 bytes, checksum: 2608439ba585a23431d2aa295b1b8876 (MD5) Previous issue date: 2014 / Resumo: Neste trabalho, abordamos o Teorema de Frege sob uma perspectiva exclusivamente técnica. Primeiramente, propomos uma caracterização geral de linguagens de segunda ordem que sejam adequadas para formalizar quaisquer teorias fregeanas ¿ teorias que resultam da introdução de um ou mais princípios de abstração a um sistema dedutivo de lógica de segunda ordem; fornecemos uma semântica e um sistema dedutivo para essas linguagens e elaboramos alguns resultados metateóricos acerca desse sistema. Em segundo lugar, apresentamos uma exposicão detalhada da prova do Teorema de Frege, enunciado como uma relação entre a Aritmética de Frege e a Aritmética de Dedekind-Peano. Por fim, provamos a equiconsistência entre essas teorias e a Aritmética de Peano de Segunda Ordem / Abstract: In this work, we discuss Frege¿s Theorem under an exclusively technical perspective. First, we propose a general caracterization of second-order languages suitable to formalize all Fregean theories ¿ theories that result from the introduction of one or more abstraction principles to a deductive system of second-order logic; we also furnish a semantics and a deductive system for these languages and establish a few metatheorical results about the system. Second, we present a detailed proof of Frege¿s Theorem, formulated as a relation between Frege¿s Arithmetic and Dedekind-Peano Arithemtic. Finally, we prove the equiconsistency between these theories and Peano Second-Order Arithmetic / Mestrado / Filosofia / Mestre em Filosofia

Problem solving is a central activity of mathematics and has been throughout its history. Recognizing the problem of problem solving, however, seems to be less explicit in the historical record. In studying three principal contributors to the study of problem solving-Rene Descartes, John Dewey, and George Polya-I have found that problems arise in two broad categories. Mathematics itself generates more mathematical problems, and problems embedded in a wider context can generate mathematics. Recognizing a mathematical problem in a rich context-problem finding-has received much less attention. John Dewey recognized the importance of problem finding and emphasized its role in problem solving. Descartes and Polya spent less time on problem finding, Polya the least of all. / Department of Mathematical Sciences

This thesis is about the nature of proofs in mathematics as it is practiced, contrasting the informal proofs found in practice with formal proofs in formal systems. In the first chapter I present a new argument against the Formalist-Reductionist view that informal proofs are justified as rigorous and correct by corresponding to formal counterparts. The second chapter builds on this to reject arguments from Gödel's paradox and incompleteness theorems to the claim that mathematics is inherently inconsistent, basing my objections on the complexities of the process of formalisation. Chapter 3 looks into the relationship between proofs and the development of the mathematical concepts that feature in them. I deploy Waismann's notion of open texture in the case of mathematical concepts, and discuss both Lakatos and Kneebone's dialectical philosophies of mathematics. I then argue that we can apply work from conceptual engineering to the relationship between formal and informal mathematics. The fourth chapter argues for the importance of mathematical knowledge-how and emphasises the primary role of the activity of proving in securing mathematical knowledge. In the final chapter I develop an account of mathematical knowledge based on virtue epistemology, which I argue provides a better view of proofs and mathematical rigour.

The philosophy of linguistics is a rich philosophical domain which encompasses various disciplines. One of the aims of this thesis is to unite theoretical linguistics, the philosophy of language, the philosophy of science (particularly mathematics and modelling) and the ontology of language. Each part of the research presented here targets separate but related goals with the unified aim of bringing greater clarity to the foundations of linguistics from a philosophical perspective. Part I is devoted to the methodology of linguistics in terms of scientific modelling. I argue against both the Conceptualist and Platonist (as well as Pluralist) interpretations of linguistic theory by means of three grades of mathematical involvement for linguistic grammars. Part II explores the specific models of syntactic and semantics by an analogy with the harder sciences. In Part III, I develop a novel account of linguistic ontology and in the process comment on the type-token distinction, the role and connection with mathematics and the nature of linguistic objects. In this research, I offer a structural realist interpretation of linguistic methodology with a nuanced structuralist picture for its ontology. This proposal is informed by historical and current work in theoretical linguistics as well as philosophical views on ontology, scientific modelling and mathematics.

Orientador: Walter Alexandre Carnielli / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias Humanas / Made available in DSpace on 2018-08-12T22:46:52Z (GMT). No. of bitstreams: 1 Freire_RodrigodeAlvarenga_D.pdf: 761227 bytes, checksum: 3b1a0de92aa93b50f2bfc602bf6173bc (MD5) Previous issue date: 2009 / Resumo: Esta Tese tem como objetivo elucidar, ao menos parcialmente, a questão do significado da Teoria de Modelos para uma reflexão sobre o conhecimento matemático no século XX. Para isso, vamos buscar, primeiramente, alcançar uma compreensão da própria reflexão sobre o conhecimento matemático, que será denominada de Fundamentos do Pensamento Matemático no século XX, e da própria relevância fundacional. Em seguida, analisaremos, dentro do contexto fundacional estabelecido, o papel da Teoria de Modelos e da sua interação com a Álgebra, em geral, e, finalmente, empreenderemos um estudo de caso específico. Nesse estudo de caso mostraremos que a Teoria de Galois pode ser vista como um conteúdo lógico, e buscaremos compreender o significado fundacional desse enquadramento modelo-teórico para uma parte da Álgebra clássica. / Abstract: The aim of the present Thesis is to bring some light to the question about the status and relevance of Model Theory to a reflection about the mathematical knowledge in the twentieth century. To pursue this target, we will, first of all, try to reach a comprehension of the reflection about the mathematical knowledge, itself, what will be designated as Foundations of Mathematical Thought in the twentieth century, and of the foundational relevance, itself. In the sequel, we will provide an analysis, of the role of Model Theory and its interaction with Algebra, in general, within the established foundational setting and, finally, we will discuss a specific study case. In this study case we will show that Galois Theory can be seen as a logical content, and we will try to understand the foundational meaning of this model-theoretic framework for some part of classical Algebra. / Doutorado / Logica / Doutor em Filosofia

Text in Afrikaans, abstract in Afrikaans and English / Hierdie studie is daarop gemik om te bepaal tot welke mate wiskundeleerlinge op skool en onderwysstudente in wiskunde, onderrig in logika ontvang as agtergrond vir strenge bewysvoering. Die formele aspek van wiskunde op hoerskool en tersiere vlak is besonder belangrik. Leerlinge en studente kom onvermydelik met hipotetiese argumente in aanraking. Hulle leer ook om die kontrapositief te gebruik in bewysvoering. Hulle maak onder andere gebruik van bewyse uit die ongerymde. Verder word nodige en voldoende voorwaardes met stellings en hulle omgekeerdes in verband gebring. Dit is dus duidelik dat 'n studie van logika reeds op hoerskool nodig is om aanvaarbare wiskunde te beoefen. Om seker te maak dat aanvaarbare wiskunde beoefen word, is dit nodig om te let op die gebrek aan beheer in die ontwikkeling van 'n taal, waar woorde meer as een betekenis het. 'n Kunsmatige taal moet gebruik word om interpretasies van uitdrukkings eenduidig te maak. In so 'n kunsmatige taal word die moontlikheid van foutiewe redenering uitgeskakel. Die eersteordepredikaatlogika, is so 'n taal, wat ryk genoeg is om die wiskunde te akkommodeer. Binne die konteks van hierdie kunsmatige taal, kan wiskundige toeriee geformaliseer word. Verskillende bewystegnieke uit die eersteordepredikaatlogika word geidentifiseer, gekategoriseer en op 'n redelik eenvoudige wyse verduidelik. Uit 'n ontleding van die wiskundesillabusse van die Departement van Onderwys, en 'n onderwysersopleidingsinstansie, volg dit dat leerlinge en studente hierdie bewystegnieke moet gebruik. Volgens hierdie sillabusse moet die leerlinge en studente vertroud wees met logiese argumente. Uit die gevolgtrekkings waartoe gekom word, blyk dit dat die leerlinge en studente se agtergrond in logika geheel en al gebrekkig en ontoereikend is. Dit het tot gevolg dat hulle nie 'n volledige begrip oor bewysvoering het nie, en 'n gebrekkige insig ontwikkel oor wat wiskunde presies behels. Die aanbevelings om hierdie ernstige leemtes in die onderrig van wiskunde aan te spreek, asook verdere navorsingsprojekte word in die laaste hoofstuk verwoord. / The aim of this study is to determine to which extent pupils taking Mathematics at school level and student teachers of Mathematics receive instruction in logic as a grounding for rigorous proof. The formal aspect of Mathematics at secondary school and tertiary levels is extremely important. It is inevitable that pupils and students become involved with hypothetical arguments. They also learn to use the contrapositive in proof. They use, among others, proofs by contradiction. Futhermore, necessary and sufficient conditions are related to theorems and their converses. It is therefore apparent that the study of logic is necessary already at secondary school level in order to practice Mathematics satisfactorily. To ensure that acceptable Mathematics is practised, it is necessary to take cognizance of the lack of control over language development, where words can have more than one meaning. For this reason an artificial language must be used so that interpretations can have one meaning. Faulty interpretations are ruled out in such an artificial language. A language which is rich enough to accommodate Mathematics is the first-order predicate logic. Mathematical theories can be formalised within the context of this artificial language. Different techniques of proof from the first-order logic are identified, categorized and explained in fairly simple terms. An analysis of Mathematics syllabuses of the Department of Education and an institution for teacher training has indicated that pupils should use these techniques of proof. According to these syllabuses pupils should be familiar with logical arguments. The conclusion which is reached, gives evidence that pupils' and students' background in logic is completely lacking and inadequate. As a result they cannot cope adequately with argumentation and this causes a poor perception of what Mathematics exactly entails. Recommendations to bridge these serious problems in the instruction of Mathematics, as well as further research projects are discussed in the final chapter. / Curriculum and Institutional Studies / D. Phil. (Wiskundeonderwys)

In this thesis I discuss the nature of ‘measurement’ in quantum theory. ‘Measurement’ is associated with several different processes: the gradual imprinting of information about one system onto another, which is well understood; the collapse of the wavefunction, which is ill-defined and troublesome; and finally, the means by which inferences about unknown experimental parameters are made. I present a theoretical extension to an experimental proposal from Leggett and Garg, who suggested that the quantum-or-classical reality of a macroscopic system may be probed with successive measurements arrayed in time. The extension allows for a finite level of imperfection in the protocol, and makes use of Leggett’s ‘null result’ measurement scheme. I present the results of an experiment conducted in Oxford that, up to certain loopholes, defies a non-quantum interpretation of the dynamics of phosphorous nuclei embedded in silicon. I also present the theory of statistical parameter estimation, and discover that a recent trend to employ time symmetric ‘postselected’ measurements offers no true advantage over standard methods. The technique, known as weak-value amplification, combines a weak transfer of quantum information from system to meter with conditional data rejection, to surprising effect. The Fisher information is a powerful tool for evaluating the performance of any parameter estimation model, and it reveals the technique to be worse than ordinary, preselected only measurements. That this is true despite the presence of noise (including magnetic field fluctuations causing deco- herence, poor resolution detection, and random displacements), casts serious doubt on the utility of the method.