87 research outputs found

    Relations between logic and mathematics in the work of Benjamin and Charles S. Peirce.

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    Charles Peirce (1839-1914) was one of the most important logicians of the nineteenth century. This thesis traces the development of his algebraic logic from his early papers, with especial attention paid to the mathematical aspects. There are three main sources to consider. 1) Benjamin Peirce (1809-1880), Charles's father and also a leading American mathematician of his day, was an inspiration. His memoir Linear Associative Algebra (1870) is summarised and for the first time the algebraic structures behind its 169 algebras are analysed in depth. 2) Peirce's early papers on algebraic logic from the late 1860s were largely an attempt to expand and adapt George Boole's calculus, using a part/whole theory of classes and algebraic analogies concerning symbols, operations and equations to produce a method of deducing consequences from premises. 3) One of Peirce's main achievements was his work on the theory of relations, following in the pioneering footsteps of Augustus De Morgan. By linking the theory of relations to his post-Boolean algebraic logic, he solved many of the limitations that beset Boole's calculus. Peirce's seminal paper `Description of a Notation for the Logic of Relatives' (1870) is analysed in detail, with a new interpretation suggested for his mysterious process of logical differentiation. Charles Peirce's later work up to the mid 1880s is then surveyed, both for its extended algebraic character and for its novel theory of quantification. The contributions of two of his students at the Johns Hopkins University, Oscar Mitchell and Christine Ladd-Franklin are traced, specifically with an analysis of their problem solving methods. The work of Peirce's successor Ernst Schröder is also reviewed, contrasting the differences and similarities between their logics. During the 1890s and later, Charles Peirce turned to a diagrammatic representation and extension of his algebraic logic. The basic concepts of this topological twist are introduced. Although Peirce's work in logic has been studied by previous scholars, this thesis stresses to a new extent the mathematical aspects of his logic - in particular the algebraic background and methods, not only of Peirce but also of several of his contemporaries

    Goal driven theorem proving using conceptual graphs and Peirce logic

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    The thesis describes a rational reconstruction of Sowa's theory of Conceptual Graphs. The reconstruction produces a theory with a firmer logical foundation than was previously the case and which is suitable for computation whilst retaining the expressiveness of the original theory. Also, several areas of incompleteness are addressed. These mainly concern the scope of operations on conceptual graphs of different types but include extensions for logics of higher orders than first order. An important innovation is the placing of negation onto a sound representational basis. A comparison of theorem proving techniques is made from which the principles of theorem proving in Peirce logic are identified. As a result, a set of derived inference rules, suitable for a goal driven approach to theorem proving, is developed from Peirce's beta rules. These derived rules, the first of their kind for Peirce logic and conceptual graphs, allow the development of a novel theorem proving approach which has some similarities to a combined semantic tableau and resolution methodology. With this methodology it is shown that a logically complete yet tractable system is possible. An important result is the identification of domain independent heuristics which follow directly from the methodology. In addition to the theorem prover, an efficient system for the detection of selectional constraint violations is developed. The proof techniques are used to build a working knowledge base system in Prolog which can accept arbitrary statements represented by conceptual graphs and test their semantic and logical consistency against a dynamic knowledge base. The same proof techniques are used to find solutions to arbitrary queries. Since the system is logically complete it can maintain the integrity of its knowledge base and answer queries in a fully automated manner. Thus the system is completely declarative and does not require any programming whatever by a user with the result that all interaction with a user is conversational. Finally, the system is compared with other theorem proving systems which are based upon Conceptual Graphs and conclusions about the effectiveness of the methodology are drawn

    Seeing problems, seeing solutions. Abduction and diagrammatic reasoning in a theory of scientific discovery

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    This paper sketches a theory of scientific discoveries that is mainly based on two concepts that Charles Peirce developed: abduction and diagrammatic reasoning. Both are problematic. While abduction describes the process of creating a new idea, it does not, on the one hand, explain how this process is possible and, on the other, is not precisely enough defined to distinguish different forms of creating new ideas. Diagrammatic reasoning, the process of constructing relational representations of knowledge areas, experimenting with them, and observing the results, can be interpreted, on the one hand, as a methodology to describe the possibility of discoveries, but its focus is limited to mathematics. The theory sketched here develops an extended version of diagrammatic reasoning as a general theory of scientific discoveries in which eight different forms of abduction play a central role

    Can we play science?: philosophical perspectives on participation in science research

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    Tese de mestrado, História e Filosofia da Ciência, Universidade de Lisboa, Faculdade de Ciências, 2015Podemos jogar ciência? Abordagens contemporâneas oferecem a possibilidade de participar na investigação científica. Muitas destas abordagens são feitas através duma gamificação da investigação científica usando a internet e ferramentas da Web 2.0, enquanto outras têm abordagens comunitárias que não estão dependentes do on-line. Como um trabalho de Filosofia da Ciência, este estudo preocupa-se sobre o significado de tal transformação. Isabelle Stengers é próxima à prática científica e sabe como o cientista é definido pelas suas paixões, por uma forma de se reportar ao mundo (Stengers 1993). No seu trabalho encontramos um ímpeto para re-inventar, re-enquadrar como as ciências se relacionam com a especialidade e a democracia. Será que estas abordagens participativas podem fazê-lo? Será que uma nova ciência está em movimento? Considerando as três ecologias de Félix Guattari, do nível mental, ao social, ao ambiental, ele considera que um valor maior se ganha abordando os diversos níveis de prática na sua singularidade (Guattari 1989). Neste estudo, um conjunto diverso de práticas participativas são investigadas, como os jogos de ciência cidadã Foldit e CosmoQuest e as redes de Do-It-Yourself biology e Nouveaux Commanditaires Sciences. Ciência cidadã on-line lida com desafios concretos apresentados à investigação científica e coloca novas questões científicas, contando com a contribuição cognitiva de cidadãos. Há uma quantidade enorme de informação e continua a aumentar. Este “conhecimentointensivo-em-informação” dá foco a inferências sintéticas, como o processo de fazer hipóteses, a abducção. Seguindo Charles Sanders Peirce, verificamos como o raciocínio abductivo construiu muitas perspectivas de interesse na epistemologia e filosofia da ciência. Seguindo cronologicamente o pensamento Peirciano, viajamos da fundação da retroducção nos silogismos aristotélicos até à sua aplicação numa lógica de ícones, em que as premissas se tornam em imagens. A partir da interacção com o ecrã onde a ciência é um jogo, a iconicidade dos elementos ganham relevo. Em segundo lugar, focando no conceito de experiência, tomamos a filosofia de John Dewey. Ele não tem a solidez lógica de Peirce, mas parece mais sistemático. Na interacção entre sujeito e natureza, o conhecimento torna-se instrumental. “Coisas na experiência” específicas servem como guias, como características que são sinais, índices de algo que prevalece na experiência. O que guia as inferências é parte da experiência do sujeito e envolve uma ligação entre a consciência e a natureza, que substancia uma ligação ao “universo completo”. O naturalismo empírico de Dewey faz um contraste interessante com o pensamento diagramático Peirciano.Para Dewey, qualquer esperança duma lógica da descoberta está perdida. Também o Pragmaticismo de Peirce não está preocupado com consequências práticas, como o Pragmatismo clássico. Em comum, sem dúvidas, está a importância dada à experiência. Considerando o nível social, usamos a emergência de esferas públicas como enquadradas por Habermas para ter um entendimento mais fino de como ferramentas online como os forums contribuem para o esforço intelectual conjunto da ciência cidadã virtual. Para participar no uso público da razão, é preciso de ser capaz de o fazer. O modelo heavyweight de produção de pares têm altos valores limites à participação. Mais, o papel do gatekeeper é criado, que pode ser reconhecido quando se abrem as portas da prática científica em jogos on-line, tal como nos salões franceses do século XVII. Outros jogos de investigação cientifica, como CosmoQuest e Zoo Universe têm valores limite à participação mais baixos. Quem quer que se registre, consegue imediatamente uma oportunidade para 'fazer ciência', usando as suas capacidades cognitivas para com os objectos no ecrã. O que é tida em linha de conta é o voto da maioria, pois muitos jogadores recebem a mesma imagem. Cientistas profissionais já assinam artigos científicos em publicações bem cotadas com peer-review. Assim é o caso do Foldit, do Polymath e do Galaxy Zoo. Interessantemente, muitos são assinados sobre um nome colectivo, que se relaciona com este enquadramento colectivo. Em tensão, existe uma dimensão agonal muito presente na gamificação da investigação científica. Há uma relevância dada ao pacto de competição, equivalente ao contrato de Agon. Colan Duclos dá ênfase ao elementos de tensão, stress, aleatoriedade e incerteza que fazem o jogo agonal. Um terceiro nível em análise é o político. Seguindo o argumento de uma re-encenação da comunidade de iguais com Jacques Rancière vemos que a comunidade de iguais: (i) é parte da interacção aleatória entre o que está lá e o que força a mudança; (ii) é fundamentalmente um processo de partilha; (iii) refere-se a um evento equalitário anterior e a um texto equalitário. O texto equalitário do movimento Do-It-Yourself biology corresponde ao Biocommons white paper. Ali está circunscrita uma forma inclusiva de abordar os comuns, a incluir não só “bens naturais”, como água, ar, terra, mas também organismos inteiros, processos bioquímicos e outras descobertas e conceitos biológicos e bioquímicos feitos pelo Homem. Biotecologia tem, então, com o Do-It-Yourself Biology, uma nova visão política e económica baseada na igualdade. Ainda, seguido o raciocínio de Rancière, podemos ver como este movimento tem que lidar com a desigualdade da organização social, tal como os fundados de Icaria tiveram que fazer no passado. Mas isto não significa por força que um tal empreendimento está fadado a fracassar. O “significador equalitário” que é agora parte integrante da sua identidade pode-se desvainecer, tal como o antigo apeiron grego, o desejo sem-limites pode enfraquecer. Se há perspectivas de ciência cidadã em favor do progresso e aceleração, outros querem desacelerar, tal como com os Nouveaux Commanditaires Sciences (NCS), pois a desconstrucção da investigação científica, no sentido de a fazer mais socialmente inclusiva, precisa de tempo. Inspirada pela emancipação de Freire, NCS usa a investigação científica para fazer trabalho comunitário. Acreditamos que participar na investigação científica é um acto de empoderamento. A aventura da Emancipação Intelectual foi aquela que juntou Rancière e Jacotot no livro de 1987 Le maître ignorant : cinq leçons sur l’émancipation intellectuelle. A lição do poeta no âmago do método de Jacotot é feita para soltar a vontade, para ser um participante activo. As decisões que vêm da sociedade que têm decisores em tópicos que concernem à comunidade científica é um tópico em discussão nos estudos sociais da ciência. Para Funtowicz e Ravetz uma exigência que vem dum decisor seria interpretado como um caso de ciência pós-normal, no sentido de legitimar a expertise de outros actores em decisões políticas. Em oposição, Collins tem dúvidas sobre o reconhecimento de expertises locais ao mesmo nível que a investigação científica. Ele preferiria criar ambientes nos quais o foco seria reconhecer e compreender a atitude científica. Em relação à descoberta de Jacotot, a educação está em tal relação com a não-educação, tal como a emancipação intelectual está para o embrutecimento. NCS e Jacotot estão, antes de mais, focados na dimensão da emancipação, enquanto Collins, a par de muitas outras iniciativas, estão focados na pedagogia. A ciência cidadã on-line está a crescer em número de participantes, projectos e escala. Estas soluções lidam com desafios novos concretos à investigação científica que parecem fadados a ser mais desenvolvidos. Podeser mais do que uma moda ou uma linha de fuga. Podemos estar perante uma re-territorialização destas abordagens massivas à investigação científica. Do outro lado da moeda, os movimentos contra-progressistas também lidam com uma resingularização da investigação científica. Este jogo é possível, mas a escala e eficiência deste processo de heterogénese continua por qualificar.Can we play science? Contemporary approaches offer the possibility of participation in science. Many of these approaches are done through a gamification of science research done using the internet and web2.0 tools, while others, have community-based approaches that aren't exclusive to the on-line environment. As a work of Philosophy of Science, this study is concerned about the meaning of such transformation. Isabelle Stengers is a close relative to scientific practice and knows how the scientist is defined by his or hers passions, by a way of reporting to the world (Stengers 1993). Inspired by the three Ecologies of Félix Guattari, we engage the diverse levels of practice in their singularity (Guattari 1989). In this study, a diverse set of participative practices are researched in connection to relevant philosophical perspectives. “Data-intensive knowledge” brings forward the synthetic inferences, as the process of making hypothesis, abduction. From the interaction with the screen, the iconicity of the elements come forward. Following Charles Peirce, we travel from the foundation of retroduction in the Aristotelian syllogisms to the application of abduction in a logic of icons, in that the premisses become images. Focusing on the concept of experience we take John Dewey's philosophy. The experience to the subject involves a connection to the “complete universe”. Dewey's empirical naturalism, gives an interesting contrast to Peirce's diagrammatic reasoning. Considering a social level, we use the emergence of Habermasian public spheres. To participate to a public use of reason, one needs to be able to do it. Moreover, the role of the gatekeeper is crafted, that can be recognized when opening the gates of scientific practice in on-line citizen science games. In tension, there's an agonal dimension very much present in the gamifications of science research. On a political level we follow Jacques Rancière, and see how Do-It-Yourself biology statement of equality will have to deal with the inequality of social organization. Just as the “egalitarian signifier” that is part of its identity might fade away, as the old greek apeiron, the unbound desire might get dimmer. If there are perspectives of citizen science as in favor of progress and acceleration, others want to decelerate, as with Nouveaux Commanditaires Sciences (NCS). On the work of Rancière we see that education is in such relation to uneducation, as intellectual emancipation is to stultification, giving an insight into a dispute at Social Studies of Science. On-line citizen science might signify a reterritorialization of this massive approaches to science research. On the other side of the coin, the counter movements of progress also deal with a resingularisation of science research. This play seems feasible, but the scale and efficiency of this heterogenesis process remains unaccounted

    Peirce's Account of Assertion

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    One usually makes assertions by means of uttering indicative sentences like “It is raining”. However, not every utterance of an indicative sentence is an assertion. For example, in uttering “I will be back tomorrow”, one might be making a promise. What is to make an assertion? C.S. Peirce held the view that “to assert a proposition is to make oneself responsible for its truth” (CP 5.543). In this thesis, I interpret Peirce’s view of assertion and I evaluate Peirce’s reasons for holding it. I begin by reconstructing and assessing Peirce’s case for such view as it appears in (EP 2.140, 1903), (EP 2.312-313, 1904), and (CP 5.546, 1908). Then, I continue by elaborating on three aspects of Peirce’s view of assertion, namely, assertion as an act involving a certain kind of responsibility, the proposition as what is asserted, and responsibility for truth as a responsibility to give reasons. With respect to these three aspects, I argue for the following claims: (1) Peirce construed the responsibility involved in asserting as a moral responsibility; (2) Peirce held that propositions are types; and (3) Peirce was committed to a dialogical interpretation of “responsibility to give reasons”. Finally, I end by presenting two objections to Peirce’s view of assertion and its corresponding replies. I conclude that Peirce’s account of assertion is a valuable contribution to the philosophical debate on assertion

    Investigation of the failure of statistical process control in manufacturing industries in South Africa : case study - Atlantis Diesel Engines

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    Includes bibliography.This work strives to give an insight into why Statistical Process Control (SPC), a quality management tool, is not yielding desired results in some manufacturing industries such as Atlantis Diesel Engines in the Western Cape. Statistical Process Control is an improvement technique that, when properly used, can improve both the quality and the productivity levels which may subsequently improve the competitiveness of a company. SPC achieves this by highlighting when a process is out of control. This happens at the source and a very early stage. The advantage of this is that in the case of manufacturing, rejects are limited and in some cases prevented depending on the relationship between process capability and specifications. The aim of SPC is to reduce variability of characteristics of a product. Wetherill and Brown (1991) revealed that many organisations regulated the quality of their products with SPC during the Second World War. This gives an idea of how long SPC has been in existence. The widespread use of SPC nearly came to an end in the 1960s. The reason for the abandonment of SPC by leading manufacturing industries in most parts of the world was not clear but the belief was that at that time industries were prospering, with little or no competition. However, in the late 1970s, the Japanese industries took the market by storm by the use of quality management techniques and tools, which were introduced by quality gurus such as Deming, Juran, Crosby and many others. This gave the incentive for organisations that wanted to be world class players in their respective sectors to reconsider exhaustively the use of SPC and its tools. In South Africa, predominantly in the Western Cape, SPC has been reintroduced in many companies over the past eight years. The introduction of SPC in most of the industries has not been a smooth transition as it was based on the misconception that if enough of the "right" improvement activities were carried out, then actual performance improvement would improve. There have been many factors hindering the successful implementation of SPC in manufacturing industries such as ADE. This research aims to identify these factors

    Graph Theory and Universal Grammar

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    Tese arquivada ao abrigo da Portaria nº 227/2017 de 25 de Julho-Registo de Grau EstrangeiroIn the last few years, Noam Chomsky (1994; 1995; 2000; 2001) has gone quite far in the direction of simplifying syntax, including eliminating X-bar theory and the levels of D-structure and S-structure entirely, as well as reducing movement rules to a combination of the more primitive operations of Copy and Merge. What remain in the Minimalist Program are the operations Merge and Agree and the levels of LF (Logical Form) and PF (Phonological form). My doctoral thesis attempts to offer an economical theory of syntactic structure from a graph-theoretic point of view (cf. Diestel, 2005), with special emphases on the elimination of category and projection labels and the Inclusiveness Condition (Chomsky 1994). The major influences for the development of such a theory have been Chris Collins’ (2002) seminal paper “Eliminating labels”, John Bowers (2001) unpublished manuscript “Syntactic Relations” and the Cartographic Paradigm (see Belletti, Cinque and Rizzi’s volumes on OUP for a starting point regarding this paradigm). A syntactic structure will be regarded here as a graph consisting of the set of lexical items, the set of relations among them and nothing more

    Recent studies on signs: Commentary and perspectives

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    In this commentary, I reply to the fourteen papers published in the Sign Systems Studies special issue on Peirce’s Theory of Signs, with a view on connecting some of their central themes and theses and in putting some of the key points in those papers into a wider perspective of Peirce’s logic and philosophy
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