Sobre la lógica en el siglo XIX y su reconstrucción historiográfica

Pretender cubrir en una exposición el conjunto del desarrollo de la lógica en el siglo XIX resulta impensable, entre otras razones por la multitud de trabajos que han aparecido en los últimos años sobre aspectos puntuales y sobre periodos definidos del mismo. Más aún, algunas presentaciones globales que sólo intentan ser, por su misma naturaleza, esquemáticas o aún bibliográficas, contienen o aluden a tal riqueza que confirman lo difícilmente abarcable del lapso referido. No es tampoco necesario recordar la fertilidad y amplitud, perfectible como es obvio, de los trabajos monográficos sobre los aportes principales de Boole, Frege, Peana, quienes son reconocidos alternativamente como los fundadores de la lógica nuestra

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

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

Laws of Thought and Laws of Logic after Kant

George Boole emerged from the British tradition of the “New Analytic”, known for the view that the laws of logic are laws of thought. Logicians in the New Analytic tradition were influenced by the work of Immanuel Kant, and by the German logicians Wilhelm Traugott Krug and Wilhelm Esser, among others. In his 1854 work An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, Boole argues that the laws of thought acquire normative force when constrained to mathematical reasoning. Boole’s motivation is, first, to address issues in the foundations of mathematics, including the relationship between arithmetic and algebra, and the study and application of differential equations (Durand-Richard, van Evra, Panteki). Second, Boole intended to derive the laws of logic from the laws of the operation of the human mind, and to show that these laws were valid of algebra and of logic both, when applied to a restricted domain. Boole’s thorough and flexible work in these areas influenced the development of model theory (see Hodges, forthcoming), and has much in common with contemporary inferentialist approaches to logic (found in, e.g., Peregrin and Resnik)

From mathematics in logic to logic in mathematics : Boole and Frege

This project proceeds from the premise that the historical and logical value of Boole's logical calculus and its connection with Frege's logic remain to be recognised. It begins by discussing Gillies' application of Kuhn's concepts to the history oflogic and proposing the use of the concept of research programme as a methodological tool in the historiography oflogic. Then it analyses'the development of mathematical logic from Boole to Frege in terms of overlapping research programmes whilst discussing especially Boole's logical calculus. Two streams of development run through the project: 1. A discussion and appraisal of Boole's research programme in the context of logical debates and the emergence of symbolical algebra in Britain in the nineteenth century, including the improvements which Venn brings to logic as algebra, and the axiomatisation of 'Boolean algebras', which is due to Huntington and Sheffer. 2. An investigation of the particularity of the Fregean research programme, including an analysis ofthe extent to which certain elements of Begriffsschrift are new; and an account of Frege's discussion of Boole which focuses on the domain common to the two formal languages and shows the logical connection between Boole's logical calculus and Frege's. As a result, it is shown that the progress made in mathematical logic stemmed from two continuous and overlapping research programmes: Boole's introduction ofmathematics in logic and Frege's introduction oflogic in mathematics. In particular, Boole is regarded as the grandfather of metamathematics, and Lowenheim's theorem ofl915 is seen as a revival of his research programme

Architecture theory, 1960-1980 : emergence of a computational perspective

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Architecture, 2004.Leaf 175 blank.Includes bibliographical references (leaves 162-175).This thesis attempts to clarify the need for an appreciation of architecture theory within a computational architectural domain. It reveals and reflects upon some of the cultural, historical and technological contexts that influenced the emergence of a computational practice in architecture. To carry out this new reading, we focus on the pioneering research that underpinned the beginnings of the relationship between architecture and computation and which was carried out at four research Centres both in the UK and in the USA: The Land Use and Built Form Studies [LUBFS], founded at Cambridge, UK; The Center for Configurational Studies at the Open University, Milton Keynes; The Architecture Machine Group [AMG] at MIT, and the Design Research Center [DRC] at Carnegie Mellon University, Pittsburgh, USA. Moreover this thesis reinterprets the role of Leslie Martin as the founding father of LUBFS by showing the influence of the British physicist Desmond Bernal's building science research and the British avant-garde movement on Martin's work. This thesis also presents reflections on how best to use computation in architecture.by Altino João Magalhães Rocha.Ph.D

Traditional logic and the early history of sets, 1854–1908

Ministerio de Educación y Ciencia (España

The life and work of Major Percy Alexander MacMahon

This thesis describes the life and work of the mathematician Major Percy Alexander MacMahon (1854 - 1929). His early life as a soldier in the Royal Artillery and events which led to him embarking on a career in mathematical research and teaching are dealt with in the first two chapters. Succeeding chapters explain the work in invariant theory and partition theory which brought him to the attention of the British mathematical community and eventually resulted in a Fellowship of the Royal Society, the presidency of the London Mathematical Society, and the award of three prestigious mathematical medals and four honorary doctorates. The development and importance of his recreational mathematical work is traced and discussed. MacMahon's career in the Civil Service as Deputy Warden of the Standards at the Board of Trade is also described. Throughout the thesis, his involvement with the British Association for the Advancement of Science and other scientific organisations is highlighted. The thesis also examines possible reasons why MacMahon's work, held in very high regard at the time, did not lead to the lasting fame accorded to some of his contemporaries. Details of his personal and social life are included to give a picture of MacMahon as a real person working hard to succeed in a difficult context

Cambridge University and the development of Victorian ideas, 1830-1870

PhD ThesisThis thesis reconstructs and interprets the life and writings of the relatively unknown nineteenth century philosopher John Grote (1813-1866). It places his work in the intellectual contexts of the University of Cambridge of his day and discusses his place in the development of Victorian Thought. The thesis argues that John Grote, (brother of the historian George Grote) is a most original thinker in his own right and that historically he holds a crucial place in the debates that make up Victorian thought. Cambridge University between 1830 and 1870 is seen to have nurtured a dualistic intellectual movement called the Cambridge Network which rivalled intellectually, the centres of Edinburgh and London and the movements of Positivism utilitarianism -and common sense philosophy. In developing the Cambridge philosophy of his day in response to developments elsewhere in British philosophy, John Grote (like James Frederick Ferrier in Scotland) is shown to have elaborated a nascent form of indigenous philosophical idealism in England prior to the 1870's and the emergence of oxford Idealism. The introduction argues that a modern understanding and appreciation of John Grote's philosophy is unlikely without the reconstruction of the cultural, intellectual and institutional world which he inhabited. The loss of detail about this world in the twentieth century, explains why past attempts to popularize Grote's work have failed. Conventional accounts of the history of Victorian philosophy are elaborated and attacked in the introduction, as are the methodological assumptions upon which they were written. Chapter one provides details of Grote's life and writings but gives special prominence to his novel, and in retrospect revolutionary, work on language. Chapters two and three provide a historical reconstruction of the intellectual context that attended the production of Grote's corpus. The middle chapters from four to nine reconstruct Grote's analytic philosophical work in the areas of metaphysics, epistemology, ontology, ethics, and politics, revealing Grote's commitment to epistemological and ethical idealism and the production of a 'relational theory of obligation' and a 'jural theory of politics'. My arguments are synthesised in chapter ten and the conclusions and some indications as to John Grote's influence are appended.Social Science Research Council: Teesside Polytechnic