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1	Conceptual role semantics, instability, and individualism towards a neo-Fregean theory of content / Sipos, Adam. Rawling, Piers. January 2003 (has links) Thesis (Ph. D.)--Florida State University, 2003. / Advisor: Dr. Piers Rawling, Florida State University, College of Arts and Sciences, Dept. of Philosophy. Title and description from dissertation home page (viewed Apr. 8,04). Includes bibliographical references.
2	Changes of Setting and the History of Mathematics: A New Study of Frege Davies, James Edgar January 2010 (has links) This thesis addresses an issue in the philosophy of Mathematics which is little discussed, and indeed little recognised. This issue is the phenomenon of a ‘change of setting’. Changes of setting are events which involve a change in a scientific framework which is fruitful for answering questions which were, under an old framework, intractable. The formulation of the new setting usually involves a conceptual re-orientation to the subject matter. In the natural sciences, such re-orientations are arguably unremarkable, inasmuch as it is possible that within the former setting for one’s thinking one was merely in error, and under the new orientation one is merely getting closer to the truth of the matter. However, when the subject matter is pure mathematics, a problem arises in that mathematical truth is (in appearance) timelessly immutable. The conceptions that had been settled upon previously seem not the sort of thing that could be vitiated. Yet within a change of setting that is just what seems to happen. Changes of setting, in particular in their effects on the truth of individual propositions, pose a problem for how to understand mathematical truth. Thus this thesis aims to give a philosophical analysis of the phenomenon of changes of setting, in the spirit of the investigations performed in Wilson (1992) and Manders (1987) and (1989). It does so in three stages, each of which occupies a chapter of the thesis: 1. An analysis of the relationship between mathematical truth and settingchanges, in terms of how the former must be viewed to allow for the latter. This results in a conception of truth in the mathematical sciences which gives a large role to the notion that a mathematical setting must ‘explain itself’ in terms of the problems it is intended to address. 2. In light of (1), I begin an analysis of the change of setting engendered in mathematical logic by Gottlob Frege. In particular, this chapter will address the question of whether Frege’s innovation constitutes a change of setting, by asking the question of whether he is seeking to answer questions which were present in the frameworks which preceded his innovations. I argue that the answer is yes, in that he is addressing the Kantian question of whether alternative systems of arithmetic are possible. This question arises because it had been shown earlier in the 19th century that Kant’s conclusion, that Euclid’s is the only possible description of space, was incorrect. 3. I conclude with an in-depth look at a specific aspect of the logical system constructed in Frege’s Grundgesetze der Arithmetik. The purpose of this chapter is to find evidence for the conclusions of chapter two in Frege’s technical work (as opposed to the philosophical). This is necessitated by chapter one’s conclusions regarding the epistemic interdependence of formal systems and informal views of those frameworks. The overall goal is to give a contemporary account of the possibility of setting-changes; it will turn out that an epistemic grasp of a mathematical system requires that one understand it within a broader, somewhat historical context. Philosophy of mathematics history of mathematics history of logic mathematical logic Gottlob Frege Immanuel Kant
3	[en] LOGIC AND ARITHMETIC IN FREGE´S PHILOSOPHY OF MATHEMATICS / [pt] LÓGICA E ARITMÉTICA NA FILOSOFIA DA MATEMÁTICA DE FREGE ALESSANDRO BANDEIRA DUARTE 30 July 2009 (has links) [pt] Nos Fundamentos da Aritmética (parágrafo 68), Frege propõe definir explicitamente o operador-abstração ´o número de...´ por meio de extensões e, a partir desta definição, provar o Princípio de Hume (PH). Contudo, a prova imaginada por Frege depende de uma fórmula (BB) não provável no sistema em 1884. Acreditamos que a distinção entre sentido e referência e a introdução dos valores de verdade como objetos foram motivada para justificar a introdução do Axioma IV, a partir do qual um análogo de (BB) é provável. Com (BB) no sistema, a prova do Princípio de Hume estaria garantida. Concomitantemente, percebemos que uma teoria unificada das extensões só é possível com a distinção entre sentido e referência e a introdução dos valores de verdade como objetos. Caso contrário, Frege teria sido obrigado a introduzir uma série de Axiomas V no seu sistema, o que acarretaria problemas com a identidade (Júlio César). Com base nestas considerações, além do fato de que, em 1882, Frege provara as leis básicas da aritmética (carta a Anton Marty), parece-nos perfeitamente plausível que as estas provas foram executadas adicionando-se o PH ao sistema lógico de Begriffsschrift. Mostramos que, nas provas dos axiomas de Peano a partir de PH dentro da conceitografia, nenhum uso é feito de (BB). Destarte, não é necessária a introdução do Axioma IV no sistema e, por conseguinte, não são necessárias a distinção entre sentido e referência e a introdução dos valores de verdade como objetos. Disto, podemos concluir que, provavelmente, a introdução das extensões nos Fundamentos foi um ato tardio; e que Frege não possuía uma prova formal de PH a partir da sua definição explícita. Estes fatos também explicam a demora na publicação das Leis Básicas da Aritmética e o descarte de um manuscrito quase pronto (provavelmente, o livro mencionado na carta a Marty). / [en] In The Foundations of Arithmetic (paragraph 68), Frege proposes to define explicitly the abstraction operator ´the number of …´ by means of extensions and, from this definition, to prove Hume´s Principle (HP). Nevertheless, the proof imagined by Frege depends on a formula (BB), which is not provable in the system in 1884. we believe that the distinction between sense and reference as well as the introduction of Truth-Values as objects were motivated in order to justify the introduction of Axiom IV, from which an analogous of (BB) is provable. With (BB) in the system, the proof of HP would be guaranteed. At the same time, we realize that a unified theory of extensions is only possible with the distinction between sense and reference and the introduction of Truth-Values as objects. Otherwise, Frege would have been obliged to introduce a series of Axioms V in his system, what cause problems regarding the identity (Julius Caesar). Based on these considerations, besides the fact that in 1882 Frege had proved the basic laws of Arithmetic (letter to Anton Marty), it seems perfectly plausible that these proofs carried out by adding to the Begriffsschrift´s logical system. We show that in the proofs of Peano s axioms from HP within the begriffsschrift, (BB) is not used at all. Thus, the introduction of Axiom IV in the system is not necessary and, consequently, neither the distinction between sense and reference nor the introduction of Truth- Values as objects. From these findings we may conclude that probably the introduction of extensions in The Foundations was a late act; and that Frege did not hold a formal proof of HP from his explicit definition. These facts also explain the delay in the publication of the Basic Laws of Arithmetic and the abandon of a manuscript almost finished (probably the book mentioned in the letter to Marty). [pt] PRINCIPIO DE HUME [pt] AXIOMA IV [pt] AXIOMA V [pt] VALORES DE VERDADE [pt] GOTTLOB FREGE
4	Frege, Hilbert, and Structuralism Burke, Mark January 2015 (has links) The central question of this thesis is: what is mathematics about? The answer arrived at by the thesis is an unsettling and unsatisfying one. By examining two of the most promising contemporary accounts of the nature of mathematics, I conclude that neither is as yet capable of giving us a conclusive answer to our question. The conclusion is arrived at by a combination of historical and conceptual analysis. It begins with the historical fact that, since the middle of the nineteenth century, mathematics has undergone a radical transformation. This transformation occurred in most branches of mathematics, but was perhaps most apparent in geometry. Earlier images of geometry understood it as the science of space. In the wake of the emergence of multiple distinct geometries and the realization that non-Euclidean geometries might lay claim to the description of physical space, the old picture of Euclidean geometry as the sole correct description of physical space was no longer tenable. The first chapter of the dissertation provides an historical account of some of the forces which led to the destabilization of the traditional picture of geometry. The second chapter examines the debate between Gottlob Frege and David Hilbert regarding the nature of geometry and axiomatics, ending with an argument suggesting that Hilbert’s views are ultimately unsatisfying. The third chapter continues to probe the work of Frege and, again, finds his explanations of the nature of mathematics troublingly unsatisfying. The end result of the first three chapters is that the Frege-Hilbert debate leaves us with an impasse: the traditional understanding of mathematics cannot hold, but neither can the two most promising modern accounts. The fourth and final chapter of the thesis investigates mathematical structuralism—a more recent development in the philosophy of mathematics—in order to see whether it can move us beyond the impasse of the Frege-Hilbert debate. Ultimately, it is argued that the contemporary debate between ‘assertoric’ structuralists and ‘algebraic’ structuralists recapitulates a form of the Frege-Hilbert impasse. The ultimate claim of the thesis, then, is that neither of the two most promising contemporary accounts can offer us a satisfying philosophical answer to the question ‘what is mathematics about?’. Gottlob Frege David Hilbert Paul Benacerraf Category Theory Philosophy of Mathematics Categorical Foundations Foundations of Mathematics Structuralism Mathematical Structuralism History of Geometry Axiomatics Non-Euclidean Geometry
5	The Darwinian revolution as a knowledge reorganization Zacharias, Sebastian 24 February 2015 (has links) Die Dissertation leistet drei Beiträge zur Forschung: (1) Sie entwickelt ein neuartiges vierstufiges Modell wissenschaftlicher Theorien. Dieses Modell kombiniert logisch-empiristische Ansätze (Carnap, Popper, Frege) mit Konzepten von Metaphern & Narrativen (Wittgenstein, Burke, Morgan), erlaubt so deutlich präzisiere Beschreibungen wissenschaftlicher Theorien bereit und löst/mildert Widersprüche in logisch-empiristischen Modellen. (Realismus vs. Empirismus, analytische vs. synthetische Aussagen, Unterdeterminiertheit/ Holismus, wissenschaftliche Erklärungen, Demarkation) (2) Mit diesem Modell gelingt ein Reihenvergleich sechs biologischer Theorien von Lamarck (1809), über Cuvier (1811), Geoffroy St. Hilaire (1835), Chambers (1844-60), Owen (1848-68), Wallace (1855/8) zu Darwin (1859-1872). Dieser Vergleich offenbart eine interessante Asymmetrie: Vergleicht man Darwin mit je einem Vorgänger, so bestehen zahlreiche wichtige Unterschiede. Vergleicht man ihn mit fünf Vorgängern, verschwinden diese fast völlig: Darwins originärer Beitrag zur Revolution in der Biologie des 19.Jh ist klein und seine Antwort nur eine aus einer kontinuierlichen Serie auf die empirischen Herausforderungen durch Paläontologie & Biogeographie seit Ende des 18. Jh. (3) Eine gestufte Rezeptionsanalyse zeigt, warum wir dennoch von einer Darwinschen Revolution sprechen. Zuerst zeigt eine quantitative Analyse der fast 2.000 biologischen Artikel in Britannien zwischen 1858 und 1876, dass Darwinsche Konzepte zwar wichtige Neuerungen brachten, jedoch nicht singulär herausragen. Verlässt man die Biologie und schaut sich die Rezeption bei anderen Wissenschaftlern und gebildeten Laien an, wechselt das Bild: Je weiter man aus der Biologie heraustritt, desto weniger Ebenen biologischen Wissens kennen die Rezipienten und desto sichtbarer wird Darwins Beitrag. Schließlich findet sich sein Beitrag in den abstraktesten Ebenen des biologischen Wissens: in Narrativ und Weltbild – den Ebenen die Laien rezipieren. / The dissertation makes three contributions to research: (1) It develops a novel 4-level-model of scientific theories which combines logical-empirical ideas (Carnap, Popper, Frege) with concepts of metaphors & narratives (Wittgenstein, Burke, Morgan), providing a new powerful toolbox for the analysis & comparison of scientific theories and overcoming/softening contradictions in logical-empirical models. (realism vs. empiricism, analytic vs. synthetic statements, holism, theory-laden observations, scientific explanations, demarcation) (2) Based on this model, the dissertation compares six biological theories from Lamarck (1809), via Cuvier (1811), Geoffroy St. Hilaire (1835), Chambers (1844-60), Owen (1848-68), Wallace (1855/8) to Darwin (1859-1872) and reveals an interesting asymmetry: Compared to any one of his predecessors, Darwins theory appears very original, however, compared to all five predecessor theories, many of these differences disappear and it remains but a small original contribution by Darwin. Thus, Darwin’s is but one in a continuous series of responses to the challenges posed to biology by paleontology and biogeography since the end of the 18th century. (3) A 3-level reception analysis, finally, demonstrates why we speak of a Darwinian revolution nevertheless. (i) A quantitative analysis of nearly 2.000 biological articles reveals that Darwinian concepts where indeed an important theoretical innovation – but definitely not the most important of the time. (ii) When leaving the circle of biology and moving to scientists from other disciplines or educated laymen, the landscape changes. The further outside the biological community, the shallower the audience’s knowledge – and the more visible Darwin’s original contribution. After all, most of Darwin’s contribution can be found in the narrative and worldview of 19th century biology: the only level of knowledge which laymen receive. Evolution Interpretation Rudolf Carnap Ludwig Wittgenstein Beschreibung Historische Epistemologie wissenschaftliche Revolution wissenschaftlicher Fortschritt wissenschaftliche Theorie Kontinuität Diskontinuität wissenschaftliche Erklärungen Abgrenzungskriterium Unterdeterminiertheit analytische Sätze synthetische Sätze Logischer Empirismus wissenschaftlicher Realismus Metaphern Narrative wissenschaftliche Modelle Natürliche Auslese Natürliche Selektion Kampf ums Dasein Homologie Archetype Charles Darwin Robert Chambers Richard Owen Alfred Russel Wallace Georges Cuvier Jean-Baptiste Lamarck Etienne Geoffroy Saint-Hilaire Gottlob Frege Karl Popper evolution interpretation Rudolf Carnap Ludwig Wittgenstein Historical epistemology scientific revolution scientific progress scientific theory continuity discontinuity scientific explanations demarcation criterion underdetermination analytic statements synthetic statements logical empiricism scientific realism metaphors narratives description scientific models natural selection struggle for existence homology archetype Charles Darwin Robert Chambers Richard Owen Alfred Russel Wallace Georges Cuvier Jean-Baptiste Lamarck Etienne Geoffroy Saint-Hilaire Gottlob Frege Karl Popper WH 2000

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