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Les Grundgesetze der Arithmetik de Frege : idéographie : genèse, syntaxe, sémantique / Frege's Grundgesetze der Arithmetik : Ideography : Origin, Syntax, SemanticsCadet, Méven 21 June 2017 (has links)
Un important désaccord subsiste parmi les exégètes de Frege au sujet de la question suivante : quel rapport entretient l'universalisme logique de Frege avec la sémantique contemporaine ? Le premier constitue-t-il un obstacle à l'élaboration et/ou à l'exploitation de la seconde ? Face à cette interrogation deux camps s'affrontent. L'un dresse la liste considérable des passages des Grundgesetze dans lesquels Frege sembla se lancer dans de véritables raisonnements sémantiques. L'autre rétorque qu'il s'agissait à ses yeux de pures élucidations, bannies de jure de la sphère théorique. Notre objectif consiste à faire toute la lumière sur ce problème. Dans ce but, nous nous appliquons à combattre deux poncifs ancrés dans la littérature. Nous contestons (1) l'idée que Frege était toujours soucieux de signaler la moindre inflexion de sa pensée, et (2) la possibilité d'étudier ses positions philosophiques indépendamment de son symbolisme spécifique. Par conséquent, nous retraçons la genèse des idées qui ont conduit à l'élaboration de l'idéographie de 1893, avant de réaliser toutes les étapes de la construction de ce système. Ces résultats - attachés à notre rejet de (1) et (2) - jettent une lumière neuve sur le problème soulevé plus haut. Ils nous conduisent à adopter le positionnement radical selon lequel Frege faisait bel et bien droit à une sémantique dont il jeta les bases et qu'il tenta de mettre en action afin de démontrer certains théorèmes métalogiques. Nous tentons de formaliser proprement cette sémantique, puis de localiser précisément les erreurs dont il fut responsable. Cette tâche nous conduit ultimement à l'étude des célèbres §§ 29-31 des Grundgesetze. / There is still considerable disagreement among Frege's exegetes on how Frege's logical universalism relates to modem semantics; does the former obstruct the development and/or the use of the latter? Two sides exist on this issue. The first one quotes many sections of the Grundgesetze which seem to contain genuine semantic reasonings. The other one claims that Frege holds these sections to be strict elucidations excluded de jure from the realm of science. My aim is to shed light on this problem. For this purpose, I contest the following commonplaces: (1) that Frege was concerned with indicating the slightest change of his thoughts, and (2) that his philosophical theses can be studied regardless of his particular symbolism. l thus complete the two tasks of tracing back the origins of the underlying ideas in the Ideography of 1893 and of building up this very system step by step. My results, attached to my rejection of (1) and (2), shed a new light m the issue raised above. They lead us to the radical position that not only did Frege not reject semantics, but that he himself paved the way to such a semantic theory in order to prove metalogical theorems. I then try to formalize the former so as to locate his errors in the latter. This work eventually leads to a thorough study of the famous §§ 29-31 of the Grundgesetze.
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Frege's case for the logicality of his basic lawsYates, Alexander January 2017 (has links)
Frege wanted to show that arithmetical truths are logical by proving them from purely logical basic laws. But how do we know that these basic laws are logical? Frege uses generality and undeniability to make a prima facie case for logicality—if a truth is general and undeniable, then it's likely logical. I argue that Frege could, did, and had to make a deeper case for why we're right in recognizing his basic laws as logical. Implicit in his work is a view of logical laws as epistemically analytic—his arguments for his basic laws serve to elicit a reflective awareness of the fact that understanding them is sufficient for recognizing them to be true. This view both fits with Frege's comments concerning the connection between logic, truth, and normativity, and serves to explain why and in what sense he took logic to be general and conceptually undeniable. In my view, semantics must play a distinctive role in any rational reconstruction of Frege's case for logicality—the aforementioned “reflective awareness” must be an explicit appreciation of how the truth of formulas expressing Frege's laws follows quickly from his stipulations governing terms which figure in those formulas. Opposing this view is the elucidatory interpretation of Thomas Ricketts, Warren Goldfarb, and Joan Weiner, which holds that Frege's arguments for his basic laws can't be taken at face value, and must serve the merely elucidatory purpose of easing us into the language. Another reading is the correctness interpretation of Richard Heck and Jason Stanley, which holds that Frege's primary purpose in his arguments is justifying the claim that Frege's axioms, qua formulas, are true. I argue against both of these interpretations, and in doing so clarify the role and limits of semantics in Frege's enterprise.
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