Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Does syllogistic logic have the resources to capture mathematical proof? This volume provides the first unified account of the history of attempts to answer this question, the reasoning behind the different positions taken, and their far-reaching implications. Aristotle had claimed that scientific knowledge, which includes mathematics, is provided by syllogisms of a special sort: 'scientific' ('demonstrative') syllogisms. In ancient Greece and in the Middle Ages, the claim that Euclid's theorems could be recast syllogistically was accepted without further scrutiny. Nevertheless, as early as Galen, the importance of relational reasoning for mathematics had already been recognized. Further critical voices emerged in the Renaissance and the question of whether mathematical proofs could be recast syllogistically attracted more sustained attention over the following three centuries. Supported by more detailed analyses of Euclidean theorems, this led to attempts to extend logical theory to include relational reasoning, and to arguments purporting to reduce relational reasoning to a syllogistic form. Philosophical proposals to the effect that mathematical reasoning is heterogenous with respect to logical proofs were famously defended by Kant, and the implications of the debate about the adequacy of syllogistic logic for mathematics are at the very core of Kant's account of synthetic a priori judgments. While it is now widely accepted that syllogistic logic is not sufficient to account for the logic of mathematical proof, the history and the analysis of this debate, running from Aristotle to de Morgan and beyond, is a fascinating and crucial insight into the relationship between philosophy and mathematics.

Syllogism. --- Syllogisme. --- Preuve (philosophie) --- Evidence.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Les notions de vrai, véridique et vraisemblable régissent tout le droit de la preuve. Si le vrai et le véridique diffèrent peu, le vraisemblable se détache très nettement des deux premières acceptions. Deux raisons à cela : ce qui est vrai, véridique doit être vraisemblable, tandis que ce qui est vraisemblable n'est pas toujours vrai. Dans sa mission consistant à rapporter la vérité pour trancher au plus juste un désaccord ou un litige, le droit repose sur des concepts probatoires qui doivent paraître les plus vrais, les plus véridiques. Mais la vérité est parfois si insaisissable qu'il est contraint de se tourner vers la vraisemblance, ce qui n'a que l'apparence de la vérité. L'opération, aussi astucieuse soit-elle, peut être l'occasion de consacrer le faux. Friedrich Nietzsche rejetait une croyance nihiliste en la vérité absolue. Il estimait que l'art permettait de ne pas "mourir de la vérité" (Fragments posthumes).

Preuve (droit). --- Preuve (philosophie). --- Evidence (Law) --- Obligations (Law) --- Evidence. --- Truth. --- Truthfulness and falsehood. --- Nietzsche, Friedrich, --- Nietzsche, Friedrich Wilhelm, --- Nietzsche, Friedrich --- Preuve (droit) --- Obligations (droit) --- Droit --- Vérité --- Vérité et mensonge --- Philosophie --- Truth --- Truthfulness and falsehood --- Criticism and interpretation --- Vérité. --- Vérité et mensonge. --- Preuve (philosophie) --- Philosophie. --- Evidence (Law) - France --- Nietzsche, Friedrich Wilhelm, - 1844-1900 - Criticism and interpretation --- Nietzsche, Friedrich Wilhelm, - 1844-1900 --- Vérité. --- Vérité et mensonge.