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This textbook is designed for students. Rather than the typical definition-theorem-proof-repeat style, this text includes much more commentary, motivation and explanation. The proofs are not terse, and aim for understanding over economy. Furthermore, dozens of proofs are preceded by "scratch work" or a proof sketch to give students a big-picture view and an explanation of how they would come up with it on their own. This book covers intuitive proofs, direct proofs, sets, induction, logic, the contrapositive, contradiction, functions and relations. The text aims to make the ideas visible, and contains over 200 illustrations. The writing is relaxed and conversational, and includes periodic attempts at humor. This text is also an introduction to higher mathematics. This is done in-part through the chosen examples and theorems. Furthermore, following every chapter is an introduction to an area of math. These include Ramsey theory, number theory, topology, sequences, real analysis, big data, game theory, cardinality and group theory. After every chapter are "pro-tips," which are short thoughts on things I wish I had known when I took my intro-to-proofs class. They include finer comments on the material, study tips, historical notes, comments on mathematical culture, and more. Also, after each chapter's exercises is an introduction to an unsolved problem in mathematics. In the first appendix we discuss some further proof methods, the second appendix is a collection of particularly beautiful proofs, and the third is some writing advice.
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Pour R. Swinburne, spécialiste anglais de philosophie de la religion chrétienne et du théisme, l'existence de Dieu permet d'expliquer des données que les sciences de la nature n'expliquent pas, comme l'existence de l'Univers et de ses lois. Elle est aussi l'hypothèse métaphysique la plus simple pour en rendre compte, et qui a, a priori pour elle, la probabilité la plus grande.
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Religious studies --- God --- Dieu --- Proof --- Existence --- Philosophy and religion --- Proof, Ontological --- Christianity and philosophy --- Religion and philosophy --- Religion --- Ontological argument --- Ontology --- God - Proof --- God - Proof, Ontological
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God --- -Metaphysics --- Misotheism --- Monotheism --- Religion --- Theism --- Proof --- --Existence --- --God --- -Proof --- Dieux --- --Philosophie --- Proof. --- Metaphysics --- Métaphysique --- Dieu --- Existence --- Philosophie --- God - Proof
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Le philosophe s'interroge sur la cohérence et la complexité du théisme et expérimente son pouvoir prédictif. Il souhaite éprouver l'hypothèse métaphysique de l'existence de Dieu et étaye son propos avec les théories de Thomas d'Aquin, Duns Scot, Isaac Newton, etc. ©Electre 2016
God --- Theism --- Dieu --- Théisme --- Proof --- Existence --- Théisme --- Existence. --- Théisme. --- God - Proof
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"This book re-examines Anselm's famous arguments for the existence of God in his Proslogion, and in his Reply. It demonstrates how he validly deduces from plausible premises that God so truly exists that He could not be thought not to exist. Most commentators, ancient and modern, wrongly located his argument in a passage which is not about God at all. It becomes evident that, consequently, much contemporary criticism is based on misreading and misunderstanding his text. It reconstructs his reasoning through three distinct but logically connected stages. It shows that, even if Anselm's crucial premises are sceptically interpreted, his conclusions still follow. Properly understood, this argument is not vulnerable to the standard criticisms, including Gaunilo's 'Lost island' counter-example"--
God (Christianity) --- God --- History of doctrines --- Proof --- Proof, Ontological --- Proof, Ontological. --- Anselm, --- God (Christianity) - History of doctrines - Middle Ages, 600-1500 --- God - Proof - History of doctrines --- God - Proof, Ontological
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God --- Dieu --- Proof --- Early works to 1800 --- Existence --- Ouvrages avant 1800 --- -Metaphysics --- Misotheism --- Monotheism --- Religion --- Theism --- -Early works to 1800 --- -Proof --- Metaphysics --- Proof&delete& --- Early works to 1800. --- God - Proof - Early works to 1800
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Le débat philosophique sur l'athéisme semble aujourd'hui passé de mode. Il est vrai que l'affrontement entre le théisme et l'antithéisme, qui a longtemps nourri la figure de l'athéisme classique, paraît avoir été emporté avec l'écume de l'histoire, du moins dans certaines parties de notre Occident. Mais en cessant de poser problème, l'athéisme est-il devenu pour autant solution ? De toute façon, c'est aller trop vite en besogne que de tenir pour nulle et périmée la question de l'affirmation ou de la négation de Dieu. A condition de tirer au clair, autant crue faire se peut, la question de l'identité de ce Dieu. A condition, surtout, de remarquer que l'athéisme ne se réduit pas à la négation de l'existence de Dieu, hors de tout contexte. Ce qui nous plonge dans un embarras croissant, tant l'athéisme semble alors se diluer dans ses formes variées, au point de devenir insaisissable. Il peut être philosophique ou existentiel, s'exposer bruyamment ou se lover dans le silence, s'exprimer dans l'angoisse comme dans l'insouciance, prendre le visage de la barbarie comme celui de la culture. C'est finalement comme expression d'une logique à l'œuvre, opposée point par point à celle du christianisme, mais toujours en relation étroite avec elle, que l'athéisme se donne à penser.
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Mathematical logic --- 510.6 --- Proof theory. --- 510.6 Mathematical logic --- Logique mathématique --- Logique mathematique --- Proof theory --- Theorie de la preuve
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