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This new study of David Hume’s philosophy of mathematics critically examines his objections to the concept of infinity. Although infinity raises some of the most challenging paradoxes for Hume’s empiricism, there have been few detailed and no fully comprehensive systematic discussions of Hume’s critique. In a series of eight interrelated arguments, Hume maintains that we cannot experience and therefore can have no adequate idea of infinity or of the infinite divisibility of extension. He proposes to replace the notion of infinity with an alternative phenomenalist theory of space and time as constituted by minima sensibilia or sensible extensionless indivisibles. The present work considers Hume’s critique of infinity in historical context as a product of Enlightenment theory of knowledge, and assesses the prospects of his strict finitism in light of contemporary mathematics, science, and philosophy.

Infinite --- Infinity --- Finite, The --- History --- Hume, David --- Hume, David, --- Infinite - History - 18th century. --- Infini

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Number theory --- Infinite --- History --- 51 <09> --- Mathematics--Geschiedenis van ... --- Getaltheorie. --- Oneindigheid. --- History. --- 51 <09> Mathematics--Geschiedenis van ... --- Infinity --- Finite, The --- Mathematics--Geschiedenis van .. --- Mathematics--Geschiedenis van . --- Mathematics--Geschiedenis van --- Number theory - History --- Infinite - History

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God (Christianity) - History of doctrines - Middle Ages, 600-1500. --- God (Christianity) - Attributes. --- Infinite - History - To 1500. --- Dieu --- Théologie et philosophie --- Théologie --- Infinité --- Moyen âge --- Histoire des doctrines --- God (Christianity) --- Infinite

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This volume examines a selection of late medieval works devoted to the intensive infinite in order to draw a comprehensive picture of the context, character and importance of scholastic efforts to reason philosophically about divine infinity. As Dominican masters face Franciscan 'spirituals' and as university-trained theologians face evangelical laymen, the purpose and meaning of divine infinity shift, reflecting a basic tension between the Church's Petrine vocation for geopolitical orthodoxy and its more Pauline mission to promote Christian orthopraxis. The first part of the book traces the scholastic defense of divine infinity from the holocaust of Montségur up to John Duns Scotus. The second part examines the semiotic breakthrough initiated by William of Ockham and the subsequent penetration of infinist theory into a wide variety of disciplines.

Filosofie [Middeleeuwse ] --- Medieval philosophy --- Middeleeuwse filosofie --- Philosophie médiévale --- Philosophy [Medieval ] --- Infinite --- Philosophy, Medieval --- God --- Infini --- Dieu --- History --- Attributes --- Histoire --- Attributs --- Philosophy, Medieval. --- History. --- Attributes. --- 231.132.4 --- -Infinite --- -Philosophy, Medieval --- Scholasticism --- Infinity --- Finite, The --- Metaphysics --- Misotheism --- Monotheism --- Religion --- Theism --- Oneindigheid van God --- 231.132.4 Oneindigheid van God --- Philosophie médiévale --- Attributes of God --- Infinite - History. --- God - Attributes.

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Perspective (Philosophy) --- Infinite --- History --- Nicholas, --- Alberti, Leon Battista, --- History. --- -Perspective (Philosophy) --- -Ontology --- Philosophy --- Infinity --- Finite, The --- Alberti, Leon Battista --- Nicholas of Cusa, Cardinal --- Ontology --- Albert, Leon Baptiste --- Alberti, Leon Batista --- Chrypffs, Nicolaus, --- Cues, Nicolas de, --- Cues, Nikolaus von, --- Cusa, Nicolaus de, --- Cusano, Nicola, --- Cusano, Nicolò, --- Cusanus, Nicolaus, --- Khrypffs, Nicolaus, --- Krebs, Nicolaus, --- Kues, Nikolaus von, --- Kusánský, Mikuláš, --- Kuzańczyk, --- Kuzaneli, Nikoloz, --- Kuzanskiĭ, Nikolaĭ, --- Mikołaj, --- Mikuláš, --- Ni-ku-la Kʻu-sa, --- Nicholas de Cusa, --- Nicola, --- Nicolai, --- Nicolas, --- Nicolaus Cusanus, --- Nicolò, --- Nikolaĭ, --- Nikolaus, --- Nikolaus von Cusa, --- Nikoloz, --- Nikoloz Kuzanelis, --- Nikula Kʻu-sa, --- Николай, --- Кузанский, Николай, --- Cusano, Niccolò, --- Alberti, Leo Baptista, --- Alberti, Leon Batista, --- Alberti, Leonis Baptiste, --- Alberti, Leone Battista, --- Alberti, L. B. --- Alberti, Battista, --- אלברטי, ליאון באטיסטה --- Lepidus, --- Cusa, Nicolaas van, --- Nicolaas, --- Perspective (Philosophy) - History --- Infinite - History --- Nicholas, - of Cusa, Cardinal, - 1401-1464 --- Alberti, Leon Battista, - 1404-1472