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Using Dostoevsky's most radical experiment in literary form as a springboard, Gary Saul Morson examines a number of key topics in contemporary literary theory, including the nature of literary genres and their relation to interpretation. He convincingly argues that genre is not a property of texts alone but arises from the interaction between texts and readers. Observing that changing conventions of interpretation and classifciation may alter the perception of particular works, Morson considers a number of problematic texts that have been read according to two contradictory sets of conventions - "boundary works"--And a futher group of texts - "threshold works" such as Dostoevsky's Diary of a writer - that were evidently designed by their authors to exploit this kind of hermeneutic ambivalence. Morson explores the nature of the literary utopia and its parodic form, the anti-utopia, and, returning to Dostoevsky's Diary as his example, a third form which exists as a sort of open dialogue of utopia and anti-utopia
This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled ‘The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,’ reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of Harclay, Nicholas of Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter three, 'The age of continuity,’ discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel. Examining the nineteenth and early twentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Part one of the book concludes with a chapter on divergent conceptions of the continuum, with the work of nineteenth and early twentieth century philosophers and mathematicians, including Veronese, Poincaré, Brouwer, and Weyl. Part two of this book covers contemporary mathematics, discussing topology and manifolds, categories, and functors, Grothendieck topologies, sheaves, and elementary topoi. Among the theories presented in detail are non-standard analysis, constructive and intuitionist analysis, and smooth infinitesimal analysis/synthetic differential geometry. No other book so thoroughly covers the history and development of the concepts of the continuous and the infinitesimal.