front cover of At the Brink of Infinity
At the Brink of Infinity
Poetic Humility in Boundless American Space
James E. von der Heydt
University of Iowa Press, 2008

From popular culture to politics to classic novels, quintessentially American texts take their inspiration from the idea of infinity. In the extraordinary literary century inaugurated by Ralph Waldo Emerson, the lyric too seemed to encounter possibilities as limitless as the U.S. imagination. This raises the question: What happens when boundlessness is more than just a figure of speech? Exploring new horizons is one thing, but actually looking at the horizon itself is something altogether different. In this carefully crafted analysis, James von der Heydt shines a new light on the lyric craft of Emily Dickinson, Robert Frost, Elizabeth Bishop, and James Merrill and considers how their seascape-vision redefines poetry's purpose.

Emerson famously freed U.S. literature from its past and opened it up to vastness; in the following century, a succession of brilliant, rigorous poets took the philosophical challenges of such freedom all too seriously. Facing the unmarked horizon, Emersonian poets capture—and are captured by—a stark, astringent version of human beauty. Their uncompromising visions of limitlessness reclaim infinity's proper legacy—and give American poetry its edge. Von der Heydt's book recovers the mystery of their world.


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Dialogue on the Infinity of Love
Tullia d'Aragona
University of Chicago Press, 1997
Celebrated as a courtesan and poet, and as a woman of great intelligence and wit, Tullia d'Aragona (1510–56) entered the debate about the morality of love that engaged the best and most famous male intellects of sixteenth-century Italy. First published in Venice in 1547, but never before published in English, Dialogue on the Infinity of Love casts a woman rather than a man as the main disputant on the ethics of love.

Sexually liberated and financially independent, Tullia d'Aragona dared to argue that the only moral form of love between woman and man is one that recognizes both the sensual and the spiritual needs of humankind. Declaring sexual drives to be fundamentally irrepressible and blameless, she challenged the Platonic and religious orthodoxy of her time, which condemned all forms of sensual experience, denied the rationality of women, and relegated femininity to the realm of physicality and sin. Human beings, she argued, consist of body and soul, sense and intellect, and honorable love must be based on this real nature.

By exposing the intrinsic misogyny of prevailing theories of love, Aragona vindicates all women, proposing a morality of love that restores them to intellectual and sexual parity with men. Through Aragona's sharp reasoning, her sense of irony and humor, and her renowned linguistic skill, a rare picture unfolds of an intelligent and thoughtful woman fighting sixteenth-century stereotypes of women and sexuality.

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Levinas's Existential Analytic
A Commentary on Totality and Infinity
James R. Mensch
Northwestern University Press, 2015
By virtue of the originality and depth of its thought, Emmanuel Levinas’s masterpiece, Totality and Infinity: An Essay on Exteriority, is destined to endure as one of the great works of philosophy. It is an essential text for understanding Levinas’s discussion of “the Other,” yet it is known as a “difficult” book. Modeled after Norman Kemp Smith’s commentary on Kant’s Critique of Pure Reason, Levinas’s Existential Analytic guides both new and experienced readers through Levinas’s text. James R. Mensch explicates Levinas’s arguments and shows their historical referents, particularly with regard to Heidegger, Husserl, and Derrida. Students using this book alongside Totality and Infinity will be able to follow its arguments and grasp the subtle phenomenological analyses that fill it.

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Medieval Cosmology
Theories of Infinity, Place, Time, Void, and the Plurality of Worlds
Pierre Duhem
University of Chicago Press, 1987
These selections from Le système du monde, the classic ten-volume history of the physical sciences written by the great French physicist Pierre Duhem (1861-1916), focus on cosmology, Duhem's greatest interest. By reconsidering the work of such Arab and Christian scholars as Averroes, Avicenna, Gregory of Rimini, Albert of Saxony, Nicole Oresme, Duns Scotus, and William of Occam, Duhem demonstrated the sophistication of medieval science and cosmology.

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New Infinitary Mathematics
Petr Vopenka
Karolinum Press, 2023
A rethinking of Cantor and infinitary mathematics by the creator of Vopěnka's principle.
The dominant current of twentieth-century mathematics relies on Georg Cantor’s classical theory of infinite sets, which in turn relies on the assumption of the existence of the set of all natural numbers, the only justification for which—a theological justification—is usually concealed and pushed into the background.

This book surveys the theological background, emergence, and development of classical set theory, warning us about the dangers implicit in the construction of set theory, and presents an argument about the absurdity of the assumption of the existence of the set of all natural numbers. It instead proposes and develops a new infinitary mathematics driven by a cautious effort to transcend the horizon bounding the ancient geometric world and mathematics prior to set theory, while allowing mathematics to correspond more closely to the real world surrounding us. Finally, it discusses real numbers and demonstrates how, within a new infinitary mathematics, calculus can be rehabilitated in its original form employing infinitesimals.

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Rails to Infinity
Essays on Themes from Wittgenstein’s Philosophical Investigations
Crispin Wright
Harvard University Press, 2001

This volume, published on the fiftieth anniversary of Wittgenstein's death, brings together thirteen of Crispin Wright's most influential essays on Wittgenstein's later philosophies of language and mind, many hard to obtain, including the first publication of his Whitehead Lectures given at Harvard in 1996.

Organized into four groups, the essays focus on issues about following a rule and the objectivity of meaning; on Saul Kripke's contribution to the interpretation of Wittgenstein; on privacy and self-knowledge; and on aspects of Wittgenstein's philosophy of mathematics. Wright uses the cutting edge of Wittgenstein's thought to expose and undermine the common assumptions in platonistic views of mathematical and logical objectivity and Cartesian ideas about self-knowledge. The great question remains: How to react to the demise of these assumptions? In response, the essays develop a concerted, evolving approach to the possibilities--and limitations--of constructive philosophies of mathematics and mind. Their collection constitutes a major statement by one of Britain's most important philosophers--and will provide an indispensable tool both for students of Wittgenstein and for scholars working more generally in the metaphysics of mind and language.


front cover of Time Warps, String Edits, and Macromolecules
Time Warps, String Edits, and Macromolecules
The Theory and Practice of Sequence Comparision
David Sankoff and Joseph Kruskal
CSLI, 1983
Time Warps, String Edits and Macromolecules is a young classic in computational science. The computational perspective is that of sequence processing, in particular the problem of recognizing related sequences. The book is the first, and still best compilation of papers explaining how to measure distance between sequences, and how to compute that measure effectively. This is called string distance, Levenshtein distance, or edit distance. The book contains lucid explanations of the basic techniques; well-annotated examples of applications; mathematical analysis of its computational (algorithmic) complexity; and extensive discussion of the variants needed for weighted measures, timed sequences (songs), applications to continuous data, comparison of multiple sequences and extensions to tree-structures. This theory finds applications in molecular biology, speech recognition, analysis of bird song and error correcting in computer software.

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