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Author: Marcel Danesi
Publisher: Springer Nature
ISBN: 3031315820
Category : Mathematics
Languages : en
Pages : 180
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Book Description
This book treats eighteenth-century Italian philosopher Giambattista Vico’s theory of poetic logic for the first time as the originating force in mathematics, transforming instinctive counting and spatial perception into poetic (metaphorical) symbolism that dovetails with the origin of language. It looks at current work on mathematical cognition (from Lakoff and Núñez to Butterworth, Dehaene, and beyond), matching it against the poetic logic paradigm. In a sense, it continues from where Kasner and Newman left off, connecting contemporary research on the mathematical mind to the idea that the products of early mathematics were virtually identical to the first forms of poetic language. As such, this book informs the current research on mathematical cognition from a different angle, by looking back at a still relatively unknown philosopher within mathematics. The aim of this volume is to look broadly at what constitutes the mathematical mind through the Vichian lens of poetic logic. Vico was among the first to suggest that the essential nature of mind could be unraveled indirectly by reconstructing the sources of its “modifications” (his term for “creations”); that is, by examining the creation and function of symbols, words, and all the other uniquely human artifacts—including mathematics—the mind has allowed humans to establish “the world of civil society,” Vico’s term for culture and civilization. The book is of interest to cognitive scientists working on math cognition. It presents the theory of poetic logic as Vico articulated it in his book The New Science, examining its main premises and then applying it to an interpretation of the ongoing work in math cognition. It will also be of interest to the general public, since it presents a history of early mathematics through the lens of an idea that has borne fruit in understanding the origin of language and symbols more broadly.
Author: Marcel Danesi
Publisher: Springer Nature
ISBN: 3031315820
Category : Mathematics
Languages : en
Pages : 180
Get Book Here
Book Description
This book treats eighteenth-century Italian philosopher Giambattista Vico’s theory of poetic logic for the first time as the originating force in mathematics, transforming instinctive counting and spatial perception into poetic (metaphorical) symbolism that dovetails with the origin of language. It looks at current work on mathematical cognition (from Lakoff and Núñez to Butterworth, Dehaene, and beyond), matching it against the poetic logic paradigm. In a sense, it continues from where Kasner and Newman left off, connecting contemporary research on the mathematical mind to the idea that the products of early mathematics were virtually identical to the first forms of poetic language. As such, this book informs the current research on mathematical cognition from a different angle, by looking back at a still relatively unknown philosopher within mathematics. The aim of this volume is to look broadly at what constitutes the mathematical mind through the Vichian lens of poetic logic. Vico was among the first to suggest that the essential nature of mind could be unraveled indirectly by reconstructing the sources of its “modifications” (his term for “creations”); that is, by examining the creation and function of symbols, words, and all the other uniquely human artifacts—including mathematics—the mind has allowed humans to establish “the world of civil society,” Vico’s term for culture and civilization. The book is of interest to cognitive scientists working on math cognition. It presents the theory of poetic logic as Vico articulated it in his book The New Science, examining its main premises and then applying it to an interpretation of the ongoing work in math cognition. It will also be of interest to the general public, since it presents a history of early mathematics through the lens of an idea that has borne fruit in understanding the origin of language and symbols more broadly.
Author: Marcel Danesi
Publisher:
ISBN: 9783031315831
Category :
Languages : en
Pages : 0
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Book Description
This book treats eighteenth-century Italian philosopher Giambattista Vico's theory of poetic logic for the first time as the originating force in mathematics, transforming instinctive counting and spatial perception into poetic (metaphorical) symbolism that dovetails with the origin of language. It looks at current work on mathematical cognition (from Lakoff and Núñez to Butterworth, Dehaene, and beyond), matching it against the poetic logic paradigm. In a sense, it continues from where Kasner and Newman left off, connecting contemporary research on the mathematical mind to the idea that the products of early mathematics were virtually identical to the first forms of poetic language. As such, this book informs the current research on mathematical cognition from a different angle, by looking back at a still relatively unknown philosopher within mathematics. The aim of this volume is to look broadly at what constitutes the mathematical mind through the Vichian lens of poetic logic. Vico was among the first to suggest that the essential nature of mind could be unraveled indirectly by reconstructing the sources of its "modifications" (his term for "creations"); that is, by examining the creation and function of symbols, words, and all the other uniquely human artifacts-including mathematics-the mind has allowed humans to establish "the world of civil society," Vico's term for culture and civilization. The book is of interest to cognitive scientists working on math cognition. It presents the theory of poetic logic as Vico articulated it in his book The New Science, examining its main premises and then applying it to an interpretation of the ongoing work in math cognition. It will also be of interest to the general public, since it presents a history of early mathematics through the lens of an idea that has borne fruit in understanding the origin of language and symbols more broadly.
Author: Matthew Handelman
Publisher: Fordham Univ Press
ISBN: 0823283852
Category : Philosophy
Languages : en
Pages : 287
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Book Description
This book offers an archeology of the undeveloped potential of mathematics for critical theory. As Max Horkheimer and Theodor W. Adorno first conceived of the critical project in the 1930s, critical theory steadfastly opposed the mathematization of thought. Mathematics flattened thought into a dangerous positivism that led reason to the barbarism of World War II. The Mathematical Imagination challenges this narrative, showing how for other German-Jewish thinkers, such as Gershom Scholem, Franz Rosenzweig, and Siegfried Kracauer, mathematics offered metaphors to negotiate the crises of modernity during the Weimar Republic. Influential theories of poetry, messianism, and cultural critique, Handelman shows, borrowed from the philosophy of mathematics, infinitesimal calculus, and geometry in order to refashion cultural and aesthetic discourse. Drawn to the austerity and muteness of mathematics, these friends and forerunners of the Frankfurt School found in mathematical approaches to negativity strategies to capture the marginalized experiences and perspectives of Jews in Germany. Their vocabulary, in which theory could be both mathematical and critical, is missing from the intellectual history of critical theory, whether in the work of second generation critical theorists such as Jürgen Habermas or in contemporary critiques of technology. The Mathematical Imagination shows how Scholem, Rosenzweig, and Kracauer’s engagement with mathematics uncovers a more capacious vision of the critical project, one with tools that can help us intervene in our digital and increasingly mathematical present. The Mathematical Imagination is available from the publisher on an open-access basis.
Author: Daria Bylieva
Publisher: Springer Nature
ISBN: 3031767977
Category :
Languages : en
Pages : 369
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Book Description
Author: Yu. I. Manin
Publisher: Springer Science & Business Media
ISBN: 1441906150
Category : Mathematics
Languages : en
Pages : 389
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Book Description
1. The ?rst edition of this book was published in 1977. The text has been well received and is still used, although it has been out of print for some time. In the intervening three decades, a lot of interesting things have happened to mathematical logic: (i) Model theory has shown that insights acquired in the study of formal languages could be used fruitfully in solving old problems of conventional mathematics. (ii) Mathematics has been and is moving with growing acceleration from the set-theoretic language of structures to the language and intuition of (higher) categories, leaving behind old concerns about in?nities: a new view of foundations is now emerging. (iii) Computer science, a no-nonsense child of the abstract computability theory, has been creatively dealing with old challenges and providing new ones, such as the P/NP problem. Planning additional chapters for this second edition, I have decided to focus onmodeltheory,the conspicuousabsenceofwhichinthe ?rsteditionwasnoted in several reviews, and the theory of computation, including its categorical and quantum aspects. The whole Part IV: Model Theory, is new. I am very grateful to Boris I. Zilber, who kindly agreed to write it. It may be read directly after Chapter II. The contents of the ?rst edition are basically reproduced here as Chapters I–VIII. Section IV.7, on the cardinality of the continuum, is completed by Section IV.7.3, discussing H. Woodin’s discovery.
Author: Bertrand Russell
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 224
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Book Description
Author: John Sallis
Publisher: Indiana University Press
ISBN: 025301364X
Category : Philosophy
Languages : en
Pages : 311
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Book Description
The Shakespearean image of a tempest and its aftermath forms the beginning as well as a major guiding thread of Logic of Imagination. Moving beyond the horizons of his earlier work, Force of Imagination, John Sallis sets out to unsettle the traditional conception of logic, to mark its limits, and, beyond these limits, to launch another, exorbitant logic—a logic of imagination. Drawing on a vast range of sources, including Plato, Aristotle, Kant, Hegel, Nietzsche, and Freud, as well as developments in modern logic and modern mathematics, Sallis shows how a logic of imagination can disclose the most elemental dimensions of nature and of human existence and how, through dialogue with contemporary astrophysics, it can reopen the project of a philosophical cosmology.
Author: Patrick Bridgwater
Publisher: BRILL
ISBN: 9004490213
Category : Literary Criticism
Languages : en
Pages : 208
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Book Description
Kafka, Gothic and Fairytale is an original comparative study of the novels and some of the related shorter punishment fantasies in terms of their relationship to the Gothic and fairytale conventions. It is an absorbing subject and one which, while keeping to the basic facts of his life, mind-set and literary method, shows Kafka’s work in a genuinely new light. The contradiction between his persona with its love of fairytale and his shadow with its affinity with Gothic is reflected in his work, which is both Gothic and other than Gothic, both fairytale-like and the every denial of fairytale. Important subtexts of the book are the close connexion between Gothic and fairytale and between both of these and the dream. German text is quoted in translation unless the emphasis is on the meaning of individual words or phrases, in which case the words in question are quoted and their English meanings discussed. This means that readers without German can, for the first time, begin to understand the underlying ambiguity of Kafka’s major fictions. The book is addressed to all who are interested in the meaning of his work and its place in literary history, but also to the many readers in the English and German-speaking worlds who share the author’s enthusiasm for Gothic and fairytale.
Author: Sharon Berry
Publisher: Cambridge University Press
ISBN: 1108834310
Category : Science
Languages : en
Pages : 249
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Book Description
A new approach to the standard axioms of set theory, relating the theory to the philosophy of science and metametaphysics.
Author: Luca Tateo
Publisher: Springer Nature
ISBN: 3030380254
Category : Psychology
Languages : en
Pages : 97
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Book Description
This is a book about imaginative work and its relationship with the construction of knowledge. It is fully acknowledged by epistemologists that imagination is not something opposed to rationality; it is not mere fantasy opposed to intellect. In philosophy and cognitive sciences, imagination is generally “delimiting not much more than the mental ability to interact cognitively with things that are not now present via the senses.” (Stuart, 2017, p. 11) For centuries, scholars and poets have wondered where this capability could come from, whether it is inspired by divinity or it is a peculiar feature of human mind (Tateo, 2017b). The omnipresence of imaginative work in both every day and highly specialized human activities requires a profoundly radical understanding of this phenomenon. We need to work imaginatively in order to achieve knowledge, thus imagination must be something more than a mere flight of fantasy. Considering different stories in the field of scientific endeavor, I will try to propose the idea that the imaginative process is fundamental higher mental function that concurs in our experiencing, knowing and understanding the world we are part of. This book is thus about a theoretical idea of imagining as constant part of the complex whole we call the human psyche. It is a story of human beings striving not only for knowledge and exploration but also striving for imagining possibilities.
