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Kant's Philosophy of Mathematics
  • Language: en
  • Pages: 333

Kant's Philosophy of Mathematics

Essential for students and scholars, this book brings contemporary Kantian scholarship together with the history of philosophy of mathematics.

Kant's Mathematical World
  • Language: en
  • Pages: 317

Kant's Mathematical World

An explanation of the foundations of Kant's philosophy of mathematics and its connection to his account of human experience.

Syllogistic Logic and Mathematical Proof
  • Language: en
  • Pages: 238

Syllogistic Logic and Mathematical Proof

Does syllogistic logic have the resources to capture mathematical proof? This volume provides the first unified account of the history of attempts to answer this question, the reasoning behind the different positions taken, and their far-reaching implications. Aristotle had claimed that scientific knowledge, which includes mathematics, is provided by syllogisms of a special sort: 'scientific' ('demonstrative') syllogisms. In ancient Greece and in the Middle Ages, the claim that Euclid's theorems could be recast syllogistically was accepted without further scrutiny. Nevertheless, as early as Galen, the importance of relational reasoning for mathematics had already been recognized. Further cri...

Intuition and the Axiomatic Method
  • Language: en
  • Pages: 328

Intuition and the Axiomatic Method

Following developments in modern geometry, logic and physics, many scientists and philosophers in the modern era considered Kant’s theory of intuition to be obsolete. But this only represents one side of the story concerning Kant, intuition and twentieth century science. Several prominent mathematicians and physicists were convinced that the formal tools of modern logic, set theory and the axiomatic method are not sufficient for providing mathematics and physics with satisfactory foundations. All of Hilbert, Gödel, Poincaré, Weyl and Bohr thought that intuition was an indispensable element in describing the foundations of science. They had very different reasons for thinking this, and th...

Kant's Metaphysical Foundations of Natural Science
  • Language: en
  • Pages: 303

Kant's Metaphysical Foundations of Natural Science

New essays on Kant's complex work, considering its place in his oeuvre and in the history of science.

Deconstructing LEGO
  • Language: en
  • Pages: 318

Deconstructing LEGO

This book investigates a paradox of creative yet scripted play—how LEGO invites players to build ‘freely’ with and within its highly structured, ideologically-laden toy system. First, this book considers theories and methods for deconstructing LEGO as a medium of bricolage, the creative reassembly of already-significant elements. Then, it pieces together readings of numerous LEGO sets, advertisements, videogames, films, and other media that show how LEGO constructs five ideologies of play: construction play, dramatic play, digital play, transmedia play, and attachment play. From suburban traffic patterns to architectural croissants, from feminized mini-doll bodies to toys-to-life stories, from virtual construction to playful fan creations, this book explores how the LEGO medium conveys ideological messages—not by transmitting clear statements but by providing implicit instructions for how to reassemble meanings it had all along.

International Symposium on Fuzzy Systems, Knowledge Discovery and Natural Computation (FSKD 2014)
  • Language: en
  • Pages: 657

International Symposium on Fuzzy Systems, Knowledge Discovery and Natural Computation (FSKD 2014)

ICNC-FSKD is a premier international forum for scientists and researchers to present the state of the art of data mining and intelligent methods inspired from nature, particularly biological, linguistic, and physical systems, with applications to computers, circuits, systems, control, communications, and more. This is an exciting and emerging interdisciplinary area in which a wide range of theory and methodologies are being investigated and developed to tackle complex and challenging problems.

Cassirer
  • Language: en
  • Pages: 222

Cassirer

Ernst Cassirer (1874–1945) occupies a unique place in 20th-century philosophy. His view that human beings are not rational but symbolic animals and his famous dispute with Martin Heidegger at Davos in 1929 are compelling alternatives to the deadlock between 'analytic' and 'continental' approaches to philosophy. An astonishing polymath, Cassirer's work pays equal attention to mathematics and natural science but also art, language, myth, religion, technology, and history. However, until now the importance of his work has largely been overlooked. In this outstanding introduction Samantha Matherne examines and assesses the full span of Cassirer’s work. Beginning with an overview of his life ...

Frege's Theorem
  • Language: en
  • Pages: 322

Frege's Theorem

Richard Heck explores a key idea in the work of the great philosopher/logician Gottlob Frege: that the axioms of arithmetic can be logically derived from a single principle. Heck uses the theorem to explore historical, philosophical, and technical issues in philosophy of mathematics and logic, relating them to key areas of contemporary philosophy.

From Kant to Husserl
  • Language: en
  • Pages: 230

From Kant to Husserl

In From Kant to Husserl, Charles Parsons examines a wide range of historical opinion on philosophical questions, from mathematics to phenomenology. Amplifying his early ideas on Kant’s philosophy of arithmetic, Parsons uses Kant’s lectures on metaphysics to explore how his arithmetical concepts relate to the categories. He then turns to early reactions by two immediate successors of Kant, Johann Schultz and Bernard Bolzano, to shed light on disputed questions regarding interpretation of Kant’s philosophy of mathematics. Interested, as well, in what Kant meant by “pure natural science,” Parsons considers the relationship between the first Critique and the Metaphysical Foundations of...