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Understanding the Infinite
How can the infinite, a subject so remote from our finite experience, be an everyday tool for the working mathematician? Blending history, philosophy, mathematics, and logic, Shaughan Lavine answers this question with exceptional clarity. Making use of the mathematical work of Jan Mycielski, he demonstrates that knowledge of the infinite is possible, even according to strict standards that require some intuitive basis for knowledge.
Mathematical Thought and its Objects
Charles Parsons examines the notion of object, with the aim to navigate between nominalism, denying that distinctively mathematical objects exist, and forms of Platonism that postulate a transcendent realm of such objects. He introduces the central mathematical notion of structure and defends a version of the structuralist view of mathematical objects, according to which their existence is relative to a structure and they have no more of a 'nature' than that confers on them. Parsons also analyzes the concept of intuition and presents a conception of it distantly inspired by that of Kant, which describes a basic kind of access to abstract objects and an element of a first conception of the infinite.
The Self-Organizing Social Mind
A proposal that the basic mental models used to structure social interaction result from self-organization in brain activity. In The Self-Organizing Social Mind, John Bolender proposes a new explanation for the forms of social relations. He argues that the core of social-relational cognition exhibits beauty—in the physicist's sense of the word, associated with symmetry. Bolender describes a fundamental set of patterns in interpersonal cognition, which account for the resulting structures of social life in terms of their symmetries and the breaking of those symmetries. He further describes the symmetries of the four fundamental social relations as ordered in a nested series akin to what one...
Reflections on the Foundations of Mathematics: Essays in Honor of Solomon Feferman
Solomon Feferman has shaped the field of foundational research for nearly half a century. These papers, most of which were presented at the symposium honoring him at his 70th birthday, reflect his broad interests as well as his approach to foundational research, which places the solution of mathematical and philosophical problems at the top of his
Concise Routledge Encyclopedia of Philosophy
The most complete and up-to-date philosophy reference for a new generation, with entries ranging from Abstract Objects to Wisdom, Socrates to Jean-Paul Sartre, Ancient Egyptian Philosophy to Yoruba Epistemology. The Concise Routledge Encyclopedia of Philosophy includes: * More than 2000 alphabetically arranged, accessible entries * Contributors from more than 1200 of the world's leading thinkers * Comprehensive coverage of the classic philosophical themes, such as Plato, Arguments for the Existence of God and Metaphysics * Up-to-date coverage of contemporary philosophers, ideas, schools and recent developments, including Jacques Derrida, Poststructuralism and Ecological Philosophy * Unrivalled international and multicultural scope with entries such as Modern Islamic Philosophy, Marxist Thought in Latin America and Chinese Buddhist Thought * An exhaustive index for ease of use * Extensive cross-referencing * Suggestions for further reading at the end of each entry
Logic Colloquium 2000 (hardcover)
This compilation of papers presented at the 2000 European Summer Meeting of the Association for Symbolic Logic marks the centenial anniversery of Hilbert's famous lecture. Held in the same hall at La Sorbonne where Hilbert first presented his famous problems, this meeting carries special significance to the Mathematics and Logic communities.
The Infinite
This historical study of the infinite covers all its aspects from the mathematical to the mystical. Anyone who has ever pondered the limitlessness of space and time, or the endlessness of numbers, or the perfection of God will recognize the special fascination of the subject. Beginning with an entertaining account of the main paradoxes of the infinite, including those of Zeno, A.W. Moore traces the history of the topic from Aristotle to Kant, Hegel, Cantor, and Wittgenstein.
Model Theory of Fields
The model theory of fields is a fascinating subject stretching from Tarski's work on the decidability of the theories of the real and complex fields to Hrushovksi's recent proof of the Mordell-Lang conjecture for function fields. This volume provides an insightful introduction to this active area, concentrating on connections to stability theory.
Kurt Gödel
Kurt Gödel (1906–1978) did groundbreaking work that transformed logic and other important aspects of our understanding of mathematics, especially his proof of the incompleteness of formalized arithmetic. This book on different aspects of his work and on subjects in which his ideas have contemporary resonance includes papers from a May 2006 symposium celebrating Gödel's centennial as well as papers from a 2004 symposium. Proof theory, set theory, philosophy of mathematics, and the editing of Gödel's writings are among the topics covered. Several chapters discuss his intellectual development and his relation to predecessors and contemporaries such as Hilbert, Carnap, and Herbrand. Others consider his views on justification in set theory in light of more recent work and contemporary echoes of his incompleteness theorems and the concept of constructible sets.
