An introduction to awe-inspiring ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, and computability theory. This book introduces the reader to awe-inspiring issues at the intersection of philosophy and mathematics. It explores ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, computability theory, the Grandfather Paradox, Newcomb's Problem, the Principle of Countable Additivity. The goal is to present some exceptionally beautiful ideas in enough detail to enable readers to understand the ideas themselves (rather than watered-down approximations), but without supplying so much detail that they abandon the effort. The philosophical content requires a mind attuned to subtlety; the most demanding of the mathematical ideas require familiarity with college-level mathematics or mathematical proof. The book covers Cantor's revolutionary thinking about infinity, which leads to the result that some infinities are bigger than others; time travel and free will, decision theory, probability, and the Banach-Tarski Theorem, which states that it is possible to decompose a ball into a finite number of pieces and reassemble the pieces so as to get two balls that are each the same size as the original. Its investigation of computability theory leads to a proof of Gödel's Incompleteness Theorem, which yields the amazing result that arithmetic is so complex that no computer could be programmed to output every arithmetical truth and no falsehood. Each chapter is followed by an appendix with answers to exercises. A list of recommended reading points readers to more advanced discussions. The book is based on a popular course (and MOOC) taught by the author at MIT.

The notion of paradox dates back to ancient philosophy, yet only recently have scholars started to explore this idea in organizational phenomena. Two decades ago, a handful of provocative theorists urged researchers to take seriously the study of paradox, and thereby deepen our understanding of plurality, tensions, and contradictions in organizational life. Studies of organizational paradox have grown exponentially over the past two decades, canvassing varied phenomena, methods, and levels of analysis. These studies have explored such tensions as today and tomorrow, global integration and local distinctions, collaboration and competition, self and others, mission and markets. Yet even with both the depth and breadth of interest in organizational paradoxes, key issues around definitions and application remain. This handbook seeks to aid, engage, and fuel the expanding interest in organizational paradox. Contributions to this volume depict how paradox studies inform, and are informed, by other theoretical perspectives, while creating a resource that enables scholars to learn about and apply this lens across varied organizational phenomena. The increasing complexity, volatility, and ambiguity in our world continually surfaces paradoxical dynamics. Thus, this handbook offers insights to scholars across organizational theory.

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Consider the sentence 'This sentence is not true'. Certain notorious paradoxes like this have bedevilled philosophical theories of truth. Tim Maudlin presents an original account of logic and semantics which deals with these paradoxes, and allows him to set out a new theory of truth-values and the norms governing claims about truth.

In this groundbreaking comparative study, Matthew Bagger investigates the role of paradox in Western and Asian religious discourse. Drawing on both philosophy and social scientific theory, he offers a naturalistic explanation of religion's oft-noted propensity to sublime paradox and argues that religious thinkers employ intractable paradoxes as the basis for various techniques of self-transformation. Considering the writings of Kierkegaard, Pseudo-Dionysus, St. John of the Cross, N'g'rjuna, and Chuang-tzu, among others, Bagger identifies two religious uses of paradox: cognitive asceticism, which wields the psychological discomfort of paradox as an instrument of self-transformation, and mysticism, which seeks to transform the self through an alleged extraordinary cognition that ineffably comprehends paradox. Bagger contrasts these techniques of self-transformation with skepticism, which cultivates the appearance of contradiction in order to divest a person of beliefs altogether. Bagger further contends that a thinker's social attitudes determine his or her response to paradox. Attitudes concerning crossing the boundary of a social group prefigure attitudes concerning supposed truths that lie beyond the boundaries of understanding. Individuals who fear crossing the boundary of their social group and would prohibit them tend to use paradox ascetically, while individuals who find the controlled incorporation of outsiders enriching commonly find paradox revelatory. Although scholars have long noted that religious discourse seems to cultivate and perpetuate paradox, their scholarship tends to ratify religious attitudes toward paradox instead of explaining the unusual reaction paradox provokes. A vital contribution to discussions of mystical experience, The Uses of Paradox reveals how much this experience relies on social attitudes and cosmological speculation.

Dictionary of Paradox is a fascinating reference work for scholars, students, and the general public. It describes those paradoxes that are either especially interesting today or that have a continuing interest from the historical point of view. Each main entry consists of four parts: a statement of the paradox, an explanation of its paradoxicality, a discussion of attempted or accepted resolutions, and a list of readings. In addition, there are other entries explaining terms relating to paradoxes, listing alternative names for the main entries, or discussing variants of the entries. All information is extensively cross-referenced.

Provides therapists with an understanding of the principles, applications and implications of paradoxical therapy, the rationale for the use of paradox in family therapy and the therapist's role in paradoxical interventions.