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Computability
Computer scientists, mathematicians, and philosophers discuss the conceptual foundations of the notion of computability as well as recent theoretical developments. In the 1930s a series of seminal works published by Alan Turing, Kurt Gödel, Alonzo Church, and others established the theoretical basis for computability. This work, advancing precise characterizations of effective, algorithmic computability, was the culmination of intensive investigations into the foundations of mathematics. In the decades since, the theory of computability has moved to the center of discussions in philosophy, computer science, and cognitive science. In this volume, distinguished computer scientists, mathematic...
The Many Valued and Nonmonotonic Turn in Logic
The present volume of the Handbook of the History of Logic brings together two of the most important developments in 20th century non-classical logic. These are many-valuedness and non-monotonicity. On the one approach, in deference to vagueness, temporal or quantum indeterminacy or reference-failure, sentences that are classically non-bivalent are allowed as inputs and outputs to consequence relations. Many-valued, dialetheic, fuzzy and quantum logics are, among other things, principled attempts to regulate the flow-through of sentences that are neither true nor false. On the second, or non-monotonic, approach, constraints are placed on inputs (and sometimes on outputs) of a classical conse...
Kant's Philosophy of Mathematics: Volume 1, The Critical Philosophy and its Roots
The late 1960s saw the emergence of new philosophical interest in Kant's philosophy of mathematics, and since then this interest has developed into a major and dynamic field of study. In this state-of-the-art survey of contemporary scholarship on Kant's mathematical thinking, Carl Posy and Ofra Rechter gather leading authors who approach it from multiple perspectives, engaging with topics including geometry, arithmetic, logic, and metaphysics. Their essays offer fine-grained analysis of Kant's philosophy of mathematics in the context of his Critical philosophy, and also show sensitivity to its historical background. The volume will be important for readers seeking a comprehensive picture of the current scholarship about the development of Kant's philosophy of mathematics, its place in his overall philosophy, and the Kantian themes that influenced mathematics and its philosophy after Kant.
Kant on Causality, Freedom, and Objectivity
Kant on Causality, Freedom, and Objectivity was first published in 1984. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. Kant's account of causation is central to his views on objective truth and freedom. The Second Analogy of Experience, in the Critique of Pure Reason,where he provides his defense of the causal principle, has long been the focus of intense philosophical research. In the past twenty years, there have been two major periods of interest in Kantian themes, The first coincided with a general turn away from positivism by analytic philosoph...
Omaha Orange
Essential reading for anyone who has ever wondered how EMS in America evolved into its present state.
Humanizing Mathematics and its Philosophy
This Festschrift contains numerous colorful and eclectic essays from well-known mathematicians, philosophers, logicians, and linguists celebrating the 90th birthday of Reuben Hersh. The essays offer, in part, attempts to answer the following questions set forth by Reuben himself as a focus for this volume: Can practicing mathematicians, as such, contribute anything to the philosophy of math? Can or should philosophers of math, as such, say anything to practicing mathematicians? Twenty or fifty years from now, what will be similar, and what will, or could, or should be altogether different: About the philosophy of math? About math education? About math research institutions? About data proces...
Rethinking Kant 5
The series Rethinking Kant, now in its fifth volume, has become a mirror of Kantian studies in North America. It gathers papers presented at the various study groups of the North American Kant Society, along with contributions from hosts, session chairs, and keynote speakers. Because of its broad and unique composition, it offers a sample of a whole generation of Kantian thought, ranging from recent PhD recipients, to up-and-coming young scholars, to some well-established and influential players in the field. Contributions are subjected to strenuous peer-review, and are, without exception, examples of the most innovative and cutting-edge research done in this area. As such, this collection will appeal to anyone interested in taking the pulse of contemporary Kantian scholarship and engaging in the humbling, but rewarding task of rethinking Kant.
Wittgenstein on Rules and Private Language
Table of Contents " Preface " Introductory " The Wittgensteinian Paradox " The Solution and the 'Private Language' Argument " Postscript Wittgenstein and Other Minds " Index.
Language and the Ineffable
One's conception of language is central in fields such as linguistics, but less obviously so in fields studying matters other than language. In Language and the Ineffable Louis S. Berger demonstrates the flaws of the received view of language and the difficulties they raise in multiple disciplines. This breakthrough study sees past failures as inevitable, since reformers retained key detrimental features of the received view. Berger undertakes a new reform, grounded in an unconventional model of individual human development. A central radical and generative feature is the premise that the neonate's world is holistic, boundary-less, unimaginable, impossible to describe_in other words, ineffab...
