LetA be any nonrecursive set. We define a hierarchy of sets (and a corresponding hierarchy of degrees) that are reducible toA based on bounding the number of queries toA that an oracle machine can make. WhenA is the halting problemK our hierarchy of sets interleaves with the difference hierarchy on the r.e. sets in a logarithmic way; this follows from a tradeoff between the number of parallel queries and the number of serial queries needed to compute a function with oracleK.

The purpose of the book is to attempt to ascertain the views of President Barack Obama related to the field of education. This is done by first studying his own personal education and then following his spoken and written comments as a social worker, college professor, and as a state and federal legislator. In addition, there is an analysis of the positions he has taken during his political campaigns. Following this, there is a description of the actions he has taken (...) thus far in the field of education during his presidency. Using this background the author seeks to suggest his likely initiatives in education during the remainder of his presidency. (shrink)

The rise of progressive education -- John Dewey -- Other pioneers in the progressive education movement -- The progressive education movement during the first half of the twentieth century -- The fifties -- The sixties and seventies -- A nation at risk (1983) -- The eighties and nineties -- No child left behind -- Maria Montessori -- Teacher education programs -- Middle schools -- Choice -- Education of the gifted and talented -- Progressive education today -- The future of progressive (...) education. (shrink)

Every month some one pronounces that science must be rejected if we are to preserve a belief in human freedom, or that only by a faith in freedom that flies in the face of logic and the principle of causality can democracy be justified. Equally often other authors insist that the increase of knowledge in the science of human behavior makes plain the irrelevance and sentimentality of pious talk about free and rational choice. What is the source of this dispute? (...) Why is no resolution of it arrived at? (shrink)

Most handbooks on statistics and the theory of probability leave the reader in a mysterious tangle of mathematical rules for computing apparently arbitrarily chosen numerical functions. At first sight, then, a treatise on the Logical Foundations of Probability raises hopes that it will be a guide to clarity in these matters. These hopes are strengthened if the reader remembers that the author, Professor Rudolph Carnap of the University of Chicago, is noted for his thesis that philosophy is the study of (...) the logic of science. On the other hand, a first glance into this book may discourage a reader who, though familiar with statistics, is not familiar with modern logic and its notation. For this reason particularly I shall try to give an account of this book that will enable the interested student to form some opinion of its usefulness to him. (shrink)

In this book, authors Alyssa Magee Lowery and William Hayes trace the history of teaching from Greek philosophy to twenty-first century educational issues in an effort to provide some perspective in the long art versus science debate, ultimately finding that the two components may be able to coexist peacefully.

Charles Avison's Essay on Musical Expression, first published in 1752, is a major contribution to the debate on musical aesthetics which developed in the course of the 18th century. Considered by Charles Burney as the first essay devoted to 'musical criticism' proper, it established the primary importance of 'expression' and reconsidered the relative importance of harmony and melody. Immediately after its publication it was followed by William Hayes's Remarks (1753), to which Avison himself retorted in his Reply. Taken together these (...) three texts offer a fascinating insight into the debate that raged in the 18th century between the promoters of the so-called 'ancient music' (such as Hayes) and the more 'modern' musicians. Beyond matters of taste, what was at stake in Avison's theoretical contribution was the assertion that the individual's response to music ultimately mattered more than the dry rules established by professional musicians. Avison also wrote several prefaces to the published editions of his own musical compositions. This volume reprints these prefaces and advertisements together with his Essay to provide an interesting view of eighteenth-century conceptions of composition and performance, and a complete survey of Avison's theory of music. (shrink)

A philosopher who is influential owes his influence to dealing with questions which his readers recognize as questions of importance to themselves as well. It might be thought that since Dewey was so influential in his lifetime, his philosophy is not likely to have much of relevance to generations rising in 1964. It is, however, my belief that the study of Dewey’s writings on certain topics has enabled me to come by ideas that are helpful in getting a clearer understanding (...) of reasoning, choice, and freedom. (shrink)