Constructive mathematics is based on the thesis that the meaning of a mathematical formula is given, not by its truth-conditions, but in terms of what constructions count as a proof of it. However, the meaning of the terms construction' and proof' has never been adequately explained (although Kriesel, Goodman and Martin-Lof have attempted axiomatisations). This monograph develops precise (though not wholly formal) definitions of construction and proof, and describes the algorithmic substructure underlying intuitionistic logic. Interpretations of Heyting arithmetic and constructive analysis...

This volume contains a wide-ranging survey of musics of the world in historical and social contexts, from ancient times to the present day. It begins by describing aspects of musical style and function in relation to the early developments of civilizations, as background to a study of later transformations. It then describes, in some detail, musical traditions of Africa and Asia, in relation to history/geography and to other aspects of culture. A compendium of information currently available as well as a dialectical examination of musical causation and function, this book aims to lead...