Combinatorics 79. Part I

This is the second edition of an important introduction to Leibniz's philosophy of logic and language first published in 1972. It takes issue with several traditional interpretations of Leibniz (by Russell amongst others) while revealing how Leibniz's thought is related to issues of great interest in current logical theory. For this new edition, the author has added new chapters on infinitesimals and conditionals as well as taking account of reviews of the first edition.

Richard Dawkins's formulation of the meme concept in his 1976 classic The Selfish Gene has inspired three decades of work in what many see as the burgeoning science of memetics. Its underpinning theory proposes that human culture is composed of a multitude of particulate units, memes, which are analogous to the genes of biological transmission. These cultural replicators are transmitted by imitation between members of a community and are subject to mutational-evolutionary pressures over time. Despite Dawkins and several others using music in their exemplifications of what might constitute a meme, these formulations have generally been quite rudimentary, even na?. This study is the first musicologically-orientated attempt systematically to apply the theory of memetics to music. In contrast to the two points of view normally adopted in music theory and analysis - namely those of the listener and the composer - the purpose of this book is to argue for a distinct and illuminating third perspective. This point of view is metaphorical and anthropomorphic, and the metaphor is challenging and controversial, but the way of thinking adopted has its basis in well-founded scientific principles and it is capable of generating insights not available from the first two standpoints. The perspective is that of the (selfish) replicated musical pattern itself, and adopting it is central to memetics. The approach taken is both theoretical and analytical. Starting with a discussion of evolutionary thinking within musicology, Jan goes on to cover the theoretical aspects of the memetics of music, ranging from quite abstract philosophical speculation to detailed consideration of what actually constitutes a meme in music. In doing so, Jan draws upon several approaches current in music theory, including Schenkerism and Narmour's implication-realization model. To demonstrate the practical utility of the memetic perspective, Chapter 6 applies it analytically, tracing the transmission o

Because our own historical moment continues to be indebted to romanticism, such a shift in understanding prompts a rethinking in our ideas of the interrelation of literature, philosophy, and science."--Jacket.

This text presents the ideas of a particular group of mathematicians of the late 18th century known as “the German combinatorial school” and its influence. The book tackles several questions concerning the emergence and historical development of the German combinatorial analysis, which was the unfinished scientific research project of that group of mathematicians. The historical survey covers the three main episodes in the evolution of that research project: its theoretical antecedents (which go back to the innovative ideas on mathematical analysis of the late 17th century) and first formulation, its consolidation as a foundationalist project of mathematical analysis, and its dissolution at the beginning of the 19th century. In addition, the book analyzes the influence of the ideas of the combinatorial school on German mathematics throughout the 19th century.

This is the first full English translation, with a critical introduction and a comprehensive commentary, of the Dissertation on Combinatorial Art (1666), in which Leibniz introduces some of his most important ideas in philosophy, logic, and mathematics.

The ability to improvise represents one of the highest levels of musical achievement. Yet what musical knowledge is 3equired for improvisation? How does a musician learn to improvise? What are the neural correlates of improvised performance? These are some of the questions explored in this unique and fascinating new book.