This book is the third component in the ROAL model; it suggests a relation between language and mathematical models of totality relying on verifiability and observability/objectivity models of the linguistic text. In addition of the biomathematical hypothesis, rules of observability and objectivity have been extended to both objective and non-objective models toward a manifolded dimension of the structure within a field dimension of consciousness in which dwells the paradigm of the text as a meta-observability domain for language and natural/individual languages.

This book is the third component in the ROAL model; it suggests a relation between language and mathematical models of totality relying on verifiability and observability/objectivity models of the linguistic text. In addition of the biomathematical hypothesis, rules of observability and objectivity have been extended to both objective and non-objective models toward a manifolded dimension of the structure within a field dimension of consciousness in which dwells the paradigm of the text as a meta-observability domain for language and natural/individual languages.

Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.

Karl Bühler (1879–1963) was one of the leading theoreticians of language of the twentieth century. Although primarily a psychologist, Bühler devoted much of his attention to the study of language and language theory. His masterwork Sprachtheorie (1934) quickly gained recognition in the fields of linguistics, semiotics, the philosophy of language and the psychology of language. This new edition of the English translation of Bühler’s theory begins with a survey on ‘Bühler’s legacy’ for modern linguistics (Werner Abraham), followed by the Theory of Language, and finally with a special ‘Postscript: Twenty-five Years Later ...’ (Achim Eschbach). Bühler’s theory is divided into four parts. Part I discusses the four axioms or principles of language research, the most famous of which is the first, the organon model, the base of Bühler's instrumental view of language. Part II treats the role of indexicality in language and discusses deixis as one determinant of speech. Part III examines the symbolic field, dealing with context, onomatopoeia and the function of case. Part IV deals with the elements of language and their organization (syllabification, the definition of the word, metaphor, anaphora, etc).The text is accompanied by an Introduction (Achim Eschbach); Translator's preface (Donald Fraser Goodwin); Glossary of terms; and a Bibliography of cited works.

The first book to explore and bring together both Phenomenological and analytic-empirical approaches to a central issue in our understanding of consciousness.