The Foundations of Arithmetic - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Foundations of Arithmetic write by Gottlob Frege. This book was released on 1980-12. The Foundations of Arithmetic available in PDF, EPUB and Kindle. The Foundations of Arithmetic is undoubtedly the best introduction to Frege's thought; it is here that Frege expounds the central notions of his philosophy, subjecting the views of his predecessors and contemporaries to devastating analysis. The book represents the first philosophically sound discussion of the concept of number in Western civilization. It profoundly influenced developments in the philosophy of mathematics and in general ontology.
The Basic Laws of Arithmetic
The Basic Laws of Arithmetic - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Basic Laws of Arithmetic write by Gottlob Frege. This book was released on 1967. The Basic Laws of Arithmetic available in PDF, EPUB and Kindle.
Frege, Dedekind, and Peano on the Foundations of Arithmetic (Routledge Revivals)
Frege, Dedekind, and Peano on the Foundations of Arithmetic (Routledge Revivals) - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Frege, Dedekind, and Peano on the Foundations of Arithmetic (Routledge Revivals) write by Donald Gillies. This book was released on 2013-01-11. Frege, Dedekind, and Peano on the Foundations of Arithmetic (Routledge Revivals) available in PDF, EPUB and Kindle. First published in 1982, this reissue contains a critical exposition of the views of Frege, Dedekind and Peano on the foundations of arithmetic. The last quarter of the 19th century witnessed a remarkable growth of interest in the foundations of arithmetic. This work analyses both the reasons for this growth of interest within both mathematics and philosophy and the ways in which this study of the foundations of arithmetic led to new insights in philosophy and striking advances in logic. This historical-critical study provides an excellent introduction to the problems of the philosophy of mathematics - problems which have wide implications for philosophy as a whole. This reissue will appeal to students of both mathematics and philosophy who wish to improve their knowledge of logic.
Foundations of Arithmetic Differential Geometry
Foundations of Arithmetic Differential Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Foundations of Arithmetic Differential Geometry write by Alexandru Buium. This book was released on 2017-06-09. Foundations of Arithmetic Differential Geometry available in PDF, EPUB and Kindle. The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is “intrinsically curved”; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.
The Foundations of Mathematics
The Foundations of Mathematics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Foundations of Mathematics write by Ian Stewart. This book was released on 2015. The Foundations of Mathematics available in PDF, EPUB and Kindle. The transition from school mathematics to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory. The authors have many years' experience of the potential difficulties involved, through teaching first-year undergraduates and researching the ways in which students and mathematicians think. The book explains the motivation behind abstract foundational material based on students' experiences of school mathematics, and explicitly suggests ways students can make sense of formal ideas. This second edition takes a significant step forward by not only making the transition from intuitive to formal methods, but also by reversing the process- using structure theorems to prove that formal systems have visual and symbolic interpretations that enhance mathematical thinking. This is exemplified by a new chapter on the theory of groups. While the first edition extended counting to infinite cardinal numbers, the second also extends the real numbers rigorously to larger ordered fields. This links intuitive ideas in calculus to the formal epsilon-delta methods of analysis. The approach here is not the conventional one of 'nonstandard analysis', but a simpler, graphically based treatment which makes the notion of an infinitesimal natural and straightforward. This allows a further vision of the wider world of mathematical thinking in which formal definitions and proof lead to amazing new ways of defining, proving, visualising and symbolising mathematics beyond previous expectations.
