[PDF] The Objective Or Synthetic Arithmetic eBook

Author : Gottlob Frege
Publisher : Northwestern University Press
Page : 144 pages
File Size : 13,90 MB
Release : 1980-12
Category : Mathematics
ISBN : 0810106051

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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.

Author : Daniel Adams
Publisher : Forgotten Books
Page : 190 pages
File Size : 35,43 MB
Release : 2017-11-02
Category : Mathematics
ISBN : 9780260151995

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Excerpt from Adam's New Arithmetic: Arithmetic, in Which the Principles of Operating by Numbers and Analytically Explained, and Synthetically Applied; Thus Combining the Advantages to Be Derived Both From the Inductive and Synthetic Mode of Instructing The numerical Enragra hs are chiefly for the purpose of reference; these references t e pup: should not be allowed to neglect. His attention also ought to re particularly directed, by his instructer, to the illustration of each particular principle, from which general rules are deduced: for this purpose, recitations by classes ought to be instituted in every school where arithmetic is taught. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Author : Burt C. Hopkins
Publisher : Indiana University Press
Page : 593 pages
File Size : 26,26 MB
Release : 2011-09-07
Category : Philosophy
ISBN : 0253005272

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Burt C. Hopkins presents the first in-depth study of the work of Edmund Husserl and Jacob Klein on the philosophical foundations of the logic of modern symbolic mathematics. Accounts of the philosophical origins of formalized concepts—especially mathematical concepts and the process of mathematical abstraction that generates them—have been paramount to the development of phenomenology. Both Husserl and Klein independently concluded that it is impossible to separate the historical origin of the thought that generates the basic concepts of mathematics from their philosophical meanings. Hopkins explores how Husserl and Klein arrived at their conclusion and its philosophical implications for the modern project of formalizing all knowledge.

Author : Giovanni Sommaruga
Publisher : Springer Science & Business Media
Page : 312 pages
File Size : 38,40 MB
Release : 2011-03-24
Category : Mathematics
ISBN : 9400704313

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The book "Foundational Theories of Classical and Constructive Mathematics" is a book on the classical topic of foundations of mathematics. Its originality resides mainly in its treating at the same time foundations of classical and foundations of constructive mathematics. This confrontation of two kinds of foundations contributes to answering questions such as: Are foundations/foundational theories of classical mathematics of a different nature compared to those of constructive mathematics? Do they play the same role for the resp. mathematics? Are there connections between the two kinds of foundational theories? etc. The confrontation and comparison is often implicit and sometimes explicit. Its great advantage is to extend the traditional discussion of the foundations of mathematics and to render it at the same time more subtle and more differentiated. Another important aspect of the book is that some of its contributions are of a more philosophical, others of a more technical nature. This double face is emphasized, since foundations of mathematics is an eminent topic in the philosophy of mathematics: hence both sides of this discipline ought to be and are being paid due to.