Iconic Arithmetic Volume II

Iconic Arithmetic  Volume II

The Image is the cover of Iconic Arithmetic Volume II: Symbolic and Postsymbolic Formal Foundations.
This book is the second of three volumes and is available on Amazon (ISBN 978-1-7324851-4-3).
Volume II compares the conventional symbolic forms of equality, composition and concurrency to the iconic perspective of James algebra. Then the structure of James algebra is compared to the foundations of arithmetic developed by Hilbert, Frege and Peano; to weaker arithmetics (Presburger, Robinson and Primitive Recursive Arithmetic); and to symbolic formalism and digital computation in general. These contrasts support a postsymbolic perspective that sets, logic and functional thinking are not necessary for formal arithmetic. Only the single concept of distinction, expressed by the single iconic relation of containment, is necessary.

Here is the text on the back cover:

Arithmetic evolves.
Symbolic mathematics was designed before film, before TV, before music videos, before smart phones.
Our media are coupled to how we think and what we do.
Symbolic abstraction is too detached for this century.
Postsymbolic math reintegrates our bodies and our minds.
Sets and logic and functional thinking need to evolve to incorporate global unity and ecological diversity.
Concept is embodied, concrete, incorporated, lived.
Meaning comes from experience.
Arithmetic is multisensory pattern.


The first volume of this series, Iconic Arithmetic Volume I: The Design of Mathematics for Human Understanding, is also available from both Amazon (ISBN 978-1-7324851-3-6) and PayPal under an adjacent tile on the home page of this site.

The third volume of this series, Iconic Arithmetic Volume III: The Structure of Infinite and Imaginary Forms should be ready in late 2019.

A PDF sample of Iconic Arithmetic Volume Two is available below. It has been designed for two-page layout, with a distinct right and left page format. Please set your PDF viewer (probably Acrobat) for View>PageDisplay>TwoPageView.



The Iconic Arithmetic Volume II Sample includes the contents, preface, bibliography and index of Volume II, as well as Chapters 16, 26 and 30. The first Chapter 16 introduces the objectives of iconic mathematics. Chapter 26 describes the postsymbolic perspective that symbols are not necessary for the expression of mathematical concepts. The final Chapter 30 summarizes the volume and introduces the content of Volume III.



Chapters 17-20 explore some of the structure and tools of computation.
Chapters 21-25 examine the historical origins of formal arithmetic.
Chapters 27-30 make the case for postsymbolic formal structure.



Iconic Arithmetic Volume Two is now available for sale in two formats.
The softcover physical book can be purchased directly from Amazon ($30), ISBN 978-1-7324851-4-3.
An electronic PDF file can be purchased via the PayPal button below ($20).
These prices are intended only to cover some of the development overhead. Thanks!





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