Philosophy of Arithmetic

psychological and logical investigations with supplementary texts from 1887-1901

Edmund Husserl

This volume is a window on a period of rich and illuminating philosophical activity that has been rendered generally inaccessible by the supposed "revolution" attributed to "Analytic Philosophy." 

Available in hardcover and paperback (, Barnes & Noble).

(Dordrecht: Kluwer Academic Publishers, 2003) 580 pp., ISBN 1-4020-1546-1 (Hardbound) ISBN 1-4020-1603-4 (Paperback). A translation of Edmund Husserl's Philosophie der Arithmetik, and the other shorter works published with it in "Husserliana XII" (The Hague, Netherlands:Martinus Nijhoff, 1970).


In his first book, Philosophy of Arithmetic, Edmund Husserl provides a carefully worked out account of number as a categorial or formal feature of the objective world, and of arithmetic as a symbolic technique for mastering the infinite field of numbers for knowledge. It is a realist account of numbers and number relations that interweaves them into the basic structure of the universe and into our knowledge of reality. It provides an answer to the question of how arithmetic applies to reality, and gives an account of how, in general, formalized systems of symbols work in providing access to the world. The "appendices" to this book provide some of Husserl's subsequent discussions of how formalisms work, involving David Hilbert's program of completeness for arithmetic. "Completeness" is integrated into Husserl's own problematic of the "imaginary", and allows him to move beyond the analysis of "representations" in his understanding of the logic of mathematics.

Husserl's work here provides an alternative model of what "conceptual analysis" should be - minus the "linguistic turn", but inclusive of language and linguistic meaning. In the process, he provides case after case of "Phenomenological Analysis" - fortunately unencumbered by that title - of the convincing type that made Husserl's life and thought a fountainhead of much of the most important philosophical work of the twentieth Century in Europe. Many Husserlian themes to be developed at length in later writings first emerge here: Abstraction, internal time consciousness, polythetic acts, acts of higher order ('founded' acts), Gestalt qualities and their role in knowledge, formalization (as opposed to generalization), essence analysis, and so forth.

This volume is a window on a period of rich and illuminating philosophical activity that has been rendered generally inaccessible by the supposed "revolution" attributed to "Analytic Philosophy" so-called. Careful exposition and critique is given to every serious alternative account of number and number relations available at the time. Husserl's extensive and trenchant criticisms of Gottlob Frege's theory of number and arithmetic reach far beyond those most commonly referred to in the literature on their views.

More about the book from the publisher.


“This translation is the crowning achievement of Dallas Willard’s monumental research into Husserl’s early philosophy … . The volume is hence a good starting point for English-speaking students from freshman to graduate level who wish to familiarise themselves with Husserl’s philosophy of mathematics … . Willard succeeds in creating a very readable English text, maintaining a good balance between correctly rendering difficult and ambiguous German terms and writing in a clear and easy way.”

What can be said about Philosophy of Arithmetic (PA), a book that has existed in its original language for over one hundred years? First, it is very good finally to have an English translation of the book, and for this we have to thank Professor Willard. It seems to me that, at every turn, Willard has put great care into the preparation of the translation. The book is now available to readers who are working primarily in Anglo-American philosophy of mathematics and logic, along with those whose interest in Husserl's work will be assisted by a well-crafted translation.

Richard Tieszen, Philosophia Mathematica




Hardcover, Paperback

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