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How Language Informs Mathematics

Bridging Hegelian Dialectics and Marxian Models

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Dirk Damsma

In How Language Informs Mathematics Damsma shows how Hegel’s and Marx’s systematic dialectical analysis of mathematical and economic language helps us understand the structure and nature of mathematical and capitalist systems. More importantly, Damsma shows how knowledge of the latter can inform model assumptions and help improve models.

His book provides a blueprint for an approach to economic model building that does away with arbitrarily chosen assumptions and is sensitive to the institutional structures of capitalism. In light of the failure of mainstream economics to understand systemic failures like the financial crisis and given the arbitrary character of most assumptions in mainstream models, such an approach is desperately needed.
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Jochen Viehoff and Friedrich L. Bauer

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The Commentary of al-Nayrizi on Book I of Euclid's Elements of Geometry

with an Introduction on the Transmission of Euclid's Elements in the Middle Ages

Edited by Anthony Lo Bello

For more than two millennia, the Elements of Geometry by the Greek mathematician Euclid of Alexandria (ca. 300 B.C.E. ) was held to be “the supreme example of the exercise of human reason” and “a paradigm of rational certainty” (from the preface, after Simon Blackburn). The Commentary of al-Nayrizi on Book I of Euclid’s Elements of Geometry introduces readers to the transmission of Euclid’s Elements from the Middle East to the Latin West in the medieval period and then offers the first English translation of al-Nayrizi’s (d. ca. 922) Arabic commentary on Book I.

The Three Volumes are also available as set (ISBN 0 391 04197 5)
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Edited by Anthony Lo Bello

The Commentary of Albertus Magnus on Book I of Euclid’s Elements of Geometry is the third in Lo Bello’s series on the Elements. Lo Bello provides the first modern translation of a key Latin text of the Elements in the Middle Ages, the commentary of the Dominican scholastic philosopher Albertus Magnus (d. 1280), the teacher of Thomas Aquinas. The volume includes a translation, notes on the translation, and a critical examination of the mathematical content of the three commentaries on Euclid’s Elements of Geometry thus far treated in this series.

The Three Volumes are also available as set (ISBN 0 391 04197 5)
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Gerard of Cremona’s Translation of the Commentary of al-Nayrizi on Book I of Euclid’s Elements of Geometry

With an Introductory Account of the Twenty-Two Early Extant Arabic Manuscripts of the Elements

Edited by Anthony Lo Bello

Anthony Lo Bello’s Gerard of Cremona’s Translation of Book I of the Commentary of al-Nayrizi on Euclid’s Elements of Geometry is the first modern translation of Gerard of Cremona’s (1114–1187) Latin version of al-Nayrizi’s famous Arabic commentary. Lo Bello gives an introductory account of the twenty-two early extant Arabic manuscripts of the Elements, an annotated English translation of Gerard’s translation of al-Nayrizi’s commentary, and finally a critical analysis of the idiosyncrasies of Gerard’s method of translation.

The Three Volumes are also available as set (ISBN 0 391 04197 5)