## On the Shoulders of Merchants: Exchange and the Mathematical Conception of Nature in Early Modern EuropeThis book shows how the universal quantification of science resulted from the routinization of commercial practices that were familiar in scientist's daily lives. Following the work of Franz Borkenau and Jacob Klein in the 1930s, the book describes the rise of the mechanistic world-view as a reification of relations of exchange in the sixteenth and seventeenth centuries. Critical of more orthodox, positivist Marxist accounts of the rise of science, it argues that commercial reckoners, in keeping with the social relations in which their activity took place, delivered a new mathematical object, "general magnitude," to the new mechanics. The book is an historical extension of the sociology of scientific knowledge and develops and refines themes found in the work of Alfred Sohn-Rethel and Gideon Freudenthal. |

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### Contents

Accounts of the Rise of Early Modern Science | 1 |

PostWorld War II Accounts of the Rise of Science | 2 |

Marxism Praxis and Science | 8 |

Social Relations Value and the Mechanistic Abstraction | 16 |

Marx The Commodity Abstraction and Mechanistic Knowledge of Nature | 31 |

Society Thought and Historical Specification | 34 |

Commodities Value Abstraction and Homogeneity | 40 |

Commodity Fetishism and the Representation of Society and Nature | 46 |

Thomas Bradwardine | 96 |

Nicole Oresme | 99 |

Robert Recorde | 104 |

John Dee | 109 |

Thomas Harriot | 111 |

Rafael Bombelli | 112 |

Exchange Labour Mathematics and Natural Philosophy The Social Roots of a Science of Mechanics | 115 |

Niccolo Tartaglia | 121 |

The Concrete Existence of Abstract Relations | 50 |

Commerce Finance Credit and the Money Economy | 53 |

Production Labour and LabourTime | 56 |

Mathematical Mechanics and Abstraction | 63 |

Ancient Mathematics Discontinuities | 65 |

The Ontological Shift to Modern Mathematics Jacob Klein | 71 |

Mathematics and Mechanics The Homogenization of Nature | 74 |

Exchange Relations Commercial Arithmetic and the Foundations of Mathematical Mechanics | 83 |

John Philoponos | 84 |

The Early European Arithmetic and RecordKeeping Traditions | 85 |

Galileo Galilei | 123 |

Francois Viete | 129 |

Rene Descartes | 135 |

Simon Stevin | 149 |

The Hartlib Circle and the Royal Society | 154 |

Social Relations and the Intellectual Appropriation of Nature | 157 |

Notes | 167 |

171 | |

185 | |

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### Common terms and phrases

abacist according algebra analysis ancient Archimedes argues Aristotelian Aristotle arithmetic body Bombelli bookkeeping Borkenau Bradwardine calculation cites claims Clavius commensurability commercial commodity abstraction concept concerned Descartes Diophantus division of labour double-entry early modern mathematics economic Egmond equal equations Euclid example exchange exchange-value expression fractions Francois Viete Freudenthal Galileo geometry Greek Greek mathematics Grossmann Harriot homogeneous homogeneous mathematical human industry Klein labour-process Luca Pacioli Marx Marx's mathematical mechanics mathematical object mathesis universalis mechanical philosophy mechanistic merchants method modern science nature notion number and magnitude Oresme period philosophy physical practical problems production properties proportion proportionality putting-out system qualities question ratio realm rela result Roover Sasaki scientific seventeenth century sixteenth century social relations society specific Stevin substance suggests Tartaglia techniques theory things Thomas Bradwardine Thomas Harriot thought tion tradition unit universal unlike kind use-value Viete world-view Young Hegelians