Cover

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Title Page, Copyright

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pp. i-vi

Contents

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pp. v-vi

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Introduction

Geoffrey Gorham, Benjamin Hill, and Edward Slowik

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pp. 1-28

No other episode in the history of Western science has been as consequential as the rise of the mathematical approach to the natural world, both in terms of its impact on the development of science during the scientific revolution but also in regard to the debates that it has generated among scholars who have striven to understand the history and nature of science. In his recent summary of this “mathematization thesis,” Michael Mahoney recounts the stunningly quick ascendancy...

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1. Reading the Book of Nature: The Ontological and Epistemological Underpinnings of Galileo’s Mathematical Realism

Carla Rita Palmerino

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pp. 29-50

On May 7, 1610, Galileo Galilei wrote to Belisario Vinta, Secretary of State of the Grand Duchy of Tuscany, about the terms of his future position as a court mathematician. In his letter Galileo expressed the wish that “His Majesty add the name of Philosopher to that of Mathematician,” motivating his request with the fact that he had “spent more years studying philosophy than months studying pure mathematics” (Galilei 1890–1909, 10:353)....

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2. “The Marriage of Physics with Mathematics”: Francis Bacon on Measurement, Mathematics, and the Construction of a Mathematical Physics

Dana Jalobeanu

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pp. 51-80

Considerations on the nature of science played a very important role in Francis Bacon’s project for a Great Instauration. On a general level, his approach was foundational; knowledge was required to grow like a pyramid, on a solid basis of natural history, sustaining physics and metaphysics: “For knowledges are as pyramides, whereof history is the basis: so of Natural Philosophy the basis is Natural History; the stage next the basis is Physic; the stage next to the...

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3. On the Mathematization of Free Fall: Galileo, Descartes, and a History of Misconstrual

Richard T. W. Arthur

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pp. 81-111

In any attempt to understand conceptual history, the cardinal rule is not to assume that thinkers in the past were trying to express what we now understand with perfect clarity. For it will almost always turn out both that their understanding was different from ours— that apparently innocuous details like using proportions instead of equations “shifts” their whole understanding with respect to ours— and that “we,” in any case, do not understand the matter...

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4. The Mathematization of Nature in Descartes and the First Cartesians

Roger Ariew

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pp. 112-133

Some of the motivation for this volume is the reevaluation of a prominent historiographical orientation of twentieth-century research on the scientific revolution, in light of the proliferation of novel methodological orientations and studies in the last generation of scholars. The historiographical orientation at issue is what is called the mathematization of nature; its exemplary proponents are Alexandre Koyré, Eduard Jan Dijksterhuis, and...

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5. Laws of Nature and the Mathematics of Motion

Daniel Garber

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pp. 134-159

Nature came to be understood through mathematics in the seventeenth century, when Galileo (1890) famously wrote: “Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures..."

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6. Ratios, Quotients, and the Language of Nature

Douglas Jesseph

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pp. 160-177

In his 1623 essay “The Assayer,” Galileo notoriously claimed that the “book of nature” was written in the language of mathematics.1 Yet when we consider his actual formulation of the laws of nature (most notably the law of free fall in the Two New Sciences) it becomes apparent that he took the language of mathematics to be something rather different than the mathematical formulations we typically use today. As is well known, Galileo used the Euclidean-Eudoxian...

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7. Color by Numbers: The Harmonious Palette in Early Modern Painting

Eileen Reeves

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pp. 178-204

Hidden amid the standard tales of rollicking adulterers and vigorous cheats of Celio Malaspina’s Two Hundred Novellas, published in 1609, is the story of a boorish Venetian pigment grinder and his tireless tormentors, a petty dealer in brass and a die cutter connected with the mint. There is neither philandering nor fleecing here: the pigment grinder has nothing but a modest shop of “different sorts of colors, chalks and minerals,” an aging mother, an excess...

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8. The Role of Mathematical Practitioners and Mathematical Practice in Developing Mathematics as the Language of Nature

Lesley B. Cormack

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pp. 205-228

The sixteenth and seventeenth centuries have long been seen as fundamentally important to an understanding of the changing study of nature. The changes in this period have been variously categorized by historians as philosophical, methodological, or mathematical, among other explanations. One of the profound transformations that took place was the introduction of mathematics into the language of description and explanation of nature. Many historians...

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9. Leibniz on Order, Harmony, and the Notion of Substance: Mathematizing the Sciences of Metaphysics and Physics

Kurt Smith

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pp. 229-249

The March 1694 edition of Acta Eruditorum included a short article by Leibniz titled “On the Correction of First Philosophy and the Notion of Substance.”1 In it Leibniz complains about an emerging trend of obscurity in metaphysics, attributing it in part to a widening rift between work in metaphysics and work in mathematics. In July of that year Leibniz wrote to Jacques-Bénigne Bossuet, including with the letter a copy of a manuscript titled...

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10. Leibniz’s Harlequinade: Nature, Infinity, and the Limits of Mathematization

Justin E. H. Smith

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pp. 250-273

René Descartes writes to Marin Mersenne in a letter of 1639 that if his account of the circulation of blood, among other things, “turns out to be false, then the rest of my philosophy is entirely worthless” (1964–76, AT 2 501). He does not say that if his account is wrong then his circulation theory, or his medicine, or his physiology will be worthless. He says that his philosophy depends on the correctness of his explanation of cardiac motion. This is, indeed, putting quite a lot...

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11. The Geometrical Method as a New Standard of Truth, Based on the Mathematization of Nature

Ursula Goldenbaum

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pp. 274-307

Use of the geometrical method has long been criticized, even before Kant, for being inappropriate in the field of philosophy. There is above all the general reluctance to accept the ponderous method of geometrical demonstration in philosophy. This method is considered to require definitions and demonstrations of propositions,1 rarely commenting and explaining, thus providing little communication with the audience, while eschewing irony and rhetoric altogether. Many philosophers

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12. Philosophical Geometers and Geometrical Philosophers

Christopher Smeenk

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pp. 308-338

It is common to regard newton as the apotheosis of mathematized natural philosophy in the seventeenth century. For example, the Principia Mathematica is the culmination of Dijksterhuis’s grand narrative of mechanization (1961), marking the transition to a thorough mathematization of science. Accounts like this reflect Newton’s transformative contributions to natural philosophy and the central role of mathematics in his achievements. Newton frequently characterized...

Contributors

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pp. 339-342

Index

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pp. 343-354