The Scaling of Speeds and Distances in Galileo's Two New Sciences: A Reply to Palmerino and Laird

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Centaurus, ISSN: 0008-8994, Vol: 54, Issue: 2, Page: 182-191

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Norton, John D., Roberts, Bryan W.
Wiley-Blackwell, John Wiley and Sons
Arts and Humanities
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We thank Drs. Laird and Palmerino for their efforts in responding to our analysis of Galileo's refutation of the speed-distance law of fall. We have studied their concerns. In sum, we stand by our account and the claims of our original text. We hope that readers will compare it with the critiques and come to their own conclusions. To assist them, we will remark here on some of the points they have raised. We will respond mostly to Palmerino's comments, since hers is the more critical reaction. The locus of her concerns is the crucial first clause of Galileo's passage: When speeds have the same ratio as the spaces passed or to be passed, those spaces come to be passed in equal times;: : : (Galilei, 1974, p. 160) It contains, we urge, an ambiguity that has misdirected the literature. Do the 'speeds' and 'spaces' refer to a single moving body or to two moving bodies? Most commentators assume the single-body reading. It results in Galileo's 'very clear proof' collapsing into a circularity. We urge the two-body reading, for then the argument that follows is cogent and powerful. Of course even a thinker as adept as Galileo can commit simple fallacies. But why would we settle for that verdict on an argument that was of such importance to Galileo's narrative, when there is a second reading that exonerates him? Here, for convenience of reference, we summarize our earlier claim: In the two-body reading of this clause, we take Galileo to be asserting a scaling result: if one takes any motion and scales up the speeds and spaces in proportion to form a new motion, the original and scaled motions occur in the same time.

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