Newton's Principia advanced the idea of a world governed by strict mathematical law. Hume's admiration for Newton's laws did not prevent him from advancing his well-known skeptical argument against the idea of necessary connections in nature. But Newton himself anticipated some of Hume's skeptical concerns. I will show how\, in facing those concerns\, Newton took a far-sighted view of the power and the limitations of mathematical laws\, and the subtle relations between natural powers and our mathematical pictures of them. Along the way\, Newton's approach suggested what it might mean to take a realist perspective on laws that are possibly\, if not probably\, wrong. This approach is illuminating for contemporary debates on the application of mathematics to physics\, and on the role of mathematics in physical explanations.

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