The disgrace of geometry: Newton on postulates and the mechanical foundations of mathematics

The essay explores Newton's assertion that geometry is grounded in mechanics, and demonstrates that this claim arises from his understanding of mathematical postulates. Several of Newton's unpublished works on the foundations of mathematics are examined, highlighting the various systems of postulates he developed throughout his lifetime as the foundations of geometry. Newton's research is placed in the broader context of seventeenth-century studies on axiomatics, particularly in relation to the works of mathematicians Viète and van Schooten. The article presents an inferential interpretation of Newton's conception of postulates, offering new insights into his philosophy of mathematics. This, in turn, clarifies the significance and implications of Newton's statement regarding the relationship between geometry and mechanics.