ABSTRACT
This chapter is dedicated to defending the plausibility of the Two-Set Reading of Rule 3. It opens by demonstrating that the Two-Set Reading can accommodate the same key selections from the Principia that are compatible with the One-Set Reading. It then shows that interpreting Rule 3 as identifying two sets of qualities that can be universalized accords with the Latin formulation of the Rule. Specifically, it is demonstrated that the Two-Set Reading is consistent with Newton’s use of the Latin quæ … quæque construction to express the third Rule and with his use of that same Latin construction elsewhere in the Principia. The chapter concludes with a sustained discussion of Newton’s one-sentence justification for Rule 3 and his two examples of cases to which the Rule can be applied. One example involves applying Rule 3 to gravity. The other involves applying it to the quality of divisibility. It is argued that the Two-Set Reading gives us a clearer view than the One-Set Reading of why Newton claims that Rule 3 can be applied to both of the cases that he presents.
