Book 1 of Newton’s Opticks opens with a set of definitions and axioms, so one might expect to find the theorems contained therein to be proved from said definitions and axioms via deductively valid rules of inference. But they’re not. Instead, Newton employs ‘proof by experiments’: each theorem is proved via a series of experiments, ...
Book 1 of Newton’s Opticks opens with a set of definitions and axioms, so one might expect to find the theorems contained therein to be proved from said definitions and axioms via deductively valid rules of inference. But they’re not. Instead, Newton employs ‘proof by experiments’: each theorem is proved via a series of experiments, which are represented by geometrical diagrams and accompanying text. Newton’s axioms and definitions do not feature explicitly in these proofs – they are not even mentioned in the discussions. This chapter addresses two questions in relation to this case. First, how does ‘proof by experiment’ function as a proof? Second, what roles do axioms and definitions play in the trajectory from experiment to proven theorem? It is argued that the probative force of the proof lies in the experience of enacting the experimental sequence and that the definitions and axioms guide and facilitate the experience.
