 The inductive principle applies to mathematics as well as physics. Shepherd takes arithmetical operations to be procedures for forming numbers out of given numbers; each different number determines somewhat different properties. Geometrical constructions are understood in the same way. A demonstration is made on a diagram constructed from lines drawn at various distances from each other. The properties of the particular construction are known by inspection. The move from a particular object to all things with similar constitutions is licensed by CPI; Shepherd calls this “reasoning on an experiment”. It is true that we are typically more certain of general theorems of mathematics than laws of physics. Shepherd explains that this is because we can often be more certain that two figures or numerical values have been formed in the same way because we construct them from known elements by known rules and procedures. There are many questions about the details of her theory of mathematical induction which have not, so far, been answered. To mention just one, it is not clear whether the method applies just to arithmetic and geometry or also the method of fluxions, and so  on.[7] 