The book only italicised; I added the majuscules.
Source: pp 226-227, Think: A Compelling Introduction to Philosophy (1 ed, 1999) by Simon Blackburn
[...] As with Boyle's law, we can say that while it is all we have got, we know something about the system. But we do not really understand WHY it is behaving as it does. Why should pressure vary inversely with volume? If it always does, why does it always do so? And why should constancy of temperature be important?
These questions were answered by providing a model in a more robust sense. The kinetic theory of gases sees gases as volumes of molecules in motion. Pressure is the result of the impact of these molecules on the walls of the container. The molecules speed up with increased temperature. Once a gas is seen like this, we have a mechanism, and given suitable assumptions, the empirical laws such as Boyle's law can be derived from the nature of the mechanism.
Finding a mechanism does not bypass the problem of induction. The continued uniform behaviour of items in a mechanism is a projection or extrapolation from what we have found so far, just as much as anything else. But it reduces the number of independent assumptions we need to make. A few stable features of things, and reliable interactions between them, might explain others. If we take the stable features for granted, we can explain the others in terms of them. These represent the EXPLANATORY and SIMPLIFYING ideals of science.
Inexperienced in the natural sciences, I do not understand the bolded. Suppose that as one equation, Boyle's Law (hereafter BL) is regarded as one independent assumption. Then any reference or use of BL means BL assumed true.
So how does a mechanism reduce 'the number of independent assumptions we need to make'?