By the time of the Leibniz-Clarke correspondence of 1716 the Newtonian and Leibnizian systems of natural philosophy had reached maturity. Each system consisted of different physical as well as metaphysical principles which, taken together, formed a world view. At the time of their famous debates, Leibniz at 70 and Newton at 74, the founders of two highly developed scientific philosophies, were struggling to establish and defend the ontological and mechanical bases of differing bodies of organized knowledge.

In the late 1810s and 1820s the Edinburgh phrenologists were largely concerned with trying to establish phrenology as the true science of mind. They challenged the accepted theories about the nature of mind and the brain; in turn, phrenology was attacked by the proponents of Scottish common-sense philosophy and by some medical men. The ensuing debate, which is discussed as an example of conflict between incommensurable world-views, involved a wide range of contentious theological, philosophical, scientific and methodological issues.