In his theological writings, Galileo maintained what might be called the “independence principle” – science and religion belong to, and are competent on, two distinct and different domains: the factual domain of natural phenomena and the domain of faith of supernatural phenomena. As he put it, a distinction is to be drawn between “purely physical propositions which are matters of faith [and] supernatural propositions which are articles of faith.” Accordingly, Galileo held the view that all factual statements about natural phenomena contained in the Scriptures have no value for salvation and, therefore, can be revised or dismissed on scientific grounds.

Bellarmine adopted a different principle, which can be called the "limitation principle." According to it, certain factual statements contained in the Scriptures are necessary for their salvation value and, therefore, cannot be revised in the light of any contrary scientific theories. This has the consequence that, if such theories are advanced, they cannot be held to be true and, at the most, have to be treated as "hypotheses," in the technical sense of devices for calculating or systematizing phenomena, deprived of truth and epistemic value.