 Corresponding to these four kinds of objects, Schopenhauer links in parallel, four different kinds of reasoning. He associates material things with reasoning in terms of cause and effect; abstract concepts with reasoning in terms of logic; mathematical and geometrical constructions with reasoning in reference to numbers and spaces; and motivating forces with reasoning in reference to intentions, or what he calls moral reasoning. In sum, he identifies the general root of the principle of sufficient reason as the subject-object distinction in conjunction with the thought of necessary connection, and the fourfold root of the principle of sufficient reason as the specification of four different kinds of objects for which we can seek explanations, in association with the four independent styles of necessary connection along which such explanations can be given, depending upon the different kinds of objects involved.