There are reams of literature addressing whether these two definitions are the same and, if not, to which of them Hume gives primacy. Robinson is perhaps the staunchest proponent of the position that the two are nonequivalent, arguing that there is an nonequivalence in meaning and that they fail to capture the same extension. Two objects can be constantly conjoined without our mind determining that one causes the other, and it seems possible that we can be determined that one object causes another without their being constantly conjoined. But if the definitions fail in this way, then it is problematic that Hume maintains that both are adequate definitions of causation. Some scholars have argued for ways of squaring the two definitions (Don Garrett, for instance, argues that the two are equivalent if they are both read objectively or both read subjectively), while others have given reason to think that seeking to fit or eliminate definitions may be a misguided project.
As indicated in the above chart, our more complex ideas of the imagination are further divided between two categories. Some imaginative ideas represent flights of the fancy, such as the idea of a golden mountain; however, other imaginative ideas represent solid reasoning, such as predicting the trajectory of a thrown ball. The fanciful ideas are derived from the faculty of the fancy , and are the source of fantasies, superstitions, and bad philosophy. By contrast, sound ideas are derived from the faculty of the understanding— or reason—and are of two types: (1) involving relations of ideas; or (2) involving matters of fact. A relation of ideas (or relation between ideas) is a mathematical relation that is “discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe,” such as the mathematical statement “the square of the hypotenuse is equal to the square of the two sides” ( Enquiry , 4). By contrast, a matter of fact, for Hume, is any object or circumstance which has physical existence, such as “the sun will rise tomorrow”. This split between relations of ideas and matters of fact is commonly called “Hume’s Fork”, and Hume himself uses it as a radical tool for distinguishing between well-founded ideas of the understanding, and unfounded ideas of the fancy. He dramatically makes this point at the conclusion of his Enquiry :