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 :
But the question arises: how can we verify if a proposition is true? How do we know that an experience of ours is veridical? There are two methods to achieve this. First, there are the standards of formal inference of arguments —Is the argument logically sound? Second, and most importantly, there is a transcendent intellect in which all the essences of things and all knowledge resides. This intellect, known as the Active Intellect, illuminates the human intellect through conjunction and bestows upon the human intellect true knowledge of things. Conjunction, however, is episodic and only occurs to human intellects that have become adequately trained and thereby actualized. The active intellect also intervenes in the assessment of sound inferences through Avicenna’s theory of intuition. A syllogistic inference draws a conclusion from two prepositional premises through their connection or their middle term. It is sometimes rather difficult to see what the middle term is; thus when someone reflecting upon an inferential problem suddenly hits upon the middle term, and thus understands the correct result, she has been helped through intuition ( hads ) inspired by the active intellect. There are various objections that can be raised against this theory, especially because it is predicated upon a cosmology widely refuted in the post-Copernican world.
Loc. cit. ( Latin , short for loco citato , meaning "in the place cited") is a footnote or endnote term used to repeat the title and page number for a given work (and author). Loc. cit. is used in place of ibid. when the reference is not only to the work immediately preceding, but also refers to the same page. Therefore, loc. cit. is never followed by volume or page numbers. Loc. cit. may be contrasted with op. cit. ( opere citato , "in the work cited"), in which reference is made to a work previously cited, but to a different page within that work.