David Hume allows that the human mind possesses the freedom to roam across all sorts of territory. But, he adds, the mind is “really confined within very narrow limits.” After all is said and done, the contents of the mind can all be reduced to the materials given by the senses and experience, materials that Hume calls perceptions. The perceptions of the mind take two forms, which Hume distinguishes as impressions and ideas.

The Logic of Impressions and Ideas

Hume opens his Treatise by considering the ways in which a human being perceives the world around him. He says that perceptions are of two kinds: impressions, which are “all our sensations, passions, and emotions as they make their first appearance in the soul,” and ideas, which are the “faint images of these impressions in thinking and reasoning.” The impression of the Beethoven sonata comes as you are listening to the music. The idea of the sonata comes to you in the hours, days, and months afterward. Impressions or ideas may be either simple or complex.

All simple ideas come from simple impressions. Impressions and ideas make up the total content of the mind. The original stuff of thought, however, is called an impression, which is similar to John Locke's “sensation.” When you look at a cup of coffee, the shape of that cup, as well as the color and other qualities of it, and the aroma of the beverage “impress” themselves upon your organs of sense. So impressions are the first building blocks of knowledge.

From impressions come ideas. Ideas, in Hume's words, are copies of impressions. If you turn your eyes away from that cup of coffee, you can still have an idea of the cylinder-shape of the cup, the steam rising from the container, even though you are not presently having an impression of it. Without impressions, which are vivid when you first have them, there can be no ideas.

Matters of Fact and Relations of Ideas

Of the many philosophical insights contributed by Hume, perhaps none is greater than his division of knowledge into “matters of fact” and “relations of ideas.” According to Hume, if some object of reason is neither a matter of fact nor a relation of ideas, then it cannot count as knowledge at all. Because he thinks that all genuine knowledge is of one or the other kind, his revelation is known as “Hume's Fork.”

One of Hume's major objectives in the treatise is to show that:

All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas and Matters of Fact. Of the first kind are the sciences of Geometry, Algebra, and Arithmetic; and in short, every affirmation which is either intuitively or demonstratively certain…. Propositions of this kind are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe.

Matters of Fact, which are the second object of human reason, are not ascertained in the same manner; nor is our evidence of their truth, however great, of a like nature with the foregoing. The contrary of every matter of fact is still possible; because it can never imply a contradiction…. That the sun will not rise tomorrow is no less intelligible a proposition and implies no more contradiction than the affirmation that it will rise.

You know propositions like 3 × 5 = 15 or that the sum of the interior angles of parallel lines cut by a transversal equal 360 degrees “by the mere operation of thought.” Put another way, you know the truth of these claims a priori, or prior to experience. They are certainties and cannot be contradicted. You know matters of fact differently.

You can never be sure of matters of fact. To follow Hume's example, you can have impressions of the sun rising on seven consecutive days. Further investigation will tell you that it has always risen. So you may think you are entitled to say “I know for certain that the sun will rise tomorrow.” But you cannot know this. All that you know — and all that anyone knows — is that it has always risen. You cannot know that it will continue to rise. You only have impressions to this point in time, not beyond this point. In addition, there is no logical contradiction in your asserting that the sun will not rise tomorrow.

As Hume says, “The contrary of every mater of fact is still possible; because it can never imply a contradiction.” It is unlikely that the sun will not rise tomorrow, but it is still a possibility. Few philosophers have stated a truth as clearly, forcefully, or profoundly. As opposed to relations of ideas, which are known a priori, you know matters of fact a posteriori, or after experience.