Hume begins by arguing for the validity of empiricism, the premise that all of our knowledge is based on our experiences, and using this method to examine several philosophical concepts. First, he demonstrates that all of our complex ideas are formed out of simpler ideas, which were themselves formed on the basis of impressions we received through our senses. Therefore, ideas are not fundamentally different from experiences. Second, Hume defines “matters of fact” as matters that must be experienced, not reasoned out or arrived at instinctually. Based on these two claims, Hume attacks metaphysical systems used to prove the existence of God, the soul, divine creation, and other such ideas. Since we have no experience of any of these things and cannot receive a direct impression of them, we have no real reason to believe that they are true.
Hume systematically applies the idea that ideas and facts come from experience in order to analyze the concepts of space, time, and mathematics. If we have no experience of a concept, such as the size of the universe, that concept cannot be meaningful. Hume insists that neither our ideas nor our impressions are infinitely divisible. If we continued to try to break them down ad infinitum, we would eventually arrive at a level too small for us to perceive or grasp conceptually. Since we have no experience of infinite divisibility, the idea that things or ideas are infinitely divisible is meaningless. Mathematics, however, is a system of pure relations of ideas, and so it retains its value even though we cannot directly experience its phenomena. Many of its principles do not hold in matters of fact, but it is the only realm of knowledge in which perfect certainty is possible anyway.
Hume introduces two of his three tools of philosophical inquiry, the “microscope” and the “razor.” The microscope is the principle that to understand an idea we must first break it down into the various simple ideas that make it up. If any of these simple ideas is still difficult to understand, we must isolate it and reenact the impression that gave rise to it. The razor is the principle that if any term cannot be proven to arise from an idea that can be broken into simpler ideas ready for analysis, then that term has no meaning. Hume uses his razor principle to devalue abstract concepts pertaining to religion and metaphysics.
Despite his apparent hostility to abstract ideas of a metaphysical nature, Hume does not deem all abstract ideas worthless. Hume argues that the mind naturally forms associations between ideas from impressions that are similar in space and time. In the mind, a general term becomes associated with further specific instances of those similar impressions and comes to stand for all of them. This process explains why we can visualize particular events that we may not have actually experienced, based on their association with those events that we have experienced.
Hume’s third philosophical tool is the “fork,” the principle that truths can be divided into two kinds. The first kind of truth deals with relations of ideas, such as true statements in mathematics—for example, that the sum of the angles in a triangle equals 180 degrees. These kinds of truth are necessary—once they’ve been proven, they stay proven. The second kind of truth deals is in matters of fact, which concerns things that exist in the world.
The theories Hume develops in the Treatise have their foundations in the writings of John Locke and George Berkeley, and Hume is associated with these two men as the third in the series of great British empiricists. Like Hume, Locke denied the existence of innate ideas, dividing the sources of our ideas into two categories: those derived from sensation through the use of our sense organs and those derived from reflection through our own mental processes. Hume makes use of Locke’s distinction in his own theory of ideas, though he alters the terminology. For Hume, sensations and reflections both fall under the term impressions, while he reserves the term ideas for the results of mental processes such as imagination and memory. Hume’s discussion of abstract ideas rests on his acceptance of Berkeley’s claim that the idea we have of a general term always springs from a specific experience, though used in a general way. Hume praised this explanation but further clarified how a general term could stand for several similar, but specific, experiences.