David Hume pushed the principles of Locke and Berkeley to their logical conclusions. Hume's most important work is Treatise on Human Nature. He also enlarged upon certain portions of this work in other publications such as An Inquiry Concerning the Principles of Morals and the Dialogues concerning Natural Religion.
Hume spoke of matters of fact (synthetic ideas) and relations of ideas (analytic ideas). Hume contended that our knowledge of "facts" about the world is based on experience (That "Some birds are yellow" as we will see in one moment). These types of claims about the world are what Hume called "matters of fact." On the other hand, judgments, statements, or propositions that are true or false by definition are not fact but they are "relations of ideas" (That "all bachelors are unmarried" as we will also see in one moment).
Hume posited that propositions used by rationalists as models for knowledge, such as "a whole is always greater than any one of its parts" and "triangles have three sides" are simply matters of definition. This type of "knowledge" does not provide us with real knowledge other than the meaning of certain terms. As long s we understand the meaning of a certain term we can analyze it and we can do so without learning anything about whether there is anything in the world that the term describes. Relations of ideas statements that identify characteristics already implicit in the meaning of a concept or object are called analytic statements. Examples of this type of statement are "all bodies take up some space" or "bachelors are unmarried males". True analytic statements are those in which the predicate is contained within the subject. In the statement "bachelors are unmarried" the term "unmarried" is the predicate and the term "bachelors" is the subject. If you try to deny this proposition or any proposition like it you contradict yourself.
Synthetic propositions stand in contrast to analytic propositions. Synthetic propositions are those in which the predicate is not part of the meaning of definition of a thing. For example, to say that some birds are yellow is to say something about birds, which are not contained within the definition of what it is that makes a bird a bird. In an analytic statement while "unmarriedness" (so to speak) is the very element that defines a "bachelor" in a synthetic statement "yellowness" is not part of that which defines a bird. By saying that a bird is yellow we add a new bit of information, which we could not know simply by knowing that something is a bird. In other words we appeal to experience. In this sense we combine or synthesize two ideas. One of those ideas, "yellow", is not already implicit within the meaning of the other, "bird." In other words, synthetic propositions are statements in which the predicate IS NOT contained within the subject and if we deny such a "matter of fact" proposition, by saying for example "It is not the case that some birds are yellow", we do not necessarily contradict ourselves.
Hume maintains that there is an important distinction to be made between analytic statements and synthetic statements and the difference between a priori statements and a posteriori statements. The difference between a priori statements and a posteriori statements lies within the matter of whether you have to rely on experience to determine whether the proposition is true or false. In other words, the distinction between a priori and a posteriori statements is experience centered. According to Hume, this is not the case with the distinction between analytic statements and synthetic statements. The distinction between these two lies is whether or not what you can say about a thing is already contained in the meaning of the thing. Since analytic judgments can be made in most cases without having to appeal to experience, the happen to be a priori judgments as well and in most cases, synthetic statements happen to be a posteriori judgments.
Therefore, every meaningful statement is known as true or false either by definition, in which case, it tells us nothing about the world, or by experience. For example, propositions such as "thre is a God" or there is a spiritual self" are not true by definition not are they based on sense experience. Therefore, they are meaningless statements.
Hume also explores the relationship of Cause and Effect. He asks what it means to say that we know that events have causes. When we try to trace such knowledge back to experience, we discover that all we mean by saying that A causes B is that A occurs before b, A seems to be near B in space and time, and in our experience events like a seem to be followed with some regularity by events like B. However Hume argues that we do not experience a "necessary" connection between A and B. We have a natural inclination to assume that A caused B and desire to assume this to be true, and there may be a high probability that A did cause B, but all we can really "know" is that A and B occurred together in close proximity of time.
In addition, Hume takes his conclusions and applies them to the issue of the continuity of self. According to Hume, we are dependent upon memories to assure us of the continuity of our "self" into the past. But we have no sense datum to provide us with the assurance of the existence of self in the past and memories not a legitimate means of knowledge. Consequently we can only know what we are presently experiencing and even that is questionable or doubtful since this might be illusion. Consequently, in the end we are compelled to doubt whether knowledge is possible at all and we are left only with skepticism.
