Hume, like Spinoza and Leibniz, Locke and Berkeley is a follower of Descartes' way of ideas. Like his predecessors, Hume distinguishes between ideas of sense and ideas of reflection, as well as simple and complex ideas. Hume, however, makes a distinction between ideas and impressions which is somewhat new, at least it is new terminology. Hume claims that ideas in memory and the imagination are derived from impressions. You might start by thinking of these as sense impressions. Impressions are more lively than ideas. Thus an impression of the sun looked at directly without filters, will cause me serious discomfort. The corresponding idea will not. There may well be something to this distinction, but this way of making it is problematic. Beyond impressions of sense there are also impressions from our minds. Every complex idea is made up of simple ideas, and with a few minor exceptions, Hume claims that every simple idea can be traced back to an antecedent impression.
If there are going to be simple and basic principles at the root of the science of man, what are they going to be? Hume holds that there are three relations which the mind uses to associate ideas together: resemblance, contiguity and cause and effect. Resemblance means that one thing is similar to another. Contiguity means that one thing is next to another in space or time. Cause and effect means that one thing is a cause of the other, or an effect of the other. So, if I say 'child', you might think 'parent' or 'mother' -- a causal relationship. If I say 'beach,' you might think 'ocean' or 'sunshine' (if, like me you are from Southern California) or 'windy and rocky' -- relations of contiguity. If I say 'Canada', you might think 'Mexico' -- a relation of resemblance, both being states neighboring the United States. It is very unlikely that all relations fit into one or another of these three categories of relations, or even that all relations could be constructed out of combinations of them. Still, it is important to understand that Hume has such simple and basic principles for his science of man.
Hume has a procedure for determining if ideas are legitimate or illegitimate.
It seems a proposition, which will not admit of much dispute, that all our ideas are nothing but copies of our impressions, or, in other words, that it is impossible for us to think of anything, which we have not antecedently felt, either by our external or internal senses. I have endeavoured to explain and prove this proposition, and have expressed my hopes, that, by a proper application of it, men may reach a greater clearness and precision in philosophical reasonings, than what they have hitherto been able to attain. Complex ideas may, perhaps, be well known by definition, which is nothing but an enumeration of those parts or simple ideas, that compose them. But when we have pushed up definitions to the most simple ideas, and find still some ambiguity and obscurity; what resource are we then possessed of?So, on Hume's account, any complex idea should be divisible into simple ideas, and any simple idea should be traceable back to an antecedent impression. So, if you have doubts about the legitimacy of an idea, you can determine if the idea is legitimate by determining what its parts are and tracing those parts back to their antecedent impressions. If you can do this the idea is a legitimate one. If you cannot do this, that is you cannot find an antecedent impression for the idea, it is very like illegitimate -- a sophistry or an illusion. Hume, as we shall see, uses his microscope in examining ideas of causality -- to search for the antecedent impression of such ideas as 'necessary connection' 'power' and 'force.'
By what invention can we throw light upon these ideas, and render them altogether precise and determinate to our intellectual view? Produce the impressions or original sentiments, from which the ideas are copied. These impressions are all strong and sensible. They admit not of ambiguity. They are not only placed in a full light themselves, but may throw light on their correspondent ideas, which lie in obscurity. And by this means, we may, perhaps, attain a new microscope or species of optics, by which, in the moral sciences, the most minute, and most simple ideas may be so enlarged as to fall readily under our apprehension, and be equally known with the grossest and most sensible ideas, that can be the object of our enquiry.
Hume distinguishes two different kinds of truths. The first are relations among ideas. These are mathematical ideas such as squares have four sides, and the three angles of a triangle are equal to two right angles. Such relations among ideas are necessary. But they also tell us nothing about the world. While we may know with certainty that the square on the side of a right triangle which subtends the right angle is equal to the squares on the other two sides, that does not tell us if there are any right triangles in the world. One mark of this kind of truth is that its negation is a contradiction. This follows from the fact that relations among ideas are necessary. So, it is possible to demonstrate that the propostion '2 + 2 does not equal 4' (the negation of '2 + 2 = 4') when combined with the definitions of numbers and other relevant propositons, leads to a contradiction. The second kind of truths are matters of fact. In contrast to relations among ideas, matters of fact are contingent, and hence their negations are not contradictions. Matters of facts provide us with genuine information about the world. Here are some examples of matters of fact: "John has a cold." "Australia is a large contintent lying in the Pacific Ocean in the Southern Hemisphere north of Antartica." "There are still a few depleted salmon runs in the rivers of the Pacific Northwest." "Some roses are not red." "NATO is bombing Serbia." Hume divides all propositions into one or another of these categories. This division into two is Hume's fork. Both the fork and the microscope play important parts in Hume's investigation into the nature of causality and the problem of induction.