In his Enquiry Concerning Human Understanding David Hume investigates the processes by which we form concepts of the world and critically examines the validity and the limits of such understanding. One of the concepts that he examines in particular is our claims about causal relations. When I say that fire causes smoke, what am I actually saying and what can I actually guarantee by my claim?

The first thing that Hume says is that we must have experience in order to know anything about the world. He uses the example of Adam, seeing the world for the first time. What would he have known about the world, other than what his senses perceived? Could he have known that water will drown a man, just from looking at it? Could he have known what foods were edible, or even that objects could have the property of being edible or inedible? The conclusion he arrives at is that Adam would have known next to nothing about the world because there is no way to reason about an object without experiencing it and its effects in different contexts. Reason cannot act without experience.1

Since we must use experience to inform us about the world, anytime I wish to reason about things I must essentially reason from my experience of what the world is like. For example when a person says that fire causes smoke, what he is really doing is examining his experience and finding that fire and smoke have always been conjoined. Whenever two events, states, or objects are conjoined in our experience, we tend to say that one causes the other. What Hume finds very interesting in this proposition is the fact that when the person sees this causal relation, there is in fact nothing that forces it to be the case. Technically, all the person can do is say "in my experience in the past, fire has always been conjoined with smoke". There is nothing inherent in the experiences that says that fire and smoke always will be together. In other words, there is no way to claim necessary connection. In essence when I make a causal claim what I am saying is:

  1. In the past, x has been associated with y
  2. Therefore, x will be associated with y in the future
There seems to be a step missing here, something that ties the two steps together. Hume says that what we are actually doing is implicitly assuming that the future will follow the way the past has been going, so that things that have happened in the past are likely to occur in a similar way in the future. If we assume that then we can reasonably conclude that x and y will occur together in the future. So now the reasoning looks like this:
  1. In the past, x has been associated with y
  2. The future follows in an orderly way from the past (the future resembles the past)
  3. Therefore, x will be associated with y in the future
(The last statement can be reformulated as "x implies y")

Now that we have a framework with which to understand our reasoning, Hume begins to question the validity of making the assumption in the first place. It is possible to reason about it? Can we show that it is correct? Perhaps one way is to put the assumption into effect and see whether or not it is effective. If we reason about the world this way, do we make accurate descriptions and predictions? As it turns out, there is no way to prove this assumption because any experimental proof that one might bring relies on the assumption that if there is proof of something in the past, it will work in the future. We rely on the same assumption that we are trying to prove, and we end up begging the question. The next approach that one might take is to reason about this through the sole use of logic, trying to escape the trap that empirical induction leads us into. The trouble is that there is nothing inherent about the assumption that we can reason in an a priori form about. It could be true, or it may not be, but there is nothing in virtue of its form that one can decide about. Thus, we are left with an assumption that cannot be proved empirically, and therefore our reasoning about causal relations is not based on logic.

What Hume has done is shown that our reasoning about causal connection has no logical necessity and ultimately has no rational basis. Always present in our judgments is an unprovable assumption. This is not to say that we shouldn't go on reasoning about the world the way we have been, just that there is a limit to the powers of causal claims.

1(For more information on why this is the case, see Matters-of-Fact and Relations of Ideas)