coincidence, correlation, and causality

Two or more things happen. What do we say about them? More and more in our public discourse, I see signs of a hasty and lazy leap to the conclusion of a causal relationship when there is barely any reason to believe in even a correlation. Some definitions:

• Coincidence - two or more things happening. For my purposes, they don't even need to be said to happen at the same time.
  
• Correlation - two or more things whose occurrence is (are?) connected. It could be that one thing always happens when one or more other thing happens, or only if something else doesn't happen, or ...
• Causality - one or more thing whose occurrence is a direct result of one or more (other) thing.
  

It is the purview of science, or at least the scientific method, to establish what relationship exists, if any, among events. A tree falls on my car and my wife calls her mother. Coincidence, probably. A tree falls on my car and the wind blows. There could be a causal relationship there but there really isn't any basis, just from these two events, to conclude that there is one.

Establishing causality, as opposed to making it up, is hard. Often in science, particularly in physics, the scientist develops a model that fits some (hopefully, all) the data associated with a particular phenomenon or observation. A model is not the same as physical reality. It is useful precisely because it is a simplification of reality. If a model works, then it is often possible to derive causal relationships (mathematically) from the model. Even then, the validity of that causality is only conditional on the model. It is frequently the case that the prediction of causal relationships is what allows a model to be tested, and discarded. Without a model, that is, in reality, establishing a causal relationship as opposed to a correlation, is often impossible.

Politicians are, in my opinion, the worst offenders, because their intellectual laziness has the broadest effect. Every time a politician says "...because...", examine the foundation for the causal relationship. Mostly, there won't be any. Bush says "the economy is strong because of our tax cuts". Wrong on so many levels. First of all, I don't see much evidence that the economy is strong. But, that aside, how do we know anything about a causal relationship between the tax cuts and the strength (or weakness) of the economy? They're just two pieces of (varyingly believable) information.