Logical Principles in Tension

Jul 11, 2011 at 6:54PM
Caleb Doxsey

Principle #1: Correlation does not imply Causation

It is not sufficient to merely offer correlation as an argument for causation. For example states in the south spend less money on education and have lower test scores than states in the northeast. You might conclude therefore that high spending causes high test scores.

The typical rebuttal here would be to offer up Washington DC as an example where spending is very high but scores are very low. But in reality you shouldn't even need to bring this up as an example. The conclusion is a fallacy from the get-go. Just because spending and high scores are correlated does not indicate a causal relationship. The causation could be an explanation (in one direction or the other) but there could also be some 3rd factor which causes both of them. Or they might just be entirely coincidental. Though in this case I would suggest that the system is far too complex to suggest a single cause.

Let's take another example. The rise in CO2 levels in the last 100 years is positively correlated with a rise in global temperature during that same time period. Therefore we are tempted to conclude that the rise in CO2 levels caused the rise in temperature. But this argument has the same problem.

But I also want to argue that these kinds of arguments are actually persuasive. We do, in fact, find them compelling. Why?

Principle #2: If it looks like a duck, swims like a duck, and quacks like a duck, then it probably is a duck.

As we grow and mature we gain a sense of how the world works. We learn what things in the world are me and what things are not me, what is dangerous and what is safe. We can discern types and relationships among objects. We develop classifications and names of things. And at some point we can even master our portion of the world we live in and bend it to our will.

But all of this begins from a very basic and simple set of general logical principles from which we deduce how the world works. We never really think too hard about this process (except when it sadly lets us down) but it undergirds almost everything we believe.

And I think that's why we think correlation implies causation. Looking at a duck-like animal and concluding that I am looking at a duck is an exercise in correlating attributes. Does it have a bill and webbed feet? Is it small and winged? Does it swim and fly and quack? Then its a duck isn't it?

In the same way if I see that your brother's been murdered, and I see you with the knife in your hand, you're the only one around, and I know you had just had an argument with him. Am I wrong to think that you killed him? All of this data is correlated with murder... but I'm suggesting that the correlation implies causation aren't I?

Isn't correlation the only way we know causation? I mean what does cause mean anyway?

I think what's missing in this picture is a theory. We suggest a hypothesis as an explanation of an event (that you with your knife caused your brother's death) and then supply correlative evidence as a means of strengthening the argument. Sure its logically fallacious. All inference is. Just because the sun came up yesterday is no proof that it will come up today. And in general we are pretty good at weighing evidence between different explanations. Between you having done it and him accidentally falling on the knife for example.

And that's where logic can really help. Not in forming perfect knowledge out of thin air. But in setting out clear the lines of inference within arguments. It's not enough to propose evidence. That evidence must be placed within the larger frame of a theory. And then that theory must be considered in relation to other competing theories.

Wikipedia suggests this an example of principle #1:

With a decrease in the number of pirates, there has been an increase in global warming over the same period. Therefore, global warming is caused by a lack of pirates.

This from pastafarianism as a parody of religious belief. (A reductio ad absurdum) But hopefully now we can see what is wrong with this parody. The believer is not necessarily claiming that because catastrophic events are happening God is displeased with us. Rather he is claiming that God is displeased with us and therefore we should expect natural calamities to befall us and lo and behold they do.

I don't think this is a very good argument (just on merely theoretical grounds alone for what it claims about God) but the point is that once taken as an abductive argument you can't just dismiss it for being deductively fallacious. Otherwise you're doomed to throw the baby out with the bath water and abolish almost anything we know. You've proven too much.

Instead what troubles me are two different problems:

  1. We have to make a decision. Most of life is full of things like this. Doing nothing is doing something. You can doubt everything, but you still have to live don't you? You ever doubt your doubting? Where does that leave you?
  2. How do we come up with the alternative explanations? If we only ever have one explanation available to us and it turns out there were hundreds of other explanations we didn't think of do you really suppose that we will make the right decisions? You can be the most logical person in the world but without knowledge you can't make good decisions. And none of us has perfect knowledge or, if we're honest, even good knowledge. We might know a lot about a small specialty or even a little about a lot of things, but who knows a lot about everything? Aren't we doomed to be wrong?

We just play at philosophy but what if we seriously considered the arguments we make and actually lived them out?