How to Interpret the Notion of Chance?

We all think we’re familiar with the notion of ‘chance‘. But are we really? And if so, what are the consequences we should attach to our interpretation of chance? For instance, are chances purely descriptive in nature – in the sense that they refer only to past events – or do they have a predictive power that might be based upon some kind of underlying ‘natural’ force producing the structured data? And why would it even matter how to interpret chance? Let’s take a look behind the curtains of a probabilistic interpretation of chance, right into its philosophical dimensions.

On average, 12,3 per 100.000 inhabitants of the USA get killed in a traffic accident. Also, 45 percent of Canadian men are expected to develop some form of cancer at some point in their lives. So, what do you think about these data? First of all: does the fact that 12.3 out of 100.000 inhabits get killed in traffic tell you anything about the likelihood that you are going to be killed in traffic? I guess not. It is merely a descriptive notion invented to condense a large amount of data into an easy to read figure. It says nothing about your future, or anyone’s future for that matter. After all: you will either die in traffic or you will not, and you will either get cancer or you will not. At this point in your life you are absolutely clueless which way it will turn out to be. For all you know, it might be a 50-50 kind of situation.

Although this interpretation of chance might feel counter-intuitive, it seems a more reasonable position to take than believing you are expected to die in traffic with a probability of 12,3/100.000. You are after all a unique person and you don’t have 100.000 ways to go. You either go one way, or the other. It is only by adding huge amounts of data together that scientists can come to compressed figures (like chances), thereby describing what has happened in the past. But description does not equal prediction, and totality does not equal uniqueness.

What are the implications of this manner of looking at chance for our interpretation of science? What about the inferences scientists make based upon data, like the one about cancer I mentioned above? Are they making unjustified claims by posing that 45 percent of men are expected to die of cancer? I believe this might indeed be the case. In case scientists want to be fully justified in getting at their conclusions, they should do away with any claims regarding the likelihood of any event happening in the future. That seems to be the only manner for staying true for 100 percent to the data available.

But watch it: this is not to say that the scientific enterprise has lost its value. Science can still be the vehicle best-suited for gathering huge amounts of data about the world, and for presenting these data in such a way that we are able to get a decent glimpse of what is going on in the world around us. And that is where – I believe – the value of science resides: in the provision of data in an easy to understand manner. Not in the making of predictions, or inferences of any kind, as many scientists might happen to believe: just the presentation of data, a job which is difficult enough in itself.

You could say that I am not justified in make this claim. You could back up your argument by saying that a difference should be made between the case of ’45 percent of men are expected to get some form of cancer’ and ‘one specific man has a 45 percent chance of getting cancer’. Where the latter might be untrue, because of the fact that one will either get cancer or not, the former might be more justified. That is because it divides a group into units that will either get cancer or not. However, although this might be true to a certain extent, it still seems to be an unjustified manner to make predictions about the way the world will turn out to be. After all, considering 100 men to be the unit of selection is only to replace the level of the individual with the level of a group. On an even higher level of abstraction, one could consider the 100 men to be one unit, which subsequently would make the conclusions reached unjustified again.

Also, when choosing to make predictions on the level of the group, why does one choose the higher- instead instead of the lower level? Why wouldn’t it be okay to say that, instead of human beings, cells are the true units that either get cancer or not? That’s only a difference in the level of analysis, right?

So, next time you read somewhere that 99 of the 100 people fail in achieving something, interpret this for what it is: a description of what has happened in the past that can inform you in making the decision about what you should do right now. So don’t interpret this as meaning that you only have a one percent chance of being able to achieve a certain goal, because that would be a totally unjustified inference to make: an inference that goes way beyond what the data can support. And don’t consider a scientific fact to be a prediction about the future. Consider it for what it is: a useful description of the past, but no legitimate claim about the future.

But what do you think?

Written by Rob Graumans