Why probabilities matter

In real life, it’s pretty rare (some would even say utterly impossible) to be sure of anything at all, like knowing it’s going to rain in one hour, that a conservative president is going to be elected, that you will be happily married in two years and so on and so forth.

We all recognize that it is only meaningful to speak of the probability or likelihood of each of these events.

The question of how to interpret their profound nature (ontoloy) is however, far from being an easy one.

I will use the basic proposition: if I roll the dice, there is a probability of 1/6 I will get a 3 in order to illustrate the two main interpretation of the probability concept out there.

1. Frequentism

According to this interpretation, the probability of an event equals its frequency if it is repeated an infinite number of times. If you roll a dice a great number of time, the frequency of the event (that is the number of 3s divided by the total number of rollings) will converge towards 1/6.

Mathematically it is a well defined concept and in many cases it can be relatively easily approximated. One of the main difficulties is that it apparently fails to account for the likelihood of unique situations, such as that (as far as we know in 2013) the Republicans are going to win the next American elections.

This brings us to the next popular interpretation of probability.

2. Bayesianism

For Bayesians, probabilities are degrees of belief and each degree of belief is a probability.

My degree of belief that the dice will fall onto 3 is 1/6.

But what is then a „degree of belief“? It is a psychological mind state which is correlated with a certain readiness for action.

According to many proponents of Bayenianism, degrees of belief are objective in so far that every rational creature disposing of a set of information would have exactly the same.

While such a claim is largely defensible for many situations such as the rolling of dices, the spread of a disaease or the results of the next elections, there are cases where it does not seem to make any sense at all.

Take for exampling the young Isaac Newton who was considering his newly developed theory of universal gravitation. What value should his degree of belief have taken on BEFORE he had begun to consider the first data of the real world?

And what would it mean ontologically to say that we have a degree of belief of 60% that the theory is true? What is the relation (in that particular situation) between the intensity of certain brain processes and the objective reality?

Such considerations have led other Bayesians to give up objectivity and define „degrees of belief“ as subjective states of mind, which might however be objectively constrained in many situations.

Another criticism of (strong) Bayesianism is that it ties the concept of probability to the belief of intelligent creatures. Yet it is clear that even in an universe lacking conscious beings, the probability of the decay of an atom and of more fundamental quantum processes would still exist and be meaningful.

For completeness, I should mention the propensity interpretation of Karl Popper who viewed the likelihood of an event as an intrinsic tendency of a physical system to tend towards a certain state of affairs.

So this was my completely unbiased (pun intended!) views on probabilities.

When debating (and fighting!) each other, theists and atheists tend to take their own epistemology (theory of knowledge) as granted.

This often leads to fruitless and idle discussions.

This is why I want to take the time to examine how we can know, what it means to know, before discussing what we can (and cannot) know.

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6 thoughts on “Why probabilities matter”

1. Andy Schueler says:

“When debating (and fighting!) each other, theists and atheists tend to take their own epistemology (theory of knowledge) as granted.

This often leads to fruitless and idle discussions.”
– In principle, I totally agree with this. Although I do think that, overall, there is much more agreement about epistemology than there is disagreement. I think the way we evaluate eyewitness accounts might be one of the points where there is a lot of disagreement. But beside that, is there really that much we disagree about when it comes to epistemology?

• Andy Schueler says:

There are always differences in the details, but overall, I think there is much more agreement than disagreement.
Re OR – yeah, we already talked about this once, and again, Occam´s razor doesn´t actually say that simpler things are more likely to be true ;-).
Re degrees of belief – I would totally agree that we don´t treat them like probabilities. In many way, most importantly because the degrees of confidence we can feel are not fine-grained. There is no feeling for “being 55.792% certain”, it´s just not meaningful to put a number on our degrees of confidence – a seven point scale or even just a five point scale from “absolutely uncertain” over “reasonably certain” to “absolutely certain” reflects our feelings much better.

• Alright but you should not view yourself as a Bayesian if that is the case.

2. […] I illustrated how this plays out in a previous post. […]

3. […] highly recommand all my reader to first read my two other posts on the concept of probability before reading what […]