Appendix 03: Chance and Spontaneity

Doug McManaman
Reproduced with Permission

Many people in the world of science will often employ terms like 'indeterminacy', 'chance', 'probability', etc., and using knowledge from the world of science they will often attempt to draw philosophical conclusions about the nature of reality as a whole.Claims typically made center around the idea that everything happens by chance, or everything is a result of probability, or that reality is fundamentally indeterminate, etc. But at the root of these claims is a vague and imprecise understanding of what these terms really mean.

Radioactivity, for example, is a statistical process. The half life of an element is defined as the time required for half of the atoms present in a given aggregate to decay. Take radon as an example. It has the half life of 3.825 days. What this means is that half of the radon atoms initially present will have decayed 3.825 days after one begins to observe them. We cannot determine statistically which of the atoms in the aggregate will decay; the fate of individual atoms is beyond our ability to know at this point.

But some people have a tendency to infer that since we cannot predict exactly which atoms will decay, the decay is a matter of chance. This conclusion, however, is unwarranted. It is true that if I were to say which atom was going to decay within the next 3.825 days, there is only a chance that I'd be correct. And if I turned out to be right, I would only be so by chance; for it is completely unpredictable which individual atom will decay. But one cannot conclude from this that the decay itself is 'by chance'.

The Meaning of Chance

In order to explain chance more thoroughly, I am going to offer a careful commentary on book two, chapters five and six of Aristotle's Physics, which treats the philosophical question of what it means for events to happen by chance. He writes:

First then we observe that some things always come to pass in the same way, and others for the most part.

In other words, John wakes up every morning at the same time and spends his morning in the same way, i.e., he goes for a half hour jog.

Aristotle continues:

It is clearly of neither of these that chance is said to be the cause, nor can the 'effect of chance' be identified with any of the things that come to pass by necessity and always, or for the most part.

Hence, it is not by chance that John gets up every morning at the crack of dawn and goes for a jog.

Already, from these first two lines of chapter five, we can begin to deal with the relationship between radioactive half life and chance. If it regularly comes to pass that half of the radon atoms in a given aggregate will decay after 3.825 days, we cannot say that their decay occurs by chance.

Aristotle continues:

...some events are for the sake of something, others not. Again, some of the former class are in accordance with deliberate intention, others not, but both are in the class of things which are for the sake of something. Hence it is clear that even among the things which are outside the necessary and the normal, there are some in connexion with which the phrase 'for the sake of something' is applicable. (Events that are for the sake of something include whatever may be done as a result of thought or of nature.)

John puts on his shoes 'for the sake of something', namely for the sake of jogging. He does not put on his shoes necessarily. It may not even be normal for John to put on his shoes and jog (perhaps it was a result of watching a special on TV). Even so, he acts 'for the sake of something'. And so what happens here does not happen by chance. It is only when things 'come to pass incidentally' that we say they have come to pass 'by chance'.

Aristotle writes:

For just as a thing is something either in virtue of itself or incidentally, so may it be a cause. For instance, the house building faculty is in virtue of itself the cause of a house, whereas the pale or the musical is the incidental cause.

The per se cause of my house is the skill (house building faculty) of the builder, which he acquired over many years of apprenticeship. It is not in virtue of his flute playing that my house was built. A flute player did indeed build my house, but the faculty of flute playing is not the per se cause, but an incidental cause. It is by chance that the carpenter who built my house is also a flute player. But it is not by chance that the carpenter who built my house owns a hammer, or is capable of reading blueprints. The joining of 'flute playing skill' and 'carpentry skill' is incidental, that is, by chance.

Now, we cannot conclude that since it is by chance that our carpenter is a flute player, his flute playing itself is an effect of chance. No, he may have wanted to be a flute player ever since he was a child, studied flute in high school and university. He became a flute player 'on purpose', so to speak. Perhaps he got interested in flute playing by chance, for instance, he was sent to the store to buy milk and decided to take a different route, upon which he stumbled upon a flute player playing his flute under a tree. But again, stumbling upon a flute player playing a flute under a tree is incidental to buying milk at the corner store. The intersection of the two events is 'by chance'.

Aristotle continues:

That which is per se cause of the effect is determinate, but the incidental cause is indeterminable, for the possible attributes of an individual are innumerable.

In other words, the cause of purchasing the milk can be determined (being sent to the store, walking towards it, and presenting the money, etc.). So too are we able to determine the cause of the house (the builder who has the faculty of building). But we cannot determine the incidental cause. It is not possible, for instance, to determine that he is a flute player by looking at the completed house. The incidental cause is indeterminate. And so Aristotle writes:

when a thing of this kind comes to pass among events which are for the sake of something, it is said to be spontaneous or by chance.

In other words, chance events come to pass among events which are not chance happenings, that is, events which are for the sake of something.

That is why it is not possible for every event to be a chance event. What is incidental can only be seen against the background of what is per se (through itself). If all was chance, no causes could be known or determined. If the causes of all the houses in the neighborhood were incidental causes, we could not determine the cause. For instance, consider that the cause of my house was a flute player having no building skills, my neighbor's a ballet dancer, John's house a truck driver not necessarily having any building skills, etc. The relationship between the effect and the cause would be unintelligible and indeterminate. Science, which is a knowledge of things through their proper causes, would be impossible.

Now, in order to say that the radon or plutonium atom decayed by chance, one would have to know the proper cause of an atom's decay. Only then would we be able to say that its decay was brought about by chance. We cannot, as was argued above, say its decay was a chance event because we cannot determine the cause. Our inability to determine the cause and 'chance' do have something in common, namely indeterminacy, that is, an inability on our part to determine the incidental cause in a chance event, and our inability to determine which atom will decay. The former belongs to the indeterminacy of chance events (the indeterminacy of incidental causes), the latter has nothing to do with incidental causes. These represent two different kinds of indeterminacy. And so we are jumping the gun, to put it mildly, when we conclude that the indeterminacy involved in knowing which atom will decay means that it decays 'by chance'.

Aristotle writes:

It is necessary, no doubt, that the causes of what comes to pass by chance be indefinite; and that is why chance is supposed to belong to the class of the indefinite and to be inscrutable to man.

This is why if all causes were reduced to incidental causes, science would be impossible. For what belongs to the class of the indefinite is inscrutable to man.

He continues: say that chance is a thing contrary to rule is correct.

Consider that the Latin word for 'rule' is regula, which means a straight length, a ruler, a pattern, model, or law, and from which are derived the words 'regular' or 'regularly'. It is not regular that builders are flute players, or that kids on their way to pick up milk become interested in flute playing. Again, if everything was a result of chance, there would be no forumulated laws (regula) of physics.

Aristotle distinguishes between 'chance' and 'spontaneity'. He limits the use of the word 'chance' to agents capable of deliberation. He writes:

...what is not capable of moral action cannot do anything by chance. Thus an inanimate thing or a lower animal or a child cannot do anything by chance, because it is incapable of deliberate intention; nor can 'good fortune' or 'ill fortune' be ascribed to them, except metaphorically,...The spontaneous on the other hand is found both in the lower animals and in many inanimate objects. We say, for example, that the horse came 'spontaneously', because, though his coming saved him, he did not come for the sake of safety.

Now if we reflect on the term 'spontaneous combustion', we see at once that he is right. The cloth soaked in oil bursts into flames not by chance, but spontaneously. There was a determinate cause of the change. No one set it on fire, and we were unable to determine when it would burst into flames. But we do not say that it happened by chance. Hence, Aristotle writes: is clear that events which (1) belong to the general class of things that may come to pass for the sake of something, (2) do not come to pass for the sake of what actually results, and (3) have an external cause, may be described by the phrase 'from spontaneity'.

Consider Aristotle's example of the horse that moves spontaneously. He moves not for the sake of avoiding the explosion that is about to take place, but because he moved and was saved as a result, we say that he was one lucky horse. He moved spontaneously. What came to pass did not come to pass for the sake of what actually resulted (the horse's life was saved). The oil soaked cloth burst into flames and burned down the shed. But the combustion did not come to pass for the sake of burning down the shed. Its combustion was spontaneous.

Aristotle uses the example of the stone that struck the man as he was walking under a bridge.

The stone did not fall for the purpose of striking him; therefore, it fell spontaneously, because it might have fallen by the action of an agent and for the purpose of striking.

The man will run and look to see if anyone is on the bridge looking down with a handful of rocks. If so, the rock did not fall spontaneously. But if there is no one around, and the man sees other loose rocks falling from the bridge's slow disintegration, he knows that the rock fell spontaneously.

We continue to use the word 'chance' with regard to situations like the one above. But it was not by chance that the rock fell. It was by chance that the rock hit the man. If a physics student was dropping stones in order to time their fall, and one of the stones or rocks hit the man under the bridge as he was passing under, we could then say that the rock hit the man by chance. Here we have two lines of action "for the sake of some end" which intersect 'by accident', that is, incidentally. But in the situation in which no person is on the bridge experimenting with rocks, and in which the rock falls spontaneously, there is a determinate reason why that rock fell at that particular time. No one but a trained engineer would be able to figure out the reason. But it was 'by chance' that it hit the man under the bridge, using chance analogously here.

Similarly, when we say the atom decayed by chance, it is only so according to our perspective, that is, in relation to us. It is only by chance that we would be able to determine which atom was about to decay. But there are no grounds for maintaining that there is no determinate reason why the atom decayed, which is what we would be saying were we to maintain that it really did decay by chance, and not merely from our perspective. In short, we might be able to predict, through probability, the number of deaths that are going to occur next year, but it in no way follows that my death (if I happen to be part of that number) was 'by chance'.

Aristotle concludes his chapter:

Spontaneity and chance are causes of effects which though they might result from intelligence or nature, have in fact been caused by something incidentally. Now since nothing which is incidental is prior to what is per se, it is clear that no incidental cause can be prior to a cause per se. Spontaneity and chance, therefore, are posterior to intelligence and nature. Hence, however true it may be that the heavens are due to spontaneity, it will still be true that intelligence and nature will be prior causes of this All and of many things in it besides.

In other words, it is not possible for chance and spontaneity to be the first cause or causes of the universe and all that happens therein.

As a further illustration of what is meant by chance, consider the following: Tom gets up every morning and opens the door of his house to get the paper. But on this day, Friday, May 18th, he didn't come to the door to get his paper. It's not that on every Friday, he doesn't come to the door to get his paper. No, he picks it up every day, including Fridays. It's just by chance that on this Friday, he did not pick it up. There is nothing in the nature of being a Friday that requires Tom to not pick up the paper. No, the fact is he got sick and couldn't get out of bed. It is "by chance" that it happens to be on a Friday. There is no connection between Tom not getting the paper and Fridays, or the 18th day of May. If on every May 18th, Tom would not come to the door to get his paper, then it would not be "by chance" that he didn't get the paper. May 18th is the anniversary of his father's death, so he does not go to the door, but has some routine he regularly engages in every year on this day. It was only by chance that May 18th fell on a Friday this year. There is nothing in the nature of being May 18th that requires that day to be a Friday.

Now, what is the probability of Tom not getting the paper in the morning due to illness? We need sample space. Once we got it, we can tell you the probability. It is highly probable that Tom will not get the paper on three occasions this year. Which day we do not know. After a year, it turns out that the mathematician was right. On three occasions, Tom did not come to get the paper due to illness. It turned out to be February 3rd, July 22nd, and December 5th.

Now, did Tom get sick by chance? What is the reason why his illness landed on February 3rd? The reason is that he went to a party on February 2nd, shook hands with one who had a bad cold, then Tom went to the table to the dish full of peanuts, grabbed a handful and ate them, the virus on his hands was transferred to the peanut and entered his body, and the next morning Tom is not feeling well. Now, probability cannot tell us this. It cannot tell us anything like this. Does that mean that this causal series was non-existent? No, it does not.

Why did he get sick on July 22nd? On July 21st, Tom was riding a street-car and was hanging on to the pole to keep himself from falling. But earlier a man with the flu was holding on to that pole. Tom picked up the virus, went home, and the next day woke up feeling sick. Why didn't his immune system destroy it? Because that night Tom had three glasses of wine, and alcohol suppresses your immune system temporarily. Hence, it was weakened.

Probability was not able to provide us with any kind of qualitative information like we have above. But that does not mean that there isn't any qualitative information to be had.

Now, we can say that it was 'by chance' that it happened to be February 3rd and July 22nd in this sense: there is nothing in this date (February 3rd) that entails illness. It has nothing to do with dates. So too, there is nothing about the date July 22nd that entails "flu". The meeting of "illness" and "July 22nd" was purely incidental. It had to do with where Tom was on this particular day and on what he was doing on this day, and on who he was in contact with. Now what some argue is that since probability has determined that there is a very high probability that Tom will not come to the door to get his paper in the morning due to illness on three separate occasions this year, Tom got sick on those particular days "by chance". But with regard to the actual days "Feb 3, July 22, Dec 5", Tom got sick by chance; for one does not get sick every single year on those days. One's sickness has nothing to do with those days as such. Nevertheless, one got sick for a determinate reason. One's getting sick is not chance.

Now, chance is involved here. For example, Tom goes to the Bills party, and Bill's party is a regular and yearly occurrence, but this year Dave came, and he has a bad cold. The intersection of "Dave having a cold" and "Bill's party" is by chance. Bill's party does not require somebody with a cold. It was by chance that someone showed up with a cold. But it was not by chance that people showed up. They were invited, and they chose to accept the invitation. Dave came because he broke up with his girlfriend and was lonely. So Dave did not come to the party by chance (but it was by chance that this party came two days after he broke up with his girlfriend).

So, Dave did not come to the party by chance, neither did Tom get a cold by chance. He got a cold on February 3rd by chance (insofar as the date February 3rd is concerned), but he did not get a cold by chance. It is not true, moreover, that Tom did not pick up his paper by chance. There was a definite reason. He was sick. But it was by chance that on Friday, he didn't get his paper. It just happened to fall on that day.

Probability leaves out a veritable universe of information. Predicting that Tom will be sick 3 times this year and will not get his paper on that morning, does not imply that everything that happens to bring that about was by chance or indeterminate. If all that information were closed off to us, it only means that it is closed off to us. That does not mean that there is nothing there for us to know. And that especially does not mean that everything that happens behind the scene (behind the scene of probability) is pure chance.

(Originally written in 2003, edited further in 2010)


Chapter: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26