On the notion of chance
and its application in natural sciences

Grzegorz Bugajak
Cardinal Stefan Wyszynski University in Warsaw
gbugajak@uksw.edu.pl

Abstract
The notion of chance plays an important role in some philosophical analyses and interpretations of scientific theories. The most obvious examples of that are the theories of evolution and quantum mechanics. This notion, however seems to be notoriously vague. Its application in such analyses, more often than not refers to its common-sense understanding, which, by definition, cannot be sufficient when it comes to sound philosophical interpretations of scientific achievements.
The paper attempts at formulating a ‘typology of chance’. It distinguishes eight different meanings of this notion. Those meanings can be found in classical philosophical accounts of chance, in the common usage of this term, or form logical possibilities of its understanding.
Subsequently, the paper points to those forms of the notion in question which may and may not be properly applied to scientific theories and ideas – given usual characteristics of natural sciences. It also shows – by the examples of particular theories mentioned above – which of the distinguished forms of the notion of chance are actually applicable in the context of these theories.

Introduction
In common speech, chance or a random event is usually described as an event that happened without our previous knowledge of what is going to occur or without us aiming at it to happen. When somebody says: ‘Yesterday in a supermarket I happened to meet my friend from high school’ (in other words: ‘I met him by chance’), he relates to the fact, that neither he had known that a friend was going to be there, nor they intended to meet. In other contexts – more theoretical perhaps – many believe that there are events in this world that occur without being triggered by any cause, and call them chance. In those simple examples we can see two important features of the notion of ‘chance’. It is defined in negative terms, as the lack of something – a cause or an aim (plan). We shall call them causeless chance and aimless chance. Also, the word ‘chance’ may refer to the lack of real influences in the world or to the lack of somebody’s knowledge or intentions. This can be called objective and subjective (meaning of the notion of) chance respectively. This gives us, in principle, four different categories of chance. As we shall see, each of them can be further distinguished as absolute and relative.

1. Causeless chance
Many accounts of chance refer to the notion of cause and describe random events as lacking any cause – at least any apparent instances of anterior phenomena that would lead to given effect. We call this type of the category in question causeless chance.
When it is maintained that the events in question lack any real, causal influences, we have objective causeless chance. On the other hand, when some antecedent phenomena leading to a given event may exist, but we do not recognize them, our notion of chance expresses then the lack of knowledge about possibly existing causes and therefore may be called subjective causeless chance.
1.1. Objective causeless chance
Such understanding of chance can be found for instance in Boethius’ works, where chance is seen as a result of many causes that coincide in one ‘thing’. Similar intuitions expresses also E. Nagel for whom chance is an event that occurs at the intersection of two independent chains of causes. 
This understanding of chance appears indeed – what is important from the point of view of this paper – in the analyses of evolutionary processes where chance may be also seen as a ‘side–effect’ of the interference of efficient causes aiming independently at their own goals. What is obvious, however, those accounts do not deny causal influences. On the contrary – events that fall under this category are causally triggered, hence they do not represent ‘pure’ chance understood as a notion opposite to the notion of cause. A chance event may be regarded as such, because in searching for a cause we do not see the whole chain of previous events. Moreover, such an event may be a result of many efficient causes that act independently and are not ordered with regard to each other. Chance in this context does not have its own cause which direct effect it would be, but assumes many causes, not related in their acting.
Such a meaning of chance is, for example, attributed to evolutionary processes where the latter are called random. In fact – as we could see – it refers rather to a special form of causal influences then to ‘real’ chance. To be in accordance with quite common way of speaking, we may call this category a relative chance (objective causeless relative chance). We need to remember, however, that such a name may be misleading, since it calls a ‘chance’ what is in fact a form of causal influence.
An account of chance described above is different from objective causeless absolute chance. This category is employed by those who maintain that there are events which are deprived of any causal relations at all. There are discussions whether this category is or is not empty. Some think that everyday experience, as well as philosophical principle of sufficient reason proves that the occurrence of such events is impossible. If it were possible, the world would be purely factual – we could only register certain phenomena, but not understand them – and, consequently, theoretical knowledge would be impossible. Obviously, one does not have to share philosophical assumptions that lay behind this reasoning and accept a possibility of the existence of beings or occurrences of phenomena that would not be causally related to anything else. It seems, however, that this discussion cannot be conclusive and a position one takes in this dispute depends on a kind of ‘philosophical creed’.
As for an important question, if this notion of chance can be applied to any discoveries in natural sciences, the answer has to be negative. Even if ‘purely’ random events can occur (objective causeless absolute chance is possible), science can never recognize them. This is so, because of the very nature of scientific knowledge: in natural sciences (as opposed here to formal ones) with their inductive methodology, it is possible to give a statement an appearance of verisimilitude, but, strictly speaking, never to prove it. So, if certain event appears to be causeless, it does not follow that it is necessarily so. In general terms, no absolute statement can be achieved in natural sciences, which follows both from meta–theoretical analysis of scientific research and from historical practice of science. For those reasons, the controversy over the category of objective causeless absolute chance will remain purely philosophical, and the category itself – useless in the analyses and interpretations of scientific discoveries.
1.2. Subjective causeless chance
This type of chance is called here ‘subjective’ because it does not refer to actual occurrences in the real world but to the knowledge of their causal relations.
Such understanding of the notion of chance can be found, for example, in Spinoza’s works, for whom the chance is the same with the unknown. If we have no knowledge of the circumstances that determine the occurrence of some event, we call this event chance. For some authors, our lack of knowledge about hypothetical causal influences on an event in question may be temporal: we just don’t know anything about those supposed influences at the time when the event occurs or – more generally – our knowledge obtained until now does not allow us to attribute such influences to the event in question. For others, our lack of knowledge is fundamental: not only actually we are unable to see any causal relations, but we cannot have such knowledge in principle. The latter form of such understanding of subjective causeless chance can therefore be called absolute, whereas the former – relative. 

2. Aimless chance
Quite often a random event is defined in opposition to a goal: if something is aimless, it is called chance. When the lack of a goal is claimed with regard to natural phenomena, outside of the context of knowledge or will, this aimless chance can be called objective. In case of the lack of conscious intention or project we have subjective aimless chance.
2.1. Objective aimless chance
According to some classic accounts of random events, a chance is an event which is not a result of any natural direction towards itself, an event, which is not ‘guided’ by any goal. In Aristotelian language, this type of chance would mean the lack of a “final cause”. Although in Aristotelian metaphysics, the final cause was one of the four fundamental factors (causes) shaping every being, and in our perspective we speak about events, not beings, it seems that – mutatis mutandis – this classical category can be used here to explain the meaning of objective aimless chance: this type of chance can be regarded as an event lacking its final cause.
In more modern language – and especially in the context of natural sciences – this ‘natural direction towards some goal’, lack of which is regarded as chance, can be seen as laws of nature which in a sense ‘direct’ phenomena that occur in the world. If this identification is justified, our type of chance here would mean an occurrence of certain phenomenon without any laws of nature guiding this event.
There are at least two reasons for which this category of chance cannot be properly applied in scientific consideration. By their very nature, natural sciences discover (or ‘impose’ – depending on the opinions about both – preferred characteristics of scientific enterprise and of the world itself) regularities in the world – the laws of nature. If they didn’t exist, science would be impossible. So, even if objective aimless chance events do occur, science is incapable of discovering them as such, because by definition, they would have to be beyond scientific perspective. Moreover, with regard to given event, science can point to the laws of nature which make this event possible, or confess ignorance. A statement ‘there is no laws of nature behind this particular event’ can be only relative (related to current state of knowledge) and never absolute. As it was mentioned above – no ‘absolute’ statement seems to be possible within the scope of science, and this general rule applies also to the type of chance described here. Its characteristics allow us to call it aimless objective absolute chance.
This is different for aimless objective relative chance, which indeed is considered in science, what can be traced in many examples, including those coming from evolutionary research.
The category of chance in question refers to the notion of ‘natural direction’ towards a goal (which we identified with the laws of nature). Whereas absolute form of this category requires that no laws at all are in action (there is no ‘natural direction’ in the occurrence of an event), its relative form points to existing laws, which are, however, directed towards goals different than actually achieved. There are many instances of this type of chance pointed to by natural sciences. The process of evolution, as it is described in contemporary theories, may serve here as an example.
Among most important evolutionary factors there are genetic changeability, genetic drift and isolation. All of them are chance in character and become a basis for claims that the whole process of evolution are governed by chance. This is true, as long as the notion of chance is properly understood in this context. And these are all instances of objective aimless relative chance.
One of the driving forces of genetic changeability are mutations. These come about due to various physical and chemical factors called mutagens. Among most active physical mutagens there are ultraviolet radiation and various forms of ionizing radiation (X and ). Currently we know also thousands of chemical mutagens, which can modify various components of DNA, acting directly or indirectly – through cell metabolic processes. The laws of nature that govern various forms of radiation and their effects, as well as the way chemical substances influence each other (here: chemical mutagens influence DNA) are certainly not directed towards such particular effects like mutations. Physical and chemical factors have their ‘natural direction’ – they act according to appropriate laws of nature – however, being a mutagenic agent is not their ‘aim’. From this point of view, mutations occur ‘unwillingly’, somehow ‘by the way’ and – together with the whole phenomenon of genetic changeability – fall into the category of objective aimless relative chance.
2.2. Subjective aimless chance
Some accounts of chance refer this notion to consciously chosen goals, intentions, or predictions. This conscious (or intentional) factor makes this type of chance category a subjective one. For example, Thomas Aquinas defined chance as a cause acting beyond an intention. In Boethius’ account we also find a subjective reference, where chance is regarded as unpredicted result of coinciding causes. Subjective aimless chance is an event that is unexpected, because it is not a result of any planned action.
Undoubtedly, this type of the category of chance cannot be used with regard to the pure results of natural sciences, because they, when dealing with natural phenomena, do not consider such subjective factors as conscious plans or predictions.
Subjective character of this type of chance is usually relative. Certain event is unpredicted, unwanted, unexpected or unplanned by somebody who makes predictions and plans, or consciously wants or expects something to happen. Acts of will or knowledge are related to given subject of those acts and, what follows, random character of some events is also related to this subject. This is different from the last form of the category of chance: absolute subjective aimless chance.
An event would fall into this category, if the lack of conscious plans, predictions or goals were absolute, that is, if there were no possible subject of the relevant acts of will or knowledge. However, even if there are such events, which is logically possible, natural sciences cannot decide, with regard to any individual event, that it has such a character. This is so basically for the same reasons, for which any absolute form of the chance category is inapplicable in purely scientific context. In this case: the lack of recognition of a conscious plan or will behind given phenomena does not imply that such a plan or will is non-existent. And science (together, perhaps, with all forms of natural knowledge) – again here – can confess its ignorance, or rather admit its boundaries: ‘I know that I don’t know’.

Conclusion
The typology of the notion of chance offered here do not form a logical division of its meaning. We considered some classical philosophical accounts of this notion as well as the most common ways of using this term, but the eight distinguished categories may well not be exhaustive. It seems, however, that they sufficiently determine those meanings of chance that are applicable to philosophical interpretations of scientific theories, and distinguishes them from those that are not. Our eight categories are not mutually exclusive either. For example, the same event may be regarded both – as unplanned (aimless subjective chance, relative – when we consider plans of a given subject, or absolute – when we maintain that there is no such a subject), and as lacking any causal influences (causeless objective absolute chance).
We showed that out of eight distinguished meanings of the notion of chance, only three seem to be applicable in philosophical interpretations of scientific theories. These are causeless objective relative chance (which in fact is not chance at all), aimless objective relative chance and (marginally) aimless subjective relative chance. Given this typology it becomes much more clear what is meant by such statements as ‘quantum world is governed by chance’, or ‘evolution is a process where chance plays a significant role’. Philosophical discussions concerning the theories mentioned (and perhaps also other theories in natural sciences) may obviously benefit from such clarification, by offering a tool to avoid some misunderstandings which stem from ambiguity of the notion of ‘chance’.