The definition of life is a long standing open question in science. Many people have come to believe that the it is not possible to define life. At present there exist many non-overlapping meanings of 'life' (which is largely a question of semantics, see e.g. Figure 1). We suggest that a biological definition can make use of how the operator theory defines different types of organisms. Having defined all the organisms, life can be defined by referring in a generic way to certain properties of organisms.

The following papers offer more information:
Towards a hierarchical definition of life, the organism, and death.
Jagers op Akkerhuis G.A.J.M. (2010). Foundations of Science 15: 245-262.
Explaining the origin of life is not enough for a definition of life.
Jagers op Akkerhuis G.A.J.M. (2010). Foundations of Science 16: 327-329.
Bringing the definition of 'life' to closure.
Astrobiology Magazine 2010
The Role of Logic and Insight in the Search for a Definition of Life
Jagers op Akkerhuis G.A.J.M. (2012). J. Biomol Struct Dyn 29(4), 619-620 (2012).
Contributions of the Operator Hierarchy to the field of biologically driven mathematics and computation.
Jagers op Akkerhuis G.A.J.M. (2012). In: Integral Biomathics: Tracing the Road to Reality

Figure 1: Definition of life according to Joost Halbertsma (2005)

People hold many different viewpoints on the definition of life (e.g. Figure 1). Here we focus on life from a structural point of view.

The literature offers many definitions of life. One definition involves a list of seven fundamental principles, regarded as the pillars of life. Another demands reproduction and evolution (e.g. NASA). Yet another focuses on the presence of a container, of metabolism and a genetic program. Also popular is 'autopoiesis', which is defined as the capacity of an entity to remake all its constituents by itself (mostly acknowledging that energy rich compounds from the environment are required as input and waste as output). Additionally the concept of 'far from thermodynamic equilibrium' has been used.

As long as these definitions are based on a posteriori criteria, and generally show incomplete overlap, the concept of life will remain elusive. This elusiveness has frustrated some scientists so much, that they have started advocating that the endeavour of defining life should be given up and would do harm to science. They say the focus should be on understanding 'living processes'. This does not solve the problem, however, as long as it is not defined what 'living' processes are.

But even if one would insist that a definition of life would not be of practical use, the definition would still be of fundamental scientific interest, because it would prove that sientists are capable of expressing in detail a concept that is fundamental in their communication. So, lets regard the search for a definition of life as an interesting theoretical puzzle, as an intellectual challenge. If a definition has been found, we can we can still look for practical applications.

You have to comply with the criterion of life before you can be a living being

Presuming for the moment that a bacterium complies with the criteria of life, it is quite natural to consider its dynamics as living. The dynamics of a bacterium involve for example metabolism, motion, responses to chemical gradients, growth, and the production of an offspring when conditions allow.

But before one can decide whether the dynamics of an entity represent living, one must know whether the entity itself complies with the criteria of life. For example a flame and an alarm clock also show dynamics. These dynamics, however, can only be called living when it is certain that a flame and an alarm clock comply with the criteria of life (which as we will argue, they don't).

One can also ask the question the other way around: "do you have to be living to comply with the criteria of life?" Imagine a frozen bacterium or a frozen common tree frog (Rana sylvatica). Both can be frozen in a reversible way. This means that after thawing, the bacterium revives and the frog jumps again. The same holds for desiccated seeds. After moistening, a seed can hatch. This leads to the question whether it is necessary that you are dynamically active to comply with the criteria of life. Can it be that compliance with the criteria of life depends primarily on a specific kind of organisation an entity possesses? This begs the question of what organisation would be necessary and sufficient?

The operator hierarchy: A complexity ladder that allows a non-circular definition of organisms

Figure 2: Using the operator hierarchy as a ladder of system complexity. Elements on the ladder (the 'operators') with a complexity higher or equal to the bacterial cell are organisms.
In relation to the latter question it will be analysed here what structural organisation defines the criteria of life. It may seem a logical and easy solution to begin by suggesting that only organisms possess the required structural organisation.

However, a problem now emerges, because many dictionaries define an organism as a living being, while referring under 'living' to the activity of organisms. Such circular definitions are not desirable from a philosophical/logical point of view. To solve this circularity, an external frame of reference is needed for defining the organism concept.

It is quite special that the operator hierarchy offers such an external frame. The operator hierarchy demonstrates how lower level units construct higher level units by means of particular changes in organisation called closures. At every closure step, the lower type units create a next higher type unit, and so on. In this way, a stepwise ranking emerges. One can now use the levels of this ranking, which can be viewed as a kind of 'ladder', to define different system types.

A stringent definition of what is an organisms is now possible as follows: only those physical systems are called organisms that correspond with a closure type in the operator hierarchy that is of equal or higher complexity than the single celled operator type (represented e.g. by the bacteria).

One should keep in mind that at each level,the essence of the organisation of an organism at that level, depends on what is called its 'typical closure'. Typical closure combines a typical functional and a typical structural closure. The following offers examples of the typical closures of several organism types. The typical closure of bacteria involves their membrane (structural closure) and autocatalysis (functional closure), which in interaction maintain each other. The typical closure of an endosymbiont cell involves the interplay between its proper physiology and that of the internal compartment of the endosymbiont. A multicellular organism combines communication between cells via plasma connections with a common membrane. Finally, neural network organisms (called 'memons' in the context of the operator theory) have specifically connected neurons within an interface of sensors.

Definition of life

The above definition of what is an organism, offers a basis for finally defining the abstract criteria of life from the ground up. This is possible by assuming that life relates to the presence of the typical closure in all the operators that are considered 'organisms'. It should be noted that this definition excludes all the typical closures of an operator that is not an organism.

As was indicated above, the typical closure of a specific organism depends on its position in the operator hierarchy. And there is a minimum complexity involved: the typical closure of organisms should be equal or more complex than the typical closure defining the bacterial cell. We prefer not to include an upper limit, which decision implies that it is assumed that all higher level organisms, including technical neural network organisms (which may be called 'technisms'), also can be considered to comply with the criterion of life.

The line of reasoning we have proposed for defining life can be summarised as follows: 1. we start with a definition of all the operator types and their ranking, 2. we define which operator types relate to the concept of the organism, and 3. we define the criteria for life as a group property which refers to the presence of the typical closure in organisms (hereby excluding the typical closure of operators which are not organisms). As the result of this sequence of steps, a definition can be constructed from the ground up. It is important that the resulting definition is free of circular reasoning.

Consequence of the above definition:

The first cell offers insufficient information for defining life

The first cell(s) shows 'bacterial' complexity. Higher level closures are selectively present in higher level organisms. Accordingly, any definition that limits itself to properties that are unique to the first cell, will lack the width to deal with higher level organisms.


The definition of life proposed by the operator theory does not offer a single chemical recipe for abiogenesis (the emergence of the first cell from a chemical environment). The reason is that the definitition focuses on the typical closures, irrespective the kind of chemistry involved.

The focus on closures has the advantage, however, that it applies to all life forms, also those that in astrobiology are indicated as 'life as we don't know it'. And Darwin's theory of evolution lacks the means to incorporate abiogenesis, because a new organism always is born from a parent organism. This problem is solved by the present approach.

Definition of death

Upon losing its typical closure, an organism ceases to show its highest level of organisation. It is no longer the organism that it was; it has died away from the level of organisation it had.

This does not mean that its parts now necessarily and immediately die as well. Individual parts may actually continue to live as individual organisms at the direct lower level on the ladder. For example, and assuming special treatment, a multicellular plant can be 'dissolved' into separate cells, and these individual cells can be reared in a culture medium. For example a memon (the neural network organism) is dead when its typical neural closure has deteriorated. Normally neural death will be followed by the death of all the cells in the remaining body, because the neural network is responsible for the behavior required for feeding and breathing. Cultures of humane cancer cells show that parts of the human body can live on long after their 'owner' has died.

The proof of the pudding is in the eating

The question can be asked whether the definition of life that was suggested above is a practical tool for distinguishing entities that do represent life, from entities that don't represent life. A straightforward conclusion is that a system does never represent life, if it is not an operator, or if it is an operator but of a type that is lower on the complexity ladder than the bacterial cell type.

The above demands exclude a great many things from the discussion, such as all single molecules and complexes of molecules (as long as they are not an organism). In principle this excludes all the viruses. If there is confusion on this point, this may be because the discussion focuses on an entity which we call a virus, but which represents a highly simplified cell. Only if such an entity would self-maintain its membrane and autocatalytic set (and only then!), the operator theory would regard it as an organism, and as a representative of the abstract property of life.

Systems that are not organisms are excluded, regardless their complexity or dynamics. Examples include flames, the earth (Gaia hypothesis), local parts of the global ecosystem, populations, and colonies of all sorts (by definition a colony is a group of organisms, not an organism). Moreover, anything showing the required typical closure is an organism, and represents life, regardless whether it is active or inactive. It is no longer relevant whether an organism lacks the capacity for reproduction or replication, and whether it has phosphate or arsenic in its autocatalytic molecules (this knowledge would have prevented NASA from what is viewed here as a comminicative mishap in relation to Mono Lake).

Why reproduction is not important if one defines 'life' from the ground up

There exist definitions of life that demand reproduction. Clearly, since the first cell, all organisms are the result of various processes of offspring creation. Yet, there are two problems with the use of reproduction as a requirement for life. Firstly, the abstract property of life does not always depend on the capacity to reproduce. It is easy to give examples of organisms that are not capable of reproduction, but which do comply with the concept of life, such as old aged and/or sterilised organisms, many species crosses (ligers, mules), etc. Secondly, one does not always have to be an offspring to represent life: the first cells were formed as organisms without having parents.

Why evolution is not important if one defines 'life' from the ground up

There exist definitions of life that demand evolution. However, the operator theory would emphasise that once you show the right typical closure, you are an organism, and thus represent life. From this starting point, you may or may not show dynamics, growth, reproduction and, over generations, evolution, but whether or not you show all these 'secondary' properties will not interfere with the fact that you are an organism and represent life.