The definition of life is a long standing open question in science. Currently many people believe that life cannot be defined. Indeed life has many non-overlapping meanings. Of course the operator theory cannot solve such differences. Yet the OT can contribute, because it provides a stringent, and hierarchically constructed definition of what is an 'organism'. And based on the definition of the organism one can specify organismic life (O-life) and systemic life (S-life).

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
Learning from water: two complementary definitions of the concept of life
Jagers op Akkerhuis G.A.J.M. (2016). In: Evolution and transitions in complexity. The science of hierarchical organization in nature
Why on theoretical grounds it may be likely that ‘life’ exists throughout the universe
Jagers op Akkerhuis G.A.J.M. (2017). In: Habitability of the Universe before Earth, Volume 1

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

People hold many different opinions about the definition of life (e.g. Figure 1). Here we focus on life from a structural point of view, which implies that instead of 'is there life on this planet' we suggest to use 'are there organisms on this planet'

The literature offers many definitions of life. One definition suggests 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 definitions are based on the above criteria, the concept of life will remain elusive, because these criteria show incomplete overlap. 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 even be harmful for 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, it 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 communication in the life sciences. So, lets regard the search for a definition of life as an interesting theoretical puzzle, and 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 both show dynamics. These dynamics, however, can only be called living when it is certain that a flame and an alarm clock are organisms (which they are not).

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 really necessary that you are dynamically active to comply with the criteria of life. Maybe compliance with the criteria of life depends primarily on a specific kind of organisation? This begs the question of which kind of organisation would offer necessary and sufficient criteria?

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 structure an object needs to comply with the criteria for life. Here we start suggesting that only organisms possess the required organisation.

However, a problem now emerges, because many dictionaries define an organism as a living being, while defining 'living' as an 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.

The operator hierarchy offers such an external frame. In the operator theory a lower kind of operator creates the next higher kind, 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 the organism as follows: only those operators are organisms that possess a closure kind that in the operator hierarchy is of equal or higher than that of the cell (classically referred to as the prokaryota).

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 a membrane (structural closure) and autocatalysis (functional closure), which in interaction maintain each other. The typical closure of an endosymbiont cell involves the interplay between the physiology and containment of the internal compartment by the host. 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.

Two definitions of life: O-life and S-life

The above definition of what is an organism, offers a basis for defining the concept of life from the ground up. There are two options. The first option is that of organismic life, or O-life. O-life refers 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. While the organism concept knows a lower limit, 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 second option is that of systemic life, or S-life. S-life refers to the kind of system that emerges when two or more organisms interact amongst themseves and/or with their environment.

Consequence of the above two definitions:

The first cell offers insufficient information for defining O-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 fail 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, that it allows one to deal with any kind of organisms, also the organisms that in astrobiology are indicated as 'life as we don't know it' (which in fact means 'organisms as have not been observed on earth').

Definition of death

Upon losing its typical closure, an organism ceases to show its highest level of organisation. 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. 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. Also cultures of humane cancer cells show that parts of the human body can live on long after their 'owner' has died. When a memon (the neural network organism) is dead, this means that its typical neural closure is no longer present. Normally neural death will be followed by the death of all the cells in the remaining body, because of the neural networks responsibility for behavior involved in e.g. feeding and breathing.

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 not comply with the criteria for O-life if it is not an organism. The demand that life refers only to organisms excludes 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 viruses. In analogy with liquid water, any system in which organisms interact can be viewed as an example of S-life, such as the earth, and any local parts of the global ecosystem.

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 bastards (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 a relevant criterion if one defines 'life' from the ground up

There exist definitions of life that demand evolution. However, the operator theory advocates 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.