http://star.tau.ac.il/~eshel/papers/bacterial wisdom.pdf
To refer to the genome as being self-aware is a very strong statement with far-reaching implications. The issue will be presented in a forthcoming publication [60]. I briefly describe here the main points needed for this presentation. Our logic and mathematics are based on the notion of a set composed of elements. Implicitly, the set is closed and static, the elements have a fixed identity (it does not change due to the fact that they are part of the set) and they either do not have internal structure or, if they do, it is not relevant to the definition of the set. The set is defined by an external observer, i.e., it is not a result of self-assembly of the elements under a common goal. The elements, being passive and of no structure, do not have any information about the set. The definition of sets leads to logical paradoxes (Russel-type, like the famous barber paradox) when we try to include a notion of self-reference. Russel and others have devoted much effort to construct formal axiomatic systems free of inherent logical paradoxes. Gödel's theorem [62,63] proved that they all have to be "incomplete", including the Principa Mathematica of Russell and Whitehead. It is important to emphasize that Gödel's theorem applies to closed systems which are also fixed in time. I propose that one has to take an entirely different approach and not start with the notion of sets of elements. I believe that here is exactly where the reductionist approach fails. We cannot reach self-awareness starting from passive elements, no matter how intricate their assembly. I propose to replace elements by agents, that possess internal structure, purpose and some level of self-interest, and whose identity is not fixed. The notion of a set is replaced by a cell, which refers to a collection of agents with a common goal and mutual dependence. It also implies that the system of agents is open, i.e., it exchanges energy and information with the environment. I argue that, in order for a cell of agents to be self-aware, it must have an advanced language, i.e., a language which permits self-reference to sentences and to its grammar. The language also enables the individual agents to have information about the entire system.