Figure 1. Systems view of biology. The borders (outlines surrounding boxes) and connecting lines indicate the level of derivation. Boxes with bold outlines (and bold connecting lines) are at the beginning of this particular order. Boxes with thin outlines (and thin connecting lines) indicate the second level, while boxes with dotted outlines and dotted connecting lines signify the third level (last in this diagram). Box with dashed outline and dashed arrows indicate a special role of hierarchical systems. This box should normally be at the second level (boxes with thin outlines and thin connecting lines), if it was not so special. The four main agencies, viz. (1) General system theory, (2) Rules of clear thinking, (3) Reductionism and (4) Holism, constitute the foundation for systems thinking in biology. Hierarchical systems appear to play a special role (indicated by the dashed arrows). Not only do they constitute one of two major aspects of clear thinking (the second aspect is logic) but also, at the same time, they are variants of general systems. In addition they can conform to both weak version of holism and an epistemological version of reductionism. Their conformity to causal reductionism (preference for upward causation and against downward causation) has also been prevalent in biological research to date.

Figure 2. Rosen–Hertz modeling relation. A general diagram of a modeling relation (MR) between a natural system N and a surrogate formal system F (see Rosen's Life Itself (Further Reading) for more detailed explanations). Arrow (step 1) represents an act of descriptive observation of natural system N that generally reflects casual entailments within N. Arrow 2 symbolizes the process of abstraction via which the observer encodes observations into symbols (such as numbers or words). Arrow 3 represents all acts of formal inference (permitted in F) such as derivation of conclusions from premises, solving equations or generating grammatically correct sentences from words. Arrow 4 stands for a mapping of formal constructs, such as formulae or theorems, back into the natural system. In other words, arrow 4 signifies an act of prediction about N made on the basis of its formal description generated within F. Formal system F is defined as a model of the natural system N if, and only if, the outcome of observation 1 within N is the same as a final combined outcome of formalization 2 followed by inference 3 and then followed by prediction 4 (i.e. the MR commutes).

Figure 3. Selected aspects of modeling complex systems: cascades of models. For simplicity, observations within left sides and inferences within right sides of modeling relations (MRs) are not shown. Encoding ‘lower-level’ systems into their models (‘higher level’) is indicated by broken thick arrows, while decoding from models to modeled systems is symbolized by unbroken arrows. These arrows indicate real encodings that we know about, while the thin broken arrows indicate encodings (decodings) whose existence we surmise but do not know in detail. (a) The ideal MR could occur only between the original natural system and the first model in the cascade of successive models. The real MR of type 1 occurs between a model at the level k of the cascade and the following model k + 1. We generally do not know the value of k, but in the complex system theory it is assumed that there is no limit on how high this value could be (no ultimate formal model.). (b) A realistic MR occurs again between the model k and k + 1. However, the entire situation is different because there exists the ultimate (original) natural system N as well as an ultimate formal model F (the ‘largest’ model) at the end of the cascade of models. This situation holds only for simple (even if complicated) mechanisms but is believed not to be a case for functionally complex systems.

Figure 4. Systems (relational) view of analogies and metaphors. The rectangles signify systems with internal entailment structure. Both causal and inferential entailments are taken into account. Arrows between rectangles symbolize encodings (broken) and decodings (unbroken) taking place between modeled systems and their models. (a) Natural systems (or models) N₁ and N₂ are analogous if they both are in a commuting modeling relation with the same formalism F. Thin broken arrows indicate direct encodings and decodings of unknown intensity that may or may not take place between N₁ and N₂ in addition to their firm connection through a formalism (model) F. (b) A kth model in the ith cascade does not decode into any previous model in the same cascade. Instead it decodes into a system that is modeled by a different cascade. In this sense model M_{i, k} is a metaphor. Further encodings and decodings of it are metaphors as well.