Incompleteness / Philosophy

Proteons: Types of Incompleteness


Proteons, by definition, are entities for which a complete and exact description is impossible. As a result, if you try to make a description of a proteon exact, you will have to sacrifice completeness: the description will end up being special and partial. On the other hand, if you try to make the description general, comprising the whole proteon, you will have to sacrifice exactness, ending up with a blurred picture. In a way, this vague or blurred description is also incomplete, leaving out some detail.

So when we are dealing with descriptions of proteons, exactness on one hand and generality on the other are mutually exclusive goals.

The incompleteness of a description can take several forms, for example (this list is not complete):

  • Gaps: you may describe some parts exactly, but some parts of the picture will be missing.
  • Idealizations (models, approximations): you may describe an entity exactly (as a system), but this description will only be an idealized or simplified model or approximation of the real thing (think of a map, for example, se below).
  • Faults and errors: the description might be partially wrong and might contain artifacts.
  • Inconsistencies: the description might contain inconsistencies and contradictions.
  • Vagueness – you get only a blurred picture of the whole thing because some or all of the concepts you are using will be incompletely defined and might have to be changed and adapted in different cases of their use.

In all of these cases, the proteon has more properties than can be derived from any single description of it.

We are familiar with this kind of situation from our everyday lives. Our everyday world, including ourselves, is a proteon. We cannot have complete and exact knowledge of it. We know something about it and we are learning something new all of the time.

Our description, or knowledge, of a proteon, is historically developing in time. It is incomplete in one way or another at any given time. In many cases, however, it will be possible to improve the description. But each improved version of the description of a proteon will be incomplete in some way again.

This is a problem, but normally it’s no problem.

(The picture is from It shows a section of a city map of Berlin from 1895. Several aspects of incompleteness can be illustrated by this example. I am just giving some hints here: for example, them map seems to be exact, but shows only an idealization, leaving out a lot of detail. It is drawn using a mix of words and a graphical language, the elements of which are vague in their meaning. For example, red areas represent areas with buildings, but if you look at actuall buildings in a city, buildings that would be shown like this on a map, you would notice that it is practically impossible to define the concepts of “building” or “house” exactly. So the elements of the “city map language” have a vague semantics. Moreover, most of the detail of the shape of the buildings is lost. Another aspect is that the object represented on the map changes with time (see here for a map of the same place 20 years earlier and here for a current map (the area was destroyed in WW II, so looks quite different today), so the map becomes obsolete (but is still usefull for historical purposes).

4 thoughts on “Proteons: Types of Incompleteness

  1. “This is a problem, but normally it’s no problem.”

    I think this is an important point. For us to understand anything, we have to build a mental model of it. That model will never be a complete copy of the real thing. (Except perhaps for mathematical concepts, but then what is mathematics but a modelling tool?) This is true at both the level of a manifest image (the world as it naturally appears to us) and the level of a scientific image. Both are models, and the models are all we ever get.

    All we can aspire to is to make the models ever more effective. The mechanisms we have to build manifest images evolved to be adequately predictive (usually). But with all models, the only real test we ever have is whether or not they’re predictive to at lease some level of usefulness.

  2. This post has given me several lines of thought to go over. I like the idea of something defined yet undefined. I think that is the definition of our world, to start with.

  3. This reminds me of a camera zooming in or out, capturing only what falls within its range, and blurring things out of its focus, unable to focus on both the foreground and background at the same time.

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