The Trade-Off between Explicitness and Generality

indeterminacy principle

Human thinking and human culture seems to be infinitely complex. All attempts to create a unified and exact theory of human thinking and culture seem to have failed.

In Ammon 1987, Kurt Ammon introduces a hypothesis about creative systems he calls the “indeterminacy principle”, a term inspired by the principle of quantum mechanics that bears the same name. In a nutshell, Ammon’s hypothesis states that the more general a theory about creative systems gets, the less explicit it will be and vice versa.

If we presume that the concept of “creative systems” can be applied to human beings (which I suppose it can), we can take this as a statement about theories of human cognition, i.e. human thought processes, and, as a consequence, as a statement about descriptions of human culture. If it applies to humans then general and exact theories about humans and their culture are impossible.

A very specific thought process can be described very explicitly, giving an exact account of each step of a line of thought, say, and the exact bits of knowledge that were involved. We might describe it in terms of a formal theory, akin to a calculation or logical derivation. However, if we pass on to more general descriptions, the theory will become less explicit.

If we retain high explicitness and try to get the larger picture, we will end up with a theory with gaps. We will use descriptions that can be thought of as exact but incomplete. They only describe some cases. There are gaps and to fill those gaps, we have to add additional information that cannot be derived from what we have already. The concepts used might be completely defined and exact but the description is incomplete.

If we increase generality, this can mean that we have to use vague concepts in our description, concepts that have to be interpreted, i.e. complemented with additional specifications when we apply them to special cases. This means that such concepts do not have a complete definition. The description might be complete in a superficial way, but it is blurred.

Parts of a general description may also remain implicit. They might be exact, in a similar sense as, say, a mathematical equation that has a certain solution but where  we might not know how to calculate it and where a general method to do so might even not be possible. To make the description explicit, i.e. calculate solutions, we would then need additional information again, e.g. a certain new method of calculation that enables us to calculate solutions for certain cases.

In all these cases, the more general description of creative processes is incomplete in some way. The creative system can be thought of as being able to move out of the scope of any theory we create about it. A complete, i.e. general and at the same time explicit description of the whole is not possible. It would require an infinite amount of information.

You can think of this situation metaphorically by imagining a picture of which you initially see only a very small section. This you can see completely in high resolution. However, as you zoom out of the picture and more of it comes into view, parts of it blur, or holes and gaps appear. Whatever you do to fill the gaps and increase the image’s sharpness, imperfections will remain. Even if you manage to get a high definition picture of everything without any gaps, as soon as you zoom further out you will notice there are gaps and blurred parts again. Something like this is happening if we try to describe cognitive or cultural processes. Some parts of the description will remain implicit or vague or will be missing.

We could also envision this situation in the graphical form given in the picture above, (taken from Ammon 1987, page 82. Let’s assume we had a method to measure the generality and the explicitness of descriptions in some way. That might not be possible in the strict sense but it helps to understand what this trade-off between generality and explicitness means. If you imagine a coordinate system where one axis represents the generality of descriptions on a scale between 0 and 1 and the other axis represents the explicitness of descriptions, again as a value between 0 and 1, there would be a line that cannot be crossed (see image). There is a reachable area and a “forbidden zone”.

Referring to this, Ammon writes (Ammon 1987, page 81):

Thus, the triangle marked by diagonal lines cannot be reached by theories about creative processes. This means that there is no explicit and general theory about creative processes, i.e. a theory whose explicitness and generality are equal to one. Furthermore, it means the explicitness of rather general theories and the generality of rather explicit theories about creative processes are very low.

Along the diagonal line lie descriptions that are as general as their degree of explicitness allows and as explicit as their degree of generality allows.  Our common sense ideas about psychology and culture that we employ in everyday life might be somewhere within that triangle, nearer to the left lower corner.

This graphical representation of the trade-off between generality and explicitness might itself belong somewhere near the upper left corner because it might be impossible to make the notion of a numeric measure or either generality or explicitness of descriptions explicit itself, so this is not a very exact description. However, it is useful as a visualization of this basic property of creativity: that all descriptions of it are, in some way, incomplete.


Ammon 1987:

Ammon, Kurt: “The Automatic Developments of Concepts and Methods“, Doctoral Dissertation, University of Hamburg, 1987



  1. Reblogged this on The Asifoscope and commented:
    A new article on my philosophy blog.
    Descriptions of Creative processes, cannot be general and explicit at the same time, so every description of creatiity is incomplete in some way. Either you get an explicit, exact, but incomplete description of special cases or a blurred or very implicit picture of the whole. This applies, I think, to theories about human mental processes and, as a result, to descriptions of human culture.

  2. Sometimes on gets a less blurred view in the morning :-). I decided to make a few changes to the article published yesterday. I have removed the paragraph:
    “Lack of explicitness might also mean that we use descriptions that can be thought of as exact but incomplete. They only describe some cases. There are gaps and to fill those gaps, we have to add additional information that cannot be derived from what we have already. The concepts used might be completely defined but the description is incomplete.”
    From the originally published article and replaced it with:
    “If we retain high explicitness and try to get the larger picture, we will end up with a theory with gaps. We will use descriptions that can be thought of as exact but incomplete. They only describe some cases. There are gaps and to fill those gaps, we have to add additional information that cannot be derived from what we have already. The concepts used might be completely defined and exact but the description is incomplete.”
    I have moved this paragraph then in front of the paragraph about vagueness and modified the begining of the first sentence in that paragraph to fit the paragraphs together again.

  3. I like having the holes and gaps. Maybe I don’t want to be totally understood?

    1. They are unavoidable and indeed nothing is wrong with them 🙂
      Algorithms can be totally understood, humans cannot. As humans, we are creative, so we can always add new pieces to ourselves. By doing so, we can move out of any previous understanding of ourselves. That is what makes us human. Complete understanding would mean predictability.
      Who would follow your blog if you were predictable? It would be boring. I am looking forward to your next posting. 🙂

  4. This is very interesting. I’ve been thinking about social structures versus experience via Bernard Tschumi, “The Architectural Paradox” and relating it to creative writing (I’m an MFA Writing & Poetics candidate about to enter thesis). The gaps between the structures themselves [reason] and the body that moves through them [sensual experience; implicit memory]. Do you know where I can find a copy of Ammon’s dissertation? Thank you!

    1. You might be interested in some other articles on this blog as well as some on my other blog 🙂

  5. Looking for the dissertation in the search system of my local library here in Cologne (which means: in Germany) yields several libraries that have it. Sorry, that URL is a bit long (see below). I don’t know where copies exist in other countries, but probably you can search for it online. Ask for help in the next university library available to you. You might have to order it through international interlibrary loan. That might take some time, but should be possible.
    Maybe Kurt Ammon still has some copies and can send you one. I think he also still has it in electronic form. He might publish it online, but I don’t know if and when. You can contact Kurt Ammon on If you cannot find it at all, you can contact me again. I might find the time to make some copies for you since I have my own copy. But that might take some time as well.
    Ammon’s work might indeed be relevant for your topic. However, he develops his ideas in the context of mathematics and programming. The larger part of the dissertation describes an experimental computer program that analyzes mathematical proofs and derives new proof methods from that, i.e. simple programs that can be used to find mathematical proofs. The dissertation thus contains a lot of program code and math stuff and the theory is described in that context and in the style of mathematical publications, with definitions, theorems and proofs. So this is not easy to read if you are not used to such stuff. However, there are some sections that are less formal and might indeed contain insights that are interesting for you.
    Ammon is a mathematician. I am a computer scientist and I am used to his work because I have been proofreading his publications for the past 25 years or so (including the dissertation). One of the things I am trying here on this blog is to make these ideas more accessible for philosophy in general and for areas of application outside mathematics.
    In case you get your own copy and find that it is no longer useful for you, please donate it to the next university library, maybe to the philosophy department. 🙂

  6. […] The trade-of between efficiency and generality is a special case of (or another way of expressing) the trade of between explicitness/exactness and generality described in another article. A result of it is that there is a fundamental limit to how intelligent a system can become. (see…). […]

  7. […] relies on specialization, a super-intelligence is impossible in principle. Just like there is a trade-off between expliciteness and generality, there is also a trade-off between generality and efficiency, in principle (for the same reason, […]

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

  9. […] and algorithmic mode of thinking. However, I consider logical reasoning as part of reason. But exactness and generality are mutually exclusive and if we restrict ourselves to exact thinking alone, we would be losing a large part of the […]

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