In Search of a New Philosophical Term

I am looking for a new philosophical term. A short (perhaps one, two or three syllable) word for an entity that exists but cannot be described completely by any single formal theory (or algorithm). I believe human beings, their societies and cultures are such entities, but I think many physical systems are such entities as well. The word “system” actually does not fit here because it has a connotation of something systematic, that is something that can be captured completely by some theory. I am thinking of physical entities for which the set of equations describing them cannot be solved except for special cases, i.e. where the mathematical description contains functions that are not turing-computable. In mathematics, such entities are known, entities for which it can be shown that every formal theory of them is incomplete. You may always be able to extend a given theory, but the resulting theory will be incomplete again. Such entities cannot be exhaustively described in terms of a formal theory. If physical “systems” of this kind exist, they cannot be perfectly simulated by any algorithm. They would generate new information (new with respect to any given theory). Something as simple as a set of three bodies moving around each other might already be such a system (it looks like the “three body problem” cannot be solved exactly. Kurt Ammon called (a certain kind of) such objects “creative systems” but I want to avoid the term “system”. Any suggestions? It might be a synthetic neologism, but should capture the idea in such a way that it has a chance to catch on.

Much of science is built on the tacit assumption that everything can be described in terms of formal theories. Everything is a “system” in this sense. But this is just a hypothesis and I think it is wrong. In mathematics, there are mathematical entities that are not completely formalizable (i.e. they have more true properties than can be derived in any single theory about them). If such things exists in mathematics, there is no a-priori reason they cannot exist in physical reality as well. What exists and what can be formalized is not necissarily the same. I want a short and crisp term for the unformalizable. The hypothesis that everything that exists is formalizable is built into our language. There is no short, simple word for the non-formalizable (yet). There is a large range of possibilites we cannot see because our language has been restricted.

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Vagueness and Being Human

The inherently creative nature of human beings means every exact description of what it means to be a human being is incomplete. As a result, any concept of the human that is attempting to be general must be vague. The human being can always develop, so it can develop out of the scope of any given description. So either  we get a partial exact description or one that seems to be general but where the concepts involved have incomplete definitions (vagueness being a form of incompleteness, on the level of the definitions of the concepts used).

Fixing ourselves or others into roles that are strictly and formally defined, is thus dehumanizing.

We are partial, we are vague. That is what makes us human.

The Language of Use

It is interesting to see to what extent the ideas of use, of exploitation, or resources are permeating our language. Our civilization is a parasite of our planet and it is about to destroy our biosphere and this civilization is permeating our language and our concepts and categories.

If we try to say that something has a value in itsself, we are using the concept of value that comes out of the language of use. If we say something is useless, we are using a term derived from the term “use”. The concept of “open domain” still has the idea of use inside it. We seem unable to speak or think of something that is just itself and not getting its value from what we can do with it, without using terms and concepts that come from this language of use.

We have to try to develop a totally different way of talking and thinking. We have to develop a language of the useless and valuable-in-itself that is not derived from the parasitic ontology of our growth culture, a language that does not view the useless as something negative.