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.


Notes on Metaphysics and Ethics

Reality consists of many things.1) Scientists, especially physicists, are trying to arrive at a general theory of everything (GTE). We don’t have that yet and we might never find it, but let us suppose that there actually could be such a theory, a single set of formal expressions (e.g. equations) expressed in a formal language with an exactly defined semantics.

But what we would find is that the term “general theory of everything” is not really accurate. The theory, although theoretically complete, might be computationally incomplete. It might lead to calculations too complex to be practical, so we might need a number of simplified models in its place. Moreover, the laws of physics expressed in such a GTE would still not allow you to derive every fact that might be true in reality. You could not derive, from the laws of physics, something like the last name of your mother or the date when the USA declared their independence. So the GTE would not be a complete theory of reality. There is matter (or whatever) “goverened” in some sense by the laws described in the GTE (i.e. these laws are the invariants of reality, the statements that remain true through all transformations, the final symmetries of the world) and there are facts that you would have to feed into those laws to derive any specific statement. You may think of these facts as information stored in the world, in the configuration of matter. That information cannot be derived from the laws in the GTE. The GTE, by definition, only contains a finite amount of information, while the amount of information in the world is unlimited. In physical descriptions, the information appears in the form of “initial conditions”. The initial conditions of an experiment are never derived from the laws of physics (or they could be omitted from the description).

In practice, every observable system is open (i.e. new information, not derivable from the information it already contains, can enter it from the outside) and there seem to be physical processes that generate new information (think of a Geiger-Mueller counter registering events of radioactive decay – there is no way to predict when it will tick). Experimenters may construct closed systems by carefully shielding an experiment from outside influences, but such a system can be destroyed (i.e. changed by an outside influence) and that process of destruction is a normal physical process in the system, so actually, such closed systems are only temporarily closed.

Now, when we are talking about ethics, we are taking about humans and their societies and cultures. A GTE or any other axiomatic metaphysics will not be of any help here. The reason is that human beings and human societies, cultures, organizations and institutions can be thought of as systems that can store information. Moreover, this information, taken up from the environment (or from some random process inside the system) can influence the way the system behaves from then on and the way it processes further information. In that sense, humans and human societies are programmable. This means that you cannot create a complete theory of humans and their societies in the sense of a physical theory (and you could indeed question then whether it makes sense to call such a system a “system”, but that is another question). Instead of time-invariant laws you may think of such a system as having a “program”, something that acts law-like but can be changed. Human cultures can be viewed as “programs” in this sense, as something software-like. This “software” emerges in historical processes and is constantly changing and developing.

The information contained inside a human culture at any given time might contain information about the world. This knowledge about the world will enable people to expect or predict what is going to happen, but there will be always surprises since the world contains more information than can be derived from the knowledge present at a given time. The new information that could not be derived from the information existing before can be integrated into the “software”. Any formal description of the knowledge or culture before that amendment is incomplete with respect to the process of the integration of the new information and any process afterwards in which the amendment is used. So qualitatively new things can happen, where “qualitatively new” means that these events or processes could not have been derived inside the theory that existed before. As a result, as long as there is free space to store new information, the culture can change qualitatively and new kinds of phenomena can arise.

As a result, there is no single theoretical framework in which a complete and exact description of human cognition, society and culture (including science and technology) is possible. Consequently, the academic disciplines dealing with these areas of reality do not have any unique, simple, consistent framework. The attempt to apply the model of physics in such areas does not work in principle, because humans and cultures can move out of the scope of any single theory about them by incorporating new information (or, in another way of looking at it, by being creative).

With respect to ethics, this means that it appears very unlikely that a single, finite (axiomatic) theory of ethics can be produced that enables us to derive the “right” decision for arbitrary situations that might come up, because entirely new kinds of situations might arise (e.g. by the emergence of new technologies, new kinds of media, new possibilities in medicine, new ideas, etc.). If culture and society cannot be described within a single theoretical framework, then we should expect that ethical problems will be and will remain highly context-dependent, i.e. ethical and political theories will have to incorporate specific, situation- and case-dependent information in many cases. If you just apply a fixed law, you will not arrive at fitting answers for many problems. And there can be no fixed basis to decide what a fitting answer is. You have to remain creative and open. You have to (collectively) improvise. The methods and concepts we are using are vague, i.e. must be adapted in each single instance of their use. A complete formalization of moral, ethics and political theory is not possible. And a fixed, exact, unchanging foundation for ethics does not exist and cannot be created.

Moreover, any attempt to base society on a supposed fixed foundation implies that that foundation has to be enforced. Enforcing it will normally involve actions that most people would find unacceptable (think of inquisition, censorship, GULAG camps, holy wars etc.). Such a system will be “complete” only by suppressing or destroying those parts of reality (and society) that do not fit into it (i.e. that are forbidden to exist).

However, although there is nothing onto which we can put the foundation of ethics, some ethics is necessary. It is impossible to be a nihilist. The world is real, there are many of us, we somehow have to get along with each other and we are always inside a situation and time is proceeding. Ethics is not about academic problems but about real life. It is impossible not to act. Even if we do nothing in a given situation, that is an action.


1) This article was written as a reply to PeterJ’s reply to my comment on EJWinner’s article I regard it as a very preliminary formulation of this topic since I have not yet invested much thought into questions of ethics (although I might do so in the future), although I have put a lot of time into thinking about the (im-)possibility of complete descriptions the first part of this article is dealing with. Since this article is a quick draft, I decided to put it on the “Bubbling” blog rather than the Creativistic Philosophy blog

An interesting and insightful on-line-book about ethics and related topics is, (see especially As far as I have read it, it seems to be to a large extent compatible with my own (rather preliminary) thoughts about these topics.