Regular readers of my blog may have notice that there are some recurring topics, especially the concepts of creativity, incompleteness, and as-if-constructions. What do I mean by these terms, and how are they connected?
A lot of philosophy is very abstract and, as a result, hard to understand. Normally, things become easier to understand when looking at examples. So let me take an example from one of my early blog articles, the example of a car, and try to explain my ideas in a way understandable (I hope) without having a degree in philosophy.
In this article, I am going to explore some aspects of the concepts of incompleteness and as-if-constructions. (How this is connected to creativity, as I understand it, will be explored in later articles, as well as the connection of creativity and the more fundamental type of incompleteness encountered in mathematics and computer science.)
Further concepts explored on the way in this article, among others are “implementation”, “existence”, “emulation” and “underlying systems”. But before things are becoming too abstract, let us look at the example.
So look at your car (if you have one). It is a car as long as you can drive it. But what if it breaks down, rusts or is destroyed in a crash, what if it is pressed into a lump of metal in a scrap press and molten in a furnace?
You may think of your car as two things: a physical system, and a conceptual entity. Let us first look at the physical system:
There is lump of matter of different kinds: metal, glass, plastic, oil, rubber and other things. Driving or standing around, but also rusting, crashing, or melting in a steel furnace are very normal processes for this physical system. If you heat it up to high enough temperatures, it might even evaporate (e.g. if you explode an atomic bomb just besides it, but you should not try that in your garage). Obviously, after those events that destroy the car, it is no longer a car but still the same physical system. So the physical system is more than the car.
If you describe it as a car, that thing you can control by steering wheel and pedals and that you can use to drive somewhere, that description of it must be incomplete. It does not comprise, for example, what is happening if you put it into a scrap press and squeeze it into a lump of scrap. But for the physical system, these are normal processes.
So the description of the car as a car is incomplete. You can destroy the car and turn it into something no longer describable as a car. There are processes not covered by the description as a car (like rusting, wear and tear) that turn it into something that can still be re-paired, brought back, but beyond some limit, this becomes more and more costly and finally, you would no longer denote it as a car. More generally, anything (read “car”) that can be destroyed (read: “squeezed into a lump in a scrap press”) has more properties than are covered by its description as what it is (read: “a car”). A complete description must also comprise all other states after its destruction and before its construction.
So let us now look at the car as a conceptual entity. In a sense, it exists only in your imagination. There is a conceptual description of what you, as a user, recognize as your car, and there is a conceptual description of the car as seen by the engineers designing it. At first, the engineer has this in his mind, or in his computer in the design and simulation software he is using. When the car is being built, a real physical system is shaped in such a way that it now behaves as the envisioned car. The conceptual car is “implemented” in the physical system. The physical system, let us call it the “underlying system”, “emulates” the conceptual car, i.e. it behaves as if it where the car, but only until the car is “destroyed”. Destruction means that the system moves out of that part of the set of all its possible states (the “state-space”) where the description as a car can be applied.
For an object to “exist” could then be defined as “having an implementation in a physical system”. As we have seen, the underlying system, behaving as if it were a car, has more properties and possible states than the emulated system. The real car can rust and fall apart; the ideal car does not do that. The emulated system is thus an as-if-construction. We have it in mind and we can treat the real, underlying system as a car until it (the car, not the underlying system) is destroyed. The car is a projection of a conceptual structure onto a physical system emulating that conceptual structure.
The physical system has more properties than are covered by the conceptual description as a car. On the other hand, the conceptual description may contain properties not actually implemented by the real physical system. For example, you might think that the tank of your car is full. Then, half an hour later, on the highway, you find out that this is not so when your car suddenly stops. So there might be a mismatch between the conceptual structure (the as-if-construction) and the actual physical implementation. When your car breaks down on the way, nothing is wrong with the physical system, it just moved out of being a car, but the underlying system did what it had to do (e.g. some part broke because a crack (a property not described by the car-theory projected into the system) widened and the part broke (“failed” from the point of view of the as-if-construction). That the “car” broke down is your problem, not the problem of the underlying system. It is not the physical system that brakes down, it is the conceptual system, because it no longer agrees with reality.
As-if-constructions, this example shows, are fictions and these fictions might or might not agree with reality or fit more or less well and only for a limited time or under limiting conditions. If your interface with reality is narrow, you can keep up wrong aspects of fictions because you don’t test them. You might live in a world of imagined objects. For example, if you never watch the news and you never leave your village, you might continue thinking that the world is flat. If your car with the nearly empty tank is just standing in the garage and not being used, you might continue thinking that the tank is full. If you use something a lot and in different ways, i.e. if your interface with reality is wider, you will run against the flaws of these as-if-constructions and they collapse.
(The picture is from http://commons.wikimedia.org/wiki/File:Schrottauto.jpg)