Primitive objects and explanations
TL;DR: Every explanation derives facts from a set of primitives, therefore, before looking for any explanation, it is crucial to ask what primitives will you find acceptable
It seems to me that the fundamental questions that fascinate people the most are what-is questions. What is time? What is consciousness? What is reality? The sense is that these objects are difficult to define with the current scientific knowledge, which, in a sense, is just descriptive. We have equations for fundamental forces, can describe what happens, but any deeper explanation is out of bounds. Still, if we just knew more…
My sense is that the limits of our scientific explanations are the symptom of a more general problem that affects any type of logical or formal system. In any of these, the starting point is going to be a set of primitives and a set of suppositions on those primitives. The problem, then, is twofold: first, the primitives must be taken as is; second, the same primitives may not be useful in all cases.
Let us show this with an example. Suppose we ask: what is a table? An online dictionary defines it as “an article of furniture supported by one or more vertical legs and having a flat horizontal surface”. Now consider a drawing table. Its surface is inclined, not horizontal. Some tables have no legs, but are attached to the wall or suspended from the ceiling. They may even be retractable. Many of us have built a table with Lego at some point, and ended up with a toy, not an article of furniture. Conversely, suppose we construct a standard four legged table, but with gold and diamonds. It is unlikely that, for tax or custom purposes, it will simply be consided a piece of furniture. Or suppose we are in the middle of moving, no table is unpacked so we put our sandwiches and drinks on a box. Is the box a table?
The example shows that even defining something trivial, like a table, is not trivial at all. Are we describing a shape? A function? A category of pieces of furniture? What elements are critical to consider something a table, what are optional and what minimum combination is necessary? It’s complicated because it depends on the situation, on the function the definition is supposed to serve to reach a particular goal. There is no single idea of what a table must be, and it is likely that whatever definition you come up with, you are going to create exceptions. In my experience, the people that tend to be more aware of this are lawyers and comedians.
Now suppose we have agreement on the context and the goal. A definition for something is still going to be made in terms of something else. What is an article of furniture? What is a leg? If we try to define these, we are going to bump into the same problems. In fact, in some context, we might be better off simply taking table as a primitive. That is, which objects we take as primitive, and therefore are the basis of our explanations, is a choice and will depend on context. In our work on the Assumptions of Physics, for example, experimental tests play a fundamental role but do not even appear in the formal framework. The primitive in the formal system is the experimentally verifiable statement, which is a statement that can be found to be true experimentally. The experimental test itself is cumbersome to characterize formally and, in the end, only adds problems. We tried. So the definition of anything will depend on the goal, both in terms of the type of definition and the choice of primitives.
Now, suppose we want to ask: what is time? Can we provide a physical, mechanistic explanation in terms of more fundamental constituents? What can physics tell us about it? Well, physics is an experimental science. So we should ask: what is the relationship between time and experiments? Can we make experiments that tell us what time is? Or is time a precondition to be able to do physics? Can we perform experiments without the notion of time, so that we have primitives that are not defined in terms of time, and define time on top of those? It seems to me that any experiment we make is at a particular time. In fact, the precision of our definition of time defines also the precision of our experiments. Therefore, we first need to define what time is before we can do any physics, write any law. For example, Newton’s first law states “Every object perseveres in its state of rest, or of uniform motion in a right line.” Uniform motion means constant velocity, which requires time. If time is a precondition for physics, then it must be a primitive in physics. Therefore time cannot be defined by physics, because physics is defined by time.
Whether you agree or not with the previous assessment is not important. The important thing is that you must make, implicitly or explicitly, such an assessment. If you want to know what something is, how it can be explained in terms of other things, first you have to decide in what terms, or you are going to be forever stuck with an unsatisfactory answer.