This is my second post in a series that discusses science, its significance, and the manner in which scientific knowledge is derived. It discusses the manner in which scientific theories and laws are formed, and the fundamental flaw of inductive logic. For the rest of the series of posts, look here.
Science yields two types of fruit: the scientific theory, and the scientific law. The difference between the two is oft misunderstood, though I trust the concise definition presented in the article will clear up such confusion.
In philosophy, one comes up with an idea via rational thought, and subjects it to the scrutiny of his mind and those of his peers. In science, theories and laws are built in reference to experimental data, and the patterns discovered therein. Only hypotheses, which are never held as remotely accurate, are composed before the experimental data is derived, and whether they hold or not is not important to the scientific process.
Because both theories and laws are built with inductive logic, they can never be proven for every single instance. To demonstrate this, I will present a thought experiment.
Imagine that before us stood a black box. The box is perfectly regular, and adorned with one red button, and one light bulb. Curious, I press the red button. Immediately, the light bulb begins to glow. The bulb glows until I let go of the button. I do this several times, and we note that, every time, the exact same thing happened; while the button was pressed, the light bulb was on.
We will note ‘pressing the button’ was, essentially, an experiment, albeit a simple one. Let’s imagine that I continued to perform this experiment an arbitrary, but finite number of times. Every time, we noted the same thing; while the button was pressed, the light bulb was on. Using inductive logic, we can reasonably assume that, as long as the button is pressed, the light bulb will be on.
This, essentially, is a scientific law. In fact, this is the only way in which a scientific law can be discovered. However, note that we have never proven that it truly applies in all cases, only in some of them. In fact, no matter the number of times the experiment was performed, it’s very possible that if the button is pressed a still greater number of times, the light bulb will no longer turn on. It’s quite easy to design such a box.
Another comparison could be made with mathematics. Unlike in science, inductive logic is not acceptable in mathematics (what we call induction does not rely on this type of reasoning). Imagine we had a function, f(x). For a given, finite set A, every element a of A yields f(a) = 0. Those of us who are versed in mathematics, know that no matter how big set A is, we could never conclude that the function f(x) is, in fact, f(x) = 0.
Thus, the logic by which we assemble our theories and laws is necessarily flawed, because of its inductive nature. In fact, it is more accurate to view a scientific law as a pattern, observed in great amounts of experimental evidence, rather than some principle by which the universe operates. Thus, obtaining a perfect body of knowledge that describes the universe is impossible not only in practice, but also in theory.
But the problem is even deeper than that. Let’s think back to the box analogy again. Let’s embrace the notion of scientific proof, and formulate the scientific law, that pressing the red button will always cause the light bulb to turn on. To explain this law, we can try to compose a scientific theory.
We’ll use Occam’s razor and our basic knowledge of electricity to claim that the inside the box contains a simple electric circuit, where the button acts as a switch. None of our experiments -- that is, the presses of the button -- preclude this theory, and it explains the mechanism of the box fairly well. In fact, we could even make the additional assumption that the box will, in all cases, work as though it contained such a circuit.
However, once we open the box, we could see all sorts of things inside it. While the idea of an electrical circuit seems simple to us, it may not have been the way in which the box was designed. I’m sure many of us could think of a myriad of exotic ways to design a box that matches the specification.
However, if we take the box to be analogous to a physical phenomenon, the act of opening the box is denied to us. In fact, we do not even know if such a thing is possible, or if the physical phenomenon actually has a mechanism that governs it. As such, our only way to study such a physical phenomenon is via empirical data, gathered by performing experiments. Here we can see the necessary evil in inductive logic; it is simply the only means available.
