# The induction problem

The induction problem is, to me, the most amusing axiom with which one can characterize science. If research suffers from it, it is scientific. If it doesn't then it's not.

So what is the induction problem? Put succinctly it is simply the problem that you can never confirm an a-specific hypothesis, no matter how much evidence you gather that supports it. This may sound weird, but really it makes absolutely crystal clear sense. As an example, imagine we have formed the a-specific hypothesis that "swans are white". The induction problem says that we cannot prove this.

The naive course of action would be to just look at a couple of swans, notice they're all white, and consider the matter closed " "they are". However, this answer is not scientific: you cannot just decide that all swans are white just by looking at a few. If we look at one swan and see it is white, then we know that the one we saw is white. If we then look at another swan and see it is white, we know that two of all swans that ever have, do and will exist so far are white. The problem comes from the fact that we have not proven that "swans are white" until we have checked whether this is true for every possible case to which it might apply: until we have checked every swan out there, we cannot say that swans are white, because there might be one of them that"s black, which means our hypothesis is false and we need to replace it with a more specific hypothesis such as "swans can be white, or black".

However, while more specific than the original one, this hypothesis is still a-specific, since there might be yellow swans out there, or even grey ones, or worse yet, swans that are partially black and partially white. We don"t hit upon a specific hypothesis until we reach one such as "swans can be just white, or they can be something other than just white". This form of hypothesis is a classifying hypothesis, and gives us two mutually exclusive categories for (in this case) swans to fall into.

(Note that this last hypothesis is not trivial, as it tells someone who never saw a swan in their life something about the way swans look, namely that they can be white)

So this is a problem! That solves the "problem" part of the "induction problem", but what is the "induction"?

The induction comes from the fact that you need to continue checking a hypothesis one case at a time, even if all the cases you checked so far confirm it. In out swan example this would be the fact that if we look at one swan and see it is white, we aren"t done yet; we need to look at a second swan. But if that turns out the be white then we aren"t done yet, we need to check a third swan, and this goes on until we run out of swans. And this is unlikely to happen since new swans get born every day. So we will never be able to absolutely prove our hypothesis!

At this point a common thought is "Yeah but at some point you had enough swans to be reasonably certain that they're white". While a natural thought, this does not mean you proved your hypothesis, and thus that your conclusion is not scientific. While it could be that if you tested 20,000 swans for their colour, you happened to have the only set of 20,000 white lemons in the world without knowing it, and every other swan in existence is actually a shiny black. The problem here is that you just don't know whether all the evidence you gathered is really representative of what you need to prove your hypothesis. The only way to solve that is to rephrase your hypothesis to specifically apply to the 20,000 swans you had: "All 20,000 swans in my test set are white".

Does this mean that every scientific "truth" has actually never been proven? Yes, most definitely. Does this mean science is useless? No. Not in the slightest; science operates on the concept of "evidently true". Take Newton"s laws for motion: they hold until you try to apply them to sub-molecular motion, when it turns out they"re not true at all. However, if you restrict their applicability to anything macromolecular, they sure seem to describe what happens with high accuracy.

It is this "evidential truth" that is the foundation of science. Real science does not give absolute answers, only best-guesses for observations made so far. For this reason it is often shown that something that is believed to be true turns out to have wild exceptions when we make new discoveries about things. Newtonian motion, thermodynamic equilibrium, causality, none of it has ever been proven to hold for everything, because by the very nature of science this is impossible.

In fact this is also why statistics can never say more than it does: if for instance some research shows that 60% of all considered criminals are black, then all it says is that 60% of all criminals considered for the statistical research were black, and in absolute terms means nothing more.

So, if you ever run across someone who claims that the laws of science are absolute, you will know better.