The title might shock some readers, although I hope not. In fact, I will be shocked if I could not convince you that the statement in the title is a truism because the reality is this: while there are few things that we do learn from observations (or data, or experience, etc.) most of what we come to know is not learned by our own personal observations and experiences — in other words, most of what we come to know we come to know because it is true and not because of any data we see.

And here’s the proof…

Claim:

Not everything we come to know is learned from data (experience, or observation). In fact, most of what we come to know we ‘learn by instruction’ (or ‘by being told’ or ‘by consulting a knowledge repository’).

Proof (by negation):

1. Suppose that everything we know we learn from experience (from observations and from data).
2. Growing up, different people have different experiences and they make different observations — in fact, it is rarely the case that two people have exactly the same experiences.
3. By (1) and (2), we can say that, in theory, there is nothing that all people should agree on and come to know exactly the same way. (note, this is not saying there is nothing that different people would agree on, but if (1) and (2) are true then, in theory, there’s nothing that different people should or must agree on!)
4. But we know (3) is false, since no 2 human beings can — even of they wanted to — disagree on many established facts (a small sample of facts that no two humans can disagree on is shown in Figure 1 below). Those examples clearly show that there are many facts that we cannot learn differently regardless of our observations and experiences.
5. But if (3) is false, then either (1) is false or (2) is false (or of course both). But we know (2) is true, so (1) must be false — that is, there are many things that cannot be (and are not) learned by observation/data because if they were different people with different experiences might learn them differently and that cannot be the case.
6. If (1) is false, then not everything we come to know/learn we learn from experience or from observations of data, but most of what we learn we come to know by being told, or by instruction, etc.

End of proof.

Figure 1. Examples of things we come to know not by observations (or experience, or from data) but we come to know because they are true — usually, we learn these by instruction, or by being told, etc. Some of these are physical facts, some are mathematical facts, some are just commonsense facts, etc.

I really feel silly writing this article which states a scientific fact, but the ML runaway train has made many ‘scientists’ make some silly statements (e.g., ‘we can learn anything/everything from data’). And, unfortunately, some of these ‘scientists’ are award-wining scientists that are negatively effecting tens of thousands of young scientists and engineers.

Some logic, and some commonsense, goes a long way. So please, tone down your excitement — it will prove to be very useful in your journey.