All Greek males are bald.
Herodotus is a Greek male.
Therefore, Herodotus is bald.
The conclusion is false because Herodotus isn’t bald, at least not as he is portrayed.
Moreover, the conclusion depends on a premise — all Greeks are bald — which can’t be known with certainty. The disproof of the premise by a single observation exemplifies the Humean–Popperian view of the scientific method. A scientific proposition is one that can be falsified — contradicted by observed facts. If a proposition isn’t amenable to falsification, it is non-scientific.
In the Humean-Popperian view, a general statement such as “all Greek males are bald” can never be proven. (The next Greek male to come into view may have a full head of hair.) In this view, knowledge consists only of the accretion of discrete facts. General statements are merely provisional inferences based on what has been observed, and cannot be taken as definitive statements about what has not been observed.
Is there a way to prove a general statement about a class of things by showing that there is something about such things which necessitates the truth of a general statement about them? That approach begs the question. The “something about such things” can be discovered only by observation of a finite number of such things. The unobserved things are still lurking out of view, and any of them might not possess the “something” that is characteristic of the observed things.
All general statements about things, their characteristics, and their relationshships are therefore provisional. This inescapable truth has been dressed up in the guise of inductive probability, which is a fancy way of saying the same thing.
Not all is lost, however. If it weren’t for provisional knowledge about such things as heat and gravity, many more human beings would succumb to the allure of flames and cliffs, and man would never have stood on the Moon. If it weren’t for provisional knowledge about the relationship between matter and energy, nuclear power and nuclear weapons wouldn’t exist. And on and on.
The Humean-Popperian view is properly cautionary, but it doesn’t — and shouldn’t — stand in the way of acting as if we possess general knowledge. We must act as if we possess general knowledge. To do otherwise would result in stasis, or analysis-paralysis.