Knowledge: True belief based on evidence.
1. To provide a definition of "knowledge" that covers all cases where it is used sensibly is somewhat difficult, since one knows one may believe that one knows and may later find out that one was mistaken, even while having evidence that supported one's belief, and one's belief that with that evidence one knew.
Now... that one knows one may believe one knows and later find out one was mistaken is a true belief about claims of knowledge for which there is a lot of evidence, and so it seems one knows at least one may be mistaken. Consequently, it follows there are some things one knows, in the sense given, and that is a useful starting point.
Also, besides knowing one may be mistaken, there is the more positive fact that in order to express skepticism one must at least know some language to claim in it - inconsistently - that one doesn't know anything.
Furthermore, in the same connection - related to skepticism - it seems evidently true that there are many things that one does not know, and so it follows that one also knows that there is much one does not know, which is an instance of the truth about knowledge just established, and indeed also is one of the firmest certainties and best pieces of knowledge that a human being has.
And it is important to remark that True belief based on evidence - knowledge - comprises true belief in probabilities based on evidence, where the "true" in "true belief" refers to axioms of probabilities and statements of fact.
Therefore it is entirely possible that one's true theoretical beliefs, that imply things beyond one's experience, comprise only probable contingent statements and no certain ones, though one requires certainty for statements of evidence.
2. To consider knowledge in some more detail, it makes sense to distinguish three kinds of - presumed - knowledge:
1. Practical knowledge
2. Empirical knowledge
3. Theoretical knowledge
Practical knowledge is knowledge of how to do things, and so relates to action and abilities. Thus, in this sense one may know how to cycle, may know how to differentiate, and may not know how to make a pizza.
It is an interesting fact about practical knowledge that one may know perfectly well how to do something, and can prove so by doing it, while one is at loss to give a good explanation for it. The ability to cycle is one good example: It is neither easy nor does it make much sense to explain how to do this in words.
The way to establish whether someone has a certain kind of practical knowledge is to find out whether they can do the things they may claim they can do. Incidentally, one may know how to do things - such as speaking in prose, as the proverbial French Mr. Jourdain, of Molière - that one may not know that one does.
Empirical knowledge is knowledge of such facts as one may meet in experience. These are always particular and may be of many kinds, including such as need a lot of training or some apparatus to experience them.
Also, a lot of empirical knowledge one has was in fact conveyed by teaching, and comes from authorities, but may be all the same quite reliable and true. And it often is a bit vague what is empirical. Thus, one may have been in England, and thus believe one has empirical knowledge about England, but even so meeting in experience what is represented by the term "England" is a bit too much for personal experience, although one may have a lot of knowledge of the English landscapes and people. (See: Empirical term.)
The way to establish whether someone has a certain kind of empirical knowledge is to somehow test it, either using logic and by reference to other knowledge one believes one has, that may imply or refute it, or by some sort of experiment, which may be as simple as looking up a word in a dictionary, or as complicated as using a cyclotron or PET-scanner.
Theoretical knowledge is knowledge of such facts as are represented by theories that include theoretical terms. Theoretical knowledge tends to go beyond experience, if only for the reason that empirical theories that do not make predictions about future experiences - which does not exist now - cannot be tested.
Many of the vagueries and problems with the term "knowledge" concern theoretical knowledge, for the reason mentioned above: One knows, also about science, that one may have been quite justified to believe that one knew something, at least in the sense that it was far more probable than not, and even so it turns out that one was mistaken.
One of the things that is often missed in discussing these problems is that even if a theory is mistaken in the sense that it logically implies something that is not really so, even so the theory may be and have been quite adequate.
Indeed, one real test for scientific knowledge, that also distinguishes real scientific knowledge from the claims of faith of any kind, is that it can be used to produce technology that works in practice whatever one believes or knows about the theories on which it was based. (Thus, the faithful of some religion may murder their opponents with weapons that cannot exist if their faith is true, and would not have been developed by members of their faith.)
And all scientific knowledge, whether or not it will keep standing in the future, that has led to some technology that would not have existed without it, must be adequate at least in that respect.
The way to establish whether someone has a certain kind of theoretical knowledge is to somehow test it, either using logic and by reference to other knowledge one believes one has, that may imply or refute it, or by some sort of experiment of whatever empirically testable deductive consequences of the theory.