However, I see that in the english speaking philosophical world, certainty is so to say absent from discussions regarding language. I cannot see where certainty can be found in the standard definition of knowledge as true justified belief. How to explain this?
I think that the theory of knowledge as justified true belief is typical of analytical philosophy, which is hegemonic in English-speaking countries, and in particular in the United States.
Certainty, however, is a psychological condition and certainty that p doesn't imply p and therefore doesn't imply knowledge that p.
As I understand it, Descartes' idea is that doubt disproves knowledge, an idea he put to very effective use to arrive at the Cogito. However, as a psychological condition, certainty itself seems immune to analysis and therefore of little interest in particular to analytically-minded philosophers.
Is there an overlap?
Certainty applies to beliefs. We have beliefs, and we are certain of some of our beliefs while uncertain of others. Some of the beliefs we are certain of may be actual knowledge. Uncertainty, i.e. doubt, disproves knowledge, according to Descartes, but certainty doesn't prove knowledge.
So, there is perhaps an overlap.
Let's assume p is true. Let's assume further that subject A believes that p, and that A is somehow justified in believing that p. The theory of justified true belief says that, under those assumptions, subject A knows that p. However, what if A has some doubts about believing that p. Descartes would say that therefore A doesn't know that p (the slightest doubt is enough to disprove knowledge).
So, here it seems we have a clear contradiction between the two perspectives, one analytical philosophy, the other a typically "continental" philosophy.
The two perspectives are clearly very different but there is nonetheless a striking similarity in the difference...
According to the JTB theory, a justified true belief is equivalent to knowledge. However, it is unclear that we could ever know that we know p since there is no finite procedure to decide that we know that p is indeed true as required.
So, JTB is logically inconclusive since we don't know how to ascertain the truth of at least one of the premises theorised as necessary to the conclusion.
Descartes has also a problem, though. To disprove that you know p, you need to be able to doubt that p. However, how do you know that you doubt that p? Descartes doesn't offer any procedure to decide that you know something. His procedure is only effective in disproving that you know something. You can prove you don't know that p by being able to doubt that p is true. You cannot prove that you know that p. And, therefore, you cannot prove that it is true that you doubt that p is true.
So, at least as described by Descartes, his view was also logically inconclusive.
Perhaps Bertrand Russell bridged the gap. He made the distinction between propositional knowledge, i.e. subject A knows that p, and knowledge by acquaintance where subject A knows p.
For example, subject A knows that subject B is in pain: This is propositional knowledge. However, subject B is experiencing the pain: Subject B knows pain. This is knowledge by acquaintance, although only so while pain is being experienced. Knowledge by acquaintance reduces to propositional knowledge after the event.
Although I dispute the coherence of the theory of justified true belief, nonetheless it seems to me that its object is propositional knowledge, while Descartes' Cogito is typical of knowledge by acquaintance.
And perhaps the twain shall never meet.