If you came to Popper via Deutsch, you probably either don’t know about Popper’s three worlds or, if you do, you perhaps have no use for it. But Popper’s three worlds solved a specific philosophical problem that existed at the time: the difference between subjective knowledge and objective/autonomous knowledge. Popper’s three worlds are:
World 1: The Physical World
World 2: Experience / Thought / Subjective Knowledge / Organismic Knowledge
World 3: Objective Knowledge, especially the products of human thought
World 1 needs no explanation. World 2 included the traditional view of knowledge, i.e. knowledge held in the mind. So it consisted of one’s own thoughts, subjective experience, etc. World 3 included the sort of knowledge you found in textbooks, which included theories, mathematics, etc.
Popper felt World 2 was probably best called “organismic knowledge” rather than “subjective knowledge.”
Now I wish to distinguish between two kinds of “knowledge”: subjective knowledge (which should better be called organismic knowledge, since it consists of the disposition of organisms); and objective knowledge, or knowledge in the objective sense, which consists of the logical content of our theories, conjectures, guesses (and, if we like, the logical content of our genetic code.) Examples of objective knowledge are theories published in journals and books and stored in libraries; discussions of such theories; difficulties or problems pointed out in connection with such theories; and so on.Objective Knowledge, p. 73
Today you probably have little need to distinguish between World 2 and 3 because you probably interact with few philosophers. World 2 now seems to us like a special case of World 3: knowledge stored in the mind is just software after all. There is nothing to distinguish it knowledge stored on the internet today.
However, you can’t understand something like this without first understanding the problem space that led to it. At the time philosphers claimed that knowledge was purely in the mind and required a ‘knowing subject.’ A book, on its own, was just a bunch of ink on a page until someone read it. This way of thinking caused philosophers of the time (and well before Popper’s time) to make substantial philosophical errors anything from Plato’s divine realm to thinking math was just invented and we could change it any way we wanted. Popper’s three worlds make subjective knowledge (a term that among philosophers specifically means knowledge in one’s mind) distinct from objective knowledge because that was the way you have to do it to straighten out the mistakes of the philosophers of the time.
His three worlds might still be useful today, and I’m not suggesting otherwise. There are still people today that struggle to understand in what sense objective knowledge exists. But we’re no longer dealing with quite the philosophical crisis that Popper was dealing with either.
To fully understand Popper’s philosophy, it is important that you understand the history of the problems he was trying to solve. Popper’s choice of the phrase ‘degree of corroboration’ instead of ‘degree of confirmation’ was no different. Either word will do so long as you have the right idea in mind, namely that it means the theory has survived increasing attempts to test it that might have refuted it.