The idea that our intellect is a source of knowledge because God is a source of knowledge "has a long history which can easily be traced back at least to Homer and Hesiod. Plato also "plays a decisive part" in the pre-history of this doctrine, which was Descartes' starting point. The sources of knowledge for the Greek poets were divine. They were the Muses, and they guaranteed the truth of the stories. The philosophers Heraclitus and Parmenides made similar claims, and Parmenides' god even says that in order to distinguish between truth and falsehood, he must rely on the intellect to the exclusion of the senses of sight, hearing, and taste (also similar to Descartes) (9,10).
Plato sharply distinguishes between the "divine frenzy of the poet" and the "divine sources or origins of true knowledge". He "grants the inspiration to the poets but denies them any divine authority for their alleged knowledge of facts". On the other hand, Plato's idea is that each man is in some measure granted the possession of divine sources of knowledge (amemnesis), i.e. the essence or nature of a thing "rather than of a particular historical fact". At birth, our immortal soul forgets what it knew (this is an "epistemological fall" of sorts), but if we "see the truth again [we shall] recognize it. All knowledge is therefore re-cognition - recalling or remembering the essence or true nature that we once knew" (here, think of Socrates' story about Meno's slave boy being taught to recall the Pythagorean theorm). Even here, we can see the idea that the truth is manifest (which Popper opposes, 10).
Plato describes his teaching as one which "makes men eager to learn, to search, and to discover", but his optimism seems to have waned in the Republic. Here, we find the parable of the cave, and with it, the idea that obtaining true knowledge ("the divine understanding of the real world") and passing it on to others is exceedingly difficult. Here, "truth may be attained by a few - the elect", something that Popper says is "more wildly optimistic than even the doctrine that truth is manifest". Here, optimistic "anti-traditionalist, anti-authoritarian, revolutionary and Utopian rationalism" gives way to pessimistic "authoritarian traditionalism".
Popper thinks that in Plato's story of the cave (and maybe also the story of the fall of the city, "when the Muses and their divine teaching are neglected" also in the Republic) one can see an echo of "Parmenides' doctrine that the opinions of mortals are delusions, and the result of a misguided choice / convention (Popper also thinks this may come from Xenophanes' doctrine that all human knowledge is simply guesswork, with his own theories being merely similar to the truth). Parmenides essentially says that even though the fall affected all men, "truth may be revealed to the elect by an act of grace - even the truth about the unreal world of the delusions and opinions, the conventional notions and decisions, of mortals: the unreal world of the appearance that was destined to be accepted, and to be approved of, as real...: a few may reach certainty about both the unchanging world of eternal reality and the unreal and changing world of verisimilitude..." (11, 12). This, Popper believes, was Plato's inspiration for his philosophy.
What Popper is really interested in though are the more optimistic ideas of Plato's. He thinks that Plato's more optimistic epistemology (pre-Republic) contained the roots of Aristotle's theories of induction (and later, Bacon's), as well as the "germs of Descartes' intellectualism". He thinks that when Aristotle said that Socrates was the inventor of the method of induction, he was referring to the "Socratic method", i.e. the idea that judicious questions can help us to remember or recapture the forgotten knowledge of the soul (possessed in its pre-natal state of omniscience). He thinks that Both Aristotle and Bacon meant by "induction" "not so much the inferring of universal laws from particular observed instances" as a "method by which we are guided to the point where we can intuit or perceive the essence or the true nature of a thing", which is precisely the aim of Socrates' method, or art of midwifery (or maieutic). Therefore the aims of maieutic and induction were the same (12).
Socrates' method basically asks questions with the intent to destroy prejudices, or "false beliefs which are often traditional or fashionable ; false answers, given in the spirit of ignorant cocksureness". Socrates himself does not pretend to know, but aimed to teach us to "doubt our own convictions. Fundamentally, the same procedure is a part of Bacon's induction" 13.
My summary: - What underlies Bacon's method is really the Socratic method, which Plato subscribed to early on, only to fall into epistemological pessimism later. Aristotle, Bacon and Descartes all used this method to arrive at the discovery of essences.