Plato and Aristotle on knowledge

In his philosophical work, particularly in his Discourse on the Method, Descartes attacked, often implicitly, the authority of the church’s official doctrine and that of classical authors such as Plato and Aristotle, as regards knowledge acquisition. Also the authority of the church’s official doctrine much leaned on the views of Plato and Aristotle in this (and on the Bible, of course). Therefore it’s interesting to see what Plato’s and Aristotle’s views on knowledge were.
As for Plato, two parts of his epistemology are relevant: his theory of forms and his theory of innate knowledge. Plato’s theory of forms holds that things as we perceive them are reflections or imitations of ideal forms created by a deity. This deity has made an ideal form for every thing there is. A craftsman, let’s say one who makes a table, has such a form shaped by the deity in his mind and makes his personal version of the ideal form of the table, in this case. All tables are realized version of the ideal table designed by the deity. This is so for everything in the cosmos. If we want to gain knowledge, we must not investigate things as we perceive them, but we must try to find the ideal forms behind the observed phenomena, so Plato. Observation as a method of acquiring knowledge is explicitly rejected by Plato. Plato assumes that everyone already has knowledge of the ideal forms at birth but is not aware of this. It is therefore a matter of recalling this knowledge by asking specific questions (the maieutical method). In short, knowledge acquisition is not based on observation but on memory and recollection. With this approach, Plato introduced an anti-empiricist tradition into philosophy, despite later attempts, such as those of Aristotle or Archimedes, to the contrary.
For Aristotle, the idea of innate knowledge was absurd: “How can we learn from knowledge that is not yet available?”, he said. Moreover, one cannot separate an object and the concept of this object, for example because an object can have different forms, which may lead to contradictions. Knowledge acquisition consists in the reception of the observed objects, i.e. of the sensory impressions, in the soul. This reception is not material but immaterial: the soul absorbs the form of an object as the wax absorbs the imprint of a signet ring without absorbing the ring itself. As such, observation doesn’t give knowledge, for it still concerns individual objects, and so, at first, the forms in the soul do, while knowledge is general. This problem is solved, so Aristotle, because the impressions of individual objects in the soul lead to memory, and next repeated memory of the same object leads to familiarity. Finally, familiarity leads to the skill of the craftsman (techne) and to knowledge (episteme). Aristotle doesn’t clearly explain how this happens, but apparently he sees it as a kind of induction.
So, while for Plato knowledge acquisition is a kind of recalling the existing but yet hidden, for Aristotle it is the construction of what was once unknown by means of observation and induction. I use the word “construction” deliberately, for according to Aristotle knowledge is a system of coherent statements formulated as syllogisms. Higher placed syllogisms in the system serve as premises for lower ones. Or vice versa, lower syllogisms can be traced back to higher ones step by step. This tracing back cannot continue indefinitely. The entire system is ultimately founded on a number of unprovable basic statements or axioms (archai). The axioms are not arbitrary chosen but must be true, elementary and directly knowable, and clearer and more fundamental than the lower syllogisms. With this structure of knowledge, Aristotle has the structure of mathematics in mind. In essence, the system of syllogisms is based on observation and proved by observation. However, this doesn’t apply to the axioms, for the axioms cannot be proved by observation. Evidence cannot be a beginning of itself, and knowledge cannot be the beginning of knowledge. But because the mind (nous) is truer than knowledge, it’s the mind that provides the axioms that are the beginning of knowledge.
On the face of it, Aristotle’s system of knowledge established by induction and deduction does not seem to differ much from Descartes’ system developed by the methods of analysis and synthesis. Nevertheless, there is an important difference. For Aristotle, observation is based on everyday perception. It’s daily experience, maybe more sophisticated, but in fact daily experience it is. For Aristotle, knowledge experience meant the extension and objectification of knowledge acquired on the basis of pre-theoretical life experience. The observations must then be fitted into the system that, apart from these new additions, was in principle unchangeable. For Descartes and for the 17th-century scientists, knowledge experience consisted of systematic experimentation and observation using theoretical concepts. Observation has become a test of the system that is not given but that is fallible and therefore revisable, or may be rejected completely.

Sources
For Plato mainly Phaedo, Theaetetus and Politeia; for Aristotle mainly the Analytica Priora and Posteriora.