There are two Platonic ideas that Aristotle places pressure on in this extract. The first is that knowledge is superior to mere opinion and that there is a more abstract level of rational justification. The second and more skeptical element of thought is both about the notion of innate sources of knowledge and also the contrast between the visible and the intelligible realms. Aristotle believed in the universals and also believed that the premises have to be true in order for the conclusion to be true. The conclusion follows inescapably from the premises, so if the premise is false then the conclusion is false. This is where intuition comes into play because if the starting point needs to be evidentially true in order for the argument to be valid. The human brain, after a certain period of time begins to recognize patterns. For example when a baby is at a young age all he/she can really do is make noises that we hear as gibberish, but to them they are expressing them self and after learning from patterns and example they are able to recognize speech and do it themselves. All instruction, given or received by the way of argument proceeds from pre-existing knowledge. The mathematical sciences and other disciplines are learned this way, as do two ways of dialectical reasoning: syllogistic and inductive. Each of these methods uses old knowledge to bring forth new knowledge.
Demonstrative logic, the study of demonstration as opposed to persuasion, is the subject of Aristotle’s two-volume Analytics. Many examples are geometrical. Demonstration produces knowledge. Persuasion merely produces opinion. Aristotle presented a general truth and-consequence conception of demonstration meant to apply to all demonstrations. According to him, a demonstration, which normally proves a conclusion not previously known to be true, is an extended argumentation beginning with premises known to be truths and containing a chain of reasoning showing by deductively evident steps that its conclusion is a consequence of its premises. In particular, a demonstration is a deduction whose premises are known to be true. Aristotle’s general theory of demonstration required a prior general theory of deduction presented in the Prior Analytics. His immediate deduction chaining conception of deduction was meant to apply to all deductions. According to him, any deduction that is not immediately evident is an extended argumentation that involves a chaining of intermediate immediately evident steps that shows its final conclusion to follow logically from its premises. To illustrate his general theory of deduction, he presented an ingeniously simple and mathematically precise special case traditionally known as the categorical syllogistic.