A Brief Explanation of Aristotelian Logic - Excerpt from Aristotle's "Posterior Analytics" Bk II

Posterior Analytics Book II

Here is a very brief explanation of how knowledge works in Aristotelian logic. This system presupposes rational intelligibility to the universe, i.e. that knowledge is the grasping of immaterial essences in things. Thus, the process of knowing is something like this: Knowledge begins in the senses as a more general or universal perception (say approaching a forest - it's a large mass of green), then the senses move from the more universal to the particular (focusing on an individual tree), which generates a rational form of tree. As one begins to have these many inductive experiences, two things happen. One begins to develop first principles in general, and also in particular fields of knowledge. These are self-evident universal truths which are revealed through our experience of things. 

From these first principles one is able to proceed with deductive knowledge, or "scientific demonstration." Here scientific is used in an older sense of proceeding from first principles. And so when one has true first principles, and clearly understood data within those first principles, then one can proceed with certainty in unpacking truths which are implicit, but not obvious, in those things. This is the role of the syllogism. For example, "All men are mortal. Socrates is a man. Therefore Socrates is mortal." The first part is a first principle of the essence of man - it's self evident with experience that all will die - while the second is an application to a particular set of data within this realm of humans, Socrates, finally leading to the revelation of implicit knowledge, making it explicit - that Socrates is going to die. 
This is the essence of logic and its power. It is a way of harnessing the intelligibility of the universe and uncovering its secrets with the mind. 

Knowledge, and Book Two of Posterior Analytics

In book two of Posterior Analytics, Aristotle describes how one comes to learn. There are two basic forms of learning. These are called “induction” and “deduction.” 1 Deduction is probably what most thinks of when one thinks of learning. Also called “demonstrative knowledge,” it is when one deduces something from what are called “primary and true premises”. 2 Aristotle gives the example “if p and q are assumed, then something else r, different from p and q, follows necessarily through p and q.” This is saying that if p and q are true, then r must follow from them and also be true. In this example, p and q are the “primary and true premises.” 3 These are truths that are true in and of themselves and are not contingent upon other truths. 4 One cannot prove them like something is proven from deduction. 5 So how does one come to know these primary truths then if they cannot be proven? 

This is where the other process of learning comes in, called induction. 6 Aristotle says that these primary and true premises cannot be innately in a person because then one would not need demonstration because these primary and true premises are better; And that one does not start with absolutely no knowledge at all, because then one could not possibly learn anything. Rather, Aristotle says that one has an “innate discriminative potentiality called perception.” It is by our ability to perceive things in the world coupled with our memory that allows us to internalize these perceptions and to form concepts. From these concepts we get first principles. 7 Aristotle says that properly speaking we do not have knowledge of these first principles because knowledge refers to deduction and proving r based on p and q, but that we understand these first principles because they have been formed in us. 8 So from our innate ability to perceive and remember one can form concepts from which first principles are understood and from these one can make deductions and come to learn. 9
1 - Miller, Patrick and Lloyd Gerson. Introductory Readings in Ancient Greek and Roman Philosophy. Indianapolis: Hackett Pub. Co, 2006. Pg. 260
2 - 258, 264
3 - 258
4 - 258/262/265
5 - 262
6 - 260
7 - 264
8 - 265/246/7
9 - 247