 Axiomatic systems. Every axiomatic system consists of three basic components. Definitions, axioms or postulates, and rules of inference, or the rules of logical reasoning. With these, we construct a body of knowledge by deriving conclusions that we call theorems. Let us look at them more carefully. In terms of definitions, there are some definitions that we call primitive terms. Suppose we want to define the word set. And we say, set is a group of things. And we say, what's a group? A group is a collection of things. And what's a collection? It's a batch of things. And what's a batch? It's a series of things. And what's a series of things? It's a set of things. So notice that we are going around in circles at one point or another because the list of words in any vocabulary is finite. We are bound to come to one of the words we previously used to define a term. In an axiomatic system, what we do is to avoid this problem, we take some words as primitive terms. Primitive terms are undefined terms. Now, we don't want to take too many of those. We're just going to take a very few amount of these. They are so basic that we think that anybody would readily understand what we are talking about without any room whatsoever for confusion. With those definitions in mind, you create axioms. Now, these axioms are also called postulates. They are, quote unquote, self-evident truths. Clark also calls them as experimentally verifiable. He says that axioms are experimentally verifiable. We can think of them as laws. Or we can also think of them as beliefs. So we have some set of beliefs, some set of laws, some set of truths, or some set of principles that we take as true. We may argue their validity, but within the system, the assumption is that they are true, that they always hold true. And then we also have rules of inference. These are the rules that govern logical reasoning. For instance, rules for negations, rules for conditionals, rules for conjunctions, rules for disjunctions. There are so many rules. In summary, axiomatic systems have three components, definitions, axioms, and rules of inference. And with those three things, we construct a body of knowledge by deriving conclusions that we call theorems. Thank you.