The notions of extension and intension are incredibly important because they help us make sure that we define (categorematic) terms correctly in any given circumstance. In an argument, it is crucial that we understand intension and extension so that our terms are clear and unambiguous. When we evaluate arguments, it’s important to examine all the terms that are being used, and make sure that such terms are defined correctly. If terms are given a definition that is too broad or too narrow, it is easy to see that an absurd conclusion could follow. After all, since syllogisms are composed of propositions, and propositions are composed of terms, if the terms are faulty, then the entire argument could easily go wrong. Now that we know how terms relate to categories, we can begin relating categories themselves in propositions.