8. Patterns of Reasoning

Now that you know how to use logic for making statements about things and how to check whether or not a given statement is true, the next step is to study patterns of reasoning that allow true statements to be combined to give other statements that are guaranteed to be true. We’ll start with ideas that go all the way back to Aristotle, the founder of logic, who looked at simple patterns of logical argument with two premises and a conclusion, called syllogisms. The study of the sound syllogisms and the relationships between them dominated the subject for the next 2000 years. Nowadays, using the modern notation of symbolic logic, we can express what scholars were studying for all this time in a much simpler way, and see it as a straightforward combination of a couple of simple ideas. Since we’re not historians, the point of looking at syllogisms isn’t to learn about Aristotle and the history of logic. Rather, it’s to learn those simple ideas and how they fit together, as a starting point for studying the rest of symbolic logic, and to demonstrate the power of a good notation.