Recently, I've gotten interested in learning formal logic as another one of my hobbies. Formal logic is a way to take an argument, which has multiple premises and a conclusion, and convert it into a notation which allows it to be manipulated/transformed with. I came across this logic guide which recommended Teller's Logic Primer as my first step into the world of logic. The author has graciously made the book free so I've been following along. Today I've read the first three chapters, so I wanted to share a bit about what I learned. Now the type of logic covered in Teller's book focuses on arguments which have a true or false value. Particularly, it starts with sentence logic. Let me show you a bit about how that works. For example let's say we have two sentences:
A: I have a name.
B: I have a pet.
Using these two phrases we could play around with it in lots of different ways. In the first chapter, 3 different ways of manipulating these declarative sentences are shown: conjunction, disjunction, and negation. Each of these has a special symbol to go along with it. You can take a sentence and negate it to get the opposite of it. Let's say we take B and negate it. I have a pet becomes I do not have a pet. Teller shows us that we can translate that into the following symbols: ~B. "~" is the symbol for negation and B is a stand in for our sentence. Negation turns a true value into a false one and vice versa. Notice how we took so many words and converted into just 2 symbols. That showcases the terseness of formal logic. These capital letters used as a stand-in for our sentences are known as "Atomic sentences" or "Sentence letters" in this book. Next, let's look at conjunction. This allows us to take two sentences and bring them together, like we use "and" for in English. So if we brought A and B together the sentence would become: I have a name and I have a pet. Using Teller's notation we'd write this as A&B. For conjunction to be true, both of the values A and B must be true. The "&" is used to represent conjunction. If either one of them is false, the whole sentence is false. Finally comes disjunction, which is works like "or" does. If we applied disjunction to A and B then our sentence would be: I have a name or I have a pet. Using the notation we'd get: A v B. "v" is used as the symbol for disjunction.
These 3 ways to manipulate our sentences are known as truth functions. Just like in math or programming, these truth functions take an input, in this case a value that is either true or false, and return a true or false value. Now that we know the basics, we can start combining We can bring them together and create things like ~(A&B)&B. Give it a try with your own sentences and see how you can play with them using just these 3 concepts.
This was a very basic introduction to what's covered in Teller's Logic Primer, in fact, I didn't even share most of what the first chapter contained! If this note interested you at all, I highly recommend you give it a look. Until next time!