Validity is when some information, the premises, guarantee that something is true.
Logic studies the relationships between those bits of information. So anything that can carry information can be studied with logic.
For example, this Sudoku puzzle carries information. That information, plus the rules of Sudoku, guarantees that a certain number goes in the square with the question mark.
Your first task is to figure out what number goes there. If you're not familiar with the rules of Sudoku, do a quick internet search and discover a world of logic fun!
A type of information that is particularly important for logic is sentences. Sentences are wonderful things. They can be short and pithy:
"Seize the day."
--Horace (promoting Epicurus's philosophy)
They can be long and sonorous:
"Life’s but a walking shadow, a poor player that struts and frets his hour upon the stage and then is heard no more: it is a tale told by an idiot, full of sound and fury, signifying nothing."
Some sentences ask questions:
"Where should we get dinner?"
Some make commands:
"Do your logic homework!"
We are interested in sentences that make claims or assertions. Claims like these:
- "Pia is happy."
- "Water is made of oxygen and hydrogen."
- "There is only one even prime number."
Unlike questions and commands, these sentences have a truth value: they can be true or false. When we talk of sentences in this book, we usually mean sentences like these: ones that make claims that are true or false.
That is because our focus is arguments and reasoning, and only sentences that make claims that can be true or false can appear in arguments.
Logic can actually be used to study questions, commands, and other types of sentence. But studying arguments and sentences that make claims will take all our attention in this book.
Let's practice distinguishing different kinds of sentence.
Finally, let's see if you understand why this matters.