Statements give information about an object or objects.
- “I exist.”
- “It is not raining.”
- “I have two stones.”
Statements Have Truth Values
A truth value is the information that a statement gives, and says whether some statement matches “reality” (whatever you define it to be). For example, if your current reality or “situation” says that “you are currently reading this book,” “it is raining,” and “you have three stones,” then you could say:
- “I exist” is true because you are currently reading this
- “It is not raining” is false because it is actually raining
- “I have two stones” is true because you have three stones, therefore, you also have two stones
The two most basic truth values are true (matching reality) and false (not matching reality). There are more, but we’ll cover them later.
Premises Are Sets Of Statements
Have you noticed that your “reality” can also be written as statements as well? Let us state the three statements of our example situation above:
- “I am reading this”
- “It is raining”
- “I have two stones”
The formal term for “reality” or “your situation” is premises. Premises themselves are sets of statements that you hold to be already true or “accepted as common knowledge.”
Propositions Are The Ideas Behind Statements
Propositions are ideas that can have truth values. Statements assign truth values to propositions. For example:
- “I am reading this book” is a statement that says that the idea (proposition) that you are reading this book has a truth value of true.
- “It is not raining” is a statement about your current surroundings and says that it is a fact or that it is false that it is currently raining.
- “I have two stones” is a statement about yourself having two stones is correct, or true.
You can think about statements as “words on a page” or some other form of communication that talks about ideas (propositions) and whether they are true or false (truth values).
Propositions are the basic units of logic. They are not words on a page or the sounds that people say when talking, but ideas that are truthful (or not, or possibly unknown, depending on how you want to think about them). Proposition are concepts with truth values.