PHIL102: Introduction to Critical Thinking and Logic

Statements, Logical Connectives, and Logical Relations

Statements are the fundamental units of arguments and proofs in logic. These tutorials explain how to identify statements and introduce some of the basic ways that statements may be related to one another.

Complete the exercises and check your answers.

Statements

In logic we often talk about the logical properties of statements and how one statement is related to another. So what is a statement?

There are three main sentence types in English:

• Declarative sentences are used for assertions, e.g. "He is here."
• Interrogative sentences are used to ask questions, e.g. "Is he here?"
• Imperative sentences are used for making requests or issuing commands, e.g. "Come here!"

For present purposes, we shall take a statement to be any declarative sentence . A declarative sentence is a complete and grammatical sentence that makes a claim.

So here are some examples of statements in English:

• Snow is white.
• The moon is made of green cheese.
• Everyone is here.
• Whatever will be, will be.
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As you can see, statements can be true or false, and they can be simple or complex. But they must be grammatical and complete sentences. So these are not statements :

• The United Nations [ A proper name, but not a sentence ]
• Bridge over troubled waters. [ Not a complete sentence ]
• Come here right now! [ A command that is not a complete sentence making a claim ]
• Will you be available on Tuesday or Wednesday? [ A question ]
• HJGAS&*^@#JHGKJAS*&^*!@GJHGAA*&S [ Ungrammatical ]

There is an easy test to decide whether something is a statement in English. Suppose you have a sentence φ and you add "it is true that" to the front. If the resulting expression is grammatical, then φ is a statement. Otherwise it is not.

So for example, φ might be "bridge over troubled waters". We append "it is true that" to the front, and end up with "it is true that bridge over troubled waters." But this expression is not grammatical. So "bridge over troubled waters" is not a statement. However, "I am like a bridge over troubled waters" is a statement, because "it is true that I am like a bridge over troubled waters" is grammatical.