MODULE: Basic logic

TUTORIAL L02: 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?

L02.1 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 issusing 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.
• The data and information provided on this web page is for informational purposes only, and is not intended for trading or commercial purposes, unless written prior permission is obtained by the user from the author, though the author will not be liable for any errors or delays in the content, or for any actions taken in reliance thereon.

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.

L02.2 Exercises

Question 1. How about the following? Are these statements?

1. One plus one equals three. [Show answer]
   Yes. A false statement.
2. Can you come to the party please? [Show answer]
   A question and not a statement.
3. AJH$%^#@! [Show answer]
   “It is true that AJHGJH&#HJGJ” is not grammatical. So it is not a statement.
4. If it rains then the street will be wet. [Show answer]
   Yes. A conditional statement about what happens when it rains.
5. We all feel very sorry for you. [Show answer]
   Although statements are often used to convey information, they can also be used for other purposes as well, such as expressing sympathy.
6. Come here! [Show answer]
   Not a statement but a command.
7. A chicken is a song that weighs ten tons. [Show answer]
   It is a complete and meaningful sentence, even if what it says is silly and must be false since a chicken is not a song. But it is still a statement.
8. All statements are true. [Show answer]
   It is a (false) statement about statements.
9. It is true that it is raining. [Show answer]
   Yes. A statement.
10. I am ordering you to stop talking in class. [Show answer]
    Yes. It is actually both a statement and a command at the same time. The statement makes a claim about the command that is being issued at the same time the statement is made. This example tells us that some imperative sentences are also declarative.

Question 2. Rewrite these utterances or headlines as statements.

1. Inflation rising. [Show answer]
   Inflation is rising.
2. Kidnapper : no ransom, boy dies [Show answer]
   Kidnapper says that the boy will die if no ransom is paid.
3. Scientists : coffee good for health [Show answer]
   Scientists say that coffee is good for your health.
4. Paintings stolen from Presidential Palace. [Show answer]
   Some paintings have been stolen from The Presidential Palace. [This is probably better than "All paintings have been stolen from The Presidential Palace."]
5. No money, I no work. [Show answer]
   If I do not get any money, I will not work.

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