Module: Basic logic
Quote of the page
Without effort and change, human life cannot remain good. It is not a finished Utopia that we ought to desire, but a world where imagination and hope are alive and active.
- Bertrand Russell
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:
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 :
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 :
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.
Which of the following are statements?
Rewrite these utterances or headlines as statements using complete sentences.