Sentence, Statement, Proposition Glossary
Definition
In natural language, a sentence is a sequence of words, well-formed according to the grammar of the language, and standing as a complete [potential] utterance. In logic we normally consider only indicative sentences, which are those used to make statements.
Statements are an abstraction from sentences: the units which have truth values.
Propositions are the contents of statements; they are what statements express.
Comments
In the formal language of logic, the formulae play the role of sentences. More strictly, they are the forms of sentences.
It is possible to extend logic to deal with other sorts of sentences such as questions and commands. We do not consider such extensions in these notes.
One way to think of the proposition expressed by a statement is as the set of interpretations in which it is true. On this view, logically equivalent statements express the same proposition.
A statement is sometimes thought of as an indicative sentence on a particular occasion of its use. That is, the statement is the sentence with all indexical parts (i.e. parts that change their reference from one use of the sentence to another) given fixed interpretations. We could equivalently think of the statement as the sentence with the relevant non-indexical expressions substituted for the indexical ones.
Examples
- The sentence 'That man was here yesterday' might be used to make the statenent that Scott Morrison was in Parliament House on 14th October 2019. Of course, uttered in different places at different times, it could make other statements. The statement has a fixed truth value, but the sentence does not.
- 'If Alice and Bob are not both logicians, then Alice is not a logician, and if Bob isn't a logician, then Alice is' expresses the proposition that Bob is a logician. This is because (NOT(A AND B) IMP NOTA) AND (NOTB IMP A) is logically equivalent to B.