What is the definition of a statement, formally? We talk a lot about statements in math and philosophy, but I have never heard a precise definition of what a statement is. I would like some clarification of this topic.
There is no single agreed use of the terms 'statement' and 'proposition'. Some ways in which philosophers use the word 'statement' include:
- A synonym or alternative for 'proposition'.
- A meaningful declarative sentence in a particular language.
- The assertion made by (the utterance of) a meaningful declarative sentence.
- Something that conveys a meaning, but which might be more broader than a sentence, e.g. a sign or gesture.
Likewise with 'proposition', it is sometimes:
- The primary bearer of truth, i.e. those kinds of things that are fundamentally true or false.
- A meaningful declarative or descriptive sentence.
- The semantic content of a meaningful declarative or descriptive sentence.
- The language-independent meaning of a declarative or descriptive sentence.
- The meaning of a declarative or descriptive sentence with the indexicals and references resolved.
- The object of propositional attitudes, i.e. the things that stand in place of p in expressions like "believes that p", "hopes that p", "fears that p", etc.
- The object of that-clauses, i.e. the things that stand in place of p in expressions like "the fact that p", "the possibility that p", etc.
David Lewis expressed the view that 'proposition' is such a jumble of conflicting desiderata that it is impossible to give it a clear definition.
According to reference here:
proposition is the non-linguistic bearer of truth or falsity which makes any sentence that expresses it either true or false... While the term "proposition" may sometimes be used in everyday language to refer to a linguistic statement which can be either true or false, the technical philosophical term, which differs from the mathematical usage, refers exclusively to the non-linguistic meaning behind the statement.
Statement is a general linguistic concept which may or may not have truth value, such as an imperative statement. While in logic statements are usually meant to be declarative sentences that is true or false according to here which may be expressed in different languages such as English and French sentences for a same proposition corresponding to the same truth snow is white.
See John Corcoran, Sentence, Proposition, Judgment, Statement, and Fact.
The words sentence, proposition, judgment, statement, and fact are ambiguous in that logicians [and philosophers] use each of them with multiple normal meanings.
A judgment is a private epistemic event that results in a new belief and a statement is a public pragmatic event, an act of writing or speaking. Both are made by a unique person at a unique time and place.
In contrast, propositions and sentences are timeless and placeless abstractions. A proposition is an intensional entity; in some cases it is a meaning of a sentence: it is a meaning composed of concepts, a complex sense composed of simpler senses. A [declarative] sentence is a linguistic entity.