Statement (logic)

In logic and semantics, the term statement is variously understood to mean either:

a meaningful declarative sentence that is true or false,^{[citation needed]} or
a proposition. Which is the assertion that is made by (i.e., the meaning of) a true or false declarative sentence.^[1]^[2]

In the latter case, a (declarative) sentence is just one way of expressing an underlying statement. A statement is what a sentence means, it is the notion or idea that a sentence expresses, i.e., what it represents. For example, it could be said that "2 + 2 = 4" and "two plus two equals four" are two different sentences expressing the same statement. As another example, consider that the Arabic numeral '7', the Roman numeral 'VII', and the English word 'seven' are all distinct from the underlying number.^[3]

^ Millican (1994) "Central to the [Strawsonian tradition] is the distinction between a sentence and what is said by a sentence - Strawson initially called the latter a use of a sentence, and sometimes a proposition, but his most frequent term for what is said, which Wolfram consistently adopts, is the statement expressed."
^ Rouse (2005) "A statement is defined as that which is expressible by a sentence, and is either true or false... A statement is a more abstract entity than even a sentence type. It is not identical with the sentence used to express it... [That is,] different sentences can be used to express the same statement."
^ Rouse 2005.

[1] Millican (1994) "Central to the [Strawsonian tradition] is the distinction between a sentence and what is said by a sentence - Strawson initially called the latter a use of a sentence, and sometimes a proposition, but his most frequent term for what is said, which Wolfram consistently adopts, is the statement expressed."

[2] Rouse (2005) "A statement is defined as that which is expressible by a sentence, and is either true or false... A statement is a more abstract entity than even a sentence type. It is not identical with the sentence used to express it... [That is,] different sentences can be used to express the same statement."

[FOOTNOTERouse2005-3] Rouse 2005.

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