Is there any difference between declarative sentences and statements?

Question

I was reading about propositions and statements and the differences between them and saw this:

What is the difference between a statement and a proposition?

and the answer that one of the users gave is this:

Leitgeb distinguishes between statements, which are declarative sentences (he calls them 'descriptive sentences'), from propositions, which, unlike statements, are not linguistic objects. Propositions are the sort of objects that can have truth-values. E.g., [that snow is white] is a true proposition (Lecture 2-1).

Once the distinction is made, the key idea is this: statements express propositions, which are then said to be true or false. E.g. "snow is white" is a statement that itself doesn't have a truth-value, but instead expresses the proposition that snow is white, which happens to be true. That's pretty much it.

I want to know if there is any difference between declarative sentences and statements?

Answer 1

Words are used in contexts for communication.

If one is speaking to a teller in a bank the word "statement" has definite meaning, but the words "declarative sentence" and "proposition" would likely not. One should not expect words to have the same meaning in all contexts.

Even if one restricts the context to logic, the words may be used differently or not at all. One needs to make clear in which document the words being used.

In the text quoted by the OP where a distinction is made between "statements" and "propositions", Hunan Rostomyan explicitly references the following:

Leitgeb, Hartmann (2014 Spring) Introduction to Mathematical Philosophy (Coursera).

This defines the context. It is not just the author, Leitgeb, but one of the documents authored by Leitgeb. Within that document the reader can reasonably expect a consistent use of those terms which need not apply to other sources even those authored by Leitgeb.

As another example, searching Norman Megill's Metamath A Computer Language for Mathematical Proofs one can find multiple references to "proposition" and "statement", but only one use of the word "sentence": "English sentences".

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The OP would like to know if there is any difference between declarative sentences and statements in the general context of logic?

One should not expect to find a difference between these terms that applies to all contexts. But if one restricts the context to a particular document, one should expect the author(s) to use the terms consistently in that document. Then differences specific to that document could be observed.

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Megill N. Metamath A Computer Language for Mathematical Proofs. Retrieve on June 27, 2019 from http://us.metamath.org/downloads/metamath.pdf

Answer 2

Yes

For "statement" and "proposition", the terms can get jumbled depending on how each term is being defined, but the idea is clear and builds on this distinction:

1. There are expressions in languages (Schnee ist weiss, Snow is white, 雪は白い)
2. There are logical meanings and relations (S has property W)

1 and 2 are not identical. The former have to follow the rules of their natural languages and can be vague or ambiguous. In the English version, "white" could be either a noun or an adjective and this would change its logical meaning.

Conversely, propositions in logic are intended to express 1 thing precisely and to be trans-lingual entities. No proof should ever hinge on multiple senses of a word or on a vagary of a particular language.

Logical proofs (especially formal ones but in a less strict way most philosophical proofs) deal in 2. But depending on how formal the area is, we still write in natural languages (with the goal of being precise enough about our terms to prove things).

To give an analogy, the letter c can express two sounds, which we write as /k/ and /s/ but the /k/ and /s/ are not letters, they are IPA ways of writing the pronunciation. Propositions are that IPA level even if we write them as if they were natural language.

While some people use "statement" to mean what others use "proposition" or "claim", they are all angling at roughly the same idea above.

None of the people involved would mean a "declarative sentence" by "statement" because "declarative sentence" is a term of grammar -- and merely refers to the form of a sentence. What people are looking for in logic is not an understanding of grammar but an understanding of the logical meaning and how it is organized. (I can vaguely imagine someone rejecting the term "statement" because they view it as a synonym for the grammatical term "declarative sentence")

This is a big part of Russell's work.

Of course, there are philosophers who work on the philosophy of language who are interested in the relation between natural language and logic, and there are other philosophers who think the idea that there's a logic meta-language that differs from natural sentences is bunk.