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?

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    Yes declarative sentences are part of English grammar and statements dont have to be part of grammar. Propositions are intangible and Express an idea. This means propositions are not sense verifiable. Sentences are physically literal & can be sense verified. You cant SEE propositions you see a representative i.e., the declarative sentence or symbolic language as in math. Further more a proposition expresses that the idea has a truth value that is True or False. There are no unknowns propositions. You might not know if its true or false but dont get caught up into that. – Logikal Jun 27 '19 at 17:21
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    Every statement is NOT a declarative sentence. Many statements are emotionally controversial such as "abortion is murder." That statement would not be a proposition because it is missing details. It is too vague. What is murder for instance. Many things would need to be spelled out to avoid confusion. The example is emotional not logical. Some statements are NOT part of grammar. For instance me pointing a fire arm at your forehead is a statement. It expresses the use of deadly force without me saying a word or writing any demands to you. You recognize a deadly force don't you? – Logikal Jun 27 '19 at 18:00
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    Also one should note all statements dont express something that is either true or false. There are humans that speak insults to other humans and those insults are statements. Gestures can also be statements. Traffic cops do this all the time. There is a universal hand sign to STOP. There are also statements that are meaningful and statements that are NOT meaningful. My watch likes vanilla ice cream is a meaningless statement and not false. Declarative sentences are linguistic elements in ENGLISH grammar. The same grammar rules dont apply to all languages. – Logikal Jun 27 '19 at 18:21
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    Statement : a declaration, an assertion. – Mauro ALLEGRANZA Jun 27 '19 at 18:38
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    Leitgeb's use is not universal, Strawson calls "statements" what Leitgeb calls "propositions". The fine distinctions between statements and declarative sentences, if any, also vary from author to author. But the more common usage is (contrary to Logical) that statements are declarative sentences which are truth-apt. These things can be controversial, whether "Mona Lisa is beautiful" is truth-apt depends on one's views, but "something is beautiful" is not truth-apt, and hence not a statement, because "something" is a variable placeholder. – Conifold Jun 27 '19 at 18:53

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".

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.

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

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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.

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