I have spent a few days running around the internet trying to find a distinct and simple explanation of how all of these terms fit together. I'm aware it is quite nuanced.
Could someone help me resolve this issue? I'm sure there are many others who find your answer helpful.
Thank you!
A proposition is beyond language.
A statement is a referrer, that refers to a proposition. A proposition is a referent, that is symbolized by a referrer.
Examples of statements
The word premise is always used in the context of an argument.
You have an argument when it is asserted that given some set of propositions are true, another proposition follows. The former propositions are called the premises of the argument, the latter proposition is called the conclusion of the argument. The premises are the propositions given to be true. Arguments consisting of one premise are possible. To every argument there corresponds a statement called the corresponding conditional.
Argument: A1,A2,...,An; therefore B
Has corresponding conditional
If A1 and A2 and... and An then B.
So a one premise argument has a corresponding conditional
If A then B, where A is its single premise.
An assertion is a statement that is stated to symbolize a true proposition.
There is confusion about the use of the term statement. Many people use the term statement when they mean proposition. Their confusion stems from the original meaning of the word statement.
Classical Definition
A statement is that which is true or false, but not true and false in the same state.
A state is a moment in time.
Thus an equivalent definition is:
A statement is that which is true or false but not true and false simultaneously.
The SEP entry on propositions has for its point-of-departure:
The term ‘proposition’ has a broad use in contemporary philosophy. It is used to refer to some or all of the following: the primary bearers of truth-value, the objects of belief and other “propositional attitudes” (i.e., what is believed, doubted, etc.), the referents of that-clauses, and the meanings of sentences. ... Propositions, we shall say, are the sharable objects of the attitudes and the primary bearers of truth and falsity. This stipulation rules out certain candidates for propositions, including thought- and utterance-tokens, which presumably are not sharable, and concrete events or facts, which presumably cannot be false.
Insofar as a statement is an utterance-token (something done at a specific time, in a specific tone of voice, and so on), it is not a proposition, then. Or at least not in the above technical sense. Now, since one can "entertain" a proposition without advocating the same, and since we can make statements about the content of works of fiction, there is a difference between using a proposition as a premise in some piece of reasoning, and the proposition itself; and then an assertion is to a statement what use-as-a-premise is to a proposition.
The cited SEP account might seem to make of propositions a sort of "abstract object," and indeed that is the most usual way of cashing the thesis out as such. So a conceptualist or nominalist might be inclined to deny the theory of propositions and make do with sentences. Then, "In tenebris aardvark mundum accepit," "어둠의 땅돼지가 세상을 점령했습니다," and, "The dark aardvark took over the world," are not the same in meaning by corresponding to the same proposition, and perhaps they are not altogether the same in meaning otherwise anyway. But so the SEP entry on deflationism about truth includes an indirect critique of using sentences instead of propositions:
That is, since sententialism seems false in the one connection, it seems false in the other. At any rate, the distinction in theoretical results, here (that one concept leads to a false result, the other to a trivial one) showcases the sentence/proposition distinction moreso in itself, too.
In order to keep things simple, as a first step I propose the following definitions:
Statement = proposition: A sentence which can be either true or false.
Assertion: Asserting a proposition means to claim that the proposition is true, not false.
Premise: The first part A of an implication “A implies B”. Here A, B are two propositions.
In the second step, some authors discriminate between a proposition and a statement. I for myself do not understand what they mean. But I am sure, that some experts on this side can - and hopefully will - explain it :-)
