I've asked before as to what propositions count as meaningful, and, as some commentators and responders helpfully pointed out, 'meaning' and 'propositions' appear to be identical entities in the philosophical jargon. So I've decided to ask a new question and it is this: What are the propositions (or what is the meaning of sentences)? Is there a formal way of defining propositions? Or are they defined ostensibly only?
I'm not aware of a formal definition of proposition, and the issue is highly contentious, but one way to think about them is as follows. Take a sentence like "Clarissa is a fish". You can believe this, as in the sentence, "I believe Clarissa is a fish". You can hope it: "I hope Clarissa is a fish." You can doubt it: "I doubt Clarissa is a fish". These are various different propositional attitudes you take toward the proposition, but through them all the proposition is one and the same.
You can also say the sentence today and/or tomorrow. You can say it to your friend and/or to your teacher. You can write it down and/or say it. You can say it in English or translate it into German. The sentence is what changes in all these permutations but not the proposition.
In sum, the proposition is in effect the idealized content of the sentence, which is constant through time, place, translation, and propositional attitude. In this sense you can understand it as an abstraction from the sentences in which it occurs.
Well excuse the pseudo-philosophy BUT
A proposition is anything which I can express with a that in front, right?
I believe that, it is true that, that...
introducing a subordinate clause expressing a statement
It seems to me that this suggests a meta-language. e.g., if I think that A<->B then I am asserting not just a material equivalence, but a semantic (not syntactic) identity: such that it is always true in my language that A<->B.
- It is snowing iff there are snowflakes in the sky
- That it is snowing iff there are snowflakes in the sky
In 2 I am claiming the equivalence can be said in a metalanguage, that the the equivalence is "subordinate" to something else which can be expressed.
The supraordinate clause in 1 is augmented with THAT, and whatever it is which the that is about (e.g. I believe that) cannot be expressed without 1 [or something like it).
So in conclusion: a proposition is an expression which depends on some metalanguage.
I do not make a proposition