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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 declarative sentences.

Source: https://en.wikipedia.org/wiki/Proposition

If you define proposition as "objects of belief/referents of that-clauses", I believe it rains. and I believe it doesn´t rain. contain 2 different propositions, as I understand it [which would be formalized as p and q].

If proposition were defined as "the primary bearers of truth value", there would only be one proposition [formally: p and ¬p].

Am I correct in reasoning this way, does the number of distinct propositions depend on the definition of "proposition"?

  • See also Propositions. – Mauro ALLEGRANZA Mar 31 '17 at 10:27
  • If P = "I believe it rains" then ~P = "NOT(I believe it rains) = "I do not believe it rains." That is different from "I believe it doesn't rain." P = "I believe it rains," ~P = "I do not believe it rains," Q = "I believe it doesn't rain," ~Q = "I do not believe it doesn't rain." Putting that side, propositions can have multiple things that refer to them. That is the whole point of their explanation of why similar sentences have similar meanings, because they point to the same proposition. Q and ~P can be the name of the same proposition, so in that case ~P is not unique. – Not_Here Mar 31 '17 at 10:51
  • There is a difference when you're talking about actual propositions, which are purported to be ontological objects, and the logic that you are formalizing them in. "I believe it rains" is one proposition that means something, it means you believe it rains. "I do not believe it rains" is another, completely different proposition, whether or not it can be made out of a compound proposition with the negation connective in a formal language. Even if you think of them as truth bearers, that just means they're things that are true or false. You're dealing with them outside of a formal system. – Not_Here Mar 31 '17 at 10:55
  • @Not_Here I do understand that. The question I´m trying to answer is: How many propositions are there in my examples? So you´re saying "it doesn´t rain" and "it rains" are 2 different propositions (even though you could split up "doesn´t rain" in ~p if you were to formalize the expression)? – LittleD Mar 31 '17 at 11:27
  • My point is that how you split it in terms of a logical language is irrelevant because the syntax of a logical language is arbitrary. I would definitely recommend reading the particle that Mauro linked to, propositions are very intricate things. I guess I can see the misunderstanding, the propositions in what you linked to, the ones wikipedia are talking about, are different than the subjects of "propositional logic." The wiki and SEP articles are talking about the larger, abstract entities instead of just variables in a formal language. – Not_Here Mar 31 '17 at 11:33
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Some comments.

Propositions are (usually) not linguistic entities: thus they differ from statements and sentences.

This is the meaning of:

"The term proposition is used to refer to ... the referents of that-clauses, and the meanings of declarative sentences."

Propositions are (usually) not mental entities, like thoughts or states of mind.

The are (usally) some sort of abstract entites.

We have mainly two possibilites.

According to the first one, propositions are part of the furniture of the world; in this case, we often use them as the reference of (linguistic) sentences, like objects are the reference of names (see Russell's Logical Atomism).

According to this point of view, a proposition is a mind-independent object and a true proposition can be identified with a fact.

Problem: if so, a negated proposition ¬p must be idientified with a "negative" fact... but what are negative facts ?

A different point of view is to maintain that a sentence (the linguistic entity) express a "content" (see Fregean sense).

A sentence is true or false according to the correspondence of its content to facts: a true sentence is a sentence expressing a content that corresponds to an existing fact, while a false sentence express a contente that does not corerspond to a fact (see Wittgenstein's Logical Atomism).

With tis second point of view, if we equate "content" (of a sentence) with proposition, we have that the two expressions p and ¬p express the same proposition: one of them (e.g. p) is true and the other (¬p) is false.

  • Nicely put regarding "linguistic entities" – DukeZhou Mar 31 '17 at 20:52
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I was taught specifically that propositions are mental entities in the mind alone. We can not see or hear propositions for instance. You can't apply any sensory verification to a "proposition". In this way we express a proposition with a declarative sentence or propositional variable to apply sense verification. Proofs are sense verifiable because we can see them. The terms proof and demonstrate are by definition expressions that require someone to use at least one of our famous senses: sight, hearing, touch, taste or smell.

I was taught that propositions are those concepts or ideas that are expressed by meaningful declarative sentences to hold a truth value of either true or false. This does not indicate I "know" the truth value of the proposition at hand. For instance the proposition "God exists" is either true or false. How I know is not the issue. I did not say it was true and I did not say it was false. By definition a proposition must be true or false. That is to say analytically this must be or we are using the wrong word.
In the real world many people take the utterance of a proposition as a declaration or affirmation of the proposition. So when I say the proposition "God exists" they ask almost always ask "how do I know?" They immediately take the proposition as a value judgement, personal belief, or opinion. These people fail to understand by merely stating a proposition I am not making a personal stand. Even if I state a proposition as true this would still not be a personal stand but a logical one. We don't make all propositions true. Some are true by nature as logical necessarily such as all triangles have three sides. My personal experience is not involved. If there is a God that exists, then my existence is not relevant nor is what I think relevant to the truth of the proposition. Some propositions are independently true outside of any human being. My teacher took the approach that most propositions if not all propositions are independent of the speaker or messenger. This expresses that Proposition x is not true because I say so but it happens to be true in reality. No feelings, opinions, or emotions are involved regardless of the proposition expressed.

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