“...understand that a belief is propositional, which means it can be expressed in a declarative sentence—a sentence that is either true or false...Recall that in logic, a proposition has been demonstrated when it has been shown to be the conclusion of a sound argument—an argument in which (1) all premises are true and (2) it is impossible for the premises to be true and for the conclusion to be false” (Critical Thinking Moore and Parker). Aren’t these two quotes contradicting because the first one says a proposition can be true or false while the second one states that it is impossible for the proposition to be false? Am I misunderstanding this and can someone clarify this for me?
Your two quotes are consistent in classic propositional logic. Regarding your "the first one says a proposition can be true or false", according to IEP here:
The term proposition is sometimes used synonymously with statement... A statement can be defined as a declarative sentence, or part of a sentence, that is capable of having a truth-value, such as being true or false.
propositional logic is classical truth-functional propositional logic, which studies logical operators and connectives that are used to produce complex statements whose truth-value depends entirely on the truth-values of the simpler statements making them up, and in which it is assumed that every statement is either true or false and not both.
So a proposition generally have a truth value, of course it may be true or false depends on further available information.
Regarding your "second one states that it is impossible for the proposition to be false", according to IEP here:
A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid.
A deductive argument is sound if and only if it is both valid, and all of its premises are actually true. Otherwise, a deductive argument is unsound... Consider, then an argument such as the following:
All toasters are items made of gold.
All items made of gold are time-travel devices.
Therefore, all toasters are time-travel devices.
Obviously, the premises in this argument are not true. It may be hard to imagine these premises being true, but it is not hard to see that if they were true, their truth would logically guarantee the conclusion’s truth.
So an argument can be logically valid but not sound and a sound argument can demonstrate the conclusion proposition as true.