Hien B. answered • 03/21/19
Top Logic Tutor w/ Master's degree from Oxford
The difference is that statements merely express propositions. So a statement is "true" in virtue of the proposition it expresses being true. That is why only propositions are truth-bearers, while things like statements, thoughts, or ideas are not. In this sense, propositions are more fundamental and for some philosophers, they exist as abstract entities whereas statements do not. Additionally, two different statements may also express the same proposition (but not vice versa). Consider the proposition <~R>, where 'R' is defined as "it is raining". <~R> can be expressed by more than one statement. For example, it can be expressed by the statement, "It is not the case that it is raining", or the statement "It is not raining". So here, the same proposition is expressed by the two distinct statements.
Given this difference, it'd be more appropriate to say that statements are synonymous with sentences rather than propositions.
Hope that helps!
Majid S.
Hien B. has a point. Example: “y > 5” is a statement but not a proposition because Its truth value depends on the value of y, but this value is not specified, so I cannot evaluate the truthiness or falsehood of it. We call this type of statement a propositional function or open sentence.10/02/22
Majid S.
Also, statements are synonymous with sentences rather than propositions because not every statement can be treated straightforwardly as a proposition! Example, if you believe that "if a shape is a square, then it is a rectangle" How can this be evaluated then? Basically, we have two predicates here: S(x) standing for “x is a square” and R(x) standing for “x is a rectangle”. The sentence we are looking at is, S(x) → R(x). This is basically neither true nor false, as it is not a statement. Although we all know that we meant to consider the statement, ∀x(S(x) → R(x)). See Levin (http://discrete.openmathbooks.org/dmoi3.html)10/02/22
Gek Hua T.
i am shocked and surprised that the claim "statements are synonymous with sentences" is made. while a statement is expressible by a sentence and is either true or false ... a sentence like "Hien B. is stupid" can be neither true nor false (since stupidity is subjective and most important of all ... the context has not been established. Hien B. maybe clever in certain things but looks stupid to many others in other area).11/22/21