Wikipedia (note the redirect) defines 'necessary truth' as statements which "could not be untrue", and I assume that this is how the term is usually used. A search through the SEP shows that while there is no article dedicated to the topic, this phrase is used in over 100 articles.
This question is in two parts:
What is a necessary truth?
Are these three definitions equally correct:
- (A) A statement that cannot be untrue
- (B) A statement which is true in all possible worlds
- (C) A statement whose negation implies a contradiction
The only way I can imagine (A) or (B) to be applicable would be if (C) is also applicable. Is there any other way to determine if something is a necessary truth other than by showing (C)?
Do necessary truths exist?
Based on qualification (C) above, I assume that the answer hinges on whether or not logical contradictions are impossible (and is therefore closely related to a few questions already seen on this site, such as this one and this one). However, it appears to me that Quine (in "Two Dogmas of Empiricism") disagrees. Would someone care to shed light on the issue?