What is the difference (if any) between "not true" and "false"?

Question

A fairly simple question I hope someone can help me with.

Answer 1

In Buddhism, you can be here and not here

liar's paradox. this sentence is false. Is it true or not true?? if true it's false. if false, it's true

but in formal logic, P or ~P is a tautology, always true, an identity, so no difference

Answer 2

There is a difference if there were such a truth-value as "neither true nor false". There is of course a debate in philosophy whether propositions could in fact be neither true nor false.

Here are some cases that philosophers might cite as possible examples:

1. Liar Paradox: "This statement is false" (if you think about it, it seems as though this can't be true and it can't be false)
2. Propositions about the future: e.g. "Tomorrow I will have breakfast" (Some are motivated to say these types of propositions would conflict with free will if they are either true or false)
3. Vagueness: e.g. "George Costanza is bald" (Because 'bald' could be linguistically a vague term, there will be borderline cases in which it's not clear whether or not someone is bald, such that claims of baldness could be neither true nor false) See picture: https://upload.wikimedia.org/wikipedia/en/7/70/George_Costanza.jpg

Answer 3

In logic, "not true" and "false" are equivalent: ~T = F

The same holds for "not false" and "true": ~F = T

There are cases where a statement is unclear -- in which we can't really determine whether it is definitively true or false due to some ambiguity. In such cases one might say "that statement isn't true," but what should really be said is just that it is unclear, and that because of this its truth is unknown or indeterminate.