Truth and falsity are properties of propositions. A proposition is true if it corresponds to the facts, and otherwise it is false.
The statements 'Jupiter is larger than the Earth' and 'Earth is smaller than Jupiter' are different, but both exemplify the same proposition. Likewise, my belief that Jupiter is larger than the Earth is not the same thing as your belief that Jupiter is larger than the Earth, but both are about the same proposition. Propositions are abstract things. You cannot find propositions in the physical world, neither in books nor in peoples' brains, but only structures that exemplify them.
All truths are universal and objective. A proposition which is "true" for some people but "false" for others is merely false. A true proposition tolerates no exceptions, by definition. A counterexample to any proposition entails its falsity, however small the deviation from the facts. What is true is true for everyone, or else it was never true in the first place. The inherent universality and objectivity of truth is why it is valued so highly and can serve as a common goal for rational discussion.
True propositions exist independent of our beliefs about which propositions are true. We may be right or we may be wrong. Whether a proposition is true and whether we know it to be true are separate issues; the absence of certainty or knowledge does not entail the absence of truth.
A proposition may be verisimilar or truthlike. One proposition may have a higher degree of verisimilitude than another. For example, both propositions exemplified by the statements 'Jupiter is two times larger than the Earth' and 'Jupiter is ten times larger than the Earth' are false, but the latter has a higher degree of verisimilitude, i.e. it is closer to the truth. There is no precise way to quantify verisimilitude. Propositions entail other propositions, and every proposition has infinitely many logical consequences. Therefore, to entail any false proposition is to entail infinitely many.
The idea of "theories of truth" is nonsense. The question 'which theory of truth is true?' is rather facile. We can, of course, define the word 'truth' as something other than correspondence to the facts, but then we have just discreetly changed the subject. Usefulness and coherency are relevant to truth, but they are weaker standards and less precise ends. If pragmatists, coherentists, or whoever want the word 'truth', then they can have it. Words are not important, because 'troof' and 'thalzity' are fine substitutes.
