“Justification is a person-oriented activity. In trying to justify our beliefs, we often seek to persuade others and sometimes ourselves, but there is always some persuasion being attempted. As George Mavrodes has pointed out, it is possible to have an argument that is perfectly valid (the premises imply the conclusion) and perfectly sound (the premises, and therefore the conclusion, are true) that nevertheless fails to persuade. Consider his example:
Nothing exists or God exists. Something exists. Therefore God exists.
The argument is valid, and Mavrodes believes it sound because he believes in God. Evidently, however, there are many who would not be persuaded by this argument. In constructing arguments, therefore, it is important to give attention not only to their validity and soundness but also to their persuasive power. Our goal is not to establish propositions but to persuade people.
Therefore there is an existential element in justification. A proposition that is in accord with the laws of thought and with objective reality is, we might say, objectively justified. But I do not have a justification for believing it unless I have accepted those laws and realities into my own value system, unless they have become persuasive to me.
Mavrodes suggests that proof also should be defined in what he calls a “person-variable” way, so that an argument might be a proof to one person and not to another. His formulation for a proof is this: “We will have proved a statement to N if and only if we succeed in presenting N with an argument that is convincing for him.” If we ignore the element of persuasion or “convincingness,” says Mavrodes. we may find ourselves constructing perfectly valid and sound “proofs” that are of no help to anyone.”
(Frame, DKG, 151-52)