I would never die for my beliefs, because I might be wrong. -- Bertrand RussellThis is a strange statement coming from a philosopher, an English Lord, who went to jail because he openly opposed Britain's involvement in World War I. (Conceded, imprisonment is still not a death sentence.) Surely, he knew -- perhaps not at that time -- that there are beliefs that cannot be said to be true or false. They may be judged to be unworthy, precipitous, or unwise, perhaps, but not true or false.
The crucial difference is between "believing that" and "believing in." Believing that is a matter of truth or falsity. Supporting evidence is a relevant consideration
Believing in is a matter of commitment, of faith, or of hope. One may persist in such commitment in the face of strong evidence that it is wrongheaded. We may question the wisdom of such a commitment, but we do not ask for supporting evidence. One can believe in something, without believing that something else relating to it is true or false.
For example, you may insist on believing in your brother's honesty, without believing it is false that he has stolen something. Or, you can believe in being kind to all persons without believing that they personally merit such consideration.
False beliefs are beliefs that something is factually true, when it is not. A judgment that someone's belief is false depends on the authorities one invokes to claim that one knows something to be a fact belying the belief (a belief that) judged to be false.
The most one can say about beliefs in some thing, in some commitment, in some person is that this faith, this commitment, presumes the truth of facts needed to support that faith. To the extent that such facts are lacking, the faith may be at best a forlorn hope.
So it is that one may believe in a god without knowing that a god exists; or one may believe in a way of life, i.e. pacifism, Animal rights, without knowing that such a way of life is ultimately feasible. There is a lot of room between "not knowing that X" and "knowing that not-X" that permits belief in X to retain some credibility, some honor, even.
A religious belief may be foolish, -- many have died or caused others to die for such foolishness. But religious belief in, trust in, commitment to a god is not disestablished by facts based on the authority of empirical science, any more than, say, brain research can inform me that I am mistaken in believing that chocolate I am tasting at the moment tastes good, if I judge the chocolate I am tasting to taste good to me.
To examine these issues further, see The Pseudo-Science of "X is no more than Y"