A simple correspondence theory would say that belief is a relation of the mind to a fact.

So, suppose Jill believes that Paul is dead. On the simple correspondence theory that would be a relation of Jill's mind to Paul being dead.

But, Russell argues, this theory would then fail the first requirement on a theory of truth, namely that it admit of falsity too.

"... for if there were such an object [as Paul's being dead], the belief would be true. There is in fact no object [since, we are supposing, Paul is not dead], and therefore [Jill] cannot have any relation to such an object. Hence, [her] belief cannot possibly consist in a relation to this object." (P 193a)