Following his teacher, Karl Popper, the operating principle of Bartley's rationalism is the formula 'I may be wrong and you may be right, and by means of critical discussion we may get nearer to the truth of the matter'.Note that this conception of rationality is all about *how disagreements are treated*. It has an implicit "When we disagree, I may be wrong..." at the start.
Here is an equivalent statement of rationality:
Rationality is a property of how disagreements are treated, not which ideas one holds. Rational ways of approaching disagreements keep open the possibility of either party being mistaken, or both parties. Rational approaches are those that aim to eliminate errors. Irrational approaches presuppose a correct conclusion. They try to entrench it, or "make it rule". Aiming to convert people to your way of thinking is thus irrational, whereas aiming to discuss which way of thinking is true is rational.