A rational argument means using logical thinking and facts to explain or support your opinions or ideas. It involves presenting reasonable and well-thought-out points to persuade others or to come to a fair conclusion. Full definition
A shame, really, because there actually are good, rational arguments for belief, if they'd only take the time to do some questioning, criticizing, and research. (religion.blogs.cnn.com)
Most of us have at least some experience of changing beliefs, including some fundamental moral beliefs, under the pressure of rational argument. (firstthings.com)
They have a duty to demand that space for rational argument in newspapers, journals and programmes. (newscientist.com)