The relationship between wisdom and age

Generally, it is believed that people become wiser with age, and all things being equal, I would agree that this is true because the more experiences a person has, the wiser the person will become. However, I would argue that if people are close-minded and always follow traditions, then as they age, they will become more stupid because they will just accumulate more and more illogical ideas about life. By the time they die, they would have become walking oxymorons.