De Morgan in the prehistory of statistical hypothesis testing

Whereas the research of the 19th-century mathematician Augustus De Morgan in formal logic is fairly familiar to historians of mathematics, his work in probability is largely unknown to the modern reader. For this reason, few would be aware that this work contains a self-admitted error in probabilistic reasoning. This mistake is intriguing not only because it features in the work of someone who was so expert in logic but also because it appears to be an early example of hypothesis testing, which was a topic of much controversy in the development of mathematical statistics in the 20th century. The paper examines the mathematical and historical details of De Morgan’s error.