The Shroud of Turin is an old linen fabric imprinted with the image of a tortured man who lies prone with his hands crossed before him. Since for many it is related to Jesus of Nazareth, this cloth is among the most studied, controversial and enigmatic of all archaeological and religious objects. Since its radiocarbon dating at the end of the eighties of the last century, it is considered by many to be an object made in the Middle Ages. The controversy is due to the fact that there are other scientific and artistic evidences that place this object outside the medieval sphere. An argument map is a critical thinking way of representing the relationships between evidences and arguments, and is used here to represent the sequences of argumentation that defend that the Shroud of Turin is not a medieval object.