An argument against Markan priority is the belief that the four New Testament gospels were originally written by Matthew, Mark, Luke and John respectively. That being the case, it is inconceivable that Matthew, a disciple of Jesus, would have relied on a book universally agreed not to have been written by an eyewitness to the life and mission of Jesus. Against this is that there is no evidence that the gospels, which are unsigned, were ever attributed to Matthew, Mark, Luke and John until the second century.
One of the earliest attempts to assign authorship to the gospels seems to have been made by Papias early in the second century, when he attributed two gospels to Matthew and Mark respectively. He assumed that Matthew wrote his gospel in either Hebrew or Aramaic ("the Hebrew language"), which if true would rule out Markan priority. However, there is nothing extant that points to there ever having been a Hebrew or Aramaic autograph of Matthew, and linguists say that the Greek manuscripts do not appear to be translations.