AP: There are basically ten. But there are three or four that are very important:
1. Something that is attested to by more than one independent tradition should be considered historical.
These sources are: the "Q" document; Mark, the first Gospel; material that is only found in Matthew or Luke; special traditions collected by John or other sources outside the New Testament, if they are proven reliable and provide independent information.
For example, three attestations of an exorcism or healing by Jesus should not be considered historical if one of them is found in the Gospel of Mark and the same story has been copied by Matthew and Luke. In such a case, that is supported by one tradition, not three.
2. The Criterion of "Dissimilarity." Certain words and deeds of Jesus can be considered historical if it is proven that that they cannot be derived out of and they are not contrary to the concepts or interests of ancient Judaism and early Christianity.
Example: An angry Jesus (Mark 1:41), which is opposed to the traditional figure of a meek and humble Jesus (Matt. 11:29); a Jesus who doesn’t know everything (Mark 13:32), as opposed to one who is divine and omniscient.
3. The Criterion of "Difficulty." It is probable that something was said or done by Jesus when such tradition causes many problems for the church later on.
Example: Jesus was baptized as a sinner by John the Baptist for the remission of sins, something that caused the early church all sorts of theological concerns because they considered Jesus God and sinless. Because of this difficulty, it is more likely that the account of Jesus’ baptism is purely an invention of the early church.
4. The Criterion of "Coherence/Consistency." Something that is coherent and consistent with what has already been established as authentic by the above three criterion can also be accepted.
Example: By Jesus’ use of "Abba" (Mk 14:36) to address God as "Father" and the various references in the Gospels to his continuous periods of prayer, it is clear that Jesus preached the nearness of God to human beings.With material found in the Gospels, and in some cases the rest of the New Testament, properly assessed by critics, we can begin to answer questions about Jesus’ life, words, doctrine, mission, person, etc.
For a thorough discussion of the other criteria, I recommend a chapter written by D. Gonzalo del Cerro in the following book: A. Piñero (ed.), ¿Existió Jesús realmente? (Madrid: Editorial Raíces, 2009), 350 pp. ISBN 978-84-86115-64-7.
TWH: I believe that the words spoken and the acts performed by the Lord Jesus Christ as presented in the four canonical Gospels are historical. I believe that they are authentic, genuine, and veracious. I believe that they are in no way deficient, in no way incorrect, or in any way insufficient for presenting the Lord Jesus Christ. I believe that the Jesus that we see in the Gospels is the Jesus who existed in history. Why do I believe this? Well, I believe that everything that is written down in the Bible ultimately comes from God. Biblical inspiration is critical to accurately understanding the Word of God (2 Tim. 3:16).
Searches for the historical Jesus are not so much attempts to figure out what Jesus actually said or actually did; they are more so attempts to figure out what Jesus did not say and what Jesus did not do. And at the very core of searches for the historical Jesus is an attack on the veracity of the Scriptures and the doctrine of inspiration. Did Jesus say "A trainee is not above his teacher, but, after he is fully trained, he will be like his teacher" while he was teaching on the Mount/Plain? Or did Luke take those words from a different teaching setting and add some extra content to spruce up his Gospel? Did Jesus feed the 5,000? Did Jesus heal the demoniac as recorded in Mark 5? Was Jesus born of a virgin? I don't search for the historical Jesus. I am on no such quest, and I would recommend to everyone who wants to know Jesus that they just go to the Gospels. God has revealed to us everything we need to know about the life and ministry of Jesus in the Gospels of Matthew, Luke, Mark, and John.