Just to add here what I left assumed in my previous post . . . .
Enough has been written on the contradictory and inconsistent issues arising from the attempts to establish “bedrock evidence” for the life of Jesus from “criteriology”. (I am not addressing the use of criteria in other historical studies where it has a different function.)
Criteriology leaves the debate open whether Jesus was a political revolutionary, an apocalyptic prophet, a rabbi, a mystic, a teacher, a healer, a magician, a timberman (see #4 by Lemche at http://www.bibleinterp.com/opeds/sack357908.shtml).
In other words, criteriology leaves us not knowing where to even start a definitive exploration of who this Jesus was.
But in addition to failing to establish who or what Jesus was historically, it leads to the greater sin of avoiding the historical question of Christian origins. Christianity was a faith movement, and its origin and spread needs to be explained as such. The Christ that was spread through the Mediterranean and Middle East was a Christ of faith, after all. A mythical construct, in other words.
Historical method worth its salt will work with the evidence as it exists, as faith literature, and through analysis of both it and its relationships with other ideas of the time, seek to understand its origin and appeal.