I'm not going to put in much on this becuase it's very complex, voluminous, madening and takes forever to address properly. I think basically Jesus is talked about in the Talmud and that proves he at least existed. There's three reasons I assume so:
(1) Historians of the Talmud allude to it.
(2) it was self censored and the references to Jesus were blotted out or changed to certain epithets are know this to be a fact. So it did talk about him.
(3) The skeptic Celsus offers historical proof that the Talmud talked about Jesus.
The thing about the Talmud passages is the Jews wanted plausible deniable. They changed the readings so they could say It's not really him. That's understandable becuase they were being persecuted and they reason to fear. It also means that the fact that Talmudic evidence is confusing and not clear is not reaosn to discount it. Part of the maintaining of the deniable is taking Jesus name out of the text and using epithets and another part is the argument that the sourcs are from too late. This is one of Lowder's main argument.s Being late doesn't matter because the tradition was oral it was handed down it's well known the sources go back to the first century.
One of the major sources dealt with by Loweder is the "Ben Pandera" tradition. This is supposed to be a reference to Jesus through his grandfather. Then the The Baraitha tradition. Before dealing with those let's just say that these issues are too complex to settle here. I wont spend much time on them. Before getting to them I'll deal with the three Issues I laid out.
(1) historians of the Talmud recognize Jesus as part of the tradition.
The Babylonian Talmud
translated by MICHAEL L. RODKINSON
Book 10 (Vols. I and II)
The History of the Talmud
from Vol I chapter II
Thus the study of the Talmud flourished after the destruction of the Temple, although beset with great difficulties and desperate struggles. All his days, R. Johanan b. Zakkai was obliged to dispute with Sadducees and Bathueians and, no doubt, with the Messiahists also; for although these last were Pharisees, they differed in many points from the teaching of the Talmud after their master, Jesus, had broken with the Pharisees
This clearly indicates that Jesus was followed by Christians who understood him as a Rabbi in the late first century, but the Jesus myth theory says that it was only in the second century that began to put a concrete history to Jesus. Note this history indicates taht they had a history about him as they said he had been a pharisee.
The index indicates that this statment is from the time covering the late first century.
Index to the work
The Talmud is Rabbinical commentaries that begin about the second century but they draw upon even older material. Soem parts of the Jerusalem Talmud go back to the frist century and even before:
Michael L Rodkinson
"History of Talmud"
"The Talmud is a combination of Mishna and Gemara, the latter is a collection of Mishnayoth, Tosephtas, Mechilta, Siphra, Siphre and Boraithas, all of these, interpreted and discussed by the Amoraim, Saboraim, and also Gaonim at a later period. "The Mishna is the authorized codification of the oral or unwritten law, which on the basis of the written law contained in Pentateuch, developed during the second Temple, and down to the end of the second century of the common era." The author of which was R. Jehuda, the prince named "Rabbi" (flourishing toward the end of the second century), taking the unfinished work of R. Akiba and R. Meir as basis."
Christian apologists have long used the references in the Talmud to certian figures, some named "Yeshua" and others called by deogatory nick names, to prove the Jews wrote about Jesus. But modern Jewish scholars have given up that pasttime and now deny that any of these references pertian to Jesus.
Rabbis have never deneid it. Rabbis have been using the talmudis stories of Jesus for centuries to illustraet the problems with Christianity. Secondly, they were confident enough that this was Jesus that they actually took the mentions of name out at one point to avoid attacks by anti-semetic Christians.
Rodkinson was an important translator of the Talmud. His story is found here:
(2) Talmud was Self Censored
References to Jesus were expunged form it. McDowell Explains:
"... in light of the persecutions, the Jewish communities imposed censorship on themselves to remove references to Jesus in their writings so that they might no longer be a target of attack. Morris Goldstein, former Professor of Old and New Testament Literature at the Pacific School of Religion, relates: Thus, in 1631 the Jewish Assembly of Elders in Poland declared: ‘We enjoin you under the threat of the great ban to publish in no new edition of the Mishnah or the Gemara anything that refers to Jesus of Nazareth... If you will not diligently heed this letter, but run counter thereto and continue to publish our books in the same manner as heretofore, you might bring over us and yourselves still greater sufferings than in previous times.’"He has an example of such as passage that Lightfoot found. some of the epithets that replaced the name "Jesus" were:
Dr. Robert Morey continues:
"Thankfully, copies of the uncensored pre-1631 texts can be found in Oxford University and several other European libraries. Thus the statements about Jesus were never actually ‘lost.’ They were published separately in numerous editions and studied by Jewish scholars in private. No one denies these facts any more... While the Soncino edition of the Babylonian Talmud is a censored text, the editors usually give the uncensored original readings in a footnote. We have put the statements about Jesus back into the text where they originally belonged and have indicated this by [ ]." (Morey, pp. 1-2)
Celsus demonstrates a connection to the material of the Talmud, indicating that that material about Jesus was around in a leaast the second century. Since Jewish sources would not have been reidaly avaible to Celsus it seems reasonable to assume that this information had been floating around for some time, and easier to obtain. Therefore, we can at least went back to the early second, late frist century.
Origin quoting Celsus: Jesus had come from a village in Judea, and was the son of a poor Jewess who gained her living by the work of her own hands. His mother had been turned out of doors by her husband, who was a carpenter by trade, on being convicted of adultery [with a soldier named Panthéra (i.32)]. Being thus driven away by her husband, and wandering about in disgrace, she gave birth to Jesus, a bastard. Jesus, on account of his poverty, was hired out to go to Egypt. While there he acquired certain (magical) powers which Egyptians pride themselves on possessing. He returned home highly elated at possessing these powers, and on the strength of them gave himself out to be a god."
So we estabilsh:
(1) Mary was poor and worked with her hands
(2) husband was a carpenter
(3)Mary committed adultary with Roman soldier named Panthera. (where have we heard this before?)
(4) Jesus as bastard
(5) driven to Egypt where Jesus leanred magic.
All of these points are made in the Talmudic passages. This can be seen both above and on the next page. The use of the name Panthera is a dead give away. Clearly Celsus got this info from the Talmud. Christians never used the name Panthera. He could only hae gotten it form the Talmud and these are very charges the Talmudists made.
Here is a mishna passage, which makes most of the points. Being from the Mishna it would draw upon first century material:
MISHNAH.[104b] If one writes on his flesh, he is culpable; He who scratches a mark on his flesh. He who scratches a mark on his flesh, [etc.] It was taught, R. Eliezar said to the sages: But did not Ben Stada bring forth witchcraft from Egypt by means of scratches [in the form of charms] upon his flesh? He was a fool, answered they, proof cannot be adduced from fools. [Was he then the son of Stada: surely he was the son of Pandira? - Said R. Hisda: The husband was Stada, the paramour was Pandira. But the husband was Pappos b. Judah? - his mother was Stada. But his mother was Miriam the hairdresser? - It is as we said in Pumbeditha: This is one has been unfaithful to (lit., 'turned away from'- satath da) her husband.] (Shabbath 104b)
In fact Origin himself almost hints at spcial knowledge of Jesus "ture" origns, what would that knowldge be? Christian knolwege would be posative and not contian many of the poitns, such as Mary being a spinner or hair dresser. No Christians ever said that. It was suspect for a woman to work. That's an insutl to her.
The following quotes are taken from Celsus On the True Doctrine, translated by R. Joseph Hoffman, Oxford University Press, 1987:
"Let us imagine what a Jew- let alone a philosopher- might say to Jesus: 'Is it not true, good sir, that you fabricated the story of your birth from a virgin to quiet rumourss about the true and insavoury circumstances of your origins? Is it not the case that far from being born in the royal David's city of bethlehem, you were born in a poor country town, and of a woman who earned her living by spinning? Is it not the case that when her deceit was uncovered, to wit, that she was pregnant by a roman soldier called Panthera she was driven away by her husband- the carpenter- and convicted of adultery?" (57).
why a Jew? or Philospher? Celsus was obviously reading the jewish sources. This is one of the charges made in the Talmud.
Here he claims to have secret knowledge that Christians don't have:
"I could continue along these lines, suggesting a good deal about the affairs of Jesus' life that does not appear in your own records. Indeed, what I know to be the case and what the disciples tell are two very different stories... [for example] the nonsensical idea that Jesus foresaw everything that was to happen to him (an obvious attempt to conceal the humiliating facts)." (62).
where is that from? It has to be the Talmud, or sources commonly drawn upon by the Talmud.
But how does this prove it was Jesus? Celsus sure thought it was. Apparently his Jewish contracts told him this is the staright scoup on Jesus' life. We see that everywhere in the Talmud Jesus is talked about as a living person,and connections are made to his family and geneology.
Celsus pushes the knowledge back to late second century, but due to the availability or Rabbinical writtings it must have been around for some time before that. The Jews were very consicous of geneologies and family connections. why wouldthey not pick up on the fact that Jesus had none and no one had ever seen him personaly, if indeed that was the case?
Babylonian Talmud, Book 10: History of the Talmud, tr. by Michael L. Rodkinson, trans , at sacred-texts.com http://www.sacred-texts.com/jud/t10/ht105.htm
 Josh McDowell and Bill Wilson, He Walked Among Us: Evidence for the Historical Jesus (San Benardino, CA: Here's Life, 1988).
Dr. Robert A. Morey,Jesus in the Mishnah and the Talmud,California Institute of Apologetic PO Box 7447 Orange, CA 92863 1-800-41-TRUTH or (714) 630-6307--looks like private printing