Before addressing the evidence quoted in your link, note it well that no contemporary writing or immidiately following Jesus' time mention a thing about the extraordinary events surrounding his life or alleged crucifixion. Yet we have proof that Bar Kochba (another messianic claimant who came just a few years after Jesus) has archeological and historical proof of his existence.
If we turn to the primary source, the NT, we see that the over dramatization surrounding Jesus' death found in Matt27:45,51,52, which clearly was an effort by that unknown writer to connect Jesus to the prophecies of Zech14, isnt reported in other Gospels let alone contemporary historical writings, with the eclipse, earthquake and deads coming back to life to be seen by many (where did they all go by the way, did they just keep wandering around for some time like zombies in the streets of Jerusalem?), besides other spectacular events such as Jesus' triumphal entry into Jerusalem, his witnessed ascencion to heaven and other various wonderful displays allegedly seen by many. None of all this is reported in history including the works of Josephus or Philo who lived very close to the time and at the place where all these things supposedly happenned and wrote profusely about every noted personage of Palestine, describing every important event which occurred there during the first seventy years of the Christian era, even Galilee natives historians such as Tiberias who wrote detailed accounts of the period and of the Jews covering the entire time Jesus existed. Same deafening silence regarding other contemporaries of Jesus such as the Roman aristocrat and prodigious writer Seneca, and Pliny the Elder or other historians of the time who failed to mention these amazing events yet their works covered vast subjects relevant to their period. Seneca's silence was such an embarrasement even to early Christians that in the late 4th century forgeries were made in the shape of an exchange of letters between him and none other than the apostle Paul.
Romans were renouned record keepers and they recorded earthquakes which they called prodigies yet the only ones spoken about around Jesus' era happenned in 37 BCE (too early) and again in 110 CE (too late).
Partly for this reason, even many biblical scholars doubt that these cataclysms surrounding the alleged crucifixion really happened.
Even Peter who was giving his speech in Acts 2 only 50 days after the alleged event along with Paul who in 1Cor15 was trying to convince the people on Jesus' resurection never mentionned this extraordinary event to strengthen their arguments in front of an audience that badly needed it.
Although Christian apologists choose to ignore Matthew's account -for obvious reasons- when trying to prove the historicity of the crucifixion, they do try to find some basis for the alleged eclipse by refering to an obscure pagan personality of whom next to nothing is known about; Thallus. He is mentionned in a 9th century work that relies on a 3rd century Christian writer called Julius Africanus who himself paraphrases -not quotes- Thallus about a solar eclipse none knows when and where it happenned exactly and neither does Thallus link it to Jesus. As a side note the only recorded eclipse closest to Jesus' location and time of death occured in the year 29 in the Persian Gulf which doesnt fit the Jesus chronology and would have been of negligible impact in Jerusalem, 100s of miles away.
The non-Christian sources Christians reference for Jesus' crucifixion arent by contemporary historians aside from a disputed Roman passage (see below), or the few forged lines awkwardly inserted in between 2 flowing sections in Josephus' voluminous works that has pages and chapters devoted to petty personalities such as robbers or simple kings, yet this devout and zealous orthodox Jew, and who remained so until his death, ie the last person to accept Jesus as a god or as the Jewish King-messiah is said to have given a short comment in the middle of an acount about another character (Pilate) about how Jesus was indeed the wonderful, divine, and prophecied Jewish King-Messiah. Just a short passage about his long awaited Jewish King and yet he reports in much more details about John the Baptist and other self-proclaimed messiahs like Judas of Galilee, Theudas the Magician, the "Egyptian Jew" messiah? The absurdity forces some apologists to make the ridiculous claim that Josephus was a closet Christian.
There is a reason why none of the early Church fathers up to the 3rd century never quoted this most-appropriate passage in their controversies with the Jews and other works despite their familiarity with Josephus' writings; it is a late forgery. For example Origen the Church Father who spent most of his life contending with the pagan writer Celsus, and using Josephus' works failed to mention this "ultimate rebuttal". Origen even condemns Josephus for not having accepted Jesus as the messiah in his writings. It isnt until Eusebius the official propagandist for Emperor Constantine, who judged that "it may be Lawful and Fitting to use Falsehood as a Medicine, and for the Benefit of those who Want to be Deceived", the Church father notorious for his deception and distortions of evidence to advance the cause of the church, described by St Jerome himself who thought of him as well as other Church Fathers such as Origen as sometimes "compelled to say not what they think but what is useful", that we see a mention of the passage. The first ever mention of the passage unsurprisingly comes at a time where Christianity monopolised what should be the truth, torching whole libraries, yet keeping Josephus' histories which they needed to advance their cause, turning the leading Jewish historian of his day into a witness for Jesus Christ.
In fact the Latin version of Josephus' work translated by Jerome is very similar to the quote Eusebius attributes to Josephus, except of course for the crucial parts about Jesus. Even later Christian apologists and open deciever such as Chrysostom who judged that "often it is necessary to deceive", and Photius both rejected this passage in their works yet they needed evidence such as this in their writings. Not a single writer before the 4th century – not Justin, Irenaeus, Clement of Alexandria, Tertullian, Cyprian, Arnobius, etc. – in all their defences against pagan hostility, makes a single reference to Josephus’ wondrous words. Because of the overwhelming evidence against its authenticity, Christian apologists try turning to another much briefer reference in "Book 20" Yet Josephus's second reference falls both because it is dependent upon the earlier (false) reference for explanation – and because it actually refers to "Jesus, the son of Damneus" who was made "high priest by king Agrippa".
No contemporary writing or immidiately following his time mention a thing about the extraordinary events surrounding his life or alleged crucifixion. Yet we have proof that Bar Kochba (another messianic claimant who came just a few years after Jesus) has archeological and historical proof of his existance.
A passage by the Roman Tacitus (born a good 20 years after Jesus' death and started writing some 60 years later, meaning he wasnt a historical witness and only relied on hearsay if we were to accept the passage attributed to him as athentic) talking of the persecutions of early Christians, mentions how the founder of this religion "was Christus, who, in the reign of Tiberius, was punished, as a criminal by the procurator, Pontius Pilate". Besides the fact that Pilate wasnt procurator but prefect which further shows how this passage if genuenly writen by Tacitus certainly wasnt based on detailed historical research, but again, none of the Church fathers nor any Christian writer prior to the 15th century mention it, despite their familiarity with Tacitus' works and their need for such weighty evidence by a renouned historian. Not even Eusebius who in the 4th century cites all sources available from Jewish and pagan sources. In fact it is well known that Tacitus' writing dates to about 112 CE meaning 70+ years after Jesus supposed death, so definitely not proof of anything even if the quote was from Tacitus himself but even this is disputed due to the fact there is only 1 surviving copy of this writing, supposedly "copied" in the 8th century CE (700 years after it was supposedly written) by Christian hands who wrote history, meaning it was most probably another forgery. There exist no Roman records of Jesus' execution by Pontius Pilate and here we have the most renouned of Roman historians citing the alleged event, and yet he is ignored by Christian apologists up to the 15th century.
In fact the reference to Jesus is absent from a 5th century Christian writer Sulpicius Severus who quotes the passage attributed to Tacitus in nearly the same words.
Concerning the Greek satirist Lucian of Samosata (125-180 CE), his statements concerning Jesus (an assumption since he never names Jesus, keeping in mind that many were crucified in Jesus' time) were written near the end of the 2nd century, meaning he had no independent sources and relied upon Christian sources, common knowledge etc in fact Lucian does not even specify his sources.
Sulpicius Severus wrote in the 5th century about alleged Christian persecution under Emperor Nero yet no historian or any Christian writer ever confirmed this, including Josephus who did not fail describing and denouncing Nero's abuse of power.
Another funny forgery is The Lentulus Letter, attributed to a fictitious predecessor to Pontius Pilate, governor of Judaea, called "Publius Lentulus". The letter is addressed to the Roman Senate, reporting Christ's "raising of the dead", describes him as "the most beautiful of the sons of men."
Jesus in the Talmud
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Just as there are no evidence for Jesus' alleged crucifixion, there is even less evidence for the scale of persecution early Christians allegedly sufferred, and the reason why violence was directed at them. In fact it was precisely due to the religious toleration of the Roman world, that nevertheless despised Jews for their insularity and acted against religious movements only when they appeared to threaten public order, that the nascent cult of Christianity was able to develop, become organised and, ultimately, seduce the Roman state.
In total, Christians, throughout a 300 year period, lost about a little less than 2000 persons, not for solely adhering to a faith that until the early years of the 2nd century, Roman administrators were ignorant of, but due to their own provocations, stirring up of the population by refusing military service and motivating others to do the same based on the fear of eternal damnation, campaigns of psycho-terorism that consisted in seizing every possible calamity that befell the Roman world as an occasion to claim "divine retribution" and the soon destruction of "Babylon" with the emminent return of Jesus, confrontations by the church as it organized itself against a fragilized, erroded and fragmented Roman empire as a "state within a state". It was only when the empire was itself in peril that the Roman state acted violently against any hostile element from within, including Christians.
That 2000 estimate is dwarfed by the victims of the witch trials, burnings and lynchings during the period 1300-1800 numbering 35-65,000 (and many estimates are much higher) or victims of the Inquisition, though sometimes speculatively put in the millions, in any event far exceeded anything dreamed of by the cruellest of Roman emperors against Christians. This isnt even taking into consideration forced conversions of peasantry, temple-torching and shrine-smashing ordered by bishops as soon as Christianity started ruling under Emperor Constantine, Christian persecution by Christians themselves such as the 100.000 Protestant Netherlanders sent for execution by the Catholic Charles V of Spain. What modern apologetics forget is that much more Christians died for their faith at the hands of fellow Christians than had died before in all the "persecutions".
The willingness of an individual to suffer and die for a particular cause or belief doesn't prove its truthfulness or validity. For example, the willingness of the leadership of the early Mormon church to undergo persecution and even death doesn't prove the veracity of the Mormon faith system. Likewise, the New Testament description of some of the disciples undergoing suffering or death does not prove that what they preached or believed was true either.
In the words of Celsus, one of the foremost thinkers of his age whose critique of the Christians was so damaging that Christians destroyed every copy of his work they could find "Clearly the Christians have used ... myths ... in fabricating the story of Jesus' birth ... It is clear to me that the writings of the Christians are a lie and that your fables are not well-enough constructed to conceal this monstrous fiction."