This is actually a very interesting question: How can we prove whether a given personage actually existed? How can we distinguish between a man to whom legends accrued and a myth to whom bits of history became attached? How would we distinguish, in crude terms, between Alexander the Great (the former) and King Arthur (the latter)?
Spencer’s argument reduces to a few key points. These are, in essence, that Islam presents itself as having emerged fully formed when Gabriel whispered the Qur’an into Muhammad’s ear, and therefore any evidence for evolution in belief or practice is prima facie evidence that the faith is a fraud. Because the accepted facts of Muhammad’s biography, as received in medieval Islam, do not conform completely to the earliest external sources from the Dark Ages, he must therefore have never existed. This specious reasoning rests on his interpretation of a key text.
The earliest non-Islamic source for the appearance of Muhammad and Islam is the Doctrina Iacobi nuper Baptizati, a Byzantine text written in the 630s CE recording events that occurred after the forced conversion of Byzantium’s North African Jews in 632. The dialogue given in the text is said to have taken place in July 634, after the Byzantine commander (candidatus) Sergius was killed by invading Arabs at the battle of Dathin near Gaza that February. This event was recorded in multiple sources, so we know it really happened.
Here is the passage about the coming of Islam. The translation on the left is the one Spencer uses. The translation on the right is a more recent, complete, and accurate translation, which gives a slightly different flavor to the text.
When the candidatus was killed by the Saracens, I was at Caesarea and I set off by boat to Sykamina. People were saying "the candidatus has been killed," and we Jews were overjoyed. And they were saying that the prophet had appeared, coming with the Saracens, and that he was proclaiming the advent of the anointed one, the Christ who was to come. I, having arrived at Sykamina, stopped by a certain old man well-versed in scriptures, and I said to him: "What can you tell me about the prophet who has appeared with the Saracens?" He replied, groaning deeply: "He is false, for the prophets do not come armed with a sword. Truly they are works of anarchy being committed today and I fear that the first Christ to come, whom the Christians worship, was the one sent by God and we instead are preparing to receive the Antichrist. Indeed, Isaiah said that the Jews would retain a perverted and hardened heart until all the earth should be devastated. But you go, master Abraham, and find out about the prophet who has appeared." So I, Abraham, inquired and heard from those who had met him that there was no truth to be found in the so-called prophet, only the shedding of men's blood. He says also that he has the keys of paradise, which is incredible.
Justus answered and said, “Indeed you speak the truth, and this is the great salvation: to believe in Christ. For I confess to you, master Jacob, the complete truth. My brother wrote to me that a false prophet has appeared. Abraham writes, ‘When [Sergius] the candidatus was killed by the Saracens, I was at Caesarea and I went by ship to Sykamina. And they were saying, "The candidatus has been killed," and we Jews were overjoyed. And they were saying, “A prophet has appeared, coming with the Saracens, and he is preaching the arrival of the anointed one who is to come, the Messiah. And when I arrived in Sykamina, I visited an old man who was learned in the scriptures, and I said to him: "What can you tell me about the prophet who has appeared with the Saracens?" And he said to me, groaning loudly, "He is false, for prophets do not come armed with a sword and war-chariot. Truly the things set in motion today are deeds of anarchy, and I fear that somehow the first Christ to come, whom the Christians worship, was the one sent by God, and instead of him we will receive the Antichrist. Truly, Isaiah said that the Jews will have a deceived and hardened heart until the entire earth is destroyed. But go, master Abraham, and find out about this prophet who has appeared." And when I, Abraham, investigated thoroughly, I heard from those who had met him that one will find no truth in the so-called prophet, only the shedding of human blood. In fact, he says that he has the keys of paradise, which is impossible.’ These things my brother Abraham has written from the East. …”
As translated in Robert G. Hoyland,Seeing Islam as Others Saw It: A Survey and Evaluation of Christian, Jewish, and Zoroastrian Writings on Early Islam (Princeton: Darwin Press, 1997), 57
As translated in Stephen J. Shoemaker, The Death of a Prophet: The End of Muhammad's Life and the Beginnings of Islam (University of Pennsylvania Press, 2011), 22-23.
Additionally, Spencer notes that this prophet was proclaiming a new Messiah, not that he is Allah’s last prophet. He is also troubled by the keys of paradise in the passage because “it is also completely absent from the Islamic tradition, which never depicts Muhammad as claiming to hold the keys of paradise.” Even some early Islamic sources preserve the claim—well documented in other Byzantine texts—that Muhammad claimed the “keys of paradise.” Down to the end of the medieval period, Islamic texts routinely state that “thine are the keys of paradise and hell,” usually in a metaphorical sense. The same claim was made in the sixteenth century, in the records of the life of the Orthodox Serbian St. George of Kratovo, a martyr who refused conversion to Islam. A Muslim attempted to convert him, according to his hagiographer, and in so doing asked George "What wrong do we do who honor Muhammad and keep his law and believe that God entrusted to him the keys of Paradise?"
Spencer concludes, however, that the prophet was a Christian- and Jewish-influenced figure, not the Muhammad of Islam. He suggests that “the unnamed prophet of the Doctrina Jacobi was one of several such figures, some of whose historical attributes were later subsumed into the figure of the prophet of Islam under the name of one of them, Muhammad. For indeed, there is nothing dating from the time of Muhammad's activities or for a considerable period thereafter that actually tells us anything about what he was like or what he did.”
But Spencer is suggesting a false dichotomy, that either Muhammad was exactly as depicted in late medieval Islamic hagiography, or he did not exist at all. Scholars have long understood that Islam, like every faith, has undergone a process of growth and change. No first-century Christian would recognize the gilded splendor of the Vatican, and the earliest Jews would wonder why no animals today are consecrated to Yahweh in bloody sacrifice. Scholars today recognize that early Islam underwent a process of growth and development.
It is hardly controversial to suggest that Islam drew upon Jewish and Christian traditions; the Qur’an itself contains stories parallel to Jewish and Christian traditions and states clearly that it builds upon and supersedes them. The similarity was noted in the Armenian History attributed to Sebeos and written after 660 CE in which the merchant “Mahmet” (i.e. Muhammad) is said to have preached of the God of Abraham because he was well versed in the history of Moses (ch. 42). Theophanes in the Chronicle confirms that Messianic expectations accompanied Muhammad when he writes that “At the beginning of his advent the misguided Jews thought he was the Messsiah who is awaited by them.” Such expectations are also seen in The Secrets of Rabbi Shi'mon in the seventh century, though drawing on an earlier original, according to Shoemaker: "In accordance with His will He shall raise up over them a prophet. And he (the prophet) will conquer the land for them, and they [the Ishmaelites--i.e., Muslims] shall come and restore it with grandeur."
For Spencer, such texts are proof that Muhammad did not exist because in their depiction of Muhammad as a Jewish Messiah they do not conform to Islamic traditions of anti-Semitism, which he attributes to Muhammad.
But all of his arguments reduce to a false dichotomy. He feels that Islam is static, and that if Islam, as presented in a specific form at a specific date in time, is not also present at the very dawn of the faith that it therefore is fraudulent and that Muhammad therefore did not exist except as a vague, politically-convenient fiction.
It isn’t an either-or situation, and the enormous question of historicity and how we can establish criteria for evaluating ancient sources can't be reduced to a juvenile thumbing of the nose dressed up in the name of inquiry.
I will keep reading the book and see if the quality of evidence gets any better.