The next bit of evidence comes from an inscription from the same time as the Ipuwer papyrus. It read :
"And when I allowed the abominations of the gods [immigrant peoples] to depart, the earth swallowed their footprints. This was the directive of the Primeval Father [water, according to Egyptian beliefs] who came one day unexpectedly" (Pellegrino, p 230)
Comparing this with Exodus, as Pellegrino does as follows:
(Egyptian Inscription) And when I allowed the abominations of the gods [immigrant peoples] to depart,
(Exodus 12:31) He [Pharoh] summoned Moses and Aaron in the night and said, "Up, depart from among my people, you and the Israelites with you!"
(further in Exodus 12:38) Moreover, a mixed multitude went up with them
Not just the Israelites departed, but other Asiatics who were enslaved as well.
(Egyptian Inscriptian) the earth swallowed their footprints. This was the directive of the Primeval Father [water, according to Egyptian beliefs] who came one day unexpectedly
(Exodus 14:22,27) and the Israelites went into the sea on dry ground, waters forming a wall for them on their right and their left. ....at daybreak the sea returned to its normal state, and the Egyptians fled at its approach. But the L-RD hurled the Egyptians into the sea.
Finally, as to the issue of slavery, the Leningrad Papyrus (1116A) attests to the fact that some immigrant people were subjected to compulsory labor during the time after the Hyksos expulsion leading up to and during the reign of Tutmosis III, during whose reign the inscription and Ipuwer papyrus date. As stated in the Tanach, and confermed in the Leningrad Papyrus, the servitude entailed building of public building projects (like the store cities in Exodus). The Hebrews were not mentioned specifically, because they were part of a "mixed multitude" of Asiatic slave labor. (Pellegrino, p239)
By the way, there are few peoples the Egyptians mention by name, since they considered most people to be beneath their notice and inferior. The evidence, as presented above, is overwelmingly in favor of the Exodus, though by no means certain.
The argument that Joseph served during the time of the Hyksos is compelling, but, as "The Torah: A Modern Commentary" states "..the data at our disposal are not sufficient to link them securely to the Jacob-Joseph stories or to suppose, as has been suggested, that Jacob's sones -- described throughout as ivrim -- were invited to settle in Egypt because their talents and experiences, already amply demonstrated by Joseph, would prove useful to the Hyksos". Maybe it would be better to look for a record of a 7 year famine?
Some quotes from John Bright's "History of Israel":
"We are told (Ex. 1:11) that Hebrews were forced to labor at the building of Pithom and Raamses. The former lies at Tell er-Ret\a'beh, west of Lake Timsah in northeastern Egypt; the latter is none other than the ancient Hyksos capital Avaris, rebuilt and again made the capital by Sethos I and Ramesses 11, and called by the latter the 'House of Ramesses.' That Ex. 1:11 refers to this seems certain. It is interesting that the capital was regularly referred to as 'House of Ramesses' down through the eleventh century, after which the name seems to have dropped from general use, to be replaced by the familiar name of Tanis. In the reign of Haremhab (ca. 1333-1306) the four hundredth anniversary of the city’s founding was celebrated; later Ramesses II erected a stele there. Whether there is some connection between this and the traditional four hundred and thirty years (Ex. 12:40) of Israel’s stay in Egypt (in Gen. 15:13, four hundred years), and whether this would place their coming there in the Hyksos period, is uncertain and should not be pressed. But the coincidence of the figures, plus the statement (Num. 13:22) that Hebron was built seven years before Zoan (Avaris), leaves the suspicion that Hebrews knew of the era of Avaris....
"If Hebrews labored at Avaris, then they must have been in Egypt at least in the reign of Sethos I (ca. 1305-1290), and probably of Ramesses II (ca. 1290-1224), under whom the rebuilding of that city was accomplished. On the other hand, if the destruction of various Palestinian cities late in the thirteenth century (see below) is to be connected with the Israelite conquest, as many have believed, the exodus from Egypt must have taken place perhaps a generation before that. If it were certain that the Israel defeated by Marniptah in his fifth year (ca. 1220) was a part of the group that had come from Egypt, we would have something like a fixed date from which to work; but, unfortunately, it is not certain. Moreover, Israel’s encounter with the Edomites and Moabites (Num. chs. 20; 21), unless one declare the tradition unhistorical, forbids a date for Israel’s arrival before the thirteenth century (when these two peoples first appear in contemporary texts), and might be held rather to suggest a date in the twelfth, since these areas do not seem to have had an appreciable sedentary population earlier. We can set no fixed date for the exodus, nor can we be sure in the reign of which Pharaoh it took place. But a date rather well on in the thirteenth century, perhaps late in the reign of Ramesses II, seems plausible."
John Bright, A History of Israel, (Philadelphia, Pennsylvania: The Westminster Press) 1981. (From CD-ROM)
And, of course, I see problems with Bright's view as well, since there is no reason, given that not all documents made have been found, that Edom and Moab could not have existed before the thus far known "contemporary texts".
And, lastly, from the Encyclopedia Judaica:
"(1) I Kings 6:1 states that 480 years elapsed from the Exodus to the construction of Solomon's Temple in Jerusalem. Solomon reigned over Israel during the second third of the tenth century B.C.E. According to this, the Exodus occurred no later than the second third of the 15th century B.C.E., in approximately 1450-1430 B.C.E. This date is confirmed by Judges 11:26, which states that 300 years elapsed from the time of the Israelite entry into Canaan to the time of Jephthah, who judged Israel in the second half of the 12th century B.C.E. A dating of the Exodus in the 15th century B.C.E. is preferred by several scholars who identify the Habiru of the Tell el-Amarna Letters with the Israelite tribes who penetrated Canaan and waged war against its rulers. [G. Shapiro Note: Rohl sees these as speaking about the wars in the time of Saul and David instead] Most scholars, however, agree that the 15th century B.C.E. is too early for the Exodus and does not conform with other data about Israelite, Canaanite, and Egyptian history. In the second half of the 15th century B.C.E., during the reign of Thutmosis III, Egypt was too strong for the Israelites to have been able to revolt against her or to conquer Canaan. An historical basis can be ascribed to I Kings 6:1 if the numbers are considered only symbolic, marking 12 generations of 40 years each (cf. Num. 32:13; Ps. 95:10). According to priestly tradition, 12 generations of high priests passed between the Exodus and Solomon (I Chron. 6:35-37). A realistic length of time for each generation is 25 years on the average. By this calculation, the Exodus occurred in the first half of the 13th century, in approximately 1270 B.C.E. This date accords with the inscription of Merneptah ('The Israel Stela'), which speaks of Israel as being either already in Canaan or in the desert area between Egypt and Canaan (a less probable interpretation) in the second half of the 13th century (see Kaufmann, Toledot).
"(2) According to Exodus 12:40-41, 430 years elapsed from the descent of Jacob and his sons to Egypt until the Exodus. This chronology clearly contradicts the genealogical data according to which Moses was the son of Amram son of Kehath son of Levi son of Jacob. This would mean a span of at most four generations from the descent of Jacob's sons to Egypt until the Exodus, and if Genesis 46:8-11 is also taken into account, only two generations. W. F. Albright connects the number 430 with the 'Four Hundred Year Stele' erected by Ramses II at Tanis (biblical Zoan, the Hyksos Avaris, today called San al-Hajar) in honor of the 400th anniversary of the building of that city, and the establishing of the worship of the god Seth in it by the Hyksos. According to Egyptian chronology and archaeological research, it may be calculated that Zoan was built in approximately 1700 B.C.E. [G. Shapiro note: Recall that Bright says Zoan/Tanis was built by Israelite slave labor. This means the Exodus happened after 1700 BCE, something everyone agrees upon] Assuming that the 430 years mentioned in Exodus 12:40-41 date from the building of Zoan (cf. Num. 13:22), [G. Shapiro note: Num 13:22 says Hebron was founded 7 years before Zoan, but Genesis clearly places Hebron in the time of the Patriachs, so, perhaps Zoan is not Ramses after all, or we only rebuilt Zoan/Ramses?] the year 1270 B.C.E. would be the approximate date of the Exodus, and one which accords with the calculation of 12 generations noted in (1) above. The descent of Jacob and his sons to Egypt therefore would have occurred in about 1700 B.C.E., in the context of the Hyksos penetration of that country.
"(3) In Genesis 15:13-16 God tells Abraham that the Israelites will be enslaved to another nation (i.e., Egypt) for 400 years and that "they shall return here in the fourth generation." This date too, which attributes 100 years to each generation, cannot be considered realistic. Some scholars consider the number 400 to be somehow connected with the Ephraimite tradition which places ten generations (of the conventional length of 40 years each) between Jacob and Joshua (cf. I Chron. 7:20-27). A possibility of identifying the king who enslaved the Israelites is provided by the information in Exodus 1:11 regarding the construction of the cities Pithom and Ramses by the Israelites. Pithom is Per-Atum in the Land of Goshen, and it is usually identified with Tell al-Rataba west of Lake Timsah. Ramses is Per-Ra'mses in the Wadi a Tumaylat which was rebuilt by Ramses II of the 19th Dynasty, who reigned during the first two-thirds of the 13th century. Per-Ra'mses is usually identified with Zoan (Avaris = Tanis) or with Qant'r. Ramses II is well-known for his building activities. He continued the work of his father Seti I and erected a chain of border fortresses in the eastern Delta, as well as supply depots (store-cities, Ex. 1:11) for his large army. To carry out his building operations and cultivate his lands and vineyards, the king used foreign slaves, some of whom are designated as 'apir. Most scholars identify the pharaoh of the enslavement with Ramses II, but they differ as to whether the Exodus occurred during his reign or only in the days of his son Merneptah. From Exodus 2:23, it appears that the pharaoh who began the enslavement of Israel is not the same one who reigned at the time of the Exodus. If therefore Ramses II is indeed the pharaoh of the oppression, then either the enslavement was begun by his father Seti I, or the Exodus took place early in the reign of his son Merneptah. Most of the written or material evidence having a direct or indirect bearing on the Exodus leads to the conclusion that it began in the first half of the 13th century. The mention of the name "Israel" in the stele of Merneptah shows that the Exodus is not to be dated later than the end of the 13th century. From the archaeological survey conducted by N. Glueck in Transjordan, the region was apparently desolate from the 19th until the end of the 14th centuries B.C.E. The renewal of settlement in Transjordan at the end of the 14th and the beginning of the 13th centuries is to be connected with the settlement of the Edomites, Moabites, and Ammonites, and their organization into kingdoms with borders defended by a network of fortresses and strongholds (cf. Num. 21:24). Therefore, if the Israelites encountered the kingdoms of Transjordan on their way from the desert to the Land of Canaan, it follows that the Exodus did not precede the 14th century B.C.E. The conclusions of archaeological research on the date of the Israelite conquest support the theory that the Exodus took place in the first half of the 13th century. Archaeological excavations of various sites, such as Hazor in the north and Lachish in the south, reveal that many settlements were destroyed in the course of the 13th century, especially in the last third of the 13th century. The destruction of the settlements is apparently related to the conquest of the land by the Israelites."
Well, there you have all that I currently have at my disposal in my home, either summarized or quoted. So, what do we know, that the Exodus took place somewhere between 1600 (Pellegrino's date for Thera) and 1200 BCE. Many of the dates depend on the accuracy of the archeologists/Egyptologists' dating of Egyptian Pharoah's and their reign, which, as Rohl points out, is by no means certain. A great deal depends on the age of the el-Amarna Letters, which Rohl places at the time of David and Saul, but most place at what they believe to be the time of the Exodus in the 1200's BCE. If the Jewish date (1313) is correct, and Solomon ruled, as I Kings 6:1 states 480 years after the Exodus to the Temple in Jerusalem was built, then that would put Solomon's building of the Temple in 1313 - 480 = 833 BCE. If it was Ramses II who was the Pharoah of the oppression, it is completly possible that the scholars have his dates wrong by 100 years.
Well, I guess I did not clear much up. I certainly have not settled upon a date, only a range of dates for the Exodus. Nor have I come up with whom the Pharoah was. The fact remains, that for me, at least, it is clear that it did happen, and archeological evidence supports this, even if it does not allow us to date things clearly.
Addendum -- additional things I found since the original writting of the 2nd edition of this post.