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> Given what we know about how the Egyptians recorded history, we would definitely not expect to find them writing about stuff that would have embarrassed them.

That's exactly the sort of stuff they wrote about all the time. We know about the various wars and political conflicts throughout the second intermediate period precisely because that's what the Egyptians liked documenting.

And, in particular, during the supposed time of the exodus the Egyptian kingdom was fairly divided. Even if one kingdom was too proud to write about a defeat, the others would be sure to document it.

> Look up Papyrus Brooklyn 35.1446 - it shows that Egypt held slaves with Semitic names in roughly the correct time period.

Read up about the Canaanites. They were on the uprise during this period and they are also believed to be the actual origin of the Hebrews.

> Israel being one of them!

No even according to the bible. Israel didn't exist before the exodus. Definitely not for decades and even centuries afterwards. The oldest records of the exodus are nowhere near the event. The closest record we have is around 900BCE.

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Some Jewish slaves in no way corroborates "all of Israel was enslaved". The latter is demonstrably false. Jewish immigrants were hired, paid, and in some cases promoted to positions of wealth and authority.
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Important to note, Canaanites have semitic names. So, someone with a semitic name isn't even an indicator that they were a Hebrew, only that they were possibly Hebrew. Which is unlikely. The evidence we have is that Hebrews were a splinter group from the Canaanites, rather than being a distinct group of people.

What we'd expect if the exodus was real is either proto-semitic writings about the event or even Egyptian writings. Because, fun fact, slaves tend to speak the language of their masters. The fact that the only document we have about it is written in Ancient Hebrew, a language that first debuted around 900 BCE, puts a lot of this into question.

The exodus was supposed to have happened anywhere from 1400BCE to 1200BCE (the bible gives at least 2 dates).

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