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Exodus 9:3-6 and 14:9 say:
And the next day the LORD did it: All the livestock of the Egyptians died, but not one animal belonging to the Israelites died.
The Egyptians--all Pharaoh's horses and chariots, horsemen and troops--pursued the Israelites and overtook them as they camped by the sea near Pi Hahiroth, opposite Baal Zephon.
Tthe question is, where did Pharaoh get all the horses if they were all killed in the plague?
A standard solution cites Exodus 9:3 as specifying that the plague was on animals in the field -- any animals not in the field (i.e., in stables, like Pharaoh's horses certainly would have been) were not affected. But this does run aground on verse 19, which says that all of the livestock died. One might explain that, though, in terms of a universalizing hyperbole typical of ancient literature. (In other words, "all" isn't mean to mean literally "all" but "a whole lot.") Or else, "in the field" still contextualizes the latter statement, so that those in stables remained alive.
A better solution recognizes that there is a certain misconception that the Ten Plagues were right on the heels of one another. But the #2 plague (frogs) probably took place in December ("frog season" there, as they would mate during the flood season which lasted until October, and then grow to sufficient size by December) and the #7 plague (hail) occurred in January, because, according to commentators familiar with Egypt's growing seasons, the barley was ripe and the flax was in blossom (9:31). Then of course by the time of the Exodus it was April.
That gave at least 2-3 months for the Pharaoh to replenish his stables -- certainly no problem for a world power like Egypt, which could do that either by trade, conquest or by outright confiscation from the Israelites and other foreigners.
Indeed it is wrongheaded to suggest that Egypt -- perhaps the greatest power in the world at the time -- would not have the means to do this; it did not require "invasion" of another country but normal trade or confiscation from those already in the country or close by, with tens of thousands of animals being traded at any given time (and thus as well, enough around to suffer the boils of 9:8).
Objection: So what about cleaning up all the dead animals?
The wide availability of slave labor takes care of that.
You suggest they stole from the Israelites, but they are later said to have flocks and herds.
This hardly negates any point that some portion was able to be taken from them.)
You're stretching the Biblical chronology.
Hardly so. This requires no exceptional length of time or stretching of the Biblical chronology. The plagues take place in this scenario over a mere 6 months. This involves no significant delay whatsoever. Nor is it necessary to suppose that Pharaoh waited more than a few days to ask for the removal of the plague of frogs, once it became clear that his own magicians could do nothing to reverse it and once his own sense of honor had been broken sufficiently to make the request.
The place for space is between the conclusion of one plague and the start of another, and the texts offer no time markers for those, save the ones that context (knowing the seasons) would provide for the knowledgeable reader.
That the locusts ate what the hail did not destroy hardly indicates that the hail followed on the heels of the locusts, since the crops are obviously not going anywhere; any "regrowth" of vegetation is of no relevance, for it is hardly as though any regrowth would be counted as new plants. It is also beyond credulity to claim that any delay would lessen the memory of the prior plagues -- as if such things were indeed so readily forgotten.
What about Moses being as old as he is?
Appeals to texts that record Moses' age neglect the point that Moses would hardly have had more than one birthday over these few months (even if ancient persons were indeed able to precisely calculate their own ages, which was not often possible).
As an added note, since we don't know exactly how many horses there were in the pursuing army, we might reckon that some of them were originally out on military work outside Egypt at the time of the plague. Whatever the case, there is no sufficient ground for dismissing the story outright. It should furthermore be recalled that the best-trained army in the ancient world, with horses and chariots and armor and weapons, versus a mixed crowd of untrained, unarmored, on-foot pastoralists, isn't any cause to wonder why, though outnumbering the Egyptians significantly, the Israelites were concerned.