Here's the verse:
וּלְכֹ֣ל בְּנֵ֣י יִשְׂרָאֵ֗ל לֹ֤א יֶֽחֱרַץ־ כֶּ֙לֶב֙ לְשֹׁנֹ֔ו לְמֵאִ֖ישׁ וְעַד־ בְּהֵמָ֑ה לְמַ֙עַן֙ תֵּֽדְע֔וּן אֲשֶׁר֙ יַפְלֶ֣ה יְהוָ֔ה בֵּ֥ין מִצְרַ֖יִם וּבֵ֥ין יִשְׂרָאֵֽל׃
which translates as:
But against any of the children of Israel shall not a dog move (= יֶֽחֱרַץ literally "sharpen") his tongue against man or beast so that you may know how that God has made a difference between the Egyptians and Israel
Let's look at what the bold face names do with this:
Per Rashi יֶֽחֱרַץ means sharpen, and tongue is to be understood figuratively. Thus the verse is telling us that no dog will utter a sharp cry, that is a howl or a growl. An ordinary bark, presumably, is possible, but the dogs will not make any angry noise. (Among the famous English translations only the English Standard Version picks up this nuance. All the others say the dogs won't make any sound at all, reading יֶֽחֱרַץ as "move".
Problem: What about the second part of the verse? Why does a barking, but not howling or growling dog, suggest a difference exists between Israelite and Egyptian?
Its a rule of (super)nature for dogs to bark when the Angel of Death appears. The Angel didn't visit Jewish areas on the night of Exodus, so there was no barking.
Problem: Though this comment addresses the whole verse it rests on an unproven assertion. Dogs bark at the invisible, intangible angel of death? Really?
Its to be understood symbolically. Dogs represent the never-satiated forces of destruction, the Israelites at which they didn't bark represent the righteous. The verse teaches us that at times of danger, the rightuous are saved.
Problem: Great vort, but on the literal level what does the verse mean?
It was a way to determine if a stranger had mixed in with the Jewish people. The dogs would bark at Egyptians, but not at Jews. If one reacted to a group of Jews on the night of the Exodus it was a sign that an Egyptian was among them.
Problem: However, we know that others left with the Israelites. Were the dogs quiet for the erev rav, or did they bark at them? If so, was the barking ignored? If so, what was the point of the sign?
The previous Lubovitcher Rebbe.
It was a full moon, and there was commotion in every house because firstborns were dying. Under normal circumstances these two events would cause the dogs to howl. [DB: Really?] In Israelite areas the dogs were miraculously kept from growling so that the Jews would not be frightened but because God doesn't perform unnecessary miracles they did not lose the ability to bark normally. The extra distinction between Israelite and Egyptian is that, on this night, more than the plague itself recognized a difference. In addition to the survival of Israelite firstborns, the dogs didn't howl in Jewish precincts. Also, the dogs didn't bark at the cattle in fulfillment of a promise: (Ex 10: 26) "Therefore, our livestock too shall go with us; not a hoof shall be left behind" had the dogs barked and scared off a cow, Moshe would have been made into a liar. God silenced the dogs to protect his reputation.
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