Halacha

The Halachic definition of death, is Yetzias Ha Neshamah (the leaving of the soul). But since we can’t see this, the Halacha is, that one places a feather under the nose of the person.

If the feather doesn’t move, then we assume that they are dead. If it moves we say, that the person is still alive.
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Halacha only goes according to what is evident, and what we can see with our eyes, in this physical world.

But what would be the Halacha in the case, where the feather didn’t move, but the soul never left the body? According to Halacha, you would say Kaddish and bury the person. But technically speaking, they are not dead.
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This may have been the reason, that when the Rebbe wrote about the Previous Rebbe, he used the abbreviations after his name that are used when someone has passed away; but when speaking about the Previous Rebbe, he said on occasion Shlita, and many other similar statements, indicating that he is still alive.

When you write about someone who the feather didn’t move, you have to go with the visible reality; but in speaking, you can talk about the true reality.