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From what I read, 厚い is used when something is thick or abundant and 篤い is
used when describing a serious illness. But what confuses me is that in a
dictionary (Tagaini Jisho) both of these are in the same entry, is it because
the kanji can be interchangeable? Is 篤い commonly used? And which kanji would
be used for the second definition hospitable?

The entry: 厚い Alternate writings: 篤い (あつい)

  1. Thick, deep, heavy. [ 厚い (あつい) ]
  2. Kind, cordial, hospitable, warm, faithful.
  3. Serious (of an illness). [ 篤い (あつい) ]
  4. Abundant. [ 厚い (あつい) ]
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kanji word-choice
The usages of 厚い and 篤い
I guess you are referring to a dictionary entry [like this
one](http://dic.yahoo.co.jp/detail?p=%E3%81%82%E3%81%A4%E3%81%84&stype=4&dtype=0).
I think that 篤い is not a 常用 reading (only 篤 トク is 常用), so that 厚い covers the
meaning "serious illness", but 篤い is used often for this meaning. (Compare 重篤,
meaning "serious illness".) I can't find the key for 大辞泉, but I'd guess that
the little triangle means "beware, not 常用".

Note also that 篤 also means "kind", e.g. as in 懇篤, so the meanings of 篤い and
厚い do overlap (but don't overlap with 熱い or 暑い) and the choice of 漢字 is partly
a matter of personal taste. The dictionary provides an official guideline.
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It's sometimes useful to look at what the characters mean in Chinese. Here's
what I found listed in the dictionary:

厚thick / deep or profound / kind / generous / rich or strong in flavor / to
favor / to stress

篤serious (illness) / sincere / true.

So what I would conclude is that (historically) 厚 is used for physical
thickness, 篤 is used to mean sickness, and both of them can mean a good
personality. However, because one of them is a non 常用 reading, the other one
is currently used for all meanings of the word, despite what the character
meant historically.
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answer