See the usage notes for this sign:
GOD [version 1]


The version of the sign GOD above tends to generally refer to deity and/or conveys a
meaning that tends toward a "capital G" type of "God."
If you wish to be more neutral and or convey the concept of a
lowercase "god" a good option is to simply fingerspell "G-O-D."
fs-GOD [Version 2 as in "god" with a lowercase "g" in English]

Usage notes:
Dr. Bill writes: I don't think any
particular religion has a "lock" on the general sign for "GOD."
Even
if someone tells you, "No, no, no -- the traditional sign 'GOD'
only refers to Elohim" (a name for God used frequently in the Hebrew
Bible)" -- I think it is simply their opinion.
To be (perhaps) more clear (or at least more blunt) -- the sign GOD
is a sign -- not a "namesign." It doesn't belong to any
particular God.
Those of us who can
fingerspell quickly do often tend to spell "god" for general
reference to the concept of "a superhuman being or spirit worshiped
as having power over nature or human fortunes" (Source on that
definition: Lexico (dot) com).
Just now while discussing the above post with my assistant I choose
to spell "god" rather than do the full sign.
There is typically a difference between how we sign while
"discussing" vs how we sign while "worshiping." (I'll let you think
about that on your own since I don't want this thread to devolve.)
If you are signing a hymn then yes -- you should use the GOD sign.
I've seen a lot of signed hymns in my life and not once have I seen
someone just fingerspell G-O-D during a signed hymn during a Deaf
church service.
However if you "do" see someone spell G-O-D during a hymn don't fret
about it -- instead try to understand the context and/or why the
person chose to express the concept that way instead of putting in
the effort to do the sign in a large, beautiful way.
The fact is the full sign for GOD takes a lot of work compared to
the trivial amount of work it takes to do a lexicalized version of
fs-GOD-[lexicalized] that basically only moves the index finger
while twisting the wrist a bit. (Don't believe me? Try spelling
"god" 30 times and by the time you hit 30 you'll be doing a little
bend flick of the index finger.)
So when folks tell you to just spell "god" -- it isn't because there
isn't a sign for "god or God" -- it is because spelling it is
really, really fast, easy, and efficient. The extra work in signing
GOD is fitting when you want to show your God (and fellow
worshipers) that you care enough to put out the effort to do a
beautiful, large sign, that rises up and thus puts you in
subjugation.
This "extra movement" isn't "just" about religion (worship) either.
It can be to show "honor or respect" as in the Pledge of Allegiance
when we choose to "sign" GOD instead of spell "G-O-D."
Notes:
Also see:
JESUS
Also see: GOD (Youtube clip)
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