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They have near-fully overlapping meanings (I would be going out on a limb to say fully equivalent translations) with both the Arabic and German words having their primary use in expressing the meaning in "geometric shape" and also being analogous to the word form as in Platonic forms in their respective languages.

Supposedly stellen, the original verb form of gestalt, descends from the Proto-Indo-European *stel, which puts it at one t <-> k mutation away from the Arabic š-k-l (Or a shared ancestor with Hebrew š-k-l-l שכלל) based on examples like the palatalization in Modern Arabic dialects or Egyptian as an example contemporary to PIE if Loprieno p.31 can be cited:

[Proto-]Afroas[iatic] velar plosives *k, *g and 'k display two outcomes [...] either they are maintained as k [...] or they are palatalized into t, /c/ [...]

Also, mostly on pure fancy, I am interpreting the meanings conveyed in the cited Ancient Greek and Slavic descendants from *stel as containing the common conceptual element in grouping, bringing together, forming up etc. which can be a potential (even if very weak) indicator for *stel having a meaning related to form.

So this is where the too good to be true principle kicks in for me to look for factors that make it implausible for these two to have a common origin. What are some venues to exhaust for evidence on the contrary before actually pursuing this claim further?

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    A couple notes: Loprieno is talking about ṯ, not t—Egyptian ṯ was something like IPA /c/ or /tʃ/, a palatal, not /t/, an alveolar/dental. I'm also not sure how Egyptian is "contemporary" with German; Egyptian is first attested around 3000 BCE, while Old High German isn't attested until close to 1000 CE.
    – Draconis ♦
    Sep 28, 2020 at 20:18
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    Why not begin with the beginning: the Arabic ش [ʃ] descends from the Proto-Semitic [ɬ]. How does that correlate with the PIE s? «The pronunciation of [Proto-Semitic] *ś ṣ́ as [ɬ ɬʼ] is still maintained in the Modern South Arabian languages (such as Mehri), and evidence of a former lateral pronunciation is evident in a number of other languages. For example, Biblical Hebrew baśam was borrowed into Ancient Greek as balsamon (hence English "balsam")» (here)
    – Yellow Sky
    Sep 28, 2020 at 20:29
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    (As a side note—props for looking into other cognates. Most people who ask "are these words related?" questions here don't do that, and it's an important part of determining relatedness.)
    – Draconis ♦
    Sep 28, 2020 at 20:37
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    The Hebrew ש in š-k-l-l שכלל “to improve” is a prefix, at least so says A Comprehensive Etymological Dictionary of the Hebrew Language for Readers of English, 1987, by Ernest Klein. It is a borrowing from Akkadian shuklulu which is a Š-stem verb where shu- is a prefix.
    – Yellow Sky
    Sep 28, 2020 at 21:01
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    Ia! Ia! Shuklulu balsamon! In his binyan in Akkad, dead Shuklulu lies conjugating.
    – Robert Columbia
    Sep 29, 2020 at 17:23

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Where am I getting too excited and overlooking things?

Occam's razor.

Many more German words came from Proto-Indo-European than from anything Afro-Asiatic, and there are plenty of cognates to stellen in other branches of Indo-European, as you cited (see also Old Latin stlocus "place, location"). So the hypothesis that Gestalt came from Proto-Indo-European is simpler and requires fewer assumptions.

When the languages in question were spoken so many thousands of years ago (and never written down), it's difficult to be certain of anything. So showing a relationship between proto-languages requires enormous amounts of evidence. For a single pair of words like this, Occam's razor suggests instead that it's just a coincidence.

(Could, instead, PIE *stel- be borrowed from Proto-Afro-Asiatic or one of its descendants? Possibly; unfortunately, it would have happened so long ago that it's impossible to know for certain. The meanings and sounds aren't similar enough for me to put money on it, but there's also no way to definitively rule it out. So the best we can say about that is "not enough evidence to refute the null hypothesis".)

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  • "Could, instead, PIE *stel- be borrowed from Proto-Afro-Asiatic" that is the conclusion I was pretty much daydreaming about. Not sure how I implied an Arabic origin though -- I was trying to imply the PIE word as being on the divergence point with some corresponding Proto-Semitic
    – Layman
    Sep 28, 2020 at 20:37
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    @Layman In that case, you'll want to look at the reconstructed ancestor of the Arabic and Hebrew words; I don't know what that ancestor is, but Yellow Sky says it started with *ś (a lateral fricative /ɬ/), and *ɬ-k-l vs *stel is a bit of a stretch. The only thing they actually share in common is the final L.
    – Draconis ♦
    Sep 28, 2020 at 20:40
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    @Layman The issue with that is, sound change tends to be regular and universal, which means we can see patterns in it. Proto-Indo-European *p at the start of words regularly became *f in Proto-Germanic, which is why we can see dozens and dozens of examples of correspondences where Latin/Greek/Sanskrit/etc has a word starting with P and English has a word starting with F (pater~father, pyr~fire, piscis~fish, etc). But this was a regular change that affected the entire language; P and F weren't and aren't just interchangeable ("pit" and "fit" mean totally different things).
    – Draconis ♦
    Sep 28, 2020 at 21:37
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    @Layman It's possible that some Afro-Asiatic language or dialect could have turned *ś into S and *k into T, sure. But if so we'd expect to see those changes happen all across the language, not just in a single word.
    – Draconis ♦
    Sep 28, 2020 at 21:38
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    "Many more German words came from Proto-Indo-European than from anything Afro-Asiatic" is a premisses fit for circular reasoning, a truism by definition. "the hypothesis that Gestalt came from Proto-Indo-European is simpler" You can't use a comparative to deny the comparison. That's paradox like: color sleeps more furiously. "... requires fewer assumptions." Deriving everything ex nihilo requires fewest assumptions. Beyond that it's not clear how you would enumerate irrational arguments like PAA or pre-PIE. "When the languages in question were spoken" If! Your faith is strong as ever.
    – vectory
    Oct 1, 2020 at 17:16

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