FYI, Kurt Godel also provided a “proof” modeled on Anselm: https://en.wikipedia.org/wiki/G%C3%B6del%27s_ontological_proof
Avicenna (along with Averroes —more accurately Ibn Rushd as I’ve just discovered) was only a name to me in studying Dante. I’m looking forward to exploring both Islamic philosophers in more detail, thanks to your thoughtful analysis.
The issue isn’t whether a particular “proof” of the existence of X is valid, but what the social and cultural beliefs surrounding the attempt to prove that existence reveal about human history.
The fact that Dante placed both Islamic scholars in Limbo (rather than Hell) is profoundly important. (It says more about Dante and Western culture than about Islamic theology, but in the age of Trump and Islamophobia, it’s significant that we recognize common ground whenever it exists.)
You’ll probably catch lots of grief from the skeptic crowd, but I think they’re missing the point.