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The phrase "On a purely hypothetical basis" is correct and usable in written English
It can be used when discussing a situation or scenario that is not real but is being considered for the sake of argument or analysis. Example: "On a purely hypothetical basis, if we were to double our budget, we could expand our project significantly."
Similar(60)
Q. Here's a purely hypothetical question.
Then he describes a purely "hypothetical" case: a dog Buster (he has a dog Buster) who was on the way to the vet when he started whining.
Mr. Kirtzman, his eyes narrowing: "Which is, of course, a purely hypothetical situation".
This is not a purely hypothetical concern: During 2016 protests after Freddie Gray died in the custody of Baltimore police, law enforcement used facial recognition on social media images to identify protesters with outstanding warrants.
Warp, however, is a purely hypothetical service at this point, having raised only a fraction of the $40,000 it is looking for on Kickstarter.
This isn't a purely hypothetical question.
But that's a purely hypothetical story for another post.
"On a purely aesthetic basis we've gotten used to the Oushaks and Agras.
On a purely mathematical basis, it was silly to double six hearts, trying to turn plus 100 into plus 200.
On a purely statistical basis therefeore, there will be no noticeable increase in the strength of northern voices within Whitehall.
On a purely static basis, the government has lost out on $20,000 of revenue.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com