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The phrase "logically impossible" is correct and usable in written English.
You can use it to describe an idea, concept, or thing that does not make logical sense, or which is impossible due to logic. For example: "Doing both tasks at the same time is logically impossible; there are only 24 hours in a day."
Exact(60)
His position here makes it logically impossible for explanations, predictions and postdictions to not have the same logical form.
That's logically impossible.
Because, if you think about it, that's logically impossible.
They hoped to show that the alternatives were logically impossible.
It is logically impossible for heterosexual men to have more partners on average than heterosexual women.
The argument might sound improbable, but it is at least not logically impossible.
"But we cannot all be net exporters to each other that's logically impossible.
The overwhelming majority of respondents go for b), even though that's logically impossible.
The idea of there being no end to space seems logically impossible.
(Not only would this lead to depression, but it is logically impossible for all countries to be like Germany).
In fact, some scholars would say the task the world has assigned Iraq -- to prove it has no weapons of mass destruction -- is logically impossible.
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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