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The phrase "lack of rationality" is correct and usable in written English.
You can use the phrase to describe something that does not make sense, or that is not based on logical thinking. For example, "The protesters' decision to march in the middle of a snowstorm showed a lack of rationality."
Exact(8)
And he hinted at a lack of rationality in recent bond market moves.
As a captain in the Royal Navy, I was in charge of an anti-piracy task group – and I saw the same excitability and lack of rationality that we see in the characters in this film.
No doubt the clearest evidence of the lack of rationality in such a distinction is the fact that for 108 years the State of Washington has itself made no such distinction.
Their lack of rationality in this matter is a result of their misery and ignorance.
In contrast to their philosophical claims of meaning gaps and partial lack of rationality in the choice between incommensurable theories, Bohr believed not just retrospectively that quantum mechanics was a natural generalization of classical physics, but he and Heisenberg followed in practice the requirements of the correspondence rule.
"What I miss about being younger is the lack of rationality when it came to things like ghost stories or myths.
Similar(52)
Moses Finley was the chief proponent of the primitivist view that the Roman economy was "underdeveloped and underachieving," characterized by subsistence agriculture; urban centres that consumed more than they produced in terms of trade and industry; low-status artisans; slowly developing technology; and a "lack of economic rationality".
A theory lacking of rationality can never be a sound one no matter how closely it compares with experimental data in one respect or another, since a good comparison in one respect comes at a price of poor agreement in some other respects usually, either unknown for the time being or hidden deliberately.
But decency never stopped Malkin and Fox News Channel from targeting civilian children in order to satisfy their ignorant viewers and to substitute for their utter lack of integrity, rationality and reason.
But what's happening today is a total lack of marketplace rationality".
An important question is whether the "intentional and arbitrary discrimination" test, which implies the lack of any rationality, is the sole test for proving that an executive act violates Article 12, or only one possible test.
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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