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The phrase "empirical foundation" is correct and can be used in written English.
You can use it to refer to evidence collected through observation or experimentation to support a hypothesis or conclusion. For example: "This theory has a strong empirical foundation, as demonstrated by the results of our experiments."
Exact(59)
The paranoia over the deficit is particularly pernicious, and particularly lacking in empirical foundation.
One problem with this conservative view is its lack of an empirical foundation.
Although Cuvier's doctrine of catastrophism did not last, he did set the science of paleontology on a firm empirical foundation.
The UN inquiry gathered facts which are "the empirical foundation for application of international law and of universal opinion", said Kirby.
After Charles Darwin's introduction of the principles of organic evolution, Candolle's criteria provided the empirical foundation for a modern evolutionary history of plants.
There was no agreement with government assertions that the marketisation of services would improve innovation via the discipline of competition, with this idea regarded as ideological and without any empirical foundation.
American sociologist and demographer Kingsley Davis remarked that, while Malthus based his theories on a strong empirical foundation, the theories tended to be weakest in their empiricism and strongest in their theoretical formulation.
This is an empirical claim, but without much of an empirical foundation: the report insists, for instance, that the famous "courier," a key in the search for Osama bin Laden, was discovered (and certainly discoverable) not through torture at all but through normal investigative means.
The metaphors in the Barometer have an empirical foundation upon which narrative layers are built [17, 27].
In fact, the empirical foundation for much of the conventional wisdom on the underlying causes is surprisingly weak.
These findings provide an empirical foundation for AP-dependent theories and have broad biomedical and evolutionary implications.
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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