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"underlying assumption" is a correct and usable phrase in written English
You can use it to refer to a premise or belief that forms the basis of an argument or thought process, usually one that is not stated outright. For example, "The underlying assumption of his argument seems to be that all wealth is inherently bad."
Exact(60)
Do you agree with Ms. Lynch's underlying assumption that women exercise power differently?
The basic underlying assumption in robust design is that the experimental data have a normal distribution.
The unspoken, unquestioned, and underlying assumption, especially of people 75 and older, was that marriage would last forever.
10 The underlying assumption is a relation between the excitabilities of different systems.
An underlying assumption of communication CA is that dialogues are representative of underlying cognitive processes [ 8].
What is the underlying assumption of terror management?
"The underlying assumption may have changed," Mr. Smith said.
The underlying assumption is that getting more people involved isn't practical or worthwhile.
Has anyone even questioned the underlying assumption that this would be a good thing?
None of them challenges the underlying assumption that punishment is the primary tool of crime reduction.
Nothing but an underlying assumption that everyone cleans up after themselves.
More suggestions(15)
Underlying conclusion
underlining assumption
Underlying supposition
Underlying possibility
overlying assumption
Underlying presupposition
Underlying projection
Underlying conjecture
Underlying hypothesis
pivotal assumption
Underlying the premise
principle assumption
genuine assumption
grounding assumption
substantial assumption
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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