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"fundamental assumptions" is a correct and usable phrase in written English.
It is typically used to refer to the basic beliefs or principles that underlie a particular argument, theory, or system. Example: Before beginning his research, John outlined the fundamental assumptions that would guide his study, such as the belief that all individuals are inherently rational decision-makers.
Exact(60)
Epidemiology is based on two fundamental assumptions.
For more than a century artists across the board have been questioning fundamental assumptions about art.
We take a sledgehammer to the fundamental assumptions about later life in Britain.
Questioning Equiano's origins calls into doubt some fundamental assumptions made in departments of African-American Studies".
The general theory of hallucinations here delineated rests upon two fundamental assumptions.
However, the different models reflect different fundamental assumptions about human interaction and behaviour.
Fundamental assumptions about what the state should provide and how it should do it are being challenged.
So what happens to a market in which the most fundamental assumptions turn out to be lies?
The French state, once so confident in its fundamental assumptions, is undergoing a painful period of self-questioning.
Baldwin denounced the fundamental assumptions about the relationship between literature and politics underlying Stowe's self-righteous tone.
Its fundamental assumptions remain valid, and most social scientists still specialize in just one or two culture areas.
Related(20)
pivotal assumptions
fundamental presumptions
significant assumptions
primary assumptions
elementary assumptions
fundamental hypotheses
substantive assumptions
deep assumptions
crucial assumptions
substantial assumptions
foundational assumptions
essential assumptions
critical assumptions
basic assumptions
major assumptions
fundamental flaws
fundamental values
fundamental studies
fundamental questions
fundamental rights
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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