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The phrase "an undefined notion of" is correct and usable in written English.
It can be used when discussing concepts or ideas that lack a clear or specific definition.
Example: "In philosophy, there is often an undefined notion of what constitutes reality."
Alternatives: "a vague concept of" or "an ambiguous idea of".
Exact(1)
Quine (1953) explicitly criticized Lewis and the analytic/synthetic distinction in "Two Dogmas of Empiricism", and would have objected to the idea of resting the analytic/synthetic distinction on an undefined notion of meaning inclusion.
Similar(59)
However, nowhere in the piece they operationalise what precisely constitutes 'policy change' (or for that matter, 'environmental change') – it appears to be some undefined notion of modification in organisational parameters.
First, I recommended that the university require only standardized tests that assess mastery of specific subject areas rather than undefined notions of "aptitude" or "intelligence".
One thing that has been talked about by activists and members of the black community since the 1960s is 'community control', an arguably undefined notion that could mean decision-making power for citizens over their police.
We refer to [2, 4, 8, 23] for any undefined notion used along the text.
For expository purposes it is convenient to adopt two undefined notions for NBG: class and the binary relation ∊ of membership (though, as is also true in ZFC, ∊ suffices).
AVA is an undefined formulation of Bacillus anthracis culture supernatant adsorbed to aluminum hydroxide.
Again like an incubator, it provides space for an undefined amount of time.
In 2016, the company announced it was laying off an undefined number of employees.
CloudWatch measures in a one minute interval with an undefined number of values.
Service-type specialization occurs when an organization provides a niche capability across an undefined number of industries.
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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