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The phrase 'notions should be' is correct and usable in written English.
You can use it when you want to express an opinion about something that should be done. For example, "Notions of fairness should be respected by everyone."
Exact(5)
The idea that societies like Britain and the United States have reached the end of a supposed "age of civil liberties," as though such notions should be discarded when they are no longer convenient or fashionable, is nonsense.
However, the link between the two notions should be explored.
For this reason we think that in a physical theory of evolution such notions should be avoided.
In considering the role of PRKN variants in PD, two main notions should be considered.
Some notions should be noted regarding clinical decisions.
Similar(55)
This notion should be a given.
The world's most difficult problems would be greatly ameliorated if we were able to reduce population, and this notion should be discussed.
But also: it's an awards show!" She grins, as if the ridiculousness of the notion should be glaringly self-evident.
A definite stiffness notion should be established to completely reflect the track stiffness characteristics.
However, the notion should be redefined and it should be given a clear meaning by the organization itself.
How this notion should be understood more precisely is presently widely debated, and a survey of these debates can be found in the entry on logical consequence.
More suggestions(15)
interpretations should be
criteria should be
impressions should be
understandings should be
implications should be
principles should be
expressions should be
assumptions should be
visions should be
viewpoints should be
representations should be
propositions should be
opinions should be
conception should be
misconceptions should be
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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