"wider notion" is a correct and usable phrase in written English
It is typically used to describe a more general or all-encompassing idea or concept. Example: "The term 'beauty' encompasses a wider notion of not only physical appearance, but also inner qualities such as kindness and intelligence."
The importance of what might be called "debt justice" to a wider notion of fairness is not limited to Christianity and Judaism.
This is clearly a narrowing of a wider notion of logical consequence.
Feyerabend characterized this wider notion of incommensurability as a historical, anthropological thesis (1975, 271), but also applied it to different stages of the development of thought and perception in the individual (1975, 274).
A wider notion of the normativity of meaning, ME normativism, appeared on the philosophical scene more recently, and is associated with Saul Kripke's book on Wittgenstein's rule-following considerations (Kripke 1982).
It might be impossible to be cynical about Alice Pyne and the generous folks who have rallied to her comfort — but as for the wider notion of a good and noble "Internet community"?
However, Barcan Marcus has offered an alternative perspective, insisting on 'No identity without entity.' (Marcus 1993) and arguing that although '… all terms may "refer" to objects… not all objects are things, where a thing is at least that about which it is appropriate to assert the identity relation.' (ibid., p. 25) Object-reference then becomes a wider notion than thing-reference.
No such cataclysmic weather troubles the Paris of "Happenstance," though there is some rain, but Mr. Firode is quite taken with the wide-eyed notion of cause and effect that the original title metaphorically suggests.
In the book the episode has a palpably allegorical tinge that – with all the correcting of the drawing – hints at wider notions of human error.
The decision not to arrest the man has been criticised on social media, with some using it to question wider notions of public safety.
You could argue the capitulation extends to the centre-left, which is relearning the old lesson that in hard times people look to themselves and their families rather than wider notions of the common good.
Williams' thesis about moral luck is that the wider notions are more useful, and truer to experience.
