The phrase "against any notion of" is correct and usable in written English.
It can be used when expressing opposition or disagreement with a particular idea or concept.
Example: "The committee voted against any notion of increasing the budget for the upcoming year."
Alternatives: "in opposition to any idea of" or "contrary to any belief in".
The Daily pushed back Thursday against any notion of a newsroom exodus taking place.
And the Obama administration has expressed its support for both positions, having advocated for the control board and against any notion of dual sovereignty for the island.
The very existence of the Queen and her now enormous family - all supported by the British taxpayer whether the British taxpayer likes it or not - is entirely against any notion of democracy, and is against freedom of speech.
There, he endorsed the United States' Lend-Lease policy, but warned against displaying any notion of American endorsement for the USSR, which he considered to be an unfit ally.
Some will say that San Diego State, which had 13 turnovers, was so sloppy against an inferior opponent that any notion of a national title run seems unlikely.
I even disavow any notion of weighing the benefits against the losses because they're both so staggering.
"Preston Tucker lacks an ounce of common sense or any notion of the real odds against him.
Moscow pushed back hard this week against any notion that the indictment of 13 Russians proved the Kremlin was involved in a conspiracy to influence the 2016 U.S. election.
Watching Mr. Waters's movies, you always have the us-against-them notion of 1950's squares being tweaked by bohemians, hippies and freaks.
Baghdad has become a "city of ghosts", but Antoon quickly warns against any facile notions of nostalgia and bygone eras about his beloved city.
A shrinking pie generates more nationalist sentiment as each national leader fends for themselves and survives politically by railing against the very notion of yielding any ounce of sovereignty that would make Europe as a whole stronger.
