The phrase "a peculiar notion of" is correct and usable in written English.
You can use it to describe a strange or unusual perception of something. For example, "John had a peculiar notion of happiness, which included working long hours and taking few vacations."
If this seems a peculiar view for a religious person to hold it is perhaps because we in the west have a peculiar notion of religion.
But the twins and everyone else shown here are slaves to a peculiar notion of status, one that has nothing to do with money or success.
"It's a peculiar notion of fairness," said the Republican economist Douglas Holtz-Eakin, to tell affluent Americans, "You fund all of the government, and we're going to hit you harder".
There is a peculiar notion of "equity" emanating from central government and being administered locally: you set a budget to meet the needs of a particular minority, then you go to enormous trouble to share the limited funds out as equitably as possible.
Linked with this idea of the potentially destructive power of passionate will, emotion, and thought is Balzac's peculiar notion of a vital fluid concentrated inside the person, a store of energy that he may husband or squander as he desires, thereby lengthening or shortening his vital span.
Earlier this month, it was the turn, in a U.S. drone stroke in Libya, of a Tunisian terrorist called Abu Iyadh, who also spent years in Afghanistan at bin Laden's side, thanks to Mullah Omar's peculiar notion of hospitality.
It seems possible to engage in the kind of impartial thinking that is needed, not just by utilitarianism, but by any plausible morality, without going all the way to Sidgwick's very peculiar notion of "the point of view of the universe".
My beef has been not with restraint but with that peculiar notion of legalism, which squeezes the moral juice out of any commandment in order to gnaw instead on a dry husk.
Like the small-town troupers in "Guffman" and the dog-show competitors in "Best in Show," the pickers and chirpers of "A Mighty Wind" are immune to embarrassment and utterly devoted to their own peculiar notions of artistic accomplishment and show-business glory.
What I'm trying to say is, King Tut ran off to pursue his peculiar notions of happiness between the muscled thighs of our Pilates instructor.
Peculiar notions of bravery and nobility can blind you to danger.
