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The phrase "factual world" is correct and usable in written English.
The phrase can be used to describe the real world, as opposed to an imaginary one. For example, "The students had to switch from a fantasy world to the factual world in order to succeed in their studies."
Exact(10)
It provides a "setting for myth-making far removed from the factual world of common experience".
"The watch universe is a very technical, very factual world and there is not a lot of room for emotions," she said.
He mentions novelists splitting themselves in two, "creator and documentarian, teller and listener, conspiring to pass on the collective wisdom in its own language, disguised in its own enlightened bias, that of the factual world".
Every progress in science in the last decades, from the moment it was absorbed into technology and thus introduced into the factual world where we live our everyday lives, has brought with it a veritable avalanche of fabulous instruments and ever more ingenious machinery.
"At Harvard, direct cinema was the core of the film department," he says, "and most of the students were trying to make socially conscious works, but I was trying to combine fiction and non-fiction to show how our seemingly factual world is constituted through fantasy and stories".
History is understood here in its dual meaning as a factual world of phenomena and as a discipline concerned with only its relevance of life in the present.
Similar(49)
Take the column on the far left to represent worlds that could, in some sense, "turn out" to be actual: when we consider any of these worlds w, we consider the value of the sentence at various counterfactual or factual worlds represented horizontally, given that our world turns out to be w.
It was my first encounter in the United States with what we now refer to as the post-factual world.
"I told my wife, 'I don't think we know everything that happened in this story.' And I find it frustrating that we live in a post-factual world when truth doesn't matter any more.
But the government's expert, Gordon C. Rausser, a professor of economics and statistics at the University of California, Berkeley, had produced a 340-page report stating that Mr. O'Brien's conclusions were based "in a counter-factual world" and that Native Americans had generally fared as well as white male farmers.
Mr. Cohen has conjured up a counter-factual world view in which Israel is somehow to blame for these conflicts, while Hamas, Hezbollah and Iran, which have dedicated themselves to terrorism and destruction by word and deed, are somehow construed as partners for peace.
Related(20)
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molecular world
material world
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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