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"know with certainty" is a correct and usable phrase in written English.
You can use it when you want to express that you are sure of something. For example: "I know with certainty that this is the right decision."
Exact(58)
"We really don't know with certainty," Mr. Gelman said.
Wouldn't we be grateful if we could know with certainty?
How, and at what speed, we cannot know with certainty.
Researchers don't know with certainty what causes the disease.
Do you know with certainty that your formula will predict that end date accurately?
"We know with certainty that a debt crisis is coming to America.
Why Spanier felt Curley and Schultz were innocent: I don't know with certainty.
But, like those heartbroken students, I do not know with certainty what the future holds.
I will never know with certainty if that bomb would otherwise have killed me.
Still, it is impossible to know with certainty when credit card rates will be affected.
And I do know with certainty that we can defeat al-Qaida.
More suggestions(16)
know with confidence
know with conviction
known with certainty
identifying with certainty
discern with certainty
knowing with certainty
explained with certainty
knew with certainty
recognized with certainty
understanding with certainty
knows with certainty
know with terrorism
know with everything
know with everybody
know with everyone
know with surgery
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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