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The phrase "on factual grounds" is grammatically correct and can be used in written English.
It is often used to refer to the basis or evidence that supports a statement or argument. Example: "I believe that the decision to invest in the new project is sound on factual grounds, as we have thoroughly researched the market and consulted with industry experts."
Exact(8)
Ms Morgan refutes on factual grounds one of the objections – that her preferred candidate was wrong about Ofsted's responsibility for failures of child protection.
Mr. Korematsu's conviction was invalidated by a federal judge in 1984 on factual grounds.
The Court holds today that the National Labor Relations Board may not enjoin the prosecution of a state court lawsuit unless the suit lacks a "reasonable basis," ante, at 743, and, further, that to find that the suit lacks a reasonable basis on factual grounds the Board must find that there is no "genuine issue of material fact," id., at 2171-2173.
Commentator Hilary Rosen disputed Lord on factual grounds, saying that "President Obama did take on Rev. Wright and in fact alienated Rev. Wright for a long time". Candidate Sen. Barack Obama in 2008 quit his church over the remarks of former pastor Wright.
Duchesne challenges this revisionist world history on factual grounds.
Diamond's conventionally Eurocentric viewpoint has been regularly challenged by anthropologists (McAnany and Yoffee 2009), on factual grounds, on his acceptance of discredited hypotheses, and for its naively racist message.
Similar(52)
The guards' attorneys said they will fight the government on jurisdictional and factual grounds.
I believe Mr. Schmid's real concern is (to use his words) the loss of "the distinct masculine flavor of an all-male college". Here, at least, he is on solid factual ground.
On March 7 2003 the attorney general says that military intervention will only be justified if there are "strong factual grounds" for concluding that Iraq has failed to comply with UN resolutions.
After selecting the category of complaint, you must inform the state agency of the factual grounds for the dispute.
"There have been cases that have been brought on very thin factual ground," says David Roe, then as now a lawyer for Environmental Defense.
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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