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The phrase "argument is false" is correct and usable in written English.
It can be used when discussing the validity of a claim or reasoning in a debate or logical analysis.
Example: "After reviewing the evidence, I must conclude that the argument is false and lacks sufficient support."
Alternatives: "the claim is incorrect" or "the reasoning is flawed."
Exact(15)
The earlier part of this paper demonstrates that this argument is false.
Careful analysis reveals that this argument is false, and that the decree can be carried out.
Not only are their comments insulting and ignorant, the entire premise of their argument is false.
"And they can't hang me tomorrow," thought the prisoner, "because I know it today!" Careful analysis reveals that this argument is false, and that the decree can be carried out.
The argument is false".
Hence, the second premise of the original argument is false.
Similar(45)
Defense investigators and police have now confirmed, however, that there was no murder outside a recreation center in Ephrata, and the testimony and prosecutor's argument were false.
"The assurances that he was still in the country given to the (High) Court at the commencement and during the course of argument were false," the SCA judges said.
Leibniz believes, however, that there was overwhelming evidence that the conclusion of this argument was false.
Hence all the premises of Bechtel and Mundale's Central Argument are false.
All the Obama administration is doing is correcting that obvious mistake". Importantly, the premises underlying this argument are false.
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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