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The phrase "argument based on the" is correct and usable in written English.
It can be used when discussing the foundation or reasoning behind a particular argument or claim.
Example: "The argument based on the evidence presented in the study is compelling and warrants further investigation."
Alternatives: "argument founded on the" or "argument derived from the".
Exact(58)
Ashers had one last argument, based on the Human Rights Act.
For instance, the recent discovery of the Higgs Boson was established through a statistical argument, based on the idea that what is "significant" for one researcher should also be significant for another.
Using a simple argument based on the energy budget at Earth's surface one can show that a variation of terrestrial insolation with solar activity on the percentage level – as reported in [ 1] – would lead to unrealistically large temperature fluctuations which are not observed in the instrumental surface temperature record.
But once we face up to the fact that a criterion of transworld identity (if we had one) could have no such empirical use, the argument based on the epistemological assumption appears to collapse.
The first prong, he said, would be an argument based on the Clean Air Act authority.
Yet this year the argument based on the elimination of delays lost some of its punch.
The argument based on the "harm principle" is said to treat athletes as children.
Because the Bowers v. Hardwick decision did not address equal protection, instead rejecting an argument based on the right to privacy, such a decision would not necessarily require the court to overrule the 1986 precedent.
It is an argument based on the famous remark by the former US secretary of state, Dean Acheson that Britain, having lost an empire, had not found a role.
Similar(2)
He knew how to make arguments based on the law.
Will Ulster's militants prove susceptible to arguments based on the belief that most people prefer peace to war?
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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