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The phrase "argument does not establish" is correct and usable in written English.
It can be used when discussing the validity or strength of a particular argument in a debate or analysis.
Example: "While the author presents several points, the argument does not establish a clear connection between the evidence and the conclusion."
Alternatives: "argument fails to demonstrate" or "argument does not prove".
Exact(2)
The argument does not establish that there is a general connection between relativism and tolerance.
It is also important to recognize that, even if each of these claims is accurate, this argument does not establish the type of conclusion that many defenders of closed borders might want.
Similar(58)
Judge Kennedy said this argument "does not make sense" because Congress went to great lengths to establish payment rates.
That argument doesn't make sense.
The chapters of this new book do not establish and develop an argument.
(Such numbers do not establish causation).
To be sure, the rebuttal of Strawson's argument does not suffice to establish (Claim 1), but it keeps process philosophy in the running.
The remark can be read as a concession that the Sixth Meditation arguments are weaker than the earlier arguments about minds and God — that these later arguments do not "prove what they establish".
This argument does not save the analysis.
This may indicate, that the converse argument does not hold.
The same argument does not generally hold for the hLNA.
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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