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'the above argument' is correct and can be used in written English.
You can use this phrase to refer to an argument that has been previously mentioned or discussed. For example: "The above argument makes a convincing case; however, I believe there are other factors to consider as well."
Exact(60)
There is nothing scientifically invalid about the above argument.
Still, some intuitionists do not accept the above argument.
The present study uses a differential deficit design to test the above argument.
Make an argument using your cases that either supports or attacks the above argument.
What do you think of the above argument?
Consider again proposition (1) in the above argument.
The above argument is given by Percival (1990: 185).
The above argument guarantees the validity of (3.5).
Then we need to modify the above argument a bit.
Then all inequalities in the above argument must be equalities.
By using the above argument, we conclude that (3.33).
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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