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"demonstrate the argument" is correct and usable in written English.
You can use it when you are trying to give evidence or examples to prove the validity of an argument or point you are making. For example, "The findings of this study demonstrate the argument that the use of technology can lead to better educational outcomes."
Exact(1)
To explain why, we will demonstrate the argument on ψ1.
Similar(59)
However, as McNamara (1993) demonstrates, the argument rests essentially on the principle that necessarily equivalent SOAs are identical, a principle clearly at odds with the fine-grainedness of SOAs that Plantinga assumes elsewhere (and often) in various applications of his theory.
I demonstrate the general argument in the context of emerging foreign exchange markets which exhibit a particularly wide variety of trading arrangements.
Siamak spent months engaging the media and policymakers to demonstrate the fallacy of the argument, and challenged the Office on Foreign Asset Control OFACC)'s rules.
Military action in Syria would demonstrate, so the argument goes, that America is serious about enforcing its red lines.
He proposed that, unless the coherence of a supremely perfect being could be demonstrated, the ontological argument fails.
Mr. Brodsky tried to demonstrate the inconsistency of that argument.
We have developed a number of theoretical models that demonstrate the cogency of this argument, presented empirical data that suggests that the assumptions of the models are realistic, and reviewed empirical examples of cultural changes that result from competition between groups.
This illustrates Kant's efforts to demonstrate the fallacious nature of the arguments that characterize metaphysics, as well as his interest in identifying the sources of such errors.
In the context of the debate over the environmental versus genetic causes of species extinction, the present results demonstrate that the arguments of the partisans of the environment [ 1, 2, 40] and genetic [ 9- 11] hypotheses are both theoretically justified.
"On this basis Global Radio look forward to further dialogue with the CC in order to demonstrate the strength of these arguments and working to achieve the appropriate outcome".
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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