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The phrase "a conclusive argument for" is correct and usable in written English.
It can be used when presenting a strong and definitive case or reasoning in support of a particular position or conclusion.
Example: "The research provides a conclusive argument for the need to implement renewable energy sources to combat climate change."
Alternatives: "a definitive case for" or "a strong justification for".
Exact(2)
Given that thought experiments along these lines have been popular in contemporary philosophy of mind it might seem natural to suppose that Leibniz takes the thought experiment to provide a conclusive argument for his conclusion (it is sometimes referred to as "Leibniz's Mill Argument").
"Think of this as a data-point that sparks interesting discussion about hip hop and word-usage, and absolutely not a conclusive argument for rapper x is better than rapper y". .
Similar(58)
It does not say anything about whether, for a particular theory T satisfying the conditions of the theorem, the statement "T is consistent" can be proved in the sense of being shown to be true by a conclusive argument, or by a proof generally acceptable for mathematicians.
It is therefore impossible to find a conclusive argument against the suggestion of Foucault that history, like the human subject, will prove to be a transitory conception.
But this cannot be a conclusive argument here.
Rather than offering a conclusive argument in favor of one position, Kant seeks to mediate between the two parties, Leibnizian and Cartesian.
This may be due to the difference in one methyl group, but further investigation is needed in order to achieve a conclusive argument.
Nevertheless, a conclusive argument about the relative significance of postnatal and adult d-serine concentrations will require a detailed study of NMDAR activity and expression patterns in the retina at key points between birth and adulthood.
But even if we lack a conclusive argument against current DDT use, we believe we have done enough to shift the burden of proof back to the advocates of its use.
Carnap himself admits that no conclusive argument for a specific $m$ can be made.
Perhaps the most conclusive argument for the sub's indispensability comes in the first response to Greenslade's blog: "Roy: I subbed the column you used to write for MediaGuardian enough times to realise just how much you need subeditors".
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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