The phrase "a conclusive argument" is correct and usable in written English.
It can be used when referring to an argument that definitively supports a particular conclusion or position.
Example: "The researcher presented a conclusive argument that demonstrated the effectiveness of the new treatment."
Alternatives: "a definitive argument" or "a compelling argument".
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").
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.
This is not a conclusive argument for waiting-in the meantime, other equally important things, well understood at the moment, may be forgotten-but it is a major hazard of the genre.
The fact that both the great political parties of the country, in declaring their principles prior to the election, gave a prominent place to the subject of reform of our civil service, recognizing and strongly urging its necessity, in terms almost identical in their specific import with those I have here employed, must be accepted as a conclusive argument in behalf of these measures.
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.
In short, while the general ambience of modern physics may seem more friendly to perdurance than to endurance theory, it is remarkably difficult to devise any conclusive argument from physics to temporal parts.
Certainly, a more detailed study of the surface is needed to make any conclusive arguments concerning the existence of a bilayer structure.
Carnap himself admits that no conclusive argument for a specific $m$ can be made.
To state this fact is to make the most conclusive argument in favor of the civilian candidate.
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".
