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The phrase "a more general argument" is correct and usable in written English.
You can use it when discussing a broader or more inclusive point of view in a debate or analysis.
Example: "While the specific case is compelling, we must consider a more general argument that encompasses various perspectives on the issue."
Alternatives: "a broader argument" or "a more inclusive argument".
Exact(6)
There is a more general argument about the value of pluralism in the market, but this is hard to turn into criteria that apply in specific cases.
Cohen 2004, 2009 holds a similar position, though he has produced a more general argument.
It is making a more general argument.
A more general argument against the effectiveness of 'secondary-site' models is that they are vulnerable to selfish exploitation by any element that lacks the site.
For both stimuli, we use this important role of NAD(P H within the antioxidant system as a more general argument: With increasing ROS more reducing equivalents for antioxidants are needed, and indeed supplied by the NADH pool.
While access to such social goods can determine current health status, a more general argument can be made that fairness should involve consideration of prior access to such goods even without documenting a link to health.
Similar(54)
Already, he said, foes of trade liberalization and other free-market policies in Europe are citing Washington's agreement to dramatically intervene in the American economy as a precedent for advancing their more general argument — that American-style economics is at a dead end.
That these 24 are unique and represent all possible decompositions follows from the more general argument (for n mediators) given in Web Appendix A, where we show that there are ways of decomposing a TCE into a sum of path-specific effects through n mediators.
However that does not undercut the more general argument for pushing eukaryotic origins back to a very early stage of cell evolution.
For the idea of the winner's curse to hold, papers published in less-well-known journals should be more reliable; but that has not yet been established.The group's more general argument is that scientific research is so difficult the sample sizes must be big and the analysis rigorous that most research may end up being wrong.
The second, more general argument is due to Sundholm (1983, 159).
More suggestions(17)
a more general point
a more general discussion
a more general debate
a more general plea
a more general case
a more general thesis
a more general overview
a more general calibration
a more hopeful argument
a more general issue
a more convincing argument
a more bankrupt argument
a more powerful argument
a more general result
a more general paradox
a more novel argument
a more general pattern
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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