The phrase "argument depends on" is correct and usable in written English.
You can use it when discussing the basis or foundation of a particular argument or claim.
Example: "The strength of the argument depends on the quality of the evidence presented."
Alternatives: "argument relies on" or "argument is based on".
Obviously, the strength of this argument depends on how bad one takes paternalism to be.
The first argument depends on assumptions that also appear in the subsequent ones, but it further ascribes to the community an intrinsic value.
This kind of argument depends on various controversial models of salvation, such as the one on which salvation involves the "deification" or "divinization" of humans, which can only be accomplished by one who is himself divine (Rusch 1980, 22 23).
In this case, the particular argument depends on the balance between natural selection and mutation: on one side, robustness reduces sensitivity to genetic (mutational) perturbations and therefore weakens the force of natural selection; on the other side, the weakened force of selection must be balanced against the continual evolutionary pressure from new mutations.
This argument depends on a number of assumptions.
But this argument depends on a highly selective reading of the academic literature.
However, various voices are either objecting or assenting to being brought into this argument, depending on their perspective.
(Nor does the private language argument depend on taking the latter to be an effect of the former).
The U.S. may or may not get involved militarily, goes the Obama argument, depending on whether its security interests are at stake.
This year's fall pop music season offers your average 21st century bounty, one with so many colors, textures, varieties, personalities and avenues for consumption that it's pretty easy to frame an argument depending on mood or agenda.
The logical strength of such arguments depends on how well one has taken into account all the relevant information and possible objections.
