As stated in the previous post on this topic, a refutation of a thesis consists in a proof that the thesis is not the case. This can happen in two ways. The first is by proving that the thesis is false. The second is by proving that it is ill-formed or non-sensical.
In a simple statement, the proof that a statement is false is a proof that what it attributes to the subject is not attributable to it. Such a proof may occur either solely by way of explication of the being of what is named by the subject and predicate, or it may occur by way of the addition of information about other beings. In the first case, a proof will concludes to a necessary conclusion about the nature of the things in question. In the second case, the conclusion may be merely factual. In every refutation of a thesis, an explication of the nature of what is named in its terms must play at least a partial role.
For instance, utilitarianism is a view that contains, as one of its constitutive elements, the thesis that what it is for something to be good is for it to be useful. But the nature of utility is such that something is only ever called useful with respect to a given end. Hence, whenever someone calls some thing a useful, this must be read as saying that thing is useful for some end b, i.e. a is useful for achieving b. But goodness is not only said with respect to some end. Some things are good without respect to ends, viz. those ends themselves. Therefore, utility is not goodness. Therefore, utilitarianism is false.
When a constitutive part of a view is refuted, such a refutation is ipso facto a refutation of any view or thesis that implies the original view, including any subspecies of that view.
A consequence of this is that no refuted view can become unrefuted by the addition of further nuance to that view, provided it remains a species of the originally refuted view. Hence, attempts to avoid refutation by the imposition of nuance constitute a failure to understand how refutation works. Given that this is the de facto means by which views are modified over time in academic literature on philosophical questions, the implication is that this failure of understanding is widespread.