Tl;dr (still too long, I know): no, there is no such logical fallacy. Such susceptibility to refutation is important in science and in moral philosophy as well. No, infinitely qualifying your statement is bad and by that point you should just come up with another solution. There are differences between qualifications of the principle and qualifications to the situation the principle is applied to. There are good and bad ways to "qualify" a statement: one that increases knowledge and solutions (hence more susceptible potentially to counterexamples) and one that decreases knowledge and solutions (hence less susceptible potentially to counter-examples). Finally, "most of X" qualifications are, personally speaking, a distasteful tactic in argumentation especially when no new information is added. There is no such fallacy because that is in fact a very crucial part of all generalizations: at some point there might just prop up a (valid) counter-example. If his point holds, your point may also still hold because those who are not vaccinated due to that are still responsible for their actions: they have made a choice not to vaccinate and very probably will get worse because of their immuno-compromised condition, they have to live with the pandemic while not being immune or risk getting serious health problems from immuno-compromised health conditions. The difference is that we don't want them to burden the consequences of their actions, especially in the context of their options being limited arbitrarily by the actions of others and by the limits of their biological constitution. So, what we're really saying is not necessarily that they're "not responsible" for their choices (they always are) but rather that we don't want them to be in a situation where they have to be responsible for those specific consequences of their actions because it is in some sense unjust to let them do that. Although there aren't any way to avoid such a counter-example situation (you can always avoid counter-examples by endlessly qualifying it). It is just part of the logic of an "all" general statement to be susceptible to a counter-example. The "finding a single exception to my general statement" is in fact a crucial part of scientific experimentation: if we find a single experiment that refutes a hypothesis, we need to modify the purported explanation in some way (which includes both the universal laws in the scientific explanation and the initial conditions for the law to work, for example by either fixing the value of m or the value of a or both in the equation F = ma) or we should throw it all out and find another explanation. In the scientific procedure, you can say that endlessly "qualifying" the statement with "with exceptions a, b, c, d, e, f, g,..." is actually a dogmatic move: you're not trying to find the correct laws or principles but are just trying to save the law or principle at this point. If your modifications, when faced with a potential refutation, don't advance knowledge but rather only works to save the principle that's being modified, it's not really a intellectually good move. I mean, think about it, if a generalization needs that many qualifications, what's the point of that generalization? You shouldn't try to save a broken down car but buy a new one, or just use public transport, or maybe even a bike or motorbike that's cheaper. The good thing about moral principles and scientific laws is that you can keep coming up with new laws and principles with relatively little cost, especially when compared to replacing a broken-down car with another $8000 car. And then you need to understand carefully what you are "qualifying", are you qualifying the principle or the situation it's being applied to? That is to say, are you qualifying "people are responsible for their choices" or the situation where someone is made responsible for their choices? Are you saying that the principle itself is being modified, or simply that there are conditions under which the person's specific situation made them not responsible for their actions? For example, statements like "but they're not really choosing to be vaccinated or not vaccinated" usually qualify as modifying the situation and not the principle. The principle holds, but not the situation. Again, this meets the same dogmatic moves: is this modification intended to shed light on our situation and principles, or just to save the principle in question from refutation? You can replace that principle with something like "Any action is right if it can coexist with everyone’s freedom in accordance with a universal law, or if on its maxim [subjectively formulated way of carrying out an action] the freedom of choice of each can coexist with everyone’s freedom in accordance with a universal law" and the principle of "The action to which the "ought" applies must indeed be possible under natural conditions" (or "ought implies can" principle). This is Immanuel Kant's principles . With these two principles, it now makes sense of various of our moral considerations: (1) We don't want to force vaccinated people to vaccinate when they are immuno-compromised because it implies that they can vaccinate without endangering their health, which is the purpose of vaccines to improve health, but by doing so they might end up even worse; while adverse effects on health due to vaccination without immuno-compromised conditions (mild fever, for example) are permissable because it is not contrary to the principle of health which tells us that we should improve upon our health. (2) We feel like it is part of our obligation to take care of these people by vaccinating when we can (by "can", refer to (1) for clarification) because by not doing so we have unintentionally (or in some cases intentionally) put others at risk and thus restricts their freedom of movement (or risk being infected with a dangerous virus) which is a basic prerequisite for most human actions. (3) It is icky to mandate the vaccine because this restricts others' bodily autonomy and bodily integrity, which are also preconditions of most human actions, especially considering when immuno-compromised people can take other precautions (masks, staying indoors,...) to not get infected. (4) We can and ought to refrain from vaccination in cases where its efficacy is in grave doubts, for example when it's just been developed and not even tested yet or when it has shown serious defects deadlier than the thing it is intended to be defense. So, it is perfectly plausible on these principles, with the reality of the COVID situation of course, to derive that: (1) it is a moral duty of everyone to get vaccinated whenever they can and as soon as possible for your own health and for others' freedom; (2) it is morally permissable for immuno-compromised people to not get vaccinated, although the virus is deadly; (3) it is impermissable for the government to impose a government mandate demanding everyone, who is not immuno-compromised, to be vaccinated and (4) Vaccine skepticism, to an extent, is morally justified especially in cases of doubtful efficacy. Of course, you can see that my principles do not have minimal qualifications and yet it sheds light on our intuitions on a wide range of the vaccine debates. And of course I am not even claiming that they are infallible, because I might have gotten the situation wrong in cases of application (the vaccine is indeed doubtful, this disease is not that dangerous compared to the vaccine, government mandate might be justified by these principles with enough modifications,...) but I try to keep the modifications of both the situation and the principles in to a minimum. And, of course, modifications of the situation don't count as a "dogmatic move" if the situation really is changing (the virus has gotten deadlier, the vaccine's efficacy has significantly improved, government mandate is no longer necessary because everyone's doing it voluntarily,...). Edit: Personally I absolutely despise the qualifications of the form "in most cases" and "except for a few cases" because those are actually very vague qualifications and they usually detract from moral principles into empirical investigations (which are valid if you want to discuss the science, but not when you're arguing the morals). Like, what do you mean by "most"? 95%? 80%? 60%? 50.1? And what do you mean by "except for a few cases"? 9 cases? 9% of cases? 0.9% of cases? Remember, you are "most likely" to be the average, but you are also on the spectrum of all other statistical probabilities. If I have an average likelihood of only getting a mild bruise in getting into traffic at 30%, but 10% of dying on the streets for no obvious cause by just stepping outside of my house, I'd think twice about stepping outside of my house. Furthermore, even if you've successfully argued that this one particular objection is a low probability case, that doesn't mean the rest of the cases are good. Your generalization is still susceptible to being false and falsified (shown false) because they always are. We should do our best to find these "exceptions" and to correct our overall judgments, not just trying to "defend" our original position by endlessly qualifying it. I'd argue that it is on the person doing the generalization do find for themselves as many counter-examples as possible and deal with them as non-dogmatically as possible (and this, too, is the procedure in science: you don't get to propose a theory without finding ways to test their truth, and no one will take you seriously if you keep qualifying your theory or "adding epi-cycles" as the hip people used to say).