Is it possible to draw the line with "hasty generalization"?

Question

At what point does a generalization become fallacious and hasty? If I say people who smoke get cancer and the data shows that 90% of smokers get cancer, is that still a hasty generalization? Or 60%? Would that be a hasty generalization? And what about %50 and %40?

Is it possible to draw the line when considering "people who smoke get cancer"?

Answer 1

There is no particular percentage of smokers getting cancer that will justify the claim that "people who smoke get cancer". The latter amounts to a causal claim, i.e. that smoking causes cancer. So, you are asking, in effect, about the relationship between correlation and causation. Even in a relatively simple example such as the connection between smoking and cancer, we cannot simply infer that smoking causes cancer from the fact that they are correlated. It was known back in the 1930s that smoking was correlated with cancer, but it took over 20 years of scientific research to demonstrate that smoking causes cancer.

In general, if two properties or phenomena are correlated, there are a number of possibilities. It could be that A causes B, B causes A, some third thing C causes both, or each causes the other in a circular fashion. It could also be more complex and involve many factors. It could also just be a case of random error, or of systematic error. Without understanding which of these holds, any generalization may lead to an unsafe inference.

Determining which holds, and untangling all the connections between the relevant factors is typically difficult and requires considerable scientific work. The ideal circumstance for doing this involves conducting controlled experiments in which the individual factors and variables can be isolated and manipulated independently. Often, particularly in cases involving human beings, doing this is infeasible or unethical.

Answer 2

This is like asking "when can I say that an apple is big? 270g? 281g?". There are no absolute truths in nature.

All truths are relative and more importantly, subjective. Apples will be big for you according to your experience with them. The only way your question would get an objective answer would be to make a survey. Only at that point you could objectively say the weight which make apples big and if saying that 90% could imply that people get cancer.

But objective truths like that are useless in multiple contexts. We survive day by day with subjective truths.

For example, at what point we can "hasty-generalize" that smoking gets cancer? It was just false in case of a person I know, who smoked a pack a day until dying in peace, old and healthy. It is just true in other cases.

Answer 3

Expanding on conifold's comment, the statement "People who smoke get Cancer" is vague. By vague I mean we don't know what quantifier, if any, precedes the formalization of "people who smoke." Do you mean that: "every person who smokes get cancer, which will include a "∀" (universal quantifier) binding the variable, or do you mean a certain, well quantified (percentagewise), subset of people who smoke get cancer?

Former is elementary we can use Hempelian Confirmation, and we get an easy counterexample to the universal generalization. From that we can conclude that the generalization is false, but can we say the person committed a fallacy?

For the latter, however, we need a much finer system than crude predicate logic (we will need Probability Theory). Which, by the way, comes with its own set of fallacies one ought to avoid. Do statisticians commit hasty generalizations?

Before going any further, we know for certain that "hasty generalization" is not a formal fallacy. Therefore, since it's not, it's to an extent subjective. Subjective in the sense that a person hastily generalizing isn't quantifying some sample size, nor are they bothered to include a control group. So what does that mean?

Simply put, almost every generalization beyond authoritative studies are hasty generalizations. A generalization might turn out to be true, but that would be nothing other than a fluke. That said, statisticians sometimes commit hasty generalizations too, it's just that their fallacies are not so easy to catch. All this, then, boils down to (a) credibility (do you believe the person who is generalizing to be a credible/honest individual, do you believe they are truthfully conveying their experience, etc.), and (b) authority (Medical studies, Statistics, etc).

Credibility is more for informal arguments/settings.

I would say 3 easiest ways to catch a hasty generalization are:

1. Counterexample.
2. Credibilty. (Noncredible doesn't necessarily mean every generalization they make is hasty)
3. Authority. (Authoritative doesn't necessarily mean every generalization they make is "non-hasty")