Most people, when they hear, read, or whatever, that all members of group A are members of group B, will tend to assume (wrongly) that all members of group B are also members of group A.
For example, many years ago it was true that most criminals in American prisons were black. A lot of people thought this meant that most blacks were criminals.
This fallacy is easily countered simply by creating a Venn diagram of the two groups.
I don’t know that it has a specific name. Broadly it’s just an inaccurate generalisation.
Affirming the Consequent.
Illict Conversion; see Hurley and the fallacy files for more info.
Well, that is the name of the fallacy you give in your first sentence. The second sentence switches to using “most” instead of “all”.
These are the same, or the first is a subset of the second but either applies in the OP’s cases. I think.
No, they aren’t. (Nor is the first a subset of the second. I also don’t think this is an instance of affirming the consequent.)
You might be right.
Remember to keep a true or* formal* fallacy separated from a* informal* or debating-club 'fallacy" .
For example, “appeal to authority” is perfectly OK (outside of a high school debating club) assuming said authority really is a expert on the subject. Einstein on physics is one thing, Einstein on Capital Punishment is another. Many "informal fallacies’ are not fallacies at all, just weak arguments.
However, in the OP case,* Affirming the consequent* is a* formal logical fallacy. *
Agreed: it’s “Affirming the Consequent,” a.k.a. the “fallacy of the converse.”
ETA: This is in response to the OP’s first sentence. The OP’s second paragraph, which substitutes “most” for “all,” isn’t quite the same thing.
Do you think “all A are B, thus all B are A” is an instance of affirming the consequent? The same question goes out to all the other supporting this position.
Yes I do, since “All A are B” is equivalent to “If it’s A, then it’s B.”
OK, so would I be right in thinking that you think that “if p then q, thus if q then p” is an instance of affirming the consequent? I don’t, and as far as I can tell, your citation doesn’t say that it is.
Does this cite make it any clearer?
“If p then q, q, thus p” is not the same thing as “if p then q, thus if q then p”. I see why people think they are related, but they really aren’t the same (mistaken) form of argument.
They’re certainly logically equivalent.
I’m assuming that “If p then q, q, thus p” means “((p -> q) ^ q) -> p”
and that “if p then q, thus if q then p” means “(p -> q) -> (q -> p)”
To me, they’re the same logical fallacy: assuming (wrongly) that the converse of a true statement must be true. Anybody else want to weigh in?
They are logically equivalent to a whole lot of things.
In this context I don’t think one should be invoking the deduction theorem to equate “if,then” with “therefore”. Compare, modus tollens “if p then q, not-q, thus not-p” to one direction of contraposition “if p then q, then, if not-q then not-p”. By the deduction theorem, modus tollens is equivalent to “if p then q, thus if not-q then not-p”. Again by the deduction theorem, this is equivalent to “if p then q, then, if not-q then not p”. So by this reasoning modus tollens is just one direction of contraposition. To equate forms by invoking strings of reasoning in this manner seems to me a mistake.
Affirming the consequent is a formal fallacy, and that means the precise form matters. If we want to explain a mistake one may point out the relationship to affirming the consequent. In this case this is useful. But as a formal fallacy, they are not the same thing (after all, they aren’t the same form!)
Okay, I’m inclined to concede that you’re correct.
Now this, the OP’s second paragraph, looks to me like Confusion of the Inverse. That’s described in terms of conditional probabilities (specifically, confusing “the probability of A, given B” with “the probability of B, given A”). Is confusing “the proportion of A’s who are B” with “the proportion of B’s who are A” essentially the same thing?