“Black people are typically criminals. My evidence is, look at the jail population–most people in jail are black.”
This is fallacious reasoning. Most x’s being y’s does not imply that most y’s are x’s.
But I can’t remember the name of it.
What’s it called?
Although “hasty generalization” doesn’t seem to have a authoritative scientific twang to it. So, maybe that’s not the term you’re thnking of.
It includes fallacy of quantification in some sense, or the affirming the consequent. You’re really saying most x’s are y’s because most z’s are x’s. The proportion of x’s that are z’s is unrelated to the proportion of x’s that are y’s. Even if you qualify x’s and z’s as the same thing, it’s the proportion of x’s that are y’s compared to the proportions of x’s that are z’s, because z’s are then the prison population, not the population of black people.
Also, its the fallacy of race.
Confusing causation with correlation?
My previous post sounds like a mess.
x’s number of ‘black’ people
y’s number of ‘black’ people in jail
z’s number of people in jail
x/y is not related to x/z
“Confusion of the inverse”, or “the conditional probability fallacy”.
Though probably the simplest way to get someone to recognize what you’re talking about is to say out “The mistake of conflating ‘Most Xs are Ys’ with ‘Most Ys are Xs’”.
I agree–I only wanted to know the name of it because someone else asked me what it was called.
This can’t be expressed with just 2 terms. Assuming all ‘black’ criminals are in jail:
Most ‘black’ people are criminals is is x/y where x is the number of ‘black’ criminals, and y is the total number of ‘black’ people.
Most ‘black’ people in jail is x/z where x in the number of ‘black’ criminals, and z is the number of people in jail.
It’s conflating most x’s are y’s with most x’s are z’s.
I am specifically looking for the name of the following fallacious form of reasoning:
P: Most X’s are Y’s, therefore, most Y’s are X’s.
I think Indistinguishable gave me the right name.
You’re right, though, that
Q: “Black people are typically criminals. My evidence is, look at the jail population–most people in jail are black”
can’t strictly be interpreted as an instance of P, since Q is most naturally thought to be equivalent to:
R: “Most people in jail are black, therefore, most black people are criminals.”
As you say, R involves three terms, whereas P only involves two.
But P-shaped reasoning is certainly involved in the thought process of someone who would utter Q. They’ve surely got something like this in mind:
S: Most criminal types are black, therefore, most black people are criminal types.
Where “most people in jail are black” is offered as evidence for the claim that most criminal types are black.
Ok, S fits the fallacy you were looking for.
I don’t agree with your conclusion about the hypothetical utterer. Instead the question specifically evokes the logic I represented, in order to make it more difficult to recognize as a fallacy. People that apply any reasoning at all have a natural skepticism for the inverse fallacy, so instead a fallacious comparison is made, something that will be a liitle harder to detect or argue against. But this isn;t GD or even the topic of the thread.
If you rephrase a little, it’s affirming the consequent:
If P, then Q.
Q.
Thus, P.
“If Black people are criminals, then there would be many Blacks in jail.”
“There are many black in jail.”
“Thus, blacks are criminals.”
The error becomes obvious when you say something like:
“If I am talking, then I am alive.”
“I am alive.”
“Thus, I am talking.”
which only holds true for teenagers and mothers-in-law, obviously.
And for people uttering syllogisms, of course.
I think that would be the intent of either the modified or original statement anyway.
The subtlety with removing the probabilistic element in one’ s analysis of arguments in the vein of the OP’s is that it allows one to paper over various fallacies which are intrinsically connected to intermediate probabilities.
For example, one can legitimately move from “P implies Q” and “Q implies R” to “P implies R”. You might think this correspondingly means one can move from “A high percentage of Ps are Qs” and “A high percentage of Qs are Rs” to “A high percentage of Ps are Rs”, but that would be fallacious. Indeed, even moving from “P implies Q” and “A high percentage of Qs are Rs” to “A high percentage of Ps are Rs” is fallacious. Indeed, even concluding the existence of a single P which is an R is fallacious. [Consider P = human albinos, Q = humans, and R = non-albinos]
Or consider contraposition (in some sense, just a rephrasing of the special case of the last example where R is a contradiction): one can legitimately move from “P implies Q” to “(Not Q) implies (Not P)”. But moving from “The probability of Q given P is high” to “The probability of (Not P) given (Not Q) is high” (i.e., “The probability of P given (Not Q) is low”) is fallacious. It’s the sort of reasoning undergirding p-value based null hypothesis significance testing, but it’s fallacious all the same…
Frylock, you may be thinking of the Prosecutor’s Fallacy. It involves confusing the probability of X, given Y, with the probability of Y, given X. Here’s one fairly clear explanation involving a hypothetical example, but I’ve seen several authors describe the real-life case The People of the State of California v. Collins as an example of this fallacy.
I’d say you’ve accurately described Frylock’s fallacy, but not quite done justice to describing the Prosecutor’s fallacy. I’ve always heard “the Prosecutor’s fallacy” used to describe situations which, while they may incidentally involve some amount of “confusion of the inverse”, more significantly demonstrate the use of an unconditional probability where a conditional probability is called for (or, put another way, conflating a probability conditioned on just A with a probability conditioned on A & B, using the former where the latter is more relevant), as in your linked examples.
You’re probably right.
Let me just point out that there is an additional fallacy in conflating being a criminal with being in jail. A non-violent drug user is much more likely to be put in jail if he is black rather then white. I cannot give a cite offhand, but the white drug users I know have never given a thought to being arrested and expect that, if they are, they will be let off with a warning. I did read recently that the percentage of drug users is no higher among blacks than among whites.
Self-fulfilling prophecy: if X-type people are assumed to be criminals, then any X-type person arrested mistakenly has a much higher chance of wrongly being imprisoned. The jails then become full of X-type people only because the jails started out with a slight majority of X-type people.
Hmm, also we usually assume criminal=convict. Perhaps replace the term “criminal” with “committed a crime.” After all, if you’re wrongly convicted and jailed, then you’re a “criminal” by definition, even if you’re innocent.