# Affirming the consequent

 Part of the series on Key articles General logic Bad logic v - t - e

Affirming the consequent is a formal logical fallacy confusing the directionality of if-then propositions, and named after the consequent in the conditional statement (Q in "if P, then Q"). It is a special case of the non sequitur.

## Forms of the argument

### Propositional logic

• If P, then Q.
• Q.
• Therefore, P.

In formal terms, the fallacious argument is stated as $\left(P\rightarrow Q\right), Q \vDash P$.

### First-order logic

• If P is true of x, then Q is true of x.
• Q is true of x.
• Therefore, P is true of x.

In formal terms, the fallacious argument is stated as $\forall x.\left(P(x)\rightarrow Q(x)\right), Q(a)\vDash P(a)$.

## Fallaciousness

Affirming the consequent related to the generic phrase that "all x are y, but not all y are x" in that the formal fallacy fails to recognise the "not all y are x" part. Its statistical equivalent is confusion of the inverse, where two conditional probabilities are mistaken to be equal when this is not necessarily true.

As a formal fallacy, it is an error in the underlying logic of an argument or proposition and, similar to how denying the antecedent can be remedied, is corrected by replacing the directional condition "if" with the bidirectional equivalence of the "if and only if" statement. This would mean that P necessitates Q and, equally, Q necessitates P. While this will correct the formal logic and the hypothetical assertions made, it can still form a not even wrong argument if the "if and only if" premise happens to be not well founded.

## Examples of the argument

### Propositional form

1. If it is sunny today, then I will go swimming.
2. I will go swimming.
3. Therefore, it is sunny today.

1. If Bill Gates owns Fort Knox, then he is rich.
2. Bill Gates is rich.
3. Therefore, Bill Gates owns Fort Knox.

1. If the Bible is true, then Jerusalem is a real city.
2. Jerusalem is a real city.
3. Therefore the Bible is true.

1. If God answers prayers, then the tumor will be benign.
2. The tumor is benign.

1. If the bible is true, then a One World Government will emerge.
2. [Insert bogeyman here] is starting a One World Government[1]/there is a currently a One World Government[2]
3. Therefore the bible is true.[3][4]

### First-order form

1. Fascists support a strong military.
2. John Q. Warhawk supports a strong military.
3. Therefore, John Q. Warhawk is a fascist.

## Footnotes

1. Assuming us Skeptics are wrong, to which there is no evidence
2. For future readers just in case it does happen.
3. This also falls under self-fulfilling prophecy since the bible never states when. If the prophecy doesn't state when, then it is self-fulfilling, as it could happen in any time period and be considered "fulfilled". Another bible prophecy like this is the city of Damascus being destroyed.
4. Of course they realized this, so now they're going on about how other religions were created by the Illuminati, how Evolution and Atheism were created by Them, complete with fake whistleblowers! Of course when someone even suggests Christianity was created by the Illuminati, they talk about how much of a lie that is, and how the person who dared to say that is a shill. Special pleading at its finest.