# Fallacy of affirming the consequent or of denying the antecedent? [closed]

If patient has condition X, then we would see symptoms A, B and C. We do see symptoms, A, B and C. So the patient must have condition X.

Is it the fallacy of affirming the consequent or the fallacy of denying the antecedent?

## closed as off-topic by YiFan, Eliran, Conifold, Jishin Noben, virmaiorApr 8 at 5:25

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• I just read it as "Which fallacy (of AtC and DtA) is represented in this statement?" – Josiah Mar 25 at 22:56
• @Josiah It is one of those HW questions that we close for missing context. Please do not answer them. – Conifold Mar 25 at 23:17
• Why "denying the antecedent" ? there is no negation in the expression... – Mauro ALLEGRANZA Mar 26 at 13:11

This is, a classic case of affirming the consequent.

Because they're never used apart, "Symptoms A, B, and C" can be taken together as a proposition S.

The structure is

X -> S
S
Therefore X

For contrast an example of denying the antecedent might be

If patient has condition X, then we would see symptoms A, B and C. The patient does not have condition X. Therefore we cannot see A, B, or C.

Note that in both cases the reason that these are a fallacy is the same: it is possible for two diseases to have the same set of symptoms.

Affirming the consequent: If patient has condition X, then we would see symptoms A, B and C. We do see symptoms, A, B and C. So the patient must have condition X. -- Wrong, because the patient could have condition Y which also causes A, B, and C.

Denying the antecedent: If patient has condition X, then we would see symptoms A, B and C. The patient does not have condition X. Therefore we cannot see A, B, or C. -- Wrong because the patient could have condition Y which also causes A, B, and C.

However, the fallacies differ because what is being claimed is different. Affirming the consequent is "The effect happens, so it must be because of that specific cause" whereas denying the antecedent is "The cause did not happen, so the effect is impossible."

(I say cause and effect very informally, the fallacies are actually given in terms of implications rather than causes)