Affirming the consequent

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‘Affirming the consequent’ is a logical fallacy of the form:

  1. If P, then Q.
  2. Q.
  3. Therefore, P.

An example of this error is:

  1. If John has disease X, then he’ll have symptom Y.
  2. John has symptom Y.
  3. Therefore, John has disease X.

This logic is invalid because the fact that P implies Q doesn’t mean that Q implies P. That is, in the example, the fact that Y is a symptom of disease X doesn’t mean that Y isn’t also a symptom of another disease, and so symptom Y doesn’t imply disease X. One way to make this kind of argument valid would be to begin the first premise with ‘If, and only if, …’ instead of just ‘If ...’.

The name ‘affirming the consequent’ is due to the second premise affirming the consequent of the first.

This consistent logical error is actually a form of availability bias, and can therefore be explained by credulism, the certainty of belief, and the speed of the brain. In the example, the first premise claims that there’s an exact correlation between disease X and symptom Y. And this exact correlation will be readily available to our thought processes when we learn, immediately afterwards, of the claim, in the second premise, that John has symptom Y. And an obvious possibility, given these two claims, is that John’s symptom is due to him having disease X. And, given the speed of the brain, and the obviousness of this possibility, it tends to enters our thought processes, via our reasoning or imagination, within moments of us learning of the claim in premise 2. And, given credulism, this possibility will enter our thought processes as reality, and, as explained in Confirmation bias - in the section Belief is self-preserving - the certainty of belief will then effectively provide a degree of protection to our belief, directly and via the confirmation bias. Specifically, while our certainty exists, we’re unlikely to question our conclusion, and are therefore biased against realising the logical flaw in it - that is, that the exact correlation between disease X and symptom Y is only one way. Thus, we’re biased, due to availability bias, towards committing this logical error.