15. Post Hoc Ergo Propter Hoc
Wireless Philosophy, Fallacies, 5:42. Original title: CRITICAL THINKING - Fallacies: Post Hoc Ergo Propter Hoc [HD]
Summary
Paul Henne (Duke University) explains the informal fallacy post hoc ergo propter hoc ("after this, therefore because of this"), using a broken bicycle to show that establishing that one event followed another is not the same as establishing that it was caused by it.
A broken bike
Henne lends his bike to his roommate Alex, who returns it with a broken chain. Henne's first reaction, that Alex broke it, seems obvious: the bike broke after Alex rode it. But Henne argues this conclusion is premature without further evidence that Alex was negligent, since the chain could simply have been defective, so that whoever rode the bike that day would have come home with the same broken chain.
Formalising the fallacy
He sets out the bare structure of the fallacy:
Premise 1: X happened after Y.
Conclusion: Therefore, Y caused X.
Applied to the bike: my bike broke after Alex rode it, therefore Alex caused it to break. As it stands the argument is invalid; Henne's counterexample is that the sun sometimes comes out after it rains, without the rain causing the sun to come out.
Adding premises, then testing them
Henne tries to rescue the argument by adding an implicit premise: usually, the person who rode the bike before it broke caused it to break. This turns the argument into an inductive one, but Henne notes it still needs more evidence to be convincing, so he compares two cases: one where his other roommate Aleah witnessed Alex hitting the chain with a hammer (strong evidence), and one where she saw nothing (weak evidence, only "likely"). A stronger premise, that a bike breaking after someone rides it means the rider caused it, makes the argument valid, but Henne shows it is not sound: the premise is false, since bikes often break from ordinary wear and tear without any negligence.
Beyond the bike
Henne closes by extending the point beyond his own example: a cat scratch occurring right before a fever does not mean the scratch caused the fever, since the fever could equally have come from a roommate's flu. The sequence of two events alone never establishes a causal relation between them.
Key takeaway
Concluding that Y caused X merely because X followed Y is the post hoc fallacy; only additional evidence, not the order of events, can establish that a causal relationship actually exists.