Grain of Salt

Post hoc ergo propter hoc: after it, therefore because of it

Post hoc ergo propter hoc

Struck diagram on assay stock: Post hoc ergo propter hoc

Post hoc ergo propter hoc is the false cause fallacy of treating one event as the cause of another simply because it happened first. The Latin translates as "after this, therefore because of this", and the fallacy is committed the moment a sequence in time is accepted as a causal chain without anything else being checked. It is usually shortened to post hoc, and in English it is read as post hock, air-go, prop-ter hock.

Grain of Salt is interested in how a causal claim is tested, not in settling any particular one. The examples below are invented so that the reasoning stays visible.

What post hoc ergo propter hoc is

Post hoc ergo propter hoc is the error of promoting a sequence to an explanation. Two events occur in order, the second is interesting, and the first is handed the credit or the blame because it was standing nearby at the time. The fallacy belongs to the family that logicians call false cause, or non causa pro causa, and it has exactly one sibling in that family that matters in practice: cum hoc ergo propter hoc, "with this, therefore because of this", which does the same job with two things that merely occur together.

What distinguishes post hoc from the wider category of logical fallacies is how respectable it looks. An ad hominem is visibly rude and a non sequitur is visibly broken, but a post hoc argument has the shape of a proper causal claim. It has a mechanism-sized hole in it and nothing in the sentence points at the hole.

The claim in one sentence, and the two parts it always has

Every post hoc argument has two parts: a sequence that is genuinely true, and a causal conclusion resting on nothing except that sequence. The first part is why the fallacy survives scrutiny for so long. Nobody is lying about the order of events.

A hardware shop repaints its front in April and takes more money in May than in any previous May. The repaint is real, the increase is real, and the order is real. What the shop owner has not looked at is that a large office block opened two streets away in the last week of April, that May had one more trading Saturday than the year before, and that the shop next door closed. 3 candidate causes were available and one of them got the credit for being first in the diary.

The five forms the false cause takes

The false cause takes 5 forms in everyday reasoning, and the fifth is the one that fools careful people.

  • The single sequence. One event, one later event, one conclusion, as in the repainted shop front.
  • The ritual. A repeated action followed by a wanted outcome, kept because the outcome kept arriving: the lucky shirt, the particular order in which a machine is switched on.
  • The fix applied at the worst moment. Something is done when a measure is at its extreme, and the measure then improves.
  • The change made during a trend. A new procedure is introduced while the number it targets is already moving, and the trend is credited to the procedure.
  • The delayed blame. A machine fails a week after a service, and the service is blamed, with no account of what actually broke.

Form three has a name of its own: regression to the mean. Extreme values are followed, on average, by less extreme values, whatever anyone does in between. Any intervention applied at a peak will therefore look effective, and any intervention applied at a trough will look harmful.

A worked example, and the repair

Take the raw claim: "The council resurfaced Mill Lane in March, collisions on Mill Lane fell over the following year, therefore resurfacing prevents collisions." Every factual element in that sentence can be true and the conclusion still unsupported, because of why Mill Lane was chosen. Roads are resurfaced after a bad year. A bad year is an extreme value. The following year was likely to be better even if nothing had been done at all.

The repair does not delete the claim, it adds the comparison the claim was missing: "Collisions on Mill Lane fell over the year after resurfacing. On the 6 comparable roads that were assessed as candidates and not resurfaced, collisions fell by a similar amount over the same period, so the resurfacing cannot yet be credited." That is a real answer, and it may be disappointing. The general shape of the repair is always the same. Find the cases where the first event did not happen, and see whether the second event happened anyway.

What post hoc is confused with

4 things sit close enough to post hoc ergo propter hoc to be mistaken for it, and telling them apart is most of the skill.

  • Cum hoc ergo propter hoc uses co-occurrence rather than sequence. Correlation with no time order at all.
  • Non sequitur is the general category of conclusions that do not follow. Post hoc is one specific way of not following.
  • A genuine causal inference also contains a sequence. It differs by carrying a mechanism, a comparison group, or a dose response as well.
  • Confirmation bias is what keeps a post hoc belief alive. The fallacy makes the first link; the bias supplies the later cases that fit and quietly loses the ones that do not.

When the same reasoning is not a fault

Sequence is not a fallacy on its own, because a cause must precede its effect. Temporal order is therefore a necessary condition for a causal claim and it eliminates candidates: anything that happened after the effect is out. The error is only in treating a necessary condition as a sufficient one.

There are also settings where post hoc reasoning is close to sound, and they share one feature: everything else was held still. On a production line where a single setting was changed at a known minute and the defect rate changed within the hour, with no other change logged, the sequence carries real weight. It carries that weight because of the control, not because of the order. Remove the control and the order proves nothing again.

The test to run on the next causal claim

Ask 4 questions of any claim that a change produced a result.

  1. Ask what else changed in the same window, and write down at least two other candidates before accepting the first one.
  2. Ask why this moment was chosen for the intervention: was the measure at an extreme when someone decided to act?
  3. Ask what happened to the comparable cases where nothing was done, and whether anyone looked.
  4. Ask what the proposed mechanism is, step by step, and whether each step could be checked separately.

Where the phrase turns up outside logic

The phrase is searched more often than most Latin tags because it has been used as a title outside philosophy, most visibly as the title of an early first season episode of the television drama The West Wing. That is a naming fact and nothing more: the fallacy is centuries older than the program, and this page is about the reasoning rather than the show, its plot or its cast.

The other name worth knowing is the plain English one. Textbooks list post hoc ergo propter hoc under false cause alongside cum hoc, and treat both as species of the non sequitur. If you remember one line from this page, make it the translation, because the translation is already the refutation: after this, therefore because of this. Written out in full, nobody would sign it.

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