Post hoc ergo propter hoc is a latin phrase which means ‘after this therefore because of this’. It refers to a fallacious inference (also called post hoc reasoning) that because one event occurs after another, that therefore the first event must have been the cause of the second. It is very natural for most people to draw ready inferences about causation based upon temporal sequence such as this, however one should do so cautiously since such inferences are often incorrect.
It is very easy to give examples where one event precedes another without causing it. Sunrise is always preceded by a period of relative cold and dark (the night), but it certainly isn’t the case that the cold and dark of night cause the sun to rise. In this case, both the cold and dark of night and the sunrise are caused by the regular rotation of the Earth. To give a more realistic example of fallacious post hoc reasoning, it is very common for people to make claims of the form ‘just after the president was elected the economy improved considerably, so clearly the president is a good economic manager’. This argument is fallacious because it assumes that because the economic recovery occurred after the election of the president, that therefore it must have been caused by the president. This may be true, but economic recoveries can also have numerous other causes, many of which are outside the control of the president. To know whether the president was truly the cause of the recovery, we would have to know what would have happened to the economy if a different presidential candidate had been elected instead. This sort of reasoning is called counterfactual reasoning, because one is considering what would have happened if some fact had turned out differently.
Counterfactual reasoning can be very difficult to engage in without simply degenerating into wild speculation, but is often necessary in order to make many types of causal claims. For example, we can say that a murderer caused the death of their victim because if they had not (for instance) pulled the trigger of their gun, then the victim would not have died. This counterfactual reasoning allows us to conclude that in this case, the murderer pulling the trigger of the gun both preceded and caused the death of the victim. On the other hand, if we consider the victim’s daughter who (let us suppose) ate breakfast immediately prior to the murder, we would (presumably) conclude that even if she hadn’t eaten breakfast, the victim would still have died. Such reasoning allows us to conclude in this case that eating breakfast did not cause the death of the victim, even though it did precede it. In many real-world examples it is very difficult to know what would have happened in the counterfactual case (e.g. if the president wasn’t elected). In such cases, therefore, we should be very cautious about inferring causation merely because one event occurred after some event of interest, since we cannot be confident about what would have happened if the possible cause had not occurred.
Post hoc fallacy: Brief description of the fallacy from LogicalFallacies.info
Post hoc fallacy: Description of the problems with post hoc reasoning with some examples
Post hoc reasoning: A discussion of the problems with post hoc reasoning in relation to scientific practise