Capaldi and Smit claim there are "at least" two ways to identify a post hoc fallacy in the following statement: (page 260)
I am opposed to charging tuition for college. Without tuition-free education, I could never have become mayor of this city.
The authors of The Art of Deception describe a post hoc fallacy of causal reasoning as follows: (page 206)
It is a fallacy of causal reasoning in that it is based on the mistaken belief that mere temporal priority constitutes a causal relation. It completely neglects the other criteria of spatial connection and a history of regularity.
They provide two examples.
In one example, someone prays that another person recovers from an illness. When the person recovers, the claim that the prayer was the cause of the cure is the post hoc fallacy. In the other example, someone takes snake oil for a cure and then is cured. Claiming the snake oil was the cure is the post hoc fallacy.
In both examples temporal priority implied a causal connection. This is not to deny that there might have been some connection, perhaps a placebo effect, but there may have been other causes as well. Indeed, it is easy to imagine that without either the prayer or the snake oil the sick person might have been cured.
Let's consider the question:
One instance of this fallacy is the mayor's implicit argument that no tuition-free education ⇒ Not becoming mayor. But why does the answer state "at least twice"?
We need to identify something with temporal priority that the listeners might imagine the mayor needed to become mayor. Here are three:
- Having a college education at all regardless of how it was paid
- Having a tuition-free college education paid for by one's family rather than through student savings or loans
- Having a tuition-free college education paid for by the government
It is easy to imagine that someone could become mayor without having one's family pay for the college education, or without having the government pay for the college education or without having a college education at all.
This provides three ways one might find a post hoc fallacy in the statement provided by Capaldi and Smit.
Capaldi, N., Smit, M. (2007). The art of deception: an introduction to critical thinking. Prometheus Books.