I'm a bit perplexed; I've read examples about the "post hoc ergo propter hoc" fallacy such as when a person sneezes and then an earthquake happens. However, I'm confused as to why more mundane examples haven't been showcased, such a when someone drops something and it breaks.
P1. I dropped Object A.
P2. Object A broke after I dropped it.
C. Therefore Object A broke because I dropped it.
How is this not a "post hoc" fallacy? How do I know that some other force didn't cause the object to break after I dropped it? i.e., where do you draw the line here? Thanks for answering.
This question is answered studying the logic of causation.
If one thing (B) follows another (A), A may or may not be a cause or the cause of B.
In the most obvious case (complete necessary causation), if the presence of A is invariably followed by the presence of B, and the absence of A is invariably followed by the absence of B, you can say for sure that A caused B (for sure, so long as the generalizations implied by the modality "invariably" are found to hold).
In lesser cases (partial-necessary, complete-contingent, partial-contingent), the conditions for this inference become more complicated, but are still formally expressible.
You can read more about this here: http://www.thelogician.net/4_logic_of_causation/4_chapter_01.htm
The fallacy of "post hoc ergo propter hoc" occurs when we do not apply the formal rules for identifying causation or, worse still, when we breach them. Thus, we claim that A caused B just because B followed A, even though we have not established that there is a causative relation between such things.
Matters become more complicated still when we take into consideration volition. But I won't get into that here. For this issue see here: http://www.thelogician.net/4b_volition/4b_chapter_01.htm