There are generally two types of fallacy. The first is nice and clean — formal fallacies. These are clearly wrong by the rules of logic. The classic is the well known fallacy that: If p then q, does not mean that if q then p. If all cats are mammals does not imply that all mammals are cats.
The second type of fallacy is much less clean. Informal fallacies include ideas such as an appeal to authority. The reason why it isn’t as clean is that sometimes it makes sense to accept authority. Obeying rules, unless you have a great reason not to, helps society function and may be better for you – generally you should listen to doctors when they give medical advice. This means it isn’t always wrong to heed appeals to authority. That said, following any authority whenever it is simply claimed by the speaker is a recipe for disaster, especially when the authority isn’t an authority in what they are talking about.
Another similarly messy classic logic mistake is the Post Hoc Fallacy:
“1. A occurs before B, 2. Therefore A is the cause of B.” (LaBossiere, 2013, page 97).
The problem arising is that it makes sense to use temporal consideration in causation. Something that comes after something else sometimes might be caused by it. Unfortunately, many things that come after other things simply aren’t caused by them at all. The thing to bear in mind is that while coming first is generally a pre-requisite of causing something else it isn’t enough. While informal logical fallacies are messy and sometimes tricky to spot we should all bear in mind that the post hoc fallacy is a real problem. The solution is to ask for more evidence of causation than simply accepting that because something came before something else it caused it.
Read: Michael LaBossiere (2013) 76 Fallacies