Fallacy fallacy and the big picture

The fallacy fallacy, apart from being a little more meta than its cousins, essentially boils down to this: the existence of a fallacy in an argument does not make the conclusion false. This is quite a straightforward fallacy once you have your head around it, essentially, an argument can be complete rubbish and/or the premises false, and the conclusion correct. To give a flippant example:

All envy is purple, therefore 2+2=4.

In reality, the fallacy is naturally more subtle. An argument is often a large set of premises and lines of logic, naturally, one line could be wrong but the argument could still stand on just one line of argumentation. If you're reading an article and the writer makes an error in an argument, we are often more dismissive of the surrounding arguments and general point. When a mistake spills overs from an arguments, tainting our opinion of the writer and in turn the article, you could argue that it is an ad hominem. Of course, I would like to stress again, this is a decent heuristic. If I read about a guy trying to prove gay marriage is morally wrong because of how magnets work; I am going to completely disregard everything else he says there.

To stretch the spirit of the fallacy a little further, we often mistake flaws in a system for conclusive evidence the system should change. Law is a common example. People will point out one example of a miscarriage of justice and declare the whole system to be wrong or requiring change. In reality, law, a reflection of the complexity of human interaction, is also complex. To change a law to fix that perceived mistake, could produce net negative effects. The fallacy fallacy here is that we are misjudging the complexity of the situation, systems and arguments do not rely on one logical support. Of course, even one miscarriage of justice is worthy of consideration but it must be taken in context.

In a small meta twist, I would like to highlight a nested fallacy fallacy when considering fallacies (buffalo buffalo buffalo...). When we highlight fallacies, we can react to them by doing the opposite, which although may be the correct direction is not necessarily the right amount. The proper reaction to error is not to do a big jump in the other direction, but to reconsider that area of thought.

Sometimes, when an error is found, the conclusion is still completely correct. Although it is a decent heuristic to then consider the argument weaker, an even better reaction is to completely reconsider the whole argument, system or methodology to get the bigger picture.