Folk Symmetry
I take the bus to work so I have time to read, listen to music, and think. When I use that time to think, dangerous things sometimes happen. Today en route to work I thought. On thinking, I realized that there is an interesting symmetry between Folk Philosophy and Formal Philosophy. Specifically, there is a Folk Tool that is a Formal Fallacy and there is a Formal Tool that is a Folk Fallacy. Cool huh?
Folk Philosophy is the philosophy that people do without resorting to formal training and rigour. It's when you trust your instincts or local mythology (often the same thing) rather than derive or deduce solutions. So a Folk Tool is something we can categorize as a good trick in Folk Philosophy and a Folk Fallacy is a common pitfall that is readily identified as a failed folk argument. "Folk" is not intended to be derogatory in the slightest, it just indicates untrained thought. I engage in Folk Physics all the time -- it seems obvious to me that if you slam on the brakes in your car, your helium balloon will lurch forward with the passengers. Turns out it won't -- it lurches in the opposite direction.
So, reductio ad absurdum is a Folk Fallacy and a Formal Tool.
When constructing a Folk Argument, you assemble premises and axioms in a very informal fashion but most importantly, though your logic might be rigorous, your premises are usually not carefully stated. That means that they have a kind of margin of error based on facts and interpretation. So, when you folk-argue that "If A then B, and if B then C, and if C then D" and assert A therefore D, you commit a fallacy -- reductio ad absurdum -- because although your logic is fine, the error on your premises is multiplied for each premise. Your conclusion is therefore most likely false even though the logic looks good. The more inferences in your chain, the wronger you probably are.
Formally, however, reductio ad absurdum is not only okay, it's one of the core building blocks of formal logic systems! As a tool it works like so: if you suppose premise A and can, in supposing it, derive a contradiction, then A must be false. It's a test through hypothesis and it can, with a small number of operators, be used to construct all more complex formal logical rules.
More interesting to me is post hoc ergo propter hoc.
As a Formal Fallacy this is simply the assertion that the order of events does not imply a causal relationship. Just because A happens before B, there is precisely zero rationale to assert that A causes B.
In Folk Philosophy, however, post hoc ergo propter hoc isn't just a tool -- it's a survival trait! When developing a strategy to survive, say, testing food for edibility, there are a couple of criteria that will be strongly selected for. The most strongly selected for (especially in an area with lots of delicious looking poisonous fruity) is fail-safety.
Something fails safely (exhibits the property of fail-safety) when its failure does not result in an unsafe state. For automatic trains, for example (my own field), most devices fail in such a way as to halt the train because there are precious few more safe trains than ones that are not moving. In Folk Philosophy, fail safety is very valuable because you use it to reflexively run your life and post hoc ergo propter hoc has it in spades. It's so powerful that most animals use it too.
Let's say you eat a berry and get sick. Now as everyone knows thanks to Maple Leaf, listeria has an onset of up to 10 weeks, so it's entirely possible that the berry you just ate had nothing to do with it. If, however, you reflexively apply post hoc ergo propter hoc, one of two things will happen: you will stop eating that perfectly good berry or you will stop eating that berry that makes you sick. Whether right or wrong, you are safe.
Now, for long term operation of humans and their communities this sucks because you will eventually rule out away everything and starve to death. But in the short term it's a great strategy: it's right often enough and it's safe when it's wrong. That also makes it the go-to logical tool when you're scared, which is why people make profoundly improbable leaps based on next to no evidence when they are analyzing something dangerous looking like thimerosal in vaccines or weapons of mass destruction in Iraq or having too much toothpaste on an airplane. It's no good for building a civilization but if you find yourself having to test berries in the wilderness, it's a keeper.
Folk Philosophy is the philosophy that people do without resorting to formal training and rigour. It's when you trust your instincts or local mythology (often the same thing) rather than derive or deduce solutions. So a Folk Tool is something we can categorize as a good trick in Folk Philosophy and a Folk Fallacy is a common pitfall that is readily identified as a failed folk argument. "Folk" is not intended to be derogatory in the slightest, it just indicates untrained thought. I engage in Folk Physics all the time -- it seems obvious to me that if you slam on the brakes in your car, your helium balloon will lurch forward with the passengers. Turns out it won't -- it lurches in the opposite direction.
So, reductio ad absurdum is a Folk Fallacy and a Formal Tool.
When constructing a Folk Argument, you assemble premises and axioms in a very informal fashion but most importantly, though your logic might be rigorous, your premises are usually not carefully stated. That means that they have a kind of margin of error based on facts and interpretation. So, when you folk-argue that "If A then B, and if B then C, and if C then D" and assert A therefore D, you commit a fallacy -- reductio ad absurdum -- because although your logic is fine, the error on your premises is multiplied for each premise. Your conclusion is therefore most likely false even though the logic looks good. The more inferences in your chain, the wronger you probably are.
Formally, however, reductio ad absurdum is not only okay, it's one of the core building blocks of formal logic systems! As a tool it works like so: if you suppose premise A and can, in supposing it, derive a contradiction, then A must be false. It's a test through hypothesis and it can, with a small number of operators, be used to construct all more complex formal logical rules.
More interesting to me is post hoc ergo propter hoc.
As a Formal Fallacy this is simply the assertion that the order of events does not imply a causal relationship. Just because A happens before B, there is precisely zero rationale to assert that A causes B.
In Folk Philosophy, however, post hoc ergo propter hoc isn't just a tool -- it's a survival trait! When developing a strategy to survive, say, testing food for edibility, there are a couple of criteria that will be strongly selected for. The most strongly selected for (especially in an area with lots of delicious looking poisonous fruity) is fail-safety.
Something fails safely (exhibits the property of fail-safety) when its failure does not result in an unsafe state. For automatic trains, for example (my own field), most devices fail in such a way as to halt the train because there are precious few more safe trains than ones that are not moving. In Folk Philosophy, fail safety is very valuable because you use it to reflexively run your life and post hoc ergo propter hoc has it in spades. It's so powerful that most animals use it too.
Let's say you eat a berry and get sick. Now as everyone knows thanks to Maple Leaf, listeria has an onset of up to 10 weeks, so it's entirely possible that the berry you just ate had nothing to do with it. If, however, you reflexively apply post hoc ergo propter hoc, one of two things will happen: you will stop eating that perfectly good berry or you will stop eating that berry that makes you sick. Whether right or wrong, you are safe.
Now, for long term operation of humans and their communities this sucks because you will eventually rule out away everything and starve to death. But in the short term it's a great strategy: it's right often enough and it's safe when it's wrong. That also makes it the go-to logical tool when you're scared, which is why people make profoundly improbable leaps based on next to no evidence when they are analyzing something dangerous looking like thimerosal in vaccines or weapons of mass destruction in Iraq or having too much toothpaste on an airplane. It's no good for building a civilization but if you find yourself having to test berries in the wilderness, it's a keeper.