On False Logic

[Canberra Times 6 April. This is a re-post of an earlier version scrubbed up for publication]

Coming out of my kitchen cupboard at the moment is a terrible smell. A miasma of rotting potatoes threatening to inflict upon me some awful disease. At least, that’s what I might think if I believed the old theory that foul smells can spread disease.

Now we could all chuckle, thinking patronising thoughts about how quaint it is for anybody to believe such a thing. We know that infection is caused by microbes, and no one is going to contact Yellow Fever from a smell.

Still, you can see the logic. I went to a swamp. Thick gloopy anaerobic mud, and it smelled disgusting. Next week I fell sick. Ergo the smell infected me with Yellow Fever. Here we have an example of false logic, which is what I want to talk about in this story.

You know what’s missing in the story above. The smell is associated with the swamp, but I forgot to mention the mosquitos.

Aristotle might’ve known about Yellow Fever, but he’s very unlikely to have known of its connection to mosquitos. He mightn’t have known much about disease, but he sure knew logic, so once learning his mistake he would probably say the Greek equivalent of non causa pro causa, otherwise known as the fallacy of false cause.

A variant is reductio ad absurdum, which literally means “reduce to absurdity”. A body builder might say if some muscle is good, then lots of muscle must be really good. In fact, if I bound myself up in so many layers of muscle that I can hardly move, I must be the pinnacle of health. Yet body builders can be so focused on muscle development aided by steroids and diet restrictions, they die of heart failure.

Meanwhile, Aristotle has been scratching out on parchment a catalogue of the forms of false logic. Some wag titled this his Sophistic Refutations, probably in the hope of making it sound impressive. Here’s my interpretation.

The General to the Particular: Violent spectators have been a problem at English soccer matches, therefore English soccer fans are hooligans.

The Particular to the General: People find football entertaining, therefore I find football entertaining.

Irrelevant Conclusion: There are a few variants of this, but they all revolve around unrelated causes: Ad Hominem, against the man; Ad Misericordiam, an appeal to pity; Ad Populem, “most people say…”; Ad Vericumdiam, an appeal to authority (Rod says…); Ad Ignorantiam, in the absence of evidence; Ad Baculum: agree with me or else.

Circular Argument: Paula is bad because she is racist. She’s racist because she’s bad.

Many Questions: Have you stopped beating your wife? Is actually two questions posing as one.

False Cause: The miasma theory of disease.

Non Sequitur: Sue is wrong, therefore Bill must be right. Actually they’re both wrong. (Perhaps Rod is right.)

Strictly speaking the Sophistic Refutations are about formal logic, which leaves no room for intuition or judgement based balance of probability. Circumstantial evidence is not permitted. Unfortunately in the real world, pure logic is limited because are forced to operate on imperfect information. We don’t have all the data, and we don’t understand all the mechanisms, so often we can only guess that A causes B.

In other words, in science you need logic and evidence. Understanding false logic only gives you a clue to the traps to avoid when drawing conclusions. Science has had to invent methods to overcome the little logic traps nature sets for us. Deep breath, here’s one – smoking.

I remember great aunt Betty’s withered hand holding a Capstan cigarette, but did that kill her? Or perhaps it was old age. Perhaps it was because she had polio. To say with confidence that A causes B, we need to control the variables. We need to untangle what’s significant amid the confounding noise.

Betty is only one case, and we can’t run her life again as a non-smoker to see the result. Instead we try to find a large number of people like her, and use statistics and say that on the balance of probabilities, we think smoking is a cause of early death.

Ultimately this story comes down to a question of what is inherently knowable. I don’t know that logic will solve this problem, but I do know that without it we are left with a smelly miasma of diseased science.

Sadly, all we’ve achieved with all this is to help cull failed ideas, and the Nobel Prize is not yet ours. We still haven’t covered the creative spark, the flash of insight that generates truly great discoveries. Where that comes from is a bit of a mystery, and formal logic is probably not a good place to find it.