Abstract: Exactly what is fallacious about a claim like ”ghosts exist because no one has proved that they do not”? And why does a claim with the same logical structure, such as ”this drug is safe because we have no evidence that it is not”, seem more plausible? Looking at various fallacies – the argument from ignorance, circular arguments, and the slippery slope argument - we find that they can be analyzed in Bayesian terms, and that people are generally more convinced by arguments which provide greater Bayesian evidence. Arguments which provide only weak evidence, though often evidence nonetheless, are considered fallacies.

As a Nefarious Scientist, Dr. Zany is often teleconferencing with other Nefarious Scientists. Negotiations about things such as ”when we have taken over the world, who's the lucky bastard who gets to rule over Antarctica” will often turn tense and stressful. Dr. Zany knows that stress makes it harder to evaluate arguments logically. To make things easier, he would like to build a software tool that would monitor the conversations and automatically flag any fallacious claims as such. That way, if he's too stressed out to realize that an argument offered by one of his colleagues is actually wrong, the software will work as backup to warn him.

Unfortunately, it's not easy to define what counts as a fallacy. At first, Dr. Zany tried looking at the logical form of various claims. An early example that he considered was ”ghosts exist because no one has proved that they do not”, which felt clearly wrong, an instance of the argument from ignorance. But when he programmed his software to warn him about sentences like that, it ended up flagging the claim ”this drug is safe, because we have no evidence that it is not”. Hmm. That claim felt somewhat weak, but it didn't feel obviously wrong the way that the ghost argument did. Yet they shared the same structure. What was the difference?

The argument from ignorance

Related posts: Absence of Evidence is Evidence of Absence, But Somebody Would Have Noticed!

One kind of argument from ignorance is based on negative evidence. It assumes that if the hypothesis of interest were true, then experiments made to test it would show positive results. If a drug were toxic, tests of toxicity of reveal this. Whether or not this argument is valid depends on whether the tests would indeed show positive results, and with what probability.

With some thought and help from AS-01, Dr. Zany identified three intuitions about this kind of reasoning.

1. Prior beliefs influence whether or not the argument is accepted.

A) I've often drunk alcohol, and never gotten drunk. Therefore alcohol doesn't cause intoxication.

B) I've often taken Acme Flu Medicine, and never gotten any side effects. Therefore Acme Flu Medicine doesn't cause any side effects.

Both of these are examples of the argument from ignorance, and both seem fallacious. But B seems much more compelling than A, since we know that alcohol causes intoxication, while we also know that not all kinds of medicine have side effects.

2. The more evidence found that is compatible with the conclusions of these arguments, the more acceptable they seem to be.

C) Acme Flu Medicine is not toxic because no toxic effects were observed in 50 tests.

D) Acme Flu Medicine is not toxic because no toxic effects were observed in 1 test.

C seems more compelling than D.

3. Negative arguments are acceptable, but they are generally less acceptable than positive arguments.

E) Acme Flu Medicine is toxic because a toxic effect was observed (positive argument)

F) Acme Flu Medicine is not toxic because no toxic effect was observed (negative argument, the argument from ignorance)

Argument E seems more convincing than argument F, but F is somewhat convincing as well.

"Aha!" Dr. Zany exclaims. "These three intuitions share a common origin! They bear the signatures of Bayonet reasoning!"

"Bayesian reasoning", AS-01 politely corrects.

"Yes, Bayesian! But, hmm. Exactly how are they Bayesian?"

Abstract: "Close-call counterfactuals", claims of what could have almost happened but didn't, can be used to either defend a belief or to attack it. People have a tendency to reject counterfactuals as improbable when those counterfactuals threaten a belief (the "I was not almost wrong" defense), but to embrace counterfactuals that support a belief (the "I was almost right" defense). This behavior is the strongest in people who score high on a test for need for closure and simplicity. Exploring counterfactual worlds can be used to reduce overconfidence, but it can also lead to logically incoherent answers, especially in people who score low on a test for need for closure and simplicity.

”I was not almost wrong”

Dr. Zany, the Nefarious Scientist, has a theory which he intends to use to achieve his goal of world domination. ”As you know, I have long been a student of human nature”, he tells his assistant, AS-01. (Dr. Zany has always wanted to have an intelligent robot as his assistant. Unfortunately, for some reason all the robots he has built have only been interested in eradicating the color blue from the universe. And blue is his favorite color. So for now, he has resorted to just hiring a human assistant and referring to her with a robot-like name.)

”During my studies, I have discovered the following. Whenever my archnemesis, Captain Anvil, shows up at a scene, the media will very quickly show up to make a report about it, and they prefer to send the report live. While this is going on, the whole city – including the police forces! - will be captivated by the report about Captain Anvil, and neglect to pay attention to anything else. This happened once, and a bank was robbed on the other side of the city while nobody was paying any attention. Thus, I know how to commit the perfect crime – I simply need to create a diversion that attracts Captain Anvil, and then nobody will notice me. History tells us that this is the inevitable outcome of Captain Anvil showing up!”

But to Dr. Zany's annoyance, AS-01 is always doubting him. Dr. Zany has often considered turning her into a brain-in-a-vat as punishment, but she makes the best tuna sandwiches Dr. Zany has ever tasted. He's forced to tolerate her impundence, or he'll lose that culinary pleasure.

”But Dr. Zany”, AS-01 says. ”Suppose that some TV reporter had happened to be on her way to where Captain Anvil was, and on her route she saw the bank robbery. Then part of the media attention would have been diverted, and the police would have heard about the robbery. That might happen to you, too!”

Dr. Zany's favorite belief is now being threatened. It might not be inevitable that Captain Anvil showing up will actually let criminals elsewhere act unhindered! AS-01 has presented a plausible-sounding counterfactual, ”if a TV reporter had seen the robbery, then the city's attention had been diverted to the other crime scene”. Although the historical record does not show that Dr. Zany's theory would have been wrong, the counterfactual suggests that he might be almost wrong.

There are now three tactics that Dr. Zany can use to defend his belief (warrantedly or not):

1. Challenge the mutability of the antecedent. Since AS-01's counterfactual is of the form ”if A, then B”, Dr. Zany could question the plausibility of A.

”Baloney!” exclaims Dr. Zany. ”No TV reporter could ever have wandered past, let alone seen the robbery!”

That seems a little hard to believe, however.

2. Challenge the causal principles linking the antecedent to the consequent. Dr. Zany is not logically required to accept the ”then” in ”if A, then B”. There are always unstated background assumptions that he can question.

”Humbug!” shouts Dr. Zany. ”Yes, a reporter could have seen the robbery and alerted the media, but given the choice of covering such a minor incident and continuing to report on Captain Anvil, they would not have cared about the bank robbery!”

3. Concede the counterfactual, but insist that it does not matter for the overall theory.

”Inconceivable!” yelps Dr. Zany. ”Even if the city's attention would have been diverted to the robbery, the robbers would have escaped by then! So Captain Anvil's presence would have allowed them to succeed regardless!”

Empirical work suggests that it's not only Dr. Zany who wants to stick to his beliefs. Let us for a moment turn our attention away from supervillains, and look at professional historians and analysts of world politics. In order to make sense of something as complicated as world history, experts resort to various simplifying strategies. For instance, one explanatory schema is called neorealist balancing. Neorealist balancing claims that ”when one state threatens to become too powerful, other states coalesce against it, thereby preserving the balance of power”. Among other things, it implies that Hitler's failure was predetermined by a fundemental law of world politics.