What we don’t know we don’t know

Thinking is a difficult affair. Nobody is free from making mistakes when using arguments. Nobody is free from committing fallacies. Also professionals commit them, although they are supposed to argue correctly, since it may be a matter of death or life, or acquittal or conviction, if they don’t. But also judges commit fallacies, with sometimes disastrous consequences. Innocent people are sometimes sentenced to death. Or take some cases that now pop up in my mind: Nurses got long sentences as if they were mass murderers, because they were too often present when patients died. But isn’t it one of their tasks to help dying people and isn’t it obvious then that a nurse is more often present at the death of a patient than an average person? Nevertheless, it has happened several times that nurses were accused of murder (and sentenced) on grounds of a badly understood – so false – statistical analysis.
Also in politics fallacies abound. Politicians often don’t understand what they say; they don’t understand their own arguments. Nor do their followers. Even worse are the cases that politicians intentionally use fallacies and try to manipulate the people.
Also in less dramatic cases, it is important to know what is a correct argument and what is a fallacy. It can make life more pleasant, since it can help you avoid making mistakes, which are maybe not dramatic, but annoying anyway. Therefore, now and then I pay attention to fallacies, for everybody can commit them.
This time I want to discuss the fallacy that is called “Appeal to Ignorance”, or in Latin “Argumentum ad Ignorantiam”. As often, my description of the fallacy is based on a chapter from Robert Arp et al. 2019 (see source below) and also a bit on the Wikipedia.
The term “Appeal to Ignorance” was coined by the British philosopher John Locke (1632-1704). You commit this fallacy, if you think that a statement must be true because it has not yet proven false, or the other way round. In logical symbols:

~[proof that ~p] → p
~[proof that p] → ~p

Especially the version in logical symbols makes clear that “the fallacy uses lack of evidence as the grounds for accepting some claim” (McCraw, p. 106). It is a confusion between the categories “lack of evidence” and “presence of disconfirming evidence”. (106-7) That this fallacy is really an appeal to ignorance is illustrated by an example mentioned by McCraw (106). It’s a statement by the American senator Joe McCarthy from the early 1950s, when many people were falsely accused of being communist (implying that such a person is an enemy of the state): “I do not have much information on this except the general statement of the agency that there is nothing in the files to disapprove his Communist connections.” (106) Paraphrased: “I do not know that he is not X, so he must be X.” In fact, if I do not know that someone is not X, all options are open, besides being X, so also that he could be A or B or …or W or Y or Z or AA … etc.
The form of the Appeal to Ignorance just discussed is the basic form of this fallacy. However, it can have different forms that can all, in one way or another, be reduced to its basic form. I mention some:

May it not be that ~p? → p

In this “interrogative form” of the fallacy the ignorance in the argument is implied in the question. (107) For instance: “Isn’t it likely that John is a thief?” [although I actually have no proof that he is], implying that John is a thief.
Or take this case, which, I think, everyone will have encountered once:

  A: p
            B: Why?
            A: Why not?

Here the burden of proof is shifted by A to his opponent, while actually the burden of proof should be with A. (108) And if, as often happens, B doesn’t know how to answer the question “Why not?” (or doesn’t want to answer it), this is falsely seen by A as proof that p is the case (or A says so for manipulative reasons).
The upshot is that we only know that something is the case or not the case if we have evidence for it. Ignorance can never proof facts.

Source
- McCraw, Benjamin W., “Appeal to Ignorance”, in: Arp, Robert; Steven Barbone; Michael Bruce (eds.), Bad arguments. 100 of the most important fallacies in Western philosophy. Oxford, etc.: Wiley Blackwell, 2019; pp. 106-111.