ARGUMENT FROM IGNORANCE

1. Argument from ignorance and the legitimacy of doubt

Argument from ignorance [1] is defined by Locke as one of the four basic forms of argumenta, see Collections (II):

Secondly, another way that men ordinarily use to drive others, and force them to submit to their judgment, and receive the opinion in debate, is to require the adversary to admit what they allege as a proof or to assign a better. And this I call argumentum ad ignorantiam. ([1690]; Vol. II, p. 410-411)

This argument is considered to be fallacious:

It proves not another man to be in the right way, nor that I ought to take the same way, because I know not a better. (Id., p. 411)

The following dialogue schematizes the situation where S1‘s conclusion is based  on S2‘s ignorance:

S1₁  – A, therefore C
S2₁   – This is a bad argument. I do not admit that A proves C.
S1₂  – Do you have any reason to conclude anything other than C? Do you have a better argument for C?
S2₂   – Well, no
S1₃   – Then you must accept my own proof and my conclusion.

(i) First round: S1₁ suggests a justified proposition C.

(ii) Second round: S2₁ refuses to ratify the claim C.

(iii) Third round: S1₂ asks S2 to explain the reasons for his or her doubt. According to the conversation principle which requires justification for non-preferred second turns, S1 is perfectly justified in doing so. S2 could respond:

(a) by refuting S1₁‘s argumentation outright, or by raising objections to it.
(b) by constructing a counter-argument that provides what Locke calls “a better proof”. The text does not say for which conclusion; so we can therefore assume the following two cases:

(b1) Inferring from A something different from C;
(b2) Providing a “better proof” than A for C.

(iv) Fourth turn: S2₂ admits that he or she cannot elaborate anything along the lines of (a), (b1) or (b2).

(v) Fifth turn: S1 may accordingly:

(a) Acknowledge S2’s reluctance, while maintaining his argumentation: “Okay, this is not a very good argument, but it is still interesting, in fact, it is the only one we have”;
(b) Asking S2 to accept his (A, C) argument, considering that his partner’s incapacity is a kind of second-order evidence to add to his previous substantive one, A, and thus committing an ad ignorantiam fallacy (even if his previous argument is not so bad, after all).

A pure ad ignorantiam fallacy would be based only on the partner’s failure “to assign a better [proof]”. Under conversational circumstances, S2₁ does not ratify S1₁’s turn; normally, this should prompt S1 to clarify and elaborate upon his proposal. The crude reaction seems  to be rare: “Since you cannot articulate anything against my argumentation, you have to accept it in its entirety”.

Seen from S2’s perspective, this situation also seems a bit bizarre, a kind of borderline case where S2 has only his or her inner conviction to oppose to an argument. Under normal conditions, a conversationalist and a fortiori a dialectician, knows how to elaborate upon a strong inner conviction. In essence, Locke seems to ascribe to S2 a kind of radical clause of conscience.

Leibniz moderates this radical position: “The argument ad ignorantiam is valid in cases of presumption where it is reasonable to hold to an opinion till the contrary is proved” ([1765], p. 576).
Presumption here has the meaning of burden of proof. The pretension of L1‘s presumption may be exaggerated and misleading, but his argument still creates a preference in the area, and in practice we can hold to it until something else is proven.
This “for want of anything better” reasoning seems to be the standard case in practical argumentation when a decision has to be made and a possibly urgent action has to be taken:

S1_i:     — On such and such basis, I propose 1) that we take such and such a disposition; 2) that we explore such and such a hypothesis. Now, the floor is yours

S2:        [Long silence]

S1_j     — Nothing to say? Silence means agreement,
1) In the absence of objection, my proposal is adopted.
2) In the absence of any other hypothesis, mine will serve as the working hypothesis.

It is difficult to disagree with S1_j’s conclusions. He does not claim that his proposal is the only viable one, nor that his hypothesis should be taken as true.

2. Ignorance and principle of the excluded middle

The argument from ignorance is also defined, regardless to the quality of the argument, as an illegitimate application of the principle of the excluded middle:

P is true, because you cannot prove that it is false.

The argument is inconclusive. If we consider that “not-P is not proved” is equivalent to “not-(not-P)”, we conclude that P is true by applying the principle of the excluded middle. But the two nots are not of the same kind: “not-P is not proved” does not mean “not-P is false”, which would be a confusion between what is true (alethic) and what is knowable (epistemic), see absurd.

3. Ignorance, burden of proof, precautionary principle

I am innocent, because you cannot to prove that I am guilty.
You are guilty because you cannot prove your innocence.

To admit that P is true, or to act “as if” it were true in the absence of proof that it is not true is a decision for the institution empowered to discuss and decide such matters in the field concerned. In the law, the presumption of innocence places the burden of proof on the prosecution and gives the benefit of the doubt to the accused.

Precautionary principle
In the debate about the safety or toxicity of new products, a decision has to be made in a situation of insufficient knowledge. The presumption of safety would be:

The product may have toxic effects, but this has not been proven. Therefore, it has no toxic effects.

The precautionary principle is easiest to refute when it is maximized:

Any new product is presumed toxic and remains banned until its safety is proven.

In its most common form, it simply reverses the burden of proof:

The precautionary principle (or precautionary approach) to risk management states that when an action or policy is suspected of causing harm to the public, or the environment, in the absence of scientific consensus (that the action or policy is not harmful), the burden of proof that it is not harmful falls on those taking an action that may or may not pose a risk.
Wikipedia, Precautionary Principle

Situation: No scientific consensus about the safety of a particular product
Decision: The burden of proof is on those who use it.

4. Argument from ignorance and argument from silence

See Silence

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[1] Latin ad ignorantiam argument ignorantia, “ignorance”