However, if “inferring” is read as meaning inductively or abductively inferring, that argumentative move is not necessarily a fallacy.³ This is common sense. There are cases in which it is reasonable to infer the truth of a claim from the absence of evidence against it, and cases in which it is reasonable to infer the falsity of a claim from the absence of evidence in favor of it. So, if we move from the class of deductive fallacies to that of non-deductive ones, the question we face is how to distinguish the cases in which it is reasonable to draw some non-deductive inferences from ignorance, from those in which it is not. In short, we have to determine when and why that argumentative move is not fallacious any longer.

Now an argument is an inductive fallacy when a weak conclusion is presented as strong, or vice versa. (Here for simplicity I skip considerations on abductive fallacies, which are similar to inductive ones).⁴ To put it in a more abstract way, such a fallacy occurs when contrary to appearances the inductive justification standards are not met. That happens when the inductive support given by the premises to the conclusion is disguised, misconstrued, or altered in some significant way.

That could be cast in different terms according to the theory of fallacies and argumentation agreed upon. Locke was apparently the first to use the name argumentum ad ignorantiam.⁵ Today the argument is usually included in the list of fallacies that theories of argumentation try to cast and explain. Let us consider the pragma-dialectical theory of argumentation, which regards a fallacy as a deficient move in an argumentative discourse or text (not just as an error of reasoning, i.e. not only a violation of logical standards of validity).⁶ The authors who support this theory claim that a pragma-dialectical treatment of fallacies provides a more systematic account of them (including in the picture the so-called informal fallacies) than the standard, logical treatment. For, according to the pragma-dialectical approach, a fallacy is a violation of any of the rules for a critical discussion.⁷ On the one hand, this view is taken to be broader than the standard conception, and, on the other, it is taken to be more specific:

Our view is broader because we do not link the fallacies exclusively to one particular discussion stage, which we call the argumentation stage, in which the reasoning of the protagonist is tested for its correctness. It is more specific because it links the fallacies specifically and explicitly with the process of resolving a difference of opinion (van Eemeren and Grootendorst 2004, 162).

This conception captures more fallacies than others and places them at different stages of a critical discussion. Then, what is wrong with the argument from ignorance? In the context of a conversation, or a discussion, or an exchange of reasons in general, what is wrong is the act of making a statement unsupported by evidentiary reasons. This is related to Grice’s maxim of quality (1989, 27): “Try to make your contribution one that is true”. This maxim is constituted of two more specific maxims, or sub-maxims: (1) Do not say what you believe to be false; (2) Do not say that for which you lack adequate evidence. The second sub-maxim is what interests us here. It says that we are not entitled to assert something we lack evidence for. Then, from the absence of evidence about p, we cannot conclude to the truth of p nor to its falsity. Frans van Eemeren and Rob Grootendorst (2004, 76–77) rephrase the point claiming that we must not perform any speech acts that are “insincere” (or for which we cannot accept responsibility).⁸

But arguments from ignorance are not always wrong. Douglas Walton has remarked, from the standpoint of a different but similar theory of argumentation,⁹ that some uses of that kind of argument are not fallacious. The problem is “how to determine, by some clear and useful method, which are the fallacious and which are the nonfallacious cases” (Walton 1999a, 53). He basically uses the notion of plausible inference and applies it to the absence of a certain kind of evidence in given situations. For instance: “if it were raining now I would know it (by the noise); but I do not know it; therefore, it is not raining now” (Walton 1996, 1).¹⁰ If the premises are plausible, the conclusion is plausible as well. Moreover Walton claims that some instances of the argument can be reconstructed as applications of modus tollens that provide plausible conclusions; but this is puzzling given that modus tollens provides deductive conclusions. In fact, Walton adds, it is not really modus tollens, but a kind of abductive argument (Walton 1999a, 57–58). He refines this idea saying that there is a “plausibilistic modus tollens form characteristic of typical ad ignorantiam arguments: ‘if A then one would normally expect B; not B; therefore (plausibly) not A’” (Walton 1999a, 60). Some prima facie examples of this are the dog that did not bark, the snow without footsteps outside the house, and similar cases from which a set of plausible conclusions can be drawn.¹¹ So, the argument from ignorance “is a plausible inference that makes the conclusion plausible, on the assumption that the premises are plausible” (Walton 1999a, 64); and often such arguments are defeasible bases for practical deliberation (Walton 1999a, 59).

Walton also notices that the argument from ignorance is usually construed as related to non-ordinary things such as aliens and ghosts:

it is characteristic of many of the fallacious arguments from ignorance cited in the logic textbooks that they tend to be about UFO’s, the existence of God, ghosts, the paranormal, and so forth – all subjects in which there is a verifiability problem in the sense that it would be hard to know what counts exactly as evidence either for or against the claim (Walton 1999b, 369).

Besides, there are the non-fallacious uses of the argument. But Walton (1999b, 369) conceives of them as the cases where the argument is a “presumptive guide to action”, which is a misleading account insofar as it misses the distinction between epistemic and practical considerations.¹² One thing is to have a set of epistemic reasons to uphold a (presumptive or plausible) belief, and quite another is to form a plan of action based on (i) that belief and (ii) a practical attitude such as a desire. The crucial aspects one must insist upon in order to redeem the argument from ignorance from easy criticism are (a) the nature of the evidence at stake and (b) the regulation of the burden of proof. As to (a), we have to distinguish the so-called negative evidence from the mere absence of it: “What is called negative evidence in scientific research is the kind of evidence where an outcome is tested for and does not occur”.¹³ As to (b), we need to observe that in a dialectical exchange “fallacious arguments from ignorance are often connected with first, a reversal of burden of proof, and second, a difficulty in fulfilling that burden, once it has been reversed, especially in cases where genuine evidence is difficult to find” (Walton 1999b, 375–376). (More on both points below).

In later works Walton has stressed, on the one hand, the importance of that dialectical dimension to assess what he now calls “lack of knowledge inferences”¹⁴ and, on the other hand, the importance of the epistemic distinction between negative evidence and absence of evidence. Let me focus on the latter point for the moment. If a search is scrupulous and nothing sought for is found, it is plausible to infer that what was sought for is not there. The inference is not a deductive one and the argument is not fallacious if we admit of inductive or abductive standards. “The argument from ignorance can become weak or erroneous where it is taken as a stronger form of argument than the evidence warrants” (Walton 2008, 58).

Revisiting our introductory example, with respect to (A), if the background knowledge suggests that silicone implants are safe and the relevant information is that several tests have been made and they don’t prove that such breast implants are unsafe, then by an inductive or abductive standard we can infer that silicone breast implants are safe. If, on the contrary, with respect to (B), the background knowledge suggests that silicone implants are unsafe and the relevant information is that several tests have been made and they don’t prove that such breast implants are safe, then by an inductive or abductive standard we can infer that silicone breast implants are unsafe. But these are not arguments from ignorance proper: they are arguments from negative evidence.

Walton et al. (2008, 327) provide this modus tollens scheme of the argument:

The question is in the way we read the major premise.¹⁵ How should we construe that conditional? Does it say that if A were true, then in principle A would be known to be true after a complete investigation about it? Or that if A were true, then here and now A would be known to be true as far as we are concerned? Of course the first reading is stronger and is the one that seems to be correct. But that reading transforms the argument into a sort of metaphysical claim, like Peirce’s definition of reality as that which would be known at the ideal limit of inquiry.¹⁶ Moreover, it transforms it into an argument from negative evidence; for it (counterfactually) states that a complete investigation was carried out and A was not found to be true. In fact, actual uses of the argument from ignorance are in line with the weaker reading. But then the argument is deductively fallacious, for here and now we have no deductive guarantee to know what is the case and what is not.

Logically speaking, the absence of evidence that p is not evidence that not-p, nor is the absence of evidence that not-p evidence that p.¹⁷ To put it more simply using the lawyer’s saying, “Absence of evidence is not evidence of absence”. Is this true? Perhaps it is true in general but not in particular. Or perhaps we have to make some conceptual refinements.

Let me start from a non-legal example (and indeed one of the standard and uninteresting examples that Walton criticizes). We lack evidence of the existence of aliens. What are we entitled to infer from that absence? That aliens do not exist? That they exist? Neither, from a deductive point of view. The absence of evidence about them does not imply anything about their existence. Indeed ignorance is a good ground for suspending judgment, not for taking a side (Robinson 1971, 102). Even Donald Rumsfeld would agree. Once he famously claimed that there are “unknown unknowns” beside the “known unknowns”, which meant, in the context of his remark (less silly than it seemed), that the absence of evidence of weapons of mass destruction in Iraq was not evidence of their absence.¹⁸ In logical terms, as we said, that we have no evidence that p doesn’t mean that we have evidence that not-p.

A thorough, scrupulous and possibly complete search is the key element here: “lack of confirmation after a hypothesis has been given a fair chance is equivalent to disconfirming it” (Wreen 1989, 310). Note that it is not necessary to use aliens or terrible weapons to build up examples. Imagine that someone asks me to check if Robert is in the room: now I enter the room, look for Robert everywhere (behind the door, under the bed, inside the wardrobe, etc.), but don’t find him. Could I say that I have enough evidence that he’s not there? Should I rather say that I have no evidence that he’s there? This seems to be a typical case of negative evidence, not of mere absence of it. I have a significant amount of negative evidence that he’s not in the room. A different issue¹⁹ would be to know whether he is in the next room; well, in that situation I wouldn’t know, for I would have no evidence about it.