The epistemology of absence-based inference


Our main aim in this paper is to contribute towards a better understanding of the epistemology of absence-based inferences. Many absence-based inferences are classified as fallacies. There are exceptions, however. We investigate what features make absence-based inferences epistemically good or reliable. In Section 2 we present Sanford Goldberg’s account of the reliability of absence-based inference, introducing the central notion of epistemic coverage. In Section 3 we approach the idea of epistemic coverage through a comparison of alethic and evidential principles. The Equivalence Schema–a well-known alethic principle–says that it is true that \(p\) if and only if \(p\). We take epistemic coverage to underwrite a suitably qualified evidential analogue of the Equivalence Schema: for a high proportion of values of \(p\), subject \(S\) has evidence that \(p\) due to her reliance on source \(S^{*}\) if and only if \(p\). We show how this evidential version of the Equivalence Schema suffices for the reliability of certain absence-based inferences. Section 4 is dedicated to exploring consequences of the Evidential Equivalence Schema. The slogan ‘absence of evidence is evidence of absence’ has received a lot of bad press. More elaborately, what has received a lot of bad press is something like the following idea: absence of evidence sufficiently good to justify belief in \(p\) is evidence sufficiently good to justify belief in \(\sim p\). A striking consequence of the Evidential Equivalence Schema is that absence of evidence sufficiently good to justify belief in p is evidence sufficiently good to justify belief in \(\sim p\). We establish this claim in Section 4 and show how this supports the reliability of an additional type of absence-based inference. Section 4 immediately raises the following question: how can we make philosophically good sense of the idea that absence of evidence is evidence of absence? We address this question in Section 5. Section 6 contains some summary remarks.

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  1. 1.

    The FBI example is from Copi (1953, p. 56). See also Walton (1999).

  2. 2.

    In saying that we take our cue from Goldberg we do not mean to suggest that he is the first to deny that all absence-based inferences are bad. It is widely acknowledged that some such inferences do not qualify as fallacies—indeed, this is often pointed out in logic textbooks (see, e.g., the treatment of fallacies in Copi (1953) and Hurley (2011)). However, to our knowledge, Goldberg is the first to offer a systematic and distinctively epistemological account of absence-based inferences.

  3. 3.

    Let us make a couple of remarks. First, although evidential absences strike us as a natural choice for our discussion, we grant that our target cases may well instantiate or exemplify other kinds of epistemic absences as well. For example, if you think that evidence is necessary for justification, evidential absences bring with them justificatory absences. If, in addition, you think that justification is necessary for knowledge, evidential absences bring with them two types of epistemic absences. Second, we are assuming that all four cases can be treated as involving evidence. Some people will deny this.

  4. 4.

    Strictly speaking, according to Goldberg, two further conditions must be met. Again, we agree. We present the two additional conditions in detail below.

  5. 5.

    Note that Goldberg (2010a) speaks in terms of the relied-upon source investigating, reporting, and communicating. This manner of speaking naturally carries the suggestion that the source possesses agency. In the context of Goldberg (2010a) this makes good sense since the main focus is on our reliance on others as testifiers. However, it makes for a less natural fit when we focus on sources such as vision or other perceptual capacities. In light of this we have formulated (ecc) in terms of tracking (rather than investigating) whether \(p\) and making \(p\)-relevant evidence available (rather than reporting and communicating findings of investigations).

  6. 6.

    See Gelfert (forthcoming) for an interesting and in-depth discussion of timeliness. Gelfert proposes what he calls ‘epistemic penetration’ as a necessary condition for the epistemic goodness of absence-based beliefs. What epistemic penetration amounts to is this: relevant evidence must be diffused beyond the source that initially tracks it. Sometimes only one source is involved. However, other times evidence passes through a chain of sources. For instance, a global news agency relies on its reporters in the field for information. In turn, global agencies are often relied on by national agencies for coverage of certain types of news. We agree that this kind of diffusion—or epistemic penetration—is necessary. Indeed, our agreement comes out when two observations are made: first, (ecc) is a necessary condition for the epistemic goodness of absence-based belief, and second, condition (iii) of (ecc) implies epistemic penetration in Gelfert’s sense. Putting these two observations together we get that epistemic penetration is required for the epistemic goodness of absence-based belief.

  7. 7.

    This is what Goldberg calls the ‘silence condition’

  8. 8.

    Goldberg uses the labels ‘source-existence condition’, ‘reliable-coverage condition’, ‘sufficient interval condition’, ‘silence condition’, and ‘receptivity condition’ (Goldberg 2010a, pp. 158–165). He takes these five conditions to be sufficient for what he calls ‘K-reliability’, i.e. reliability that yields knowledge when paired with true belief. They are also sufficient for what he calls ‘coverage-based beliefs’. What we refer to as the ‘Epistemic Coverage Condition’ collapses Goldberg’s source-existence, reliable-coverage, and sufficient interval conditions. Also, importantly, what we have chosen to call ‘absence-based belief’ is what Goldberg calls ‘coverage-based belief’. We prefer our label to Goldberg’s for the following reason: both beliefs based on the presence of evidence and beliefs based on the absence of evidence can be ‘coverage-based’ in the sense of satisfying the Epistemic Coverage Condition. By using the label ‘absence-based belief’ the aspect that is specific to the former kind of belief is highlighted.

  9. 9.

    Two remarks. First, many take the semantic paradoxes to show that at least some of the alethic principles must be restricted. Second, (T2), (T3), and (T4) are pairwise equivalent in a standard classical setting. However, some think that the schemas come apart in certain contexts. For example, in connection with vagueness, supervaluationists endorse (T2), but believe that (T4) fails for borderline cases.

  10. 10.

    In standard classical logic any argument with a logical truth as its conclusion is valid—a special case being the case where there are no premises. Thus, one might think that anyone who entertains a logical truth has thereby instantiated a valid argument form, namely the special case just mentioned. Since the premises of a valid argument provide evidence for the conclusion, we get the following in the special case where a subject entertains an instance of the Law of Excluded Middle: the empty set of premises gives the subject evidence for the relevant instance of the Law of Excluded Middle. This line of reasoning might be taken to support (E2). As for (E3), any instance is derivable from (T1) and (T2). Hence, anyone who buys into (T1) and (T2) should also buy into (E3).

  11. 11.

    Even when restricted to a specific discourse or domain, there may be some domains for which one could not realistically hope for anything like (E1). Arithmetical discourse—and any kind of discourse with the resources to express elementary arithmetic—might be of this kind due to the incompleteness results.

  12. 12.

    A clarificatory comment: one might think that it is impossible to offer evidence for the statement in question because Chicago has vague boundaries. However, even assuming that vagueness is not an issue, we take it that the point about evidence remains.

  13. 13.

    The counter-slogan was famously—and, we are inclined to think, unwarrantedly—invoked by former US Defense Secretary Donald Rumsfeld in response to critics of the war in Iraq. According to Rumsfeld, the absence of evidence that there were WMDs in Iraq did not amount to evidence that there were no WMDs in Iraq. For an interesting investigation of absence of evidence and evidence of absence within a probabilistic framework, see Sober (2009). This section of the present paper and the two to follow offer a discussion of the same theme. Goldberg does not engage extensively or systematically with the theme, but does touch on it in passing (see, e.g., Goldberg 2010b, p. 251).

  14. 14.

    A recent example of this is Der Spiegel’s premature online publication of an obituary for George W. Bush (Sr.) on December 30, 2012.

  15. 15.

    There are different ways to think of reliability. Some think of reliability just in terms of actual world track record. Others take reliability to consist in actual world track record plus truth in nearby worlds. We note that the latter, more demanding conception is consistent with our proposal in that the pertinent beliefs may include both actual and merely possible beliefs. In Sect. 5 we also explain how our proposal can be understood in probabilistic terms.

  16. 16.

    \(E_{S*}^S (p) \vee E_{S*}^S ({\sim }p)\) is logically equivalent to \({\sim }E_{S*}^S (p) \rightarrow E_{S*}^S ({\sim }p)\), to be derived from (E1) below. Given the noted equivalence, we could strictly speaking omit this proof and just give the one below.


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We are grateful to Axel Gelfert, Sandy Goldberg, and two anonymous reviewers for very helpful comments.

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Correspondence to Nikolaj Jang Lee Linding Pedersen.

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Pedersen, N.J.L.L., Kallestrup, J. The epistemology of absence-based inference. Synthese 190, 2573–2593 (2013).

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  • Fallacy of ignorance
  • Epistemic coverage
  • Absence-based inference
  • Absence-based belief
  • Sanford Goldberg
  • Alethic principles
  • Evidential principles
  • Absence of evidence
  • Evidence of absence
  • Reliabilism