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Absence of evidence and evidence of absence: evidential transitivity in connection with fossils, fishing, fine-tuning, and firing squads


“Absence of evidence isn’t evidence of absence” is a slogan that is popular among scientists and nonscientists alike. This article assesses its truth by using a probabilistic tool, the Law of Likelihood. Qualitative questions (“Is E evidence about H?”) and quantitative questions (“How much evidence does E provide about H?”) are both considered. The article discusses the example of fossil intermediates. If finding a fossil that is phenotypically intermediate between two extant species provides evidence that those species have a common ancestor, does failing to find such a fossil constitute evidence that there was no common ancestor? Or should the failure merely be chalked up to the imperfection of the fossil record? The transitivity of the evidence relation in simple causal chains provides a broader context, which leads to discussion of the fine-tuning argument, the anthropic principle, and observation selection effects.

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  2. Walton (1996, p. 252) says that modus tollens is the form of a basic type of ad ignorantiam argument.

  3. Chris Stephens has drawn my attention to two other examples. The administration of George W. Bush justified its 2003 invasion of Iraq by saying that there was evidence that Iraq possessed “weapons of mass destruction.” After the invasion, when none turned up, Donald Rumsfeld, who then was Bush’s Secretary of Defense, addressed the doubters by invoking the motto; see Carl Sagan (1997) does the same when he considers the fact that we have not yet found evidence that extra-terrestrial intelligence exists.

  4. Lamarck is an exception to this pattern; he held, for example, that current human beings and current dogs don’t have a common ancestor, though each line has evolved (or will evolve) through the same preordained sequence of stages. Our lineage is older since we are more complex.

  5. The same point holds for the historical association of separate ancestry and intelligent design.

  6. Since dividing by zero is not defined, perhaps the point is put better by saying that the nonexistence of an intermediate organism would refute CA (assuming gradualism) and would thereby provide the strongest possible discrimination between the two hypotheses.

  7. Developmental genetics provides numerous examples (e.g., hox genes) in which small genetic changes induce discontinuous phenotypic changes; see Carroll (2005) for an introduction.

  8. The screening-off assumption SO is a simplification. To see why it isn’t exactly right, let’s consider a version of the separate ancestry hypothesis that guarantees that the lineages leading to X and to Y will stray—just a bit and only for a little while—into the “intermediate zone” between α and β depicted in Fig. 4. Given this, the CA and the SA hypothesis both entail that there are intermediate organisms. However, the two hypotheses disagree on how many intermediates there were. If the number of organisms in a lineage is proportional to the lineage’s duration, the CA hypothesis says that there were lots more intermediate organisms than the SA hypothesis (formulated as just described) says there were. If so, when you observe an intermediate, this favors CA over SA even though both hypotheses entail that an intermediate exists. The reason this can happen is that the probability of your observing an intermediate depends, not just on whether such a thing exists, but on how many of them there are, and the two hypotheses disagree about how many. I won’t attempt to replace SO with something more realistic, since the lessons I want to extract from this model would not be affected by doing so.

  9. When we fail to observe that E is true, we often observe that some other proposition, E*, is true, where E* and E are contraries, not contradictories. For example, suppose that when we fail to observe a fossil that is intermediate, what we do observe are fossils that are not intermediate. When this happens, the principle of total evidence obliges us to use the logically stronger description O(E*) rather than ¬O(E). Although O(E) and ¬O(E) must have opposite evidential imports, O(E) and O(E*) may or may not. Even though observing fossil intermediates favors CA over SA, observing fossils that are not intermediate may or may not favor SA over CA.

  10. I’m assuming that the net will fill with fish regardless of whether the 100% or the 50% hypothesis is true.

  11. I here set aside the objection that we don’t know whether Pr(constants are right∣ID) > Pr(constants are right∣Chance). I discuss the problem of evaluating the first of these probabilities in Sober (2004) in connection with the organismic design argument. Colyvan et al. (2005) have objected that the second is suspicious as well. I will assume here that the two hypotheses are formulated so as to insure that this inequality is true.

  12. As mentioned in footnote 11, I grant this for the sake of argument.

  13. Even when you know which of the hypotheses is true, it still is possible that a given bit of evidence discriminates between them, and not always in favor of the true hypothesis.

  14. I take it that the fine-tuning argument assumes that the physical constants do not change values during the duration of our universe; the question is what gave those constants their unchanging values. The argument can of course be reformulated so that the constants are liable to change. If the Chance* hypothesis entails that the constants can flip-flop between right and wrong from moment to moment, it is arguable that ID is more likely than Chance*. However, the fact remains that ID is not more likely than Chance.

  15. Cases of amnesia can be used to make the same point. Is this a connection with the sleeping beauty problem?

  16. Note the reliance on the likelihood ratio in this definition. Other measures of strength of evidence would require other definitions.

  17. I distinguish qualitative and quantitative observation selection effects in Sober (2004). Fishing and fine-tuning are instances of the former, not just the latter.

  18. I also argued in that paper that the prisoner has other sources of information that permit him to interpret his survival in a way that bypasses questions about likelihoods; this complication can be ignored here.

  19. This is an important question to pose for the organismic design argument, as mentioned in footnote 11.

  20. This is what many Bayesians say about the raven paradox: observing a black raven and observing a non-black non-raven both confirm “All ravens are black,” but the former provides strong confirmation while the latter provides weak. Saying that non-black non-ravens don’t confirm at all is therefore a mild exaggeration. See Eells (1982, p. 61) for discussion and references.


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My thanks to Matthew Barker, Bernard Berofsky, Darren Bradley, Juan Comesaña, James Crow, Daniel Hausman, Steven Leeds, Gregory Mougin, Robert Northcott, Gregory Novack, Carolina Sartorio, Yehuda Schnall, Christopher Stephens, Michael Strevens, Martin Thomson-Jones, Michael Titelbaum, Bas Van Fraassen, Peter Vranas, Paul Weirich, Jonathan Weisberg, and Roger White for useful discussion. I am especially grateful to Martin Barrett.

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Sober, E. Absence of evidence and evidence of absence: evidential transitivity in connection with fossils, fishing, fine-tuning, and firing squads. Philos Stud 143, 63–90 (2009).

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  • Anthropic principle
  • Bayesianism
  • Common ancestry
  • Evidence
  • Fine-tuning
  • Fossils
  • Likelihood