Evidence of Absence: Completeness of Evidential Datasets
Elliott Sober presents a likelihood argument about the motto “Absence of evidence is not evidence of absence” (Sober 2009). He states the Law of Likelihood this way:
The Law of Likelihood. Evidence E favors hypothesis H1 over hypothesis H2 precisely when Pr(E│H1) > Pr(E│H2). And the degree to which E favors H1 over H2 is measured by the likelihood ratio Pr(E│H1)/Pr(E│H2).
He argues that the likelihood ratio is more useful than the difference but it has two other problems: it is not defined if Pr(E│H2) = 0 and has a wider range if the denominator is larger than the numerator than vice versa. While these are more practical than theoretical objections, they may be eliminated by the following, which we shall call the likelihood ratio index:
Likelihood Ratio Index = log((1+Pr(E│H1))/(1+Pr(E│H2))).
This index ranges from -1 to +1 and equals zero when the two probabilities are equal.
Sober uses the following scenario about the fossil record to illustrate his analysis:
Suppose you are wondering whether two species that you now observe, X and Y, have a common ancestor. … Suppose you observe that there is a fossil whose trait values are intermediate between those exhibited by X and Y. How does the discovery of this fossil intermediate affect the question of whether X and Y have a common ancestor?
His analysis is summed up in two tables, CA is where Common Ancestry and SA is Separate Ancestry.
|Figure 5. Either X and Y have a common ancestor (CA) or they do not (SA). Cells represent probabilities of the form Pr(± intermediate│±CA). Gradualism is assumed.|
|There existed an intermediate.||1||q|
|There did not.||0||1-q|
Concerning this figure, he notes:
If there is an intermediate form, this favors CA over SA, and the strength of this favoring is represented by the ratio 1/q. This ratio has a value greater than unity if q<1. On the other hand, if there is no intermediate, this infinitely favors SA over CA, since (1-q)/0 = ∞ (again assuming that q<1).6 The non-existence of an intermediate form would have a far more profound evidential impact than the existence of an intermediate.
Then he makes an assumption:
(SO) a = Pr(we have observed an intermediate │CA & there exists an intermediate) =
Pr(we have observed an intermediate │SA & there exists an intermediate).
This leads to the next figure:
|Figure 6. Either X and Y have a common ancestor (CA) or they do not (SA). Cells represent probabilities of the form Pr(± we have observed an intermediate│±CA). Gradualism is assumed.|
|We have observed an intermediate.||a||qa|
|We have not.||1-a||1-qa|
As long as there is some chance that we’ll observe an intermediate if one exists, and there is some chance that intermediates will not exist if the separate ancestry hypothesis is true, the failure to observe a fossil intermediate favors SA over CA. In this broad circumstance, absence of evidence (for a common ancestor) is evidence that there was no such thing. The motto – that absence of evidence isn’t evidence of absence — is wrong.
Suppose you look for intermediates and fail to find them. This outcome isn’t equally probable under the two hypotheses if a>0 and q< 1. Entries in each column must sum to unity in Figure 6 just as they must in Figure 5. When the two parameters fall in this rather inclusive value range, failing to observe an intermediate is evidence against the CA hypothesis, contrary to the motto. What is true, without exaggeration, is that for many values of the parameters, not observing an intermediate provides negligible evidence favoring SA, compared with the much stronger evidence that observing an intermediate provides in favor of CA.
The point to be argued for here shows that the last sentence should change in some cases, including the case of intermediate fossils.
First of all, the main question about fossils is not the existence of intermediates but the existence of long sequences of fossils. The view of “evolutionary stasis” (species fixity) was dying out in the nineteenth century and is extinct today. There is no controversy about the idea that fossils can be put into short sequences that span varieties, species, or genera. The controversy is about long sequences of fossils that span families, orders, classes, phyla, kingdoms, and domains, reaching to common (universal) ancestry. Evolutionists are committed to the existence of long sequences and creationists are committed to their non-existence.
However, this does not affect the form of the analysis. We could revise the scenario this way:
Suppose you are wondering whether two short fossil sequences that you now observe, X and Y, have a connecting sequence of fossils. To bring evidence to bear on this question, you might look at the similarities and differences (both phenotypic and genetic) that characterize the two short fossil sequences. But the traits of a third object might be relevant as well. Suppose you observe that there is a fossil (or short fossil sequence) whose trait values are intermediate between those exhibited by X and Y. How does the discovery of this intermediate fossil (or short fossil sequence) affect the question of whether X and Y have a connecting sequence of fossils?
How does this affect the motto? Consider the example Sober relates in a footnote:
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 http://en.wikiquote.org/wiki/Donald_Rumsfeld.
The Washington Post reported on January 12, 2005 (http://www.washingtonpost.com/wp-dyn/articles/A2129-2005Jan11.html):
The hunt for biological, chemical and nuclear weapons in Iraq has come to an end nearly two years after President Bush ordered U.S. troops to disarm Saddam Hussein. The top CIA weapons hunter is home, and analysts are back at Langley.
The Post article quoted an unnamed intelligence official who said:
“We’ve talked to so many people that someone would have said something. We received nothing that contradicts the picture we’ve put forward. It’s possible there is a supply someplace, but what is much more likely is that [as time goes by] we will find a greater substantiation of the picture that we’ve already put forward.”
This is how a search ends in failure: (1) there is an absence of evidence of what was sought, and (2) there is a reasonable expectation that what would be found in the future would merely substantiate what has already been discovered.
Knowledge management consists of various efforts to gather and mine information of value. A database of knowledge on a certain subject, called a knowledge base, is complete if closed-world reasoning applies to it, which means whatever it does not know to be true must be false. In other words, all relevant knowledge about that subject is in the knowledge base. This might be true for example of a company’s employee information database; if someone’s name is not in the database, they are not an employee of the company.
Let us call a knowledge base “effectively complete” precisely when all knowledge about the subject is either in the knowledge base or similar to what is in the knowledge base. The quotation from the intelligence official above presents an instance of an effectively complete knowledge base because the expectation is that as time goes by “we will find a greater substantiation of the picture that we’ve already put forward.”
Because of the common assumption of the uniformity of nature, it is common in science to consider a knowledge base what we are calling effectively complete. Essentially this means that the knowledge at hand is as all the knowledge required. So, for example, one can examine a database about the properties of copper and make conclusions about all the copper in the universe.
Something similar may be said about the fossil record. After more than two hundred years of fossil hunting, large databases of fossils are available for research [footnote]. Many interesting fossils have been discovered but there is still a complete absence of long fossil sequences. At this point, there is no substantial reason to expect that long fossil sequences will ever be found. In this sense at least, the knowledge base called the fossil record is effectively complete.
If a database is effectively complete, then the closed-world premise may be invoked: what is not currently known to be true is false, or what is not currently known to exist does not exist. In this sense, the absence of evidence is evidence of absence. What’s not in the database of evidence, must not exist; what’s not known in the database of facts, must be false.
Elliott Sober, Absence of evidence and evidence of absence: Evidential transitivity in connection with fossils, fishing, fine-tuning, and firing squads. Philosophical Studies 143 (1):63 – 90 (2009)