What can and cannot be proved? Can we prove anything at all? How close is the genealogical process to that of mathematics or the sciences?
Like a number of people with a mathematical or scientific background, I questioned the use of the term “genealogical proof” when I first came into the field. Unfortunately for me, I have since criticised it a number of times, and have been gently rebuked by long-standing genealogists who insisted it “is our jargon” and “It is currently what it is”.
Without wanting to appear belligerent, I will compare and contrast some interpretations of the term proof in order to see just how far apart genealogy and science really are in this vein. We all know there are entrenched attitudes, but there are also misconceptions too.
Fact: A thing that is known or proved to be true.
Proof: Evidence or argument establishing a fact or the truth of a statement.
These are quite specific, and it would seem that much day-to-day usage lies on the edge of, or even outside of, these descriptions. For instance, providing proof of your identity doesn’t necessarily prove beyond any doubt who you are, otherwise identity theft would not exist. The problem arises because terms such as truth and fact imply something real and immutable, and hence incontrovertible. That level of proof is more accurately referred to as an absolute proof.
Mathematics is actually the only discipline where an absolute proof is possible. A mathematical proof is reasoned not from evidence but from first principles, or from other proofs. A proof typically begins by describing what is to be proved, and concludes with the initialism QED to indicate completion. The body of a mathematical proof may draw on smaller proofs (theorems, lemmas, or even equations) to reach its goal in a hierarchical fashion, and the overall presentation is of non-sequential, labelled connections rather than plain narrative. Between 1910 and 1913, Alfred North Whitehead and Bertrand Russell published a three-volume work on the foundations of mathematics called The Principia Mathematica. It was an attempt to derive all mathematical truths from a well-defined set of axioms and inference rules in symbolic logic.
So what about scientific proof? Well, you may be surprised to hear that there’s no such thing. In a scientific context, it is an oxymoron since mathematics is a key tool of science and so they share the same interpretation of proof. Just as genealogy strives to explain the past from the available evidence, so (pure-)science tries to explain the universe from experimental evidence. Their common evidence-based aspirations lead them to the same limitation: you can never prove anything absolutely, but you can certainly disprove something.
Elizabeth Shown Mills, in her remarkable book on evidence analysis, states that “…there is no such thing as proof that can never be rebutted”, which is entirely in-keeping with the aforementioned evidence-based limitation. Mills acknowledges that the past is not directly accessible, and that any new piece of evidence could disprove our conclusions. The book clearly distinguishes the genealogical usage of words such as proof, and fact (effectively just information from a source, and usually an assertion or a claim), from any absolute interpretation. However, while differentiating a proof in genealogy from that in law and social sciences, it makes the following statement about science:
Unlike science, however, genealogy accepts no margin of error. A single error in identity or kinship will be multiplied exponentially with each generation beyond the error. Errors will occur. But family historians today approach their work with the mindset that erring is unacceptable.
This is an unfamiliar view of science to me, and I have to assume that it is referring to the applied sciences, such as engineering and technology. For example, if you were building a sky-scraper tower and your foundations were not level then the error would be compounded the higher you went. It would then be a matter of acceptable tolerances as to whether the project succeeded. From the perspective of pure science, though, the statement would be wholly wrong, and it is in pure science that the closest analogy to the genealogical ideal lies.
So let’s look at our separate vocabularies. In science, a hypothesis is a proposed explanation of some phenomenon, and is therefore based primarily on some subset of evidence relating that phenomenon. The hypothesis becomes a theory when it has been tested against a much greater set of evidence. At this point, the terms are almost identical to those presented by Mills. However, even if a scientific theory is tested against all available evidence then it does not mean that anything has been proved — there is always a chance it could be overturned later, and the history of science is full of such cases. Mills places the definition of ‘proof’ in this spot, and it is distinguished from ‘theory’ by the concept of aggregated evidence.
Remember that this is still a compare-and-contrast exercise in aligning our concepts and vocabularies, and there isn’t a great divergence so far. It is with evidence, though, that our greatest differences become manifest. Science is about the here-and-now whereas genealogy is about the been-and-gone. What this means is that genealogy only has a finite set of evidence available, and although more of that set may be discovered over time, no evidence outside of that set will ever be found. It also means that evidence cannot be created on demand in order to solve a particular problem, or to support/refute a given proposition. On the other hand, in science — technology permitting — an experiment can be conceived purposely to test a given theory, or to separate two competing theories.
The idea of competing theories is something we have in common. It is possible in both fields to have more than one theory which explains the available evidence, no matter how deeply that evidence is scrutinised. Whereas science can usually conduct a specific experiment to disprove some of the candidate theories, and so support the remainder, genealogy can only search for more items of evidence that already exist. If they don’t exist somewhere now then they never will in the future either. Part of this process of testing our theories may involve extrapolating from them, and checking what they would predict if they were true. This gives focus to the areas where we need more evidence, and is again something common to both fields.
Even the concept of Occam’s Razor is something we have in common. Put simply, the least complicated explanation is probably the correct one. This doesn’t make it absolutely true, and certainly doesn’t constitute a proof in anyone’s vocabulary, but it can help focus our research.
One area where science meets genealogy, thus showing the relevance of this post, is DNA analysis. DNA analysis compares the genetic code of someone with either specific individuals or some ethnic group. There are three types of tests: Y-Chromosome (Y-DNA), which looks at a male descent along his direct paternal line, mitochondrial DNA (mtDNA), which looks at the descent of either sex along their direct maternal line, and autosomal (atDNA), which covers all types of descent. It is important to understand that DNA testing only matches certain sequences in our genetic profile, and the relevance of the results therefore depends on how long those sequences are, how rare they are, and how far back you're looking (more intermediate generations means the results are less significant). Hence, just as with any other type of evidence — scientific or historical — there can be no absolute proof. DNA testing can support the proposition that two people are related, or completely disprove it, but it can never prove it beyond doubt. When done correctly, DNA testing does provide an objective test that is not susceptible to bias or personal agendas, but our own acceptance and interpretation is a different matter. Note that when DNA evidence is presented in court, it is also supplemented by a risk factor indicating the chances of a false positive.
One short-lived concept that illustrates the dangers of an ambiguous interpretation of proof is Definitive Tangible Proof (DTP). This was originally described as “…which can be, but is not limited to, birth/baptism records, church records, marriage records, land deals (purchases/sales), death records/certificates, grave markers, tax rolls, probate records, military records, Wills, etc.”. Rather than proof, this concept was really describing certain sources of evidence. However, no source is ever definitive, and all those listed can, and often do, contain errors. These are not special cases, and none can be taken at face value. When used in a proof argument (i.e. a written argument helping to ascertain some truth) then all such evidence must be assessed in the same way, including a consideration of the nature of the information, the nature of the underlying source, and how that evidence correlates with other evidence to support or contradict a claim.
So, in summary, I agree that historical research has a large element of precision in such areas as finding all available evidence, analysing and correlating that evidence, resolving any conflicts, and writing it up clearly and unambiguously. However, whereas science reserves the term proof for the absolute case, and doesn’t attempt to push any ideas beyond the status of theory, genealogy employs the word proof in the context of the less-precise disciplines. Despite attempts to define proof for the genealogical context, I believe this disparity of precision is at the root of many of our confusions.
 Oxford Dictionaries Online (http://www.oxforddictionaries.com/definition/english/fact : accessed 24 Dec 2013), s.v. “fact”.
 Oxford Dictionaries Online (http://www.oxforddictionaries.com/definition/english/proof : accessed 24 Dec 2013), s.v. “proof”.
 Q.E.D is an initialism of the Latin phrase: quod erat demonstrandum, which means "what was to be demonstrated”. However, the Latin was itself a translation of a Greek phrase, and translating directly from the original Greek results in “what was required to be proved”.
 Elizabeth Shown Mills, Evidence Explained: Citing History Sources from Artifacts to Cyberspace (Baltimore, Maryland: Genealogical Pub. Co., 2009), p.17.
 Mills, Evidence Explained, p.18.
 Mills, Evidence Explained, p.19.
 This concept appeared at http://generousgenealogists.com/2013/01/05/definitive-tangible-proof in May 2013. Although it has since been taken down, there are several posts still visible in the Internet that use the term as it was originally defined.