Proving Negatives, Absence of Evidence, and Ignorance as Evidence

There are certain sayings “out there” that are repeated over and over by those who want to delegitimize science and support pseudoscience and fantastical claims. One saying that you often hear is, “Science can’t prove a negative”. What is meant by this?
 
A “negative” is a claim expressed in negative form. So “ghosts exist” is the positive form of a claim whereas “ghosts do not exist” is the negative form of the claim. It is argued that the positive claim “ghosts exist” is provable, because all you have to do is demonstrate the existence of at least one ghost for it to be true. However, it is maintained that the claim “ghosts do not exist” is unprovable because no matter how many times you investigate the existence of an alleged ghost and come up empty handed, you will never exclude the possibility that there is a ghost somewhere.
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Historical marker commemorating the Michelson-Morley experiment.

However, science proves negatives all the time. The key to doing this is defining the characteristics of whatever it is we wish to find, and, if applicable, circumscribe its presence in space and time. Defining the characteristics of what we wish to investigate allows us to come up with a method of detection. Stating where and when what we wish to investigate should be, allows us to perform the detection at the right place and time. If we then proceed to perform the detection at the stated place and time and we find nothing, we can conclude that an entity with the specified characteristics that we looked for at the stated place and time doesn’t exist, because if it existed, we would have detected it. A famous example of this is the so called Michelson-Morley experiment.
 
When it was determined that light had the characteristics of a wave, the question arose as to through which medium light traveled. Sound waves travel through solids, liquids, and gases as compression waves, so light was proposed to travel forming waves in a medium that was called “aether”. Two American scientists, Albert Michelson and Edward Morley, worked out how light would interact with this alleged “aether” and performed several experiments in 1887 to measure this interaction. The overall conclusion of these experiments was that the “aether” did not exist, and similar experiments conducted since then with ever increasing precision have confirmed the results.
 
The above procedure can also be applied to things like claims for the existence of ghosts. Of course, if the proponents of the existence of ghosts and other paranormal occurrences cannot define the characteristic of the phenomena whose existence they advocate or when and where they occur with any degree of certainty, then there are serious concerns regarding whether these claims have any merits from a scientific point of view. We might as well discuss how many angels can dance on the head of a pin. Here we are better served by applying Alder’s Razor (what cannot be settled by experiment or observation is not worth debating).
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Another saying related to the one we dealt with above that is often encountered is that “The absence of evidence is not evidence of absence”. What is meant by this is that no matter how many times we perform tests or make observations to ascertain the existence of something such as, for example, a medical effect, if we find no evidence of its existence, we cannot conclude that it doesn’t exist.  This argument is frequently made by those who advocate products and treatments of dubious value or those who are hell-bent on defending disproven propositions. The idea is that no matter how much evidence to the contrary, there MAY BE an effect that the studies may have missed. The problem with this thinking is that a carefully designed series of robust studies can be carried out to evaluate the existence of an effect of a certain magnitude. The point is not whether there is a very small effect. The point is whether there is an effect of practical importance.
 
For example, many people were concerned that the vaccine against measles, mumps, and rubella (MMR) caused autism. In response to this, scientists carried out several studies evaluating possible risks of autism as a result of vaccines which all in all included hundreds of thousands of children. No significant association between autism and this vaccine was found. Could there nevertheless be a very small effect that was not detected by the studies? Yes, but such an effect would be so small as to be of no practical importance, especially compared to the risks of unvaccinated children contracting measles, mumps, and rubella.
 
One final saying that pops up among the pseudoscience crowd is that concerning products or therapies that have not yet been investigated. When unresearched products or therapies used by people come under criticism, their proponents argue that, “There is no evidence that they don’t work.” Thus what they are saying is that, because it has not been found to be ineffective, it is OK to keep on using it, even though this argument should cut both ways (if there is no evidence it works you should not use it). This line of reasoning essentially argues that ignorance is a valid reason to justify using a product or therapy. It treats ignorance as evidence!
 
Even if the effectiveness of a particular product or therapy has not been investigated, there may be grounds for serious skepticism regarding its use based on other considerations. For example, if a new untested homeopathic product is introduced into the market, we would be justified in being skeptical regarding its effectiveness because the principles on which homeopathy is claimed to work violate well-established chemical laws. Additionally, the best designed studies assessing the effectiveness of existing homeopathic products have yielded negative results, so a new product will not fare any better.
 
So to recap, science CAN prove a negative, absence of evidence CAN be evidence of absence, and ignorance IS NOT evidence.
 
Photo of the plaque commemorating the Michelson-Morley experiment by Alan Migdall is used here under an Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0).