Evidence of absence is evidence of any kind that suggests (via certain types of inference or deduction) the non-existence or non-presence of something. A simple example of evidence of absence: checking one's pocket for spare change and finding nothing but being confident that one would have found it if it were there. This is an example of modus tollens, a type of logical argument.
In this regard Irving Copi writes:
In some circumstances it can be safely assumed that if a certain event had occurred, evidence of it could be discovered by qualified investigators. In such circumstances it is perfectly reasonable to take the absence of proof of its occurrence as positive proof of its non-occurrence.
Of course, in practice, it can be difficult to agree whether a particular experiment was a sufficiently "qualified investigation".
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The difference between evidence that something is absent (e.g. an observation that suggests there are no dragons) and a simple absence of evidence (e.g. no careful research has been done) can be nuanced. Indeed, scientists will often debate whether an experiment's result should be considered evidence of absence, or if it remains absence of evidence (e.g. the experiment could have missed what it was looking for).
The confusion is worsened since arguments from ignorance and incredulity are often (wrongly) advanced in debates as proper "evidence of absence". A case in point: arguing "There is no evidence that this mysterious remedy does not work, therefore it works." Basically, this arguments from ignorance relies on a lack of research to somehow draw conclusions. While this is a powerful method of debate to switch the burden of proof, appealing to ignorance is a fallacy. Carl Sagan criticized such "impatience with ambiguity" using cosmologist Martin Rees' maxim, "Absence of evidence is not evidence of absence."[1]
Of course, in carefully designed scientific experiments, even null results can be evidence of absence. For instance, a hypothesis may be falsified if a vital predicted observation is not found empirically. At this point, the underlying hypothesis will be rejected or revised, or even rarely add ad hoc explanations. Whether the scientific community will accept a null result as evidence of absence depends on many things, including the detection power of the applied methods, and the confidence of the inference.
Philosophic arguments that depend on evidence of absence are commonly referred to in peer-reviewed literature as "noseeum arguments". The argument form is specifically inductive in that evidence is accumulated; as one collects a larger dataset the argument grows stronger. Some noseeum arguments are very strong, such as checking the fridge for milk and determining that there is none, since it is relatively easy to systematically remove every item from the fridge, verify that it is not milk, and visually inspect the empty space left over. At the other extreme are noseeum arguments about the existence, or lack thereof, of alien lifeforms. Since the universe is enormous relative to our known area, a noseeum argument stating that there are no alien lifeforms would be very weak.
Philosopher Steven Hales describes how there is widespread agreement that, as far as humans can be concerned, it seems that any inference is fallible.[2] Neither a negative claim, nor a positive claim, is ever absolutely certain (i.e. absolutely "proving" facts about reality seems impossible). For instance, someone who believes that they have seen Santa Claus may have been hallucinating, or otherwise deceived.
Philosophers acknowledge what is called the problem of induction, the idea that you never know when new information will prove you were wrong after all. Since inference in general is never certain, it may be more appropriate to say "you can't prove anything, strictly speaking (a negative or a positive)".[2] Hales also worries that people often appeal to the problem of induction in order to continue believing in less justified beliefs (i.e. pseudoscience).[2]
Notable skeptic James Randi sometimes uses the catchphrase "you can't prove a negative".[3] He uses the example of looking for Santa Claus as an unprovable negative. Philosopher Steven Hales disagrees, and says that no logician actually believes "you can't prove a negative". Hales says the rule is an oversimplification. As explained above, depending on circumstances, one can be equally as confident about a negative as a positive. [2]
Hales points out that the second law of thought is a sort of negative; "it is not the case that a thing can be X and not X at the same time". What's more, any argument can be expressed in its negative form. For example, to the extent that you can prove that you are real (a positive argument), you can also prove that you are not imaginary. Whether an argument is phrased as a positive or negative can be arbitrary.[2]
Hales acknowledges that some people understand the quote as meaning specifically: "you can't prove that something doesn't exist". Understood this way, Randi's quote is criticizing "Noseeum" arguments (mentioned in an above section). Moreover, there are many cases where we may be able to prove something does not exist with as much certainty as proving something does exist (described in the previous section).[2]
The assertion that you can't prove something doesn't exist may be a logical fallacy. Mathematicians frequently apply Proof by contradiction. This is when you assume the proposition (e.g. the negative proposition that there is no Santa Claus) is true. Then you demonstrate from that proposition either that the proposition is also false, or, alternately, that the proposition leads to some faulty conclusion. This is often trickier to perform in the real world outside of mathematics, but it's always nominally possible. It's one of the reasons we can pretty much make the assertion, "There Is No Santa Claus" with quite a high degree of reliability, despite it being a negative. For it to be otherwise leads to a whole host of rather unlikely conclusions about the real world.
Whether humans possess evidence of absence for the existence of God continues to be debated in philosophical academia. Research into the relationship between science and religion has also yielded mixed opinions.
British philosopher Antony Flew holds that some claims cannot be falsified because they are ultimately unverifiable. Flew asserts that one should test whether a certain truth claim can be falsified under a hypothetical situation. He suggests we ask "What would have to occur or to have occurred to constitute for you a disproof of the love of, or the existence of, God?" Flew also describes how deep questioning, backed up by empirical testing, can reveal a claim to at least have much less content than was originally thought (e.g. it becomes a much less detailed claim)- what he calls "death by a thousand qualifications".[4]
God's existence can mean many things to many different people. Still, some claims (which are actually contentful) about gods or their actions can be falsified, to the extent that the claims attempt to describe any facts about physical reality. For instance, the creationist claim that God created humankind in their current form has been falsified by evolution. Many (but certainly not all) other claims related to God can be similarly tested (e.g. the practice of praying to cause someone to heal has also been recognized, among scientists, as having been disproved[5]).
Some other instances of evidence of a thing's absence include: A biopsy may show the absence of malignant cells (evidence of absence of a tumour), and the result of Michelson–Morley experiment is interpreted as "strong evidence" that the luminiferous aether does not exist. Another case in point, close inspection of an attic may reveal no sign of vermin infestation and therefore evidence of vermin absence in the attic. Note however that a critic might argue, if one did not open every available box, that one still possesses an absence of evidence.
Gin Rummy, an ex-soldier character in the show The Boondocks, attempts to explain to another character what it means to say "the evidence of absence is not the absence of evidence". As Rummy puts it "Simply because you don't have evidence that something does exist does not mean you have evidence that something doesn't exist." When that rephrasing causes confusion, Rummy angrily discusses more confusing but related ideas, saying: "Well, what I'm saying is that there are known knowns and that there are known unknowns. But there are also unknown unknowns; things we don't know that we don't know."