- Evidence of absence
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".
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."
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.
Evidence vs. proof
Philosopher Steven Hales describes how there is widespread agreement that, as far as humans can be concerned, it seems that any inference is fallible. 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)". Hales also worries that people often appeal to the problem of induction in order to continue believing in less justified beliefs (i.e. pseudoscience).
"You can't prove a negative"
Notable skeptic James Randi sometimes uses the catchphrase "you can't prove a negative". He uses the example of looking for Santa Claus as an unprovable negative. A claim by philosopher Steven Hales is that no logician actually believes this, and the rule is an oversimplification. As explained above, depending on circumstances, one can be just as confident about a negative as a positive. 
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.
Hales acknowledges that people may actually mean "you can't prove that something doesn't exist". This claim is now clearer as an argument that "noseeum" arguments about the universe tend to be very weak as explained above. But it remains false as far as it concerns issues of "proof" and certainty in general as described in the previous section.
Existence of God
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".
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).
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.
In the media
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."
- Contraposition (traditional logic)
- Transposition (logic)
- Statistical significance#Pitfalls
- Argument from ignorance
- Argument from silence
- ^ Sagan, Carl (1997). The Demon-Haunted World: Science as a Candle in the Dark (1st ed.). New York: Ballantine. p. 213. ISBN 0345409469. OCLC 32855551. "Appeal to ignorance—the claim that whatever has not been proved false must be true, and vice versa (e.g., There is no compelling evidence that UFOs are not visiting the Earth; therefore UFOs exist—and there is intelligent life elsewhere in the Universe. Or: There may be seventy kazillion other worlds, but not one is known to have the moral advancement of the Earth, so we're still central to the Universe.) This impatience with ambiguity can be criticized in the phrase: absence of evidence is not evidence of absence."
- ^ a b c d e f Hales, Steven D. (2005). "Thinking Tools: You can Prove a Negative". Think 4 (4): 109–112. doi:10.1017/S1477175600001287. http://departments.bloomu.edu/philosophy/pages/content/hales/articlepdf/proveanegative.pdf.
- ^ James Randi giving one of many talks where he uses the phrase
- ^ Flew's Theology & Falsification: A Golden Jubilee Celebration (2000)
- ^ "Faith Healing". American Cancer Society. June 15, 2009. http://www.cancer.org/docroot/ETO/content/ETO_5_3X_Faith_Healing.asp. Retrieved 2011-05-01. "[...] available scientific evidence does not support claims that faith healing can actually cure physical ailments. [...] Death, disability, and other unwanted outcomes have occurred when faith healing was elected instead of medical care for serious injuries or illnesses."
- Van Inwagen, Peter (2006). "Lecture 8 The Hiddenness of God". The Problem of Evil: The Gifford Lectures given at the University of St Andrews in 2003. Oxford University Press. p. 173. ISBN 0199245606. http://books.google.com/?id=nxAP02FlE1MC&pg=PA173. "If the present argument appeals to any general epistemological principle, it is this rather obvious one: If a proposition is such that, if it were true, we should have evidence for its truth, and if we are aware that it has this property, and if we have no evidence for its truth, the fact that we have no evidence for its truth, is (conclusive) evidence for its falsity."
- Johnstone, Albert A. (1991). Rationalized Epistemology: Taking Solipsism Seriously. SUNY Press. p. 39. ISBN 079140787X. http://books.google.com/?id=IBbQtkyrLE4C&pg=PA39. "The reason why the everyday view P is not known (at least in as much as it contradicts the skeptical thesis) is not merely that the evidence for P is insufficient to warrant a knowledge claim; it is that the evidence for P is inexistent. In the absence of any such evidence, there is no reason at all to think that P is true. To claim that P is true is consequently to make a purely gratuitous claim."
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