Evidence of absence
Evidence of absence is evidence of any kind that suggests something is missing or that it does not exist.
Per the traditional aphorism, "absence of evidence is not evidence of absence", positive evidence of this kind is distinct from a lack of evidence or ignorance of that which should have been found already, had it existed. 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.— Copi, Introduction to Logic (1953), p. 95
The difference between evidence that something is absent (e.g. an observation that suggests there were no dragons here today) 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. The debate is whether the experiment would have detected the phenomenon of interest if it was there. 
The argument from ignorance for "absence of evidence" isn't necessarily fallacious, for example, that a potentially life saving new drug poses no long term health risk unless proved otherwise. On the other hand, were such an argument to rely imprudently on the lack of research to promote its conclusion, it would be considered an informal fallacy whereas the former can be a persuasive way to shift the burden of proof in an argument or debate.
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 may be rejected or revised and sometimes, additional ad hoc explanations may even be warranted.) Whether the scientific community will accept a null result as evidence of absence depends on many factors, including the detection power of the applied methods, and the confidence of the inference.
Proof and evidence
The Pyrrhonian skeptic, Sextus Empiricus, questioned the apodicticity of inductive reasoning because a universal rule cannot be established from an incomplete set of particular instances: "When they propose to establish the universal from the particulars by means of induction, they will effect this by a review of either all or some of the particulars. But if they review some, the induction will be insecure, since some of the particulars omitted in the induction may contravene the universal; while if they are to review all, they will be toiling at the impossible, since the particulars are infinite and indefinite".
Until about the middle of the previous century induction was treated as a quite specific method of inference: inference of a universal affirmative proposition (All swans are white) from its instances (a is a white swan, b is a white swan, etc.) The method had also a probabilistic form, in which the conclusion stated a probabilistic connection between the properties in question... The Oxford English Dictionary defines “induction”, in the sense relevant here, as follows: "[The] process of inferring a general law or principle from the observation of particular instances..."
[Much] of what contemporary epistemology, logic, and the philosophy of science count as induction infers neither from observation nor from particulars and does not lead to general laws or principles. [Induction] was understood to be what we now know as enumerative induction or universal inference; inference from particular instances:
- a1, a2, …, an are all Fs that are also G... [to a general law or principle] All Fs are G.
A weaker form of enumerative induction, singular predictive inference, leads not to a generalization but to a singular prediction:
- 1. a1, a2, …, an are all Fs that are also G.
- 2. an+1 is also F... [therefore]
- 3. an+1 is also G.
Singular predictive inference also has a more general probabilistic form:
- 1. The proportion p of observed Fs have also been Gs.
- 2. a, not yet observed, is an F... [therefore]
- 3. The probability that a is G is p.— John Vickers, "The Problem of Induction" in The Stanford Encyclopedia of Philosophy
Proving a negative
In 1992 during a presentation at Caltech, skeptic James Randi said "you can't prove a negative". He claims that it is impossible to 'prove' a negative assertion (such as 'telepathy does not exist'). He contends that induction is often used as a mode of proving a thesis, but if an individual assumes that something is or is not, then the person must prove so. Further, he says, he does not take an advocacy position, as a lawyer would. He says that he cannot prove that a negative is true, but he could attempt to use evidence and induction to support a claim that he is biased toward, such as a claim that something does not exist.
Philosopher Steven Hales argues that typically one can logically be as confident with the negation of an affirmation. Hales says that if one's standards of certainty leads them to say "there is never 'proof' of non-existence", then they must also say that "there is never 'proof' of existence either". Hales argues that there are many cases where we may be able to prove something does not exist with as much certainty as proving something does exist.
- Argument from ignorance
- Argument from silence
- Contraposition (traditional logic)
- Probatio diabolica
- Proof by exhaustion
- Transposition (logic)
- Turvey, B.E. (2008). Criminal Profiling: An Introduction to Behavioral Evidence Analysis. Elsevier. p. 267. ISBN 9780123741004. LCCN 2008274380.
- Martin, M. (2007). The Cambridge Companion to Atheism. Cambridge Companions to Philosophy. Cambridge University Press. p. 70. ISBN 9780521842709. LCCN 2006005949.
[Advocates] of the presumption of atheism... insist that it is precisely the absence of evidence for theism that justifies their claim that God does not exist. The problem with such a position is captured neatly by the aphorism, beloved of forensic scientists, that "absence of evidence is not evidence of absence." The absence of evidence is evidence of absence only in case in which, were the postulated entity to exist, we should expect to have more evidence of its existence than we do.
- Schreuder, Duco A. (2014). Vision and Visual Perception The Conscious Base of Seeing. p. 105.
- Walton, Douglas (1992). "Nonfallacious arguments from ignorance" (PDF). American Philosophical Quarterly: 381–387.
- Sextus Empiricus. Outlines of Pyrrhonism trans. R.G. Bury (Loeb edn) (London: W. Heinemann, 1933), p. 283.
- Vickers, John (2011). Edward N. Zalta, ed. "The Problem of Induction". The Stanford Encyclopedia of Philosophy (Fall 2011 ed.).
- on YouTube November 5, 2009, James Randi giving one of many talks where he uses the phrase
- Hales, Steven D. (2005). "Thinking Tools: You can Prove a Negative" (PDF). Think. 4 (4): 109–112. doi:10.1017/S1477175600001287.