Absence of Evidence =|= Evidence of Absence?
Absence of Evidence <=|=> Evidence of Absence?
Let: X0: = "The absence of evidence is not evidence of absence"
Let: X+: = "The absence of evidence is evidence of absence"
where X0 = Null Hypothesis = Negative Hypothesis = Negative Hypothesis
X+ = Alternative (or Test) Hypothesis = Positive Hypothesis = Affirmative Hypothesis
Line of Questioning:
Q1. Is the absence of evidence the same (i.e., identical) to evidence of absence?
Q2. Is the absence of evidence equivalent to evidence of absence?
Where: 'equivalent' refers 'materially equivalent' (i.e., material equivalence = being 'materially equal in truth value')
Q3. Is it necessarily fallacious to conclude that something is absent from the mere absence of the confirmation of its presence? Is it fallacious to affirm the truth of X+?
where: X+ := ('absence of evidence is evidence of absence')
Q4. Does there exist any possibility for the affirmation of X0 to be fallacious?
In which cases is it not fallacious to conclude something is absent from the mere absence of that thing being present? Is this necessarily fallacious?
Q5. Does the absence of evidence for some proposition count as evidence towards establishing that the proposition is not true (i.e., false)?
Absence of evidence may not be sufficient (i.e., may not materially imply) evidence of absence: absence of evidence for something existing may not be enough to confirm that it does not exist. However, does the absence of the presence of something even count as evidence for its absence?
Evidence includes reason, and is defined to be that which can be used to verify a proposition (i.e., prove that the proposition is true). Evidence = the facts indicating the truth of a given proposition are the evidence that the proposition is true.
X+ makes a positive claim (i.e., affirmative). -- the test/alt hypothesis X0 makes a negative claim (i.e., negative). -- the null hypothesis
The symbol (=|=) denotes 'not logically equal to': i.e., 'not identical to'. The symbol (<=|=>) denotes 'not (materially) equivalent to'.
- Does this proposition always hold (true), or are there exceptions?
- Is it a logical fallacy to claim: “absence of evidence is evidence of absence”?
- How is this proposition related to the argument from ignorance fallacy? Explain.
- Burden of proof, null hypothesis, negative proof, and “one cannot prove a negative”!
The statement “Absence of Evidence is not Evidence of Absence” seems to be correct.
The mere absence that something is present is not evidence that something is absent. Lacking evidence for (the presence of) something does not constitute evidence of the absence of that thing.
Negative Proof and the Burden of Proof (Onus Probandi):
The burden of proof is on the proposition, not the opposition! The one who makes a claim carries the burden of proof, regardless of the positive or negative content of the claim.
One way in which one would attempt to shift the burden of proof is by committing the fallacy "the argument from ignorance" or "the argument from personal incredulity".
Negative proof by reductio ad absurdum (reduction to absurdity), such as a proof by contradiction or proof of impossibility, are typical methods to fulfill the burden of proof for a negative claim. A proof by contradiction is a valid rule of inference called modus tollens (also proof by contraposition):
Negative Proof and the Argument from Ignorance:
The argument from ignorance: "some proposition X is true because it has not (yet) been proven false," or "some proposition is false because it has not (yet) been proven true."
To assert that "absence of evidence is evidence of absence" is a logical fallacy called the argument from ignorance.
"Something is concluded to be absent because it has not been proven to be present," or "Something is concluded to be present because it has not been proven to be absent."
Example:
Proposition G: "God exists" is accepted as true because G has not been proven false.
That is, the lack of sufficient evidence capable of constituting proof of god's existence is not sufficient evidence constituting proof of the non-existence of god.
Proposition G: "God exists" is concluded to be true because its negation ~G: ("God does not exist”) has not been proven true.
Negative Proof through Negative Claims:
A negative claim is the opposite (negation) of an affirmative (positive claim). A negative claim asserts the non-existence or exclusion of something. For a positive claim, only a single example is required to demonstrate the positive claim.
Negative Proof through Negative Evidence:
Absence of evidence: ex., no careful research has been done. Evidence of absence: ex., an observation that suggests there were no dragons in my garage.
The difference between absence of evidence and evidence of absence lies in whether investigation (i.e. scientific experiment) would have detected the phenomenon if it were there.
MODUS TOLLENS (relies on the contrapositive of the original implication to be equivalent to it).
Premise (1): P -> Q.
Premise (2): ~Q
{then}__
Conclusion: ~P.
(which reads...)
Premise (1) If P, then Q.
Premise (2) Not Q.
{then}
Conclusion: Not P.
Please note that ‘arguing from ignorance’ for ‘absence of evidence’ is not necessarily fallacious!
Example:
"This drug has no long-term risks, until proven otherwise."
Were such an argument to rely imprudently on the lack of research to promote its conclusion would be considered an informal fallacy (argument from ignorance).
Can even null results can count as evidence of absence, though not conclusive proof (in and of themselves)? Ex., A hypothesis may be falsified if an essential predicted observation is not found empirically.
In cases where there should be evidence if the hypothesis were true, absence of evidence can count as evidence (not proof) of absence, depending on the detection power of the experiment (including instruments), the confidence of the inference, limiting confirmation bias, etc.
Therefore, the argument from ignorance for "absence of evidence" is not necessarily an informal fallacy.
