Why proving a negative is harder than proving a positive
A single instance settles an existence claim. A non-existence claim requires exhausting a space, and spaces are rarely exhaustible.
Intuition test — answer before you read on
Why is a claim of non-existence evidentially harder than a claim of existence?
One photograph settles whether a black swan exists. Nothing settles whether one does not, short of inspecting every swan, and the inspection can never be reported as complete because the next unexamined swan is always available.
What everyone sees
The two claims look symmetrical, since each is the other’s denial. Their evidential requirements are not symmetrical at all. One is satisfied by a finite observation and the other requires a statement about everything not observed, which no observation can supply.
What is actually happening
Popper built his account of scientific method on this asymmetry: universal statements cannot be verified by any finite set of observations but can be falsified by one, which is why he located scientific content in what a theory forbids rather than in what it permits. The practical consequence in evidence-handling is the point Altman and Bland made about study results — a failure to detect an effect is not the same as demonstrating its absence, because the failure is also consistent with insufficient power to detect it. Wason’s experiments add why the asymmetry is so easily missed: participants testing a rule overwhelmingly sought confirming instances rather than the disconfirming ones that would have been informative, which means the search strategy people default to is the one suited to the easier claim.
Why it stays hidden
The asymmetry hides because negative claims are stated in the same confident grammar as positive ones. There is no evidence of tampering reads as a finding, with the same syntax as there is evidence of tampering. The first is a report about a search whose scope is unstated, and the scope is where all the content was.
One instance settles existence. Non-existence requires exhausting a space, so the claim is really a report about the search that was performed.
One instance settles existence. Non-existence requires exhausting a space, so the claim is really a report about the search that was performed.
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One instance settles existence. Non-existence requires exhausting a space, so the claim is really a report about the search that was performed.
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Sources & further reading 2
- Popper — the logic of scientific discovery
- Altman & Bland — absence of evidence is not evidence of absence
Cross-references
Related files
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Hidden Logic Entry #0011Why nobody calls for help in a crowd
More witnesses does not mean more help. Past a certain crowd size, the probability that any individual acts collapses — and everyone involved believes they behaved reasonably.
Adept
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